THE BOOK--Playing The Percentages In Baseball

The Fangraphs thread about the new UZR home/road splits:

http://www.fangraphs.com/blogs/index.php/uzr-home-away-splits/

My comment:

I’ll admit I’ve missed some part-time (below 100 innings in that season) players, but I’ve compiled the UZR home/road splits for Mariners outfielders from ‘02-’09.

Home: 126.3
Away: 44.6

That’s a startling difference – about 80 runs – for a stat that, as you point out, has been adjusted for park and home field advantage. And there’s nearly 2000 defensive games in each half of the split, so it strikes me as unlikely that random variance accounts for it, either.

Cross-posting:

What I would like to see is Team splits like this:

TeamX – At Home
TeamX – On Road
Opponent – At TeamX’s Home
Opponent – At Opponent Home of TeamX’s games

Only in this way can we see that the park splits make sense.

By infield/outfield.

***

Once you do that, then we can stop the park discussion.

Is there any reason to think that more information would stop the park discussion? That was the idea behind providing UZR home/road splits, wasn’t it? Nothing I’ve seen so far from the UZR splits data says I should be any less concerned about park scorer bias than I was a few days ago.

Not more information.  This specific information I am suggesting.

That’s fine to lay out that out there, Tom, if MGL for some reason wants to pick that up, but the rest of us do not have the ability to get that information from the splits information currently available on Fangraphs.  So as a request for MGL or David Appelman, that’s great.  As a request for Colin, it’s not something he can give you.  Colin’s stance seems eminently reasonable given the data available to us.

Right, I’m saying that if David/MGL gives us the data I’m suggesting, then teh park discussions will come to a close (presuming that we see the results I expect).

A counter-example.

Red Sox outfielders, 2002-2009:

Home: -50.2
Away: 17.5

Does that really make sense to anyone - a home field disadvantage in fielding, after adjusting for park?

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What I object to is this:

“Only in this way can we see that the park splits make sense.”

I would be fine with this:

“Only in this way can we see if the park splits make sense.”

What I would be jsut as interested is the Redsox opponents at Fenway and at their own home park.  IDEALLY, both splits would be close to 0.

And, this would be true for all opponents if you do it for every team.  (Within whatever sample error is implied.)

***

Colin, 67 run gap over 8 years and 3 positions, right?  So, a possible 3 run bias per position.

"Does that really make sense to anyone - a home field disadvantage in fielding, after adjusting for park?”

The home and road numbers are each zeroed out so there is no home field advantage for fielding expressed in the numbers.

Here is what I wrote I wrote on FG:

Let’s say that you were compiling park factors for a certain park, say Wenfay Park. Could be for pitching, batting, or defense (UZR) – it doesn’t matter. And let’s say that the ratio for 3 years of home plus home opponent to road plus road opponent (the usual way we do park factors) was 1.50. So the unregressed park factor for 3 years of data would be 1.50.

If we used 1.50, the unregressed PF, to adjust players in that park for those 3 years, we would find that, by definition, those players would have pretty much the same park adjusted stats at home and on the road. I say pretty much because the 1.50 includes not only the home players home and road stats, but their opponents as well. So everything looks good, right? Park adjusted home and road stats are equal, as they should be. The problem with that is that park adjustments should NOT make home and road stats equal!

Using 1.50 is a terrible PF! Certainly that has to be regressed, assuming we don’t know much about the park. Depending upon what kind of park factor it was, that 1.50 would probably get regressed to at least 1.25 for only 3 years of data. But, if we use the more correct PF, 1.25 (as an estimate of our true PF), the home players will NOT have the same park adjusted home and road stats! So which one is correct?

The second one of course. Basically, the home and road stats should NOTbe the same for in-sample data (the sample of data that is being used to generate the park factors). They should NEVER be the same unless the PF was 1.00.

Now, if you look at 2010 and beyond (data was not used to make the the PF) and we still continue to get the kind of park adjusted splits that you are getting, then we may have a problem.

But, for the 2002-209 data, OF COURSE the data is going to look like that! That is the data that the PF’s were based on and the PF’s were regressed to park adjust the stats!

Now, I am not saying that the park adjustments are not biased or certain parks are not under-adjusted, but is there any particular reason for home and road stats to be equal?  No, of course not.  Now, if the park adjustments are even close to being “correct,” we should see fluctuations between team home and road stats to be that expected by chance, more or less.  Whether those differences we see in the current UZR data are significantly different from those expected by chance for both leagues as a whole, I don’t know.  The fact that Colin cherry picked two teams whose home and road numbers are a lot different does not tell us anything at all in and of themselves, although the fact that Boston home is a lot worse than road and SEA road is a lot worse than home does suggest that the park adjustments are not enough.  I can certainly look at them again, and see if I can improve upon them.

But please don’t expect for me to make the park adjustments such that home equals road.  That is NOT correct!  In fact, that is not a park adjustment at all!  That is using road stats and throwing out home stats!  That is an important point to understand.  I’ll repeat it again.  If you make your park adjustments such that the in-sample data (the data that the park adjustments are created from) home and road stats are equal, you are simply throwing out the home stats - you are not doing a park adjustment.

MGL, it would be superlovely if you can give us the data I noted above:

teamID, parkID, yearID, pos, “Games”, total_uzr

I’ll be able to tell you if the differences are what we should expect from chance or not.

The home fielding stats, in general, should be a bit better than the road stats.  At least in TZ they are.  We know that babip is higher for the home team, it’s part of home field advantage.  UZR adjusts for the difficulty of plays (recognizes babip is higher because balls are harder hit, etc.) so it probably won’t show as much a difference as TZ.

But still, knowing babip is higher for the home team, I would expect that to be a result of a combination of better hitting, worse pitching for the road team, and worse fielding for the road team (not as familiar with park quirks.)

Rally, MGL sayeth:

Also, it is not mentioned anywhere, but road and home UZR’s are zeroed out so that they will not reflect the fact that players typically play better defense at home than on the road (HFA). IOW, if a player were an average defender (0 UZR), he would likely be around -1 per 150 on the road and +1 at home, due to the normal defensive HFA. But, the way the home and road UZR are calculated, he is going to show up on FG as zero at home and zero on the road, since again, we are trying to capture context-neutral talent and performance (so basically we are adjusting for home and away).

So what we’re seeing here is AFTER home field advantage is adjusted for.

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And MGL, how did I cherry pick the numbers? These are the only two teams I’ve looked at - I don’t KNOW what the other teams splits are!

Colin, I knew you would not like the idea of me saying that you “cherry picked” them. That sounds so pejorative. But that was probably a bad use of words by me.

What I meant was that quoting those two teams without any context doesn’t mean anything.  Plus those teams were obviously not chosen randomly.

Tango, you want each team’s UZR in every park, so a total of 196 lines in the AL and 256 in the NL?

BTW, there is no doubt that the park adjustments are far from perfect, so the distribution will NOT look like that of a random set of data.  Now, how much bias is acceptable, I have no idea. It is NOT easy to tell whether park adjustments are done well or not.  People use all kind of gross park adjustments for pitching and hitting that are clearly bad (some people use 1-year non-regressed park factors, some people use multi-year regressed numbers, some people do a regression but who the heck knows how they do it, people use different methods of computing park factors, some adjust for the imbalanced schedule, others do not, etc.), but I have never seen any research that quantifies how bad they may be.

They weren’t chosen randomly. But there were chosen for reasons unrelated to the observed UZR home-road splits, because I couldn’t know them until after I chose them!

They were chosen based upon two pieces of data:

1) The pressbox heights I measured from photos and Google Earth location data.
2) Observed LD rates from MLBAM data.

Based on the hypothesis that if there were park-scorer LD effects on UZR they would be two parks likely to show an effect, and an opposite one at that.

Tango, you want each team’s UZR in every park, so a total of 196 lines in the AL and 256 in the NL?

If you mean those sets of lines per year, then yes.

Also: are you removing IL games altogether?

I hadn’t realized until reading the primer that UZR assumes all errors are made on plays that are approx. 95% out balls.  At first blush, this seems like a reasonable assumption:  the official scorer determined the play should have been made.  On the other hand, this could penalize players with good range who get to more difficult balls but then fail to convert them. 

Jeter, for example, is -57 runs on Range UZR (and -5 for DP), but +25 on Error UZR.  Now, it’s certainly plausible that Jeter is more sure-handed than average despite limited range.  But I also wonder if SSs with better range are committing errors on balls that Jeter never would have touched.  So it might we worth exploring whether the assumption about errors is correct (if MGL hasn’t already done so): 
When high-range SSs make an error, is the UZR out% on that ball type just as high as on errors made by low-range SSs?
If you just ignored errors and used traditional UZR to rate the difficulty of the error balls, do any players see their rating change considerably?  It shouldn’t make a difference.

Right, it won’t make a difference, overall.  MGL partitions it so that we get a profile, but in the end, an error is a play not made.

It shouldn’t make a difference, but it COULD be making a difference in the current ratings, if the errors made by some players are made on balls that were in fact more difficult to field.

Jeter made just 3 fielding errors last year.  So UZR basically gives him +10 runs on that basis alone compared to Guzman, who—like every living shortstop—gets to many more balls per inning.  Only after that are their BIP rated by (relatively) more objective criteria. 

While the correlation isn’t huge, there does appear to be a positive correlation between range and error rate.  Rollins and Jeter both have terrible range yet extraordinarily low error rates (and the fact that both are huge stars may or may not be related).

Guy, it is possible that there are occasions when a good range fielder gets to a ball and makes an error that would not be an error for an average fielder, but I think this is rare and/or the overall effect is small.  For one thing, if you remember, I have mentioned several times that fielders with more range make FEWER errors on the average not more, as says conventional “wisdom.”

If I were to treat errors like any other missed ball, that would not yield good results.  That is because the data is not that accurate (fine, granular, etc.).  For example, if we just looked at the difficulty/out rate of the balls in which errors occurred, based on their buckets (location, speed, etc.), you would probably find a 60 or 70% (maybe 80%) out rate.  And clearly when any fielder makes an error, no matter how much range he has, on the average, it is a ball that gets caught 95% of the time.  Maybe it is 93% for a good range fielder and 97% for a bad range one, but it is not 70 or 80% for anyone, again, on the average.

Colin, by definition, anything that is not chosen randomly, is “cherry picked” at least according to my definition of “cherry picking.” Now whether such cherry picking biases the analysis is another story. But my main point is the fact that for two teams there is a large difference in home and road park (and HFA) adjusted numbers does not tell us much without looking at the whole enchilada.

As I explained, if you are choosing in-sample data (the data that the park factors were gotten from), it is guaranteed that the home and road numbers will NOT be different and it is guaranteed that the larger the park factor the more the difference will be, again, for in-sample data only.

So the fact that you found a large difference in Boston and in SEA is exactly what you SHOULD have found if the park effects were perfect!  Now, of course they are not perfect, and in fact, they might be much too conservative and those gaps you found might be greater than they should be.

It takes me several hours to copy down outfielder splits from Fangraphs. I only have so many hours I can devote to this sort of work, seeing as I have a job and a kid to take care of. And I have no way of generating the other half of the data (splits for visiting players).

And you’re the enchillada factory owner! If you want/need that we look at more enchilladas, well, give us some enchilladas.

MGL:
I don’t know how you can know that the error balls are in fact 95% out balls, while the bucket says 70%.  But even if that’s true, you have a problem. 

Let’s say that we have an 85% bucket of easy ground balls.  To oversimplify, 1/3 of these are really 95% balls, 2/3 really 80%.  And we have two fielders, both of whom will convert 85% of these balls, so we want UZR=0 for both.  But player A does this by converting 99% of the 95% balls, and just 78% on the 80% balls—he’s great on the sure things, but misses the tougher chances.  Player B is the reverse, converting just 91% of the sure things, but 82% of the tougher chances.

Now run your methodology.  Because player B commits more errors, and UZR now “knows” those were 95% balls, he gets hit with a big penalty.  While he makes up some ground on the remaining balls—all of which UZR assumes are 85% out balls—player B still comes out behind, even though they are in fact equal.  The problem is that UZR learned that player B had a bunch of 95% balls, but never learned that player A had the exact same number. 

Look at it this way:  Presumably, the UZR buckets do just as good a job of measuring the difficulty of balls hit to Jeter or Rollins as to other SSs, on average.  But if a SS makes 10 more errors than Jeter/Rollins, you now assume that his opportunities were a little bit easier (by 2-3 plays).  Basically, you’re assuming that more errors mean that a player had easier chances—how can that be true?  On average, the UZR buckets must be equally accurate for hi- and low-error players. 

Obviously, the players making more errors should be debited for failing to make an out.  But that would happen without adding the separate error calculation.  The current system, I think, is essentially giving extra credit to players who happen not to miss balls the scorer thinks were easy.  And that’s before we worry about any possible bias by scorers....

Guy, it is quite simple.  The BIS data gives us some information. I take that information and water it down quite a bit (in order to get some decent sample size for each bucket).  So the information that UZR uses is very watered down.  UZR does the best it can with the information it is given. If that information is watered down, so be it.

Now, the fact that the official scorer gives a player an error (or not) is great information. It is the kind of information we would love to have on every ball but we don’t.  Official scorers obviously don’t always do the best job in awarding an error or not, but basically when an error is awarded it is on a ball that is easy to field for whatever reason.  The out rate for all of those errors we know.  It is around 95% or whatever.  So, really all we have is another bucket gift wrapped to us by the official scorer.  Why would I not want to use that as a separate bucket? If I put all of those balls in my watered down buckets that would be a lot worse than using those very good, gift-wrapped buckets provided by the official scorer.  So rather than going through all the stuff you went through in your post above, just think of errors as another bucket provided by BIS - a bucket in which 95% of the balls are fielded.  That is all I am doing.

Now, you can make one argument against that, but it really won’t change anything more than a tiny amount.  That argument is that all of the buckets from BIS are independent of the fielders - they are either hard, difficult or in between for all fielders on the average.  The bucket given to us by the official scorer depends on where a fielder is positioned and how good he is at getting to the ball.  That brings us back to the previous issue about good range fielder or fielders that are positioned better than other fielders getting to some balls, making the play look easy, and then getting charged with an error, even though the ball might have been an 80% ball for the average fielder. Well, I contend that that is rarely going to occur and even if it does occasionally, the loss from that is way less than the loss from using bad information and ignoring good information.

Look at it this way.  If I were to use the BIS classifications for errors and ignore the fact that they were errors (treating them just like hits, as some defensive metrics do), if you were to look at the video for each and every ball and compare what you see to what my buckets say, you would be appalled!  Don’t forget that I am NOT using the exact location of each batted ball in the UZR engine. If I were, it would be a completely different story.  For example, let’s say that a hard hit ball went through a fielder’s legs right where he was stationed.  Certainly some not insignificant percentage of errors occur that way.  If you used my “bucket” information, the bucket might say that the ball was hit anywhere from 10 feet left of an average fielder position to 10 feet right.  Because it was hard hit, that might be a 70% ball.  If you saw that in video going through the fielder’s legs and being hit right at him, would you be happy if we scored that as a 70% out rate?  I would hope not!

And what about throwing errors?  How would you propose I change that? I assume that your arguments only apply to fielding and not throwing errors.

In any case, you are 100% wrong, Guy.  There is almost no doubt it my mind.  I’ve had 20 years to think about this.  As I said, one of the key’s (not the only key) to you being wrong is that we are using very imperfect buckets in the UZR engine.  If we were using exact locations and out rates for every ball, your argument might have some merit.  Even then, though it still would probably be better to just assume a 95% (or whatever) out rate for all errors.  And that is because the BIS data, even if it gave exactly location and I used that location and was able to associate it with an exact out rate, would not include such things as bad bounces or easy bounces.  For example, let’s say that we knew that a hard hit ball was hit directly at a fielder and BIS knew that also.  Well, the BIS out rate would include bad hops and easy hops, and might have an out rate of 90% overall.  If a fielder is awarded an error on that play, we have more information than just a hard hit ball hit right at a player.  We would know that it was likely that the ball did not take a bad hop and thus it was a 98% play and not 90%. Why would we want to ignore that information that the OS is providing us?  We wouldn’t!

"In any case, you are 100% wrong, Guy.”

Wouldn’t be the first time.  But I don’t think so.  My argument is that even if everything you say is true—every single one of these errors really was a gimme play—you are still wrong to make the adjustment.  UZR ultimately comes down to two numbers:  outs and expected outs.  We have no dispute about outs—fielding errors are not outs.  The question is how many expected outs a player had.  UZR is saying that a SS with 20 errors had 10 more 95% opportunities than a SS with 10 errors.  So your argument must be that, year after year, Jeter and Rollins have fewer of these automatic out opportunities than most SSs.  And yet, you can’t possibly believe that is true. 

Your assumption seems to be that more information is always better:  we know these plays were easy, so let’s use that information.  But that’s only true if we get this information in an unbiased way—and we don’t.  Scorers are not telling us how many 95% balls they thought a SS faced each game.  They are only telling us about these balls IF the fielder missed it—which doesn’t happen very often.  So a fielder who tends to miss these easy balls will be considered to have faced more of them.  Or you can look at it the other way: the outs this player did make were on more difficult plays than UZR recognizes, because a bunch of 95% balls have already been accounted for (on the errors).  Paradoxically, we are sometimes better off ignoring information, if it is provided selectively.

On top of all this, I think there are reasons to be concerned that errors are biased by players’ reputations, and perhaps other factors. But even if they are perfectly accurate and unbiased, you still need to leave it out of UZR.

Maybe a simple example will clarify things (or reveal that I don’t fully understand your calculations!).  Let’s say two SSs each face 100 of these 95% balls, on which an average SS will make 5 errors.  But UZR thinks these are all 80% balls (unless an error is made).  Let’s look at SSs who make 2 vs. 8 errors on these balls.

If 2 errors, UZR is 2*(-.95) + 98*.2 = +17.7 plays.

If 8 errors, UZR is 8*(-.95) + 92*.2 = 10.8.

So the 2-error SS, who is really 6 plays better, comes out +6.9.  Basically, UZR has increased the expected number of outs for the 8-error player by .9.  Have I understood the system correctly?

In other words, in UZR, errors are treated as balls that are normally fielded by that fielder and that fielder only (the one who made the error), 95% of the time, or whatever the average error rate is for that position and that type of ball.

Before I get into this at all - when you say error rate, rate of errors per what?

They way I award error runs is to take the difference between a player’s errors and how many errors a league average player at that position would make given the same number of “chances.” I don’t look at what kind of ball it was at all.  If a SS has 10 errors in 300 chances and the average SS has 20 errors in 300 chances then the SS gets credit for 10 fewer errors, or around 7-8 runs.

A “chance” in UZR is (arbitrarily) defined as the number of outs an average fielder (at that position) would make given the exact distribution of balls in play when that fielder is on the field.

Basically the number of outs a fielder makes minus his UZR converted into plays (rather than runs) is his number of chances.

I’ll have to think about Guy’s comments.  I might not be doing it 100% correctly, but I am pretty sure (99%) that ignoring errors and just treating an error as a missed ball and using the out rate for that bucket (like I do for hits) to compute the value of an error is dead wrong.  Ignoring valuable information is fine if you are using it incorrectly.  Ignoring valuing information for any other reason is crazy.  I don’t think anyone is going to dispute that knowing that a ball was an “error” is A LOT more valuable than knowing that a hard (or soft, or whatever) hit ball was hit in a zone 10 feet wide (probably, but not for sure), and we don’t really know exactly where the fielder was stationed, was not fielded.  As I said, that would be insane not to use the information that the OS is providing us with, which is that the ball was likely an easy one to field and was botched by the fielder.  Sure, there is bias by OS, and they don’t always get it right, but come on!  If we look at 100 errors scored by the OS, no matter how good or bad the OS was, we can be pretty confident that 95 of them would have been fielded on the average, if not for the “error.”

How many expected outs is an error, then?

And the reason you ignore the “information” errors gives you is twofold:

1) Scorer biases, in any number of forms.

2) You are missing that information on the majority of plays! It’s like using sac flies in a context-neutral linear weights, or measuring first baseman scoops without an idea of opportunities, or the way Fielding Bible Plus/Minus handles robbing a home run.

And I think you are conflating two ideas - the idea that errors/"chances" is .95 or whatever, and the idea that a ball where an error occurs is fielded 95% of the time on average - that really aren’t the same. And then you’re further conflating the second idea with one that says that this hold true for all players, regardless of things like park, scorer, or the observed batted ball profile!

"If a SS has 10 errors in 300 chances and the average SS has 20 errors in 300 chances then the SS gets credit for 10 fewer errors, or around 7-8 runs.”

OK, but then how do you handle the remaining 290 and 280 chances respectively?  Is each one assigned an out probability based on its bucket?  If so, it seems to me you’re double-counting the first player’s 10 non-errors, since they will again be counted as outs (at whatever value the buckets dictate).  Am I wrong?

Again, the 20 error player should clearly be debited for the 10 fewer outs he records.  The only question is whether we should ALSO assume that he also faced easier balls to field, by virtue of having committed more errors.  Isn’t that a rather odd assumption to make?

So let’s stipulate for this discussion that the OS is god-like in his wisdom and impartiality.  My argument is that it’s still wrong to treat the errors separately.  This is especially true if avoiding errors on easy balls is a discrete skill from range, which the UZR data certainly seems to indicate is true.  If so, the low-error players will be systematically overvalued by UZR, which assumes their low error total reflects fewer easy chances.

And I’m glad to see I’ve already moved you from 100% to 99% certainty.  I should be able to win this argument by Labor Day....

I don’t see why you keep saying that the assumption is that the player with more errors has more easy chances.  Not at all.

I don’t see why this is so complicated.  Let’s assume that no one makes any errors or that errors are counted as an out for the fielder, as they are for the batter.  Player A and B both fields 300 balls.  Of those, maybe 50 are difficult and 250 are fairly easy.  The ones that are difficult, if they were not fielded cleanly, the OS would not score it as an error (I am assuming for the sake of this example).

Of the 250 fairly easy ones, some players have better hands than others, obviously.  If I were out there, of those 250, I would field maybe 100 or 150 and the other ones would be scored as errors more or less.  It is similar with MLB fielders.  Jeter has great hands. Of those 250 plays, he makes 10 errors.  Someone else has bricks for hands and makes 20 errors.  That is all that is happening.  What is so complicated about that?

Now, we should all be in agreement about how to credit and debit the difference between Jeter and the guy with bricks for hands.  If the average fielder makes 15 errors, then Jeter turns 5 errors into outs and gets credit for around 4 runs.  The other guy turns 5 outs into errors and gets debited 4 runs also.  Again, where is the controversy? About the only thing that is “wrong” with that scenario is probably the fact that a player makes more errors slightly suggests that he had MORE balls that were easier to field, not LESS.  But that is ONE of many reasons why we regress things, even error runs!  And it is not that big a deal.  If I said that two fielders had the same number of outs (including errors), but that one fielder has 10 more errors than the other one, it is probably true that he is really only 9.5 errors worse, and that the other .5 was simply because he had more opportunities to make an error even though they both had exactly 300 outs + errors. 

If we treated those errors as merely missed balls like hits (which again is ridiculous - why would you treat a missed ball that is hit right at a fielder the same as a missed ball that on the average is fielded maybe 70 or 80% of the time?), then Jeter would only get credit for 70 or 80% of the errors he saves and the other guy the same.  That ain’t right.

I thought about it all night and I am back to 100% sure, so by Labor Day, I’ll probably have to come over to your house and set in on fire!

BTW, maybe some of the confusion is this (which I forgot to say in the primer).  Errors are counted as outs for all fielders before the error runs are tabulated.  Maybe that is why you thought they were being double counted!  If both players had 300 outs + errors but one player had 10 more errors (and thus 10 fewer outs), both of their “range runs” would be the same but one would have more error runs than the other. I should have explained that in the primer.  It is important.  When someone looks at anyone’s “range runs” on Gangraphs, it includes errors in a positive way, which is paradoxical of course. So UZR’s definition of “range” is getting to a ball even if you did not turn it into an out, as long as it is scored as an error (or fielder’s choice, not out) when you don’t turn it not an out.

I don’t really have anything else to say…

Other than the fact that Gangraphs = Fangraphs in an alternative universe…

"I thought about it all night and I am back to 100% sure, so by Labor Day, I’ll probably have to come over to your house and set in on fire!”

Funniest thing I’ve read this week. That escalated quickly.

Hmmm.  This may take until Christmas.  The problem here is you are focused only on these error plays, and it’s giving you tunnel vision.  They are really easy plays—easier than UZR thinks they are—and the Scorer has done us the favor of telling us that.  So let’s use the information!  Sounds good, but it’s wrong. 

You need to step back and look at the big picture.  We only care about two things in the end:  outs and expected outs.  Do the errors tell us anything new about outs?  Obviously not.  So it can only be helpful to treat errors differently if they tell us something new about expected outs.  But they don’t.  A player who makes more errors did not necessarily face easier to field balls.  He’s just someone who happened to miss a lot of easy balls.  That particular combination—miss/easy—gives us ZERO new information about his overall distribution of chances. 

Let’s finish the story of Jeter and Bricks.  Jeter is +5 plays on errors, Bricks is -5.  Let’s assume that Jeter makes 245 outs, 10 errors, and 45 hits (80% out bucket).  Brick has 235 outs, 20 errors, and 45 hits.  So Jeter is better on the easy plays, and they are equal on more difficult plays.  And they have identical range (255/300).  OK?

If we ignore errors, UZR would expect 240 outs on average, Jeter makes 245, so he is +5 plays.  Bricks is -5. To me, that seems perfect.  So please tell us how you would complete the process after treating the errors separately.  Does Jeter remain 10 plays ahead?  If so, what difference does this make?  And if not, why do you think that is more accurate?

Assuming ROE are included in the out rate (since MGL says he treats errors as outs up until the error adjustment), and assuming that I am understanding this properly, if the average fielder in the Jeter v Brick scenario is:

240 outs
15 errors
45 hits

then the out rate for the bucket would be .85, since (240+15)/300 = .85.  Jeter and Brick will both end up being 255/300 before the error adjustment, or exactly average.  Jeter is +5 plays on errors and Brick is -5 plays on errors, so it makes no difference in plays made, if all you have is one zone.  As far as I can tell, the main differences would be:

-if errors have a different run value on average than other non-outs, you can use different factors to convert hits to runs and errors to runs, sort of like how we split up IBB and nIBB so that we can use different values for each.  +5 plays on hits might not have the same value in runs as +5 plays on errors, so counting them as the same could lead to misvaluations, even if you get the same answer in plays using both methods. 

-if one of the plays is Jeter fielding a ball and the first baseman just drops it for an error, recording that as an out for Jeter and an error for the first baseman makes it easier to give the proper credit to Jeter and the proper debit to the 1B than if you just lump the error into all non-outs

-when you use multiple buckets, if the error rate for each bucket is different and you split out the errors and look at them all together, you will end up with a different number of expected errors than if you just did the errors by individual bucket like other plays

I don’t see how the first two could be controversial, and they give good enough reason to treat errors separately.  The third seems to be the crux of the disagreement, since it is the one that deals with how expected plays/opportunities are handled.  You won’t be able to see anything about the third point with a one-zone scenario, though, because it will just work out to be the same number of plays either way.

Now let’s say you have 2 zones.  For the second zone, per 300 balls, the average shortstop is:

200 outs
5 errors
95 hits

And in 300 balls, Jeter is 205 outs, 0 errors, and 95 hits.  His range will be 205/300, which is average again.  And once again he’s +5 on errors.  Now he’s +10 overall.  Brick, meanwhile, gets 300 more balls in zone 1 instead of 300 balls in zone 2, and he repeats his performance (235/20/45); he’ll be 0 plays in range and -5 in errors again, if we just treat errors as part of the zone.  However, if the typical shortstop has 20 errors in 460 balls reached, and Brick has 40 errors in 510 balls reached, then he’s not -10 in errors if we are breaking errors apart on their own.  He’ll be more like -18.  And if he instead 600 balls in zone 2 and none in zone 1, and he has 20 errors in 410 balls reached, he will be more like -2 errors instead of -10.  I think the issue becomes whether you can get a better estimate of the number of expected errors by breaking them down by bucket just like other plays, or by lumping them all together.

On that point, I have two questions for MGL:

-Is the 95% just used to get the average number of errors?  For example, if the average shortstop makes an error on 5% of the balls he gets to, you just take 95% of the balls each player gets to that you expect him to field cleanly, and then the other 5% is his expected number of errors.  Is that all the 95% is, or do you do something else with it?  Also, is that even what that figure means (the average number of errors/balls-reached), or is it something else entirely?  I can’t find anything else described for it in things you’ve written in the past, but I may be missing something.

-Is the expected number of errors equal to 5% (or whatever the percentage happens to be for the position) of the total number of balls reached by a player (outs+errors)?  Or is it based off of expected outs?  For example, if Jeter gets to 250 balls, but his distribution of balls is such that his expected plays would be 270, which figure would you use to figure the number of expected errors?  It would seem from the primer you wrote at BBTF several years back where you walked through the process for Mike Bordick that it is the former (number of balls actually reached), but maybe that has changed.

I have more thoughts on this, but I want to make sure I’m on the right page before I go rambling on.

"Or is it based off of expected outs?  For example, if Jeter gets to 250 balls, but his distribution of balls is such that his expected plays would be 270, which figure would you use to figure the number of expected errors? “

The 270.  Those are defined as “chances” (really, expected outs).  And average error rates at each position are league errors (at that position) per league chance.

It doesn’t really make much sense to use average error rate for each bucket.  Other than sample size issues, the point of knowing that something is an error is that we know it was an easy play.  So let’s say you have two buckets and one is an easy one (90% out rate) and the other is a hard one (10% out rate).  And let’s say that the error rate (errors per out) in one bucket were much different from the other, say 5% and 1%.  You still don’t want to give fielders different amount of debits for an error in each of those buckets!  An error is an error.  All errors are balls that should have been caught (95% of the time or whatever it is).  By definition, an error is in an “easy” bucket.  And error is an error and it does not matter what bucket it is in.  That is what I just use total error rates for each position and I don’t pay any attention what bucket it is in.  Again, errors are their own bucket.  Buckets tell us how easy or hard a ball was to catch.  But we already know that with errors. They were easy.  Putting them in buckets just misleads us.  Which is why one, using my method but doing it separately for individual buckets is wrong, and doing it Guy’s way, if I understand him correctly, is dead wrong!

I have to do play some golf now, and I’ll address Guy’s last post in more detail when I get back. Guy says this:

“A player who makes more errors did not necessarily face easier to field balls.  He’s just someone who happened to miss a lot of easy balls.”

That is 100% correct and that is 100% what I am doing. Why do you keep insisting that I am doing something that I am not - that is, that I am assuming that players who make more errors have gotten easier balls to field?  I am not!  I said in my last post, the assumption is that players have whatever they have (given the balls in they get in each bucket) and their number of errors has not relation to that whatsoever.  A player with more errors simply has bad hands.  NOT more easy to field balls!

When MGL finishes his round, I hope he can answer my question and tell us how to finish the process for Jeter and Bricks.  That should clear things up.  If it’s as simple as each player is zero on range, and they are +5 and -5 on errors, we have no disagreement.  But that’s the same result you would get if you treat errors the same as hits, so I’m guessing that’s not the case.

I can see advantages to separating errors, such as not penalizing a SS for a ROE if the first baseman made the error.  But that has nothing to do with the idea that errors are made on balls that are easier to field than the UZR bucket ‘thinks’ they are.  That particular information has no value and should clearly not be counted.  At this point, I can’t tell if it is.

The 270.  Those are defined as “chances” (really, expected outs).  And average error rates at each position are league errors (at that position) per league chance.

Ok, that’s good to hear.  That makes more sense than what I was thinking it was.

So doing it that way, it’s basically the same thing as doing it by individual bucket, except instead of using the actual error rate for that bucket, you just assume that the error rate should be proportional to the out rate.  This way, you are still basing the number of chances for an error on the bucket it is in, but instead of relying on the sample size of errors in the bucket, you are relying on the sample size or total balls reached in the bucket.

The only issue I would take with what is being done is the interpretation.  I think what is going on in the calculations is actually pretty close to what Guy is saying should happen.

Say you have a ball in a bucket where the out rate is .80.  You either observe an error, or you don’t; it either goes in the error count as a 1 or a 0.  The only issue is what to count for opportunities, and since MGL is using expected outs*.05 (or whatever the error rate is), for this ball, that is .80 * .05 = .04.  So that is .80 expected plays (including errors), and .04 expected errors on that particular ball.  Then, let’s say the next ball is in a bucket with only a .20 out rate, and now the error rate for this ball is .20 * .05 = .01.  You can get an expected number of errors on each play, and it will be unique for each bucket, just like the expected number of outs (the out rate).  Whether you total up the expected outs first and then multiply by .05 to get expected errors, or you first calculate the error rate for each individual bucket and then total up the expected errors, it gives you the exact same result (this is just the distributive property).

Going back to the Jeter example, we have our average fielder as reaching 255 balls and allowing 45 hits in zone 1.  The breakdown for the average fielder, using expected errors = .05*chances, would be:

242.25 outs
12.75 errors
45 hits

And for zone 2, we have 205 balls reached and 95 hits, broken down as follows:

194.75 outs
10.25 errors
95 hits

If Jeter is 245/10/45 for zone 1 and 200/5/95 for zone 2, that puts him at even on balls reached in both zones, and +2.75 on errors in zone 1 and +5.25 on errors in zone 2, or +8 plays overall.  That’s if we calculate it by individual zone.  If we go a step further and remove errors completely and just count them as non-outs, like Guy has talked about, we get:

average:

Zone1:
242.25 outs
57.75 non-outs

Zone2:
194.75 outs
105.25 non-outs

Jeter will be +2.75 plays in zone 1 and +5.25 plays in zone 2.  Same thing.

Now, if we aggregate the errors separately like MGL does, we get even on plays in both zones, and then do a separate error adjustment, based on the fact that Jeter had 255+205=460 expected plays:

460*.05 = 23 errors for the average fielder
23 - 15 = +8 plays for Jeter in errors

So his total plays will still be 0 plays reached + 8 fewer errors = +8 plays.  And, if, instead of having 300 balls in each bucket, he has 600 balls in the first (and performs the same for the second 300 as the first), then he’ll be even on balls reached and +5.5 on errors, or +5.5 plays, no matter which way you measure it.  The issue with how to combine errors from different buckets disappears when you calculate the expected error rate based on expected outs instead of just using the observed error rate for the bucket.  It is the exact same whether you do it Guy’s way or MGL’s way, as long as you don’t use the actual observed error rates for each zone and instead use expected errors = overall error rate * expected outs.

The advantages of using MGL’s method are:

-it doesn’t rely on the observed error rates in the samples, and instead uses the more reliable out rates (which have far more observances) to figure the expected error rate of each bucket

-the other advantages of having a separate error total (i.e. ability to apply different run values, easier to split up value between fielders if one makes the play but the other loses the out to an error)

But other than that, I dont’ think there’s really any difference between what MGL is doing and what Guy is talking about.  What I do disagree with is MGL’s interpretation of what is going on.  The value of each error is still dependent on the bucket it is in, because it is the expected outs that determines that value.  If the bucket has a .80 out rate, then an error costs .96 runs and a non-error (even if it is not a play made) saves .04 runs.  If the bucket has a .20 out rate, then an error costs .99 runs and a non-error saves .01 runs.  That’s exactly how the math works out:

.80 expected outs -> .05 * .80 = .04 expected errors
1 error = .96 more than expected
0 errors = .04 less than expected

.2 expected outs -> .05 * .20 = .01 expected errors
1 error = .99 more than expected
0 errors = .01 less than expected

Again, doing it that way where you get the expected errors for each individual play is the exact same as aggregating the expected outs first and then multiplying the total by .05.

The simplest way to interpret this is not that only easy plays can become errors, because this gives a certain chance for an error on every play, with the chance steadily growing the easier the play gets.  The chance of the error, using this method, is entirely dependent on the chance of getting to the ball and making a play on it, but once you get to the ball and make a play, this method gives exactly the same chance of an error no matter how hard it was to get to.  If the chance of getting to the ball is only .20, then the chance this method gives for an error is .20*.05, which is the exact same chance of getting an error, given that you have reached the ball (.05) as if you reach a ball that is reached 95% of the time.  The .95 ball just has a higher chance of becoming an error because it is much more likely to be reached.  Mathematically, that’s more or less what is happening.

Alternatively, you could expand that interpretation to say that every ball in the .20 bucket has a certain probability of really being a .95 ball that the data does not describe very well.  We know it was an easy play that was misclassified if it gets scored as an error, but if it is not scored as an error, then we only know that there is a certain probability that it was really an easy ball that was misclassified.  I think this is what Guy is talking about when he says only using that information when an error actually occurs is biasing the data; we can call the ball easy if it is scored an error, but not if it is not scored an error.  However, we can deal with that bias by assigning a probability to every non-error that it was in fact an easy play that was misclassified, which is what MGL’s method is doing.  It is saying that when there is not an error recorded, there is still a certain percentage of the time that it was in fact easy and did in fact provide an opportunity for an error, and that that percentage is proportional to the out rate we give the ball.  If we have a .80 ball, the chances we misclassified an easy play that was really an error opportunity is 4 times higher than the chance we misclassified a .20 ball in the same way.  So, in that way, MGL’s method does account for the bias Guy talks about and does give a measure of opportunity for errors based on the observed out rates for the bucket.  The inclusion of the stipulation that the probability that a ball that was not recorded as an error was still an easy play, no matter what we measure the out rate as, is a key part of the interpretation, though.  That’s the part that balances the bias Guy mentions, and without that in the interpretation, you would have to assume the bias is there.

I think that second interpretation is pretty close to reconciling what MGL and Guy are disagreeing on.  Mathematically, what MGL is doing is very close to what Guys suggests.

I said in my last post, the assumption is that players have whatever they have (given the balls in they get in each bucket) and their number of errors has not relation to that whatsoever.

I’m confused.  Are we still talking about baseball or is this about MGL at the driving range?

Kincaid: I obviously don’t know if you are describing MGL’s method accurately.  If so, then there is no disagreement and nothing to reconcile.  But in that case, it is simply not true that UZR is incorporating any additional information from Official Scorers—whether a non-out is ruled a hit or a fielding error is irrelevant.  Perhaps you’re right, and MGL is simply mistaken when he claims to be using this additional information.  However, it would surprise me if he were wrong about that....

I don’t think he is describing what I am doing correctly, but I have to go to a birthday party now and come back to this later.  Although I don’t have any money left for a birthday present after my golf round.  I definitely should have hit more buckets!

Or gambled less!

I think you guys (not pun intended) are making this way more complicated than it is.  An error is simply an easy ball to field that was not fielded.  It is its own bucket (balls that are easy and are fielded 95% of the time).  How you handle them has nothing to do with what UZR bucket it is in (location, speed, etc.).

If they are in a bucket that is 20% or a bucket that is 80%, they are treated exactly the same - an easy ball that was missed. Now, the confusion with Kinkaid’s interpretation, I think, is that because they are first treated as outs, they get more positive value in the 20% bucket and less positive value in the 80% bucket, so that when they receive the same negative value as an error in both buckets, the net value of the error is more negative in the 80% bucket than the 20% bucket.  Come to think of it, because of that, we all might be saying the same thing. Wouldn’t that have been a waste of time!

IOW, if an error is committed in a 20% bucket, first the fielder gets credited with an out.  He gets exactly .8 balls worth of credit, or around .65 runs.  Then when the errors calculations are done, he gets docked around .75 runs for the error, assuming that it is an “extra” error over and above the average player at that position (for that year and league).  So the net value of the error is -.1 run in that 20% bucket.

If he makes an extra error in a 80% bucket, at first he gets only .2 balls of credit for the out, or around .15 runs, and then he gets docked in the “errors” part of the calculation .75 runs (the same as in the other bucket, and all buckets), for a net total of -.6 runs for that error.

Does that sound reasonable to you guys?  So actually an extra error in the 80% bucket is lot worse than one in the 20% bucket.  Again, we might be saying exactly the same thing, but I did not explain how I handle the errors very well (I left out the part that the player first gets positive credit for the out, which varies according to the out rate of the bucket, and THEN he gets docked for every extra error he commits, with a constant value for all errors - the net effect being different values for an error in different buckets).

If I follow you, your player reached one extra ball in the 20% bucket, but he booted it.  He is credited with -.1.  But if the ball had been ruled a hit, he would be at zero.  Have I got that right?  If so, I believe this is mistaken:  in both cases he should be zero.  And this is why I kept saying you were assuming the player who makes an error faced easier balls—because that’s exactly what you’ve done here!  Both player have made the same number of outs, so if the guy with the error is -.1 then by definition you have—knowingly or not—decided he faced easier balls.

It’s far worse in the 80% bucket.  Again the player has reached one extra ball but failed to convert it, so we want UZR = 0.  But now he’s -.6!

And just to be clear, your examples involve a player with above-average range, but who also makes an extra error.  My examples were of players with equal range, one of whom made more errors.  I’d still be interested in hearing how Jeter and “brick hands” come out under UZR.

*

“It is its own bucket (balls that are easy and are fielded 95% of the time).”

THIS is the crux of our disagreement.  You may NOT create a 95% bucket for errors, because it’s not a random sample of observed BIP.  Every ball in this bucket had to be an error—there are no outs in this bucket.  So players with “good hands” will have smaller 95% buckets in UZR, even though we have no reason to think they actually faced fewer 95% BIP.  I hope that makes my point clear—I don’t know how else to say it.  (Having said all that, it’s still not clear to me that UZR does in fact treat these as 95% out balls.  Maybe it doesn’t. But if it does, that’s a mistake.)

As long as you are basing expected errors off of expected outs, then yes, the value of the error depends on the out rate of the bucket, because the out rate is what determines the expected outs, which is what determines the expected errors.  The value of an error/non-error on each individual play is found the same way as the value of an out/non-out; you just compare to the average rate.  If the error rate for a ball in a given bucket is .01, then the cost of the error is -.99, and the credit of not making an error is .01 (in terms of errors above or below average, and of course you add this to the range runs for the play to get the total value for that play).

Then when the errors calculations are done, he gets docked around .75 runs for the error, assuming that it is an “extra” error over and above the average player at that position (for that year and league).

The “assuming that it is an ‘extra’ error over and above the average player at that position” part is key.  You can tell precisely how far over and above the errors expected by the average player each play is, because that average error rate is based on the expected outs, which you already know for each play.  What’s more, the amount over and above the expected amount will vary for different buckets.  The value of the error itself might be the same, but the number of errors over and above the average player is not the same.  It is just like if you have an out in the .8 bucket and an out in the .2 bucket.  The out may be worth the same for each in terms of the absolute value of the out, but the one only counts as .2 outs above average while the other counts as .8 outs above average.  The same thing happens with errors.  Both might be worth the same in terms of absolute value, but an error in the .8 bucket will be .96 errors more than average while an error in the .2 bucket will be .99 errors more than average.

When you figure the average number of errors for a player based on his expected outs, you are totaling up the expected outs, and then multiplying by the error rate.  Say that the error rate is .05 and a player has 250 expected outs:

.05 * 250

And, of course, the expected outs are just the sum of the expected outs for each individual play:

.05 * (.8 + .2 +...)

Where inside the parentheses are the expected out rates for each play, which will total up to 250 when you add them all together.  By distributing the .05 factor to each term in the sum, you get:

.05*.8 + .05*.2 +....

and that gives you the expected errors for each individual play:

.04 + .01 +....

and those will of course total up to 12.5, the same as if you just took .05*250.  So taking the error rate for each individual play by multiplying the out rate by .05 is the exact same thing as just totaling up the expected outs and then multiplying by .05 to get the number of errors for the average player.

Once you know the expected error rate you are using for each individual play, you can measure errors above or below average on every single play.  It’s the exact same process you use to get outs above or below average for range once you know the expected out rate of the ball.  If you do it using the exact same process as the outs, you get the same answer as if you just aggregate the expected outs first and then calculate one total expected errors for the average player from that.

Does that sound reasonable to you guys?  So actually an extra error in the 80% bucket is lot worse than one in the 20% bucket.  Again, we might be saying exactly the same thing, but I did not explain how I handle the errors very well (I left out the part that the player first gets positive credit for the out, which varies according to the out rate of the bucket, and THEN he gets docked for every extra error he commits, with a constant value for all errors - the net effect being different values for an error in different buckets).

For the .20 bucket:

-on a play made (no error), the fielder gets .8 plays in range + .01 play for not making an error (.81 plays total)

-on an error, the fielder gets .8 plays for getting to the ball and -.99 plays for making an error (-.19 plays total)

-on a play not made, the fielder gets -.2 plays in range + .01 play for not making an error (.19 plays total)

.....
For the .80 bucket:

-on a play made (no error), the fielder gets .2 plays in range + .04 play for not making an error (.24 plays total)

-on an error, the fielder gets .2 plays for getting to the ball and -.96 plays for making an error (-.76 plays total)

-on a play not made, the fielder gets -.8 plays in range + .04 play for not making an error (-.76 plays total)

So yeah, the error in the .80 bucket is more costly, by quite a bit.  You are giving different debits for errors in different buckets, and the net effect is the exact same as what Guy has been saying it should be (at least once you throw out the observed error rates and just derive them from the out rate instead).  I don’t think it has anything to do with not explaining the positive credit of the out coming first (you did explain that in this thread, and that was a point that was incorporated into the model I was describing).  It’s just that what you are doing for the calculations is inherently giving errors different credit/debit based on the bucket they are in and is in fact matching almost exactly with what Guy was saying should happen, and saying that that is not what is happening or that that is dead wrong has been causing confusion.

If I follow you, your player reached one extra ball in the 20% bucket, but he booted it.  He is credited with -.1.  But if the ball had been ruled a hit, he would be at zero.  Have I got that right?

Why would he be at zero if it were ruled a hit?  Zero would be exactly average, which is 20% of an out.  He would get docked .2 plays for not getting the play (plus a small bonus for not making an error, so -.19 plays), which would be however many runs.  In terms of plays at least, it would be the same negative as if it had been ruled an error.

And actually, this is all just a simplified version when you are looking at only one fielder at a time.  In reality, for a hit, you would split up the debit between adjacent fielders, because you don’t know that there was one fielder responsible (unless maybe it is hit right at someone, then he’ll probably get the vast majority of the debit).  For an error, I’m guessing MGL just gives the full debit to the fielder with the error, so there actually would be a difference once you introduce the other fielders into the mix.  Just when you look only at one fielder at a time and give all the hit debit to one fielder, it simplifies to the same thing.

"Why would he be at zero if it were ruled a hit?”

Kincaid:  MGL stipulated that this was an “extra” error by the player (i.e. one more than we expected).  That’s why he initially gets positive credit.  So I’m assuming he has one more error but one less hit than average.  If the error were instead scored a hit, he’d still be average overall (assuming we give equal run value to hits and errors).  Right?

In any case, a player who makes one extra play, when that play is a fielding error, should definitely be zero and not -.1.  Agreed?

It doesn’t matter what other plays the fielder has or hasn’t made, that one play will still be worth the same.

The player initially gets positive credit because errors are included in the plays made for the range component.

In any case, a player who makes one extra play, when that play is a fielding error, should definitely be zero and not -.1.  Agreed?

Not unless the out rate of the play is 0, no, because the cost of making the error is greater than the benefit of making the play.  The expected number of errors is always going to be 5% (or whatever the error rate for the position is) of the out rate, so the number of errors made more than average on the play will always be more than the number of plays made more than average, unless they are both exactly 1 (which is when the out rate is 0).

This is basically the opposite of what you have been saying all along.  If allowing a hit is a negative, and not making the play on an error should be the same as not making one on a hit, then why are you saying now that the error should be counted as 0?

Kincaid:  The first point I’d make is that our discussion is to some extent pointless.  Only MGL can tell us what he’s doing. And I really hope he will give us a complete description of a few specific scenarios—like “jeter” and “brick hands” above—so we all have a common base of knowledge.

Second, a source of confusion is sometimes analyzing this in terms of a distribution of BIP and corresponding outcomes (my preference) vs. looking at a single hypothetical BIP as you are.  You say “it doesn’t matter what other plays” are made, but it does.  Is your hypothetical error a play that we expect to be an out, or one that we expect to be a hit?  If the former, the error is very costly; if the latter, it makes no difference.  I’m not sure it’s even possible to do this one ball at a time—how do we then know if an error is “extra?” In any case, I can’t make sense of it that way.

Here’s my bottom line:  what matters is out or non-out.  Hits and fielding errors (made by the player we’re analyzing) should be rated the same.  And if a fielder reaches a ball we didn’t expect him to but then makes an error, the UZR should be the same as if he never reached it at all.

It doesn’t matter if you do it one ball at a time or all together.  You get the same results.  All that is is the distributive property at work.

What other plays the player has made has no bearing on whether you expect a play to be a hit or an error. The only thing that matters is the data you have on that ball.  If you get a ball that is 20% out (with outs including errors) and 80% hit, then it doesn’t matter whether the fielder fielded the last ball in that bucket or not, or what he did on some other ball in another bucket.

Earlier, you described what you wanted to see as:

Let’s finish the story of Jeter and Bricks.  Jeter is +5 plays on errors, Bricks is -5.  Let’s assume that Jeter makes 245 outs, 10 errors, and 45 hits (80% out bucket).  Brick has 235 outs, 20 errors, and 45 hits.  So Jeter is better on the easy plays, and they are equal on more difficult plays.  And they have identical range (255/300).  OK?

If we ignore errors, UZR would expect 240 outs on average, Jeter makes 245, so he is +5 plays.  Bricks is -5. To me, that seems perfect.

You can get to the +5 and -5 by totaling up all the plays in that bucket and seeing Jeter made 5 more plays and that Brick made 5 fewer.  Alternatively, you can give Jeter +.2 plays for every out and -.8 plays for every non-out, and then it adds up to +5 (and do the same for Brick and it adds up to -5).  Doing it one ball at a time or in the aggregate is the exact same thing.  Again, just the distributive property.  That’s all it is.  If you prefer to do it one way or the other, that’s fine, but it’s still the same thing both ways.

If errors are handled as MGL has said where the expected number of errors is the expected outs (chances) times the error rate, then doing the errors works the same way.

Is your hypothetical error a play that we expect to be an out, or one that we expect to be a hit? If the former, the error is very costly; if the latter, it makes no difference.

You can never classify it perfectly as one or the other just from looking at the data; it will fall on some spectrum of and expected out rate somewhere between 0 and 1.  And yes, how costly it is depends on the estimated out rate for that ball based on what bucket it is in.  The more likely it is estimated to have been a hit, the more costly the error.  That is what I’ve been saying all along and what MGL said in his last post.  It will never not make any difference, because you’ll never have an error made on a play with 0 chance of an out, but as the out rate for the bucket gets closer to 0, the cost of the error will get closer to 0.  But none of that has anything to do with any other balls the fielder has fielded.  It just depends on the data you have on that ball.

Say someone has 100 balls in an 80% out rate bucket (with a 4% error rate and 76% actual out rate).  If he has made 0 plays (no outs or errors), he’ll be at -76 plays (-80 on outs, +4 on errors).  Then, if he makes an error on the next ball, he’ll have 1 play in 101 balls in the bucket, and 1 error.  The expected plays is .8*101 = 80.8 plays, and the expected errors is 4.04.  Our fielder now has 1 play and 1 error, so he is -79.8 on plays and +3.04 on errors, so -76.76 plays overall.  He was at -76 before, so that play was -.76.

If he had been 100 for 100 on those same 100 balls, with no errors, he would be +20 on plays and +4 on errors, for +24 overall.  The 101st play, he makes an error.  Now he has 101 plays with 80.8 expected and 1 error with 4.04 expected, so he’s +20.2 on plays and +3.04 on error, so +23.24 over all.  He was +24 before, so that play was worth...-.76 plays.

If he had been 100 for 100 on getting to those balls but they had all been errors, he’d be +20 on plays and -96 on errors for -76 overall.  An error on the 101st play will put him at +20.2 plays, -96.96 on errors. and -76.76 overall.  The error was worth, once again, -.76 plays. 

If you just ignore everything else the player has done, and look at that one play where he made the error, you see he is +.2 on plays and -.96 on errors, for -.76 overall.  And if you ignore errors altogether, then the out rate is 76%, and when he doesn’t make the out, he is at -.76 plays.  Same thing no matter how you do it.  It doesn’t matter what he’s done on the other balls he’s fielded:  an error on this ball, once you know what bucket it is in, has the same value.  That’s regardless of whether he had more or fewer errors than average before or after this play or whether he made more or fewer outs or allowed more or fewer hits.

Kincaid:  are you describing how you think UZR should work?  How you think it may work?  Or how you actually know it does work?  It would help a lot if you would clarify that.

I’m describing it based on what MGL has written out on it, and based on how he answered my questions earlier in this thread.

OK.  But as you describe it, the value of an additional error or additional hit in any given bucket is exactly the same.  But MGL doesn’t think he’s doing that, and said he thought you were wrong back in #39.  So are you suggesting that MGL is in fact doing this correctly after all, but is doing his best to convince us he’s doing it wrong?  :>)

I don’t have a problem with the process you’re describing, but again it has nothing to do with errors being “easier” plays, or incorporating that information in any way.  Agreed?

I’ll ask MGL this as an extension to my earlier questions:

If Jeter’s expected outs is 270 (regardless of how many balls he actually got to), and the average error rate (errors/expected outs) for shortstops in that season is 5%, then would the average number of errors you would compare Jeter against be 270*.05=13.5?  And if Jeter makes 5 errors in those 270 expected outs, then is he 8.5 plays (not runs) above average on errors?

That is how I read the answers to MGL gave to my earlier questions, but if that is inaccurate, then what I said above will probably not be true to what MGL is doing.

OK.  But as you describe it, the value of an additional error or additional hit in any given bucket is exactly the same.  But MGL doesn’t think he’s doing that, and said he thought you were wrong back in #39.  So are you suggesting that MGL is in fact doing this correctly after all, but is doing his best to convince us he’s doing it wrong?  :>)

Basically, yeah.

I don’t have a problem with the process you’re describing, but again it has nothing to do with errors being “easier” plays, or incorporating that information in any way.  Agreed?

Agreed.

The additional information would come into play for splitting up the debits on hits/errors between fielders, since on an error you can pinpoint one fielder and on a hit you can’t (the alternative would be to debit the third baseman or second baseman every time the shortstop makes an error - sometimes even moreso that you would dock the shortstop himself - if you want to just treat errors the same as hits), but that still has nothing to do with how difficult or easy the play is.

Kincaid, you have the methodology exactly down pat.

“Here’s my bottom line:  what matters is out or non-out.  Hits and fielding errors (made by the player we’re analyzing) should be rated the same.  And if a fielder reaches a ball we didn’t expect him to but then makes an error, the UZR should be the same as if he never reached it at all.”

Guy, that is 100% wrong (remember I am back to 100%), and it is shocking that you can’t see that that is wrong.  A hit is a ball that is in a certain bucket and is not fielded. It might have been a clean hit which had no chance of being fielded or it might have been a ball hit to one side of a fielder or another and he could not get to it for whatever reason.  It could even be a botched play occasionally that the OS did not rule an error.  On the average, though, it is a ball that gets fielded whatever the percentage of time it gets fielded by the average fielder.

An error is a ball hit right to a fielder and he boots it (more or less).  Yet, somehow you want to equate the two.  And somehow you can’t see that that is wrong?

Allow yourself (Guy) to enter this discussion with no pre-conceived notions and consder this and this only:

We have a bucket that has an out rate of 10%.  It has an out rate of 10% because it is a bucket where balls are really hard to field, probably hard hit (for a GB) and in a hole somewhere.  It occasionally gets fielded only because someone occasionally makes a spectacular play or someone happens to be stationed in or near the hole for whatever reason (and it is not recorded by BIS as a “shift"). 

If a player does not make a play on a ball in that bucket, it is not a big deal - he is not expected to make a play.  Thus, he only gets docked .1 plays.

Now, a player gets an error in that bucket.  Likely the ball was hit right at him or just to his right or left such that it was an easy play.  It is likely that he happened to be playing in the hole for whatever reason, or perhaps the data was not recorded real well (the stringer actually made a mistake which will occur on some small percentage of batted balls I assume).

Now, again, forget about your pre-conceived notions AND forget about UZR and how it works.  And most importantly, forget about any other plays in or out of that bucket.  For which play do you think a fielder should get greater demerits?  A hit, which is likely in the hole, nowhere near him and hardly anyone ever catches (hence a 10% out rate in that zone), or a ball which is hit right to him (again, he happens to be playing in the hole or the data was not recorded real well) that he boots?  Please rpeat that entire question and then answer it knowing nothing about UZR and having no pre-conceived notions about how you think UZR should handle errors or hits.

If you answer that the only way any reasonably thinking person can answer that question, you will immediately see the folly of the your statement that I quoted above.  But only if you release your heels from the quagmire they are buried in....

I think the one with a lot of preconceived notions about UZR here is you, MGL. And it would be really nice if we could have this conversation without the bombastic rhetoric and the appeals to authority and whatnot. But if you want to treat the rest of us as supplicants rather than peers, that’s your choice.

That said - even if I grant all your assertions about what an error means (and let’s be clear - I don’t, not by a long shot) you’re, as you say, “100% wrong.”

What an error tells us - in a perfect, ideal world where official scorers are a lot better at their jobs than they really are - is what an average fielder would have done on the play given the same positioning as the fielder.

On all other plays, UZR tells us what it thinks would have happened considering an average fielder with average position accounting for known variables.

Everyone tracking so far?

UZR does not, can not, and should not grade a fielder based upon his actual position! It doesn’t have the information to do so, and even if it did, we consider a fielder’s ability to position himself correctly in advance of the play as a skill! Now, we do take into account certain aspects of strategic positioning, but UZR (rightly!) ignores other aspects of positioning.

Except for on plays with errors, where we only concern ourselves with whether or not a ball was hit “right at” a fielder (again, if we are considering hypothetical official scorers that are much, much better than existing scorers) given his actual position!

So you have two seperate approaches to UZR:

1) Ignoring individual fielder positioning and grading against the average position for a fielder (given the known variables - count, baserunners, etc.).

2) Ignoring the average position for a fielder given known variables and grading against the fielder’s actual position.

That’s - again, as you say - 100% wrong. And hopefully it doesn’t take you another 20 years to figure it out.

"Kincaid, you have the methodology exactly down pat.

[Guy:] Here’s my bottom line:  what matters is out or non-out....

Guy, that is 100% wrong”

MGL:  You simply can’t have it both ways.  Under Kincaid’s system, UZR treats a hit and an error exactly the same.  The official scorer’s judgement has no impact whatsoever.  He and I are in agreement on this.  So you can agree with both of us, or neither of us.  But your current position is logically impossible.

I suspect UZR is in fact treating hits and errors the same, as Kincaid suggests.  But I can’t say for sure.  But if you will tell us the UZRs for these scenarios, maybe we can finally sort that out.

100 balls in 80% Range Bucket
Average Fielder
Out 75
Error 5
Hit 20

Player A
Out 75
Error 8
Hit 17

Player B
Out 72
Error 8
Hit 20

Player C
Out 72
Error 5
Hit 23

My answers (in plays):
A 0
B -3
C -3

Does UZR reach the same conclusions?  If so, then we agree (but you are not using any information from the official scorer, as you claim).  If not, please tell us the results and how they are derived.  Thanks.

"Allow yourself (Guy) to enter this discussion with no pre-conceived notions and consder this and this only:”

MGL:  I basically agree with everything you say here.  I conceded long ago that errors are easier plays than the “bucket” thinks they are.  The fact that you keep repeating this argument, again and again, in different forms, shows me that you still don’t understand my argument. So it’s you who needs to step back, stop thinking about the error plays alone, and look at the bigger picture.  (After which you can still disagree with me.)

My point is that your “95% bucket” is biased.  Furcal has made 30 more FE than Jeter since 2002.  Is it your contention that he has faced 30 more easy plays?  Obviously he hasn’t (or at least, we don’t know that).  All we know is Furcal misses a higher % of easier plays.  That information thus has NO value to UZR, even though it increases our accuracy on the small number of balls resulting in an error.

Tango:  can you help mediate here?  I’m obviously not getting thru.....

"Is it your contention that he has faced 30 more easy plays? “

No, I already said that.

“All we know is Furcal misses a higher % of easier plays.”

Yes, of course.

“That information thus has NO value to UZR, even though it increases our accuracy on the small number of balls resulting in an error.”

I don’t know what you mean y, “increases our accuracy on..” but of course the information has value to UZR.  It tells us that Furcal had 30 easy plays that he missed.  If they were simply treated as outs (let’s say that BIS didn’t even distinguish between an out and a hit), Furcal would be given a lot more credit than he deserves.  UZR would think that those errors were hits and that they were a lot harder, on the average, to field then they were, depending on the out rate of their bucket of course.

I think I already explained in many venues exactly how UZR treats errors, hits, and outs, do I don’t know why you keep asking me that.  Later, I’ll tell you again exactly how UZR treats your above examples.  Maybe we will arrive at the exact same answer, I don’t know.  Regardless, your contention that an error (such as if we didn’t even know that it was an error - only that it was not fielded, just like a hit) can be treated the same way as a hit is wrong, I believe.  And I gave you a perfect example of how is has to be wrong.

I’m trying to figure out how to jump in here, and haven’t figured out how.

Tango:  keep trying.

“It tells us that Furcal had 30 easy plays that he missed.”

Exactly right.  So what?  We already know which plays Furcal missed.  The only thing we’re trying to figure out is how many plays he SHOULD have made.  And you acknowledge that the error data sheds no additional light on this—it doesn’t necessarily mean Furcal faced easier balls.  So if the errors tell us nothing about outs recorded, and nothing useful about expected outs, how can it be helpful?  I keep asking this question, but you’ve never answered it.

Guy: Isn’t the argument that errors do actually tell you something useful about expected outs?  As you’ve conceded, the plays with errors recorded would be generally “easier” plays than the buckets would otherwise think they are.  So you’d have to increase your expected outs on those particular balls. 

I don’t know if this is the best way to do it--it seems on error plays, you pretty much take any ranginess credit away from the fielder.  Instead, you assume the ball was easy to get to.  This would mean the player does not get any credit for whatever-it-is-that-made-the-ball-easier, which I assume most of the time would be positioning.  That may be correct, but it seems inconsistent to give the player credit for positioning in all other circumstances (except where “shift” is marked).

"you” in my second paragraph = UZR, not Guy.  Or at least it = UZR as I tentatively grasp it after having read most of the thread.  Sorry for any confusion.

Those 30 extra errors were easy balls.  Had they been hits, they would have been average balls to field in that bucket.  How is that not extra information that we can use to dock the player runs?  If those 30 balls were hits, he would get docked maybe a total of .7 times 30 balls (if his average bucket had a 70% out rate).  If they were errors, he would get docked .95 times 30 balls.  I just don’t get what you are trying to say.  And the fact that one player has more errors DOES actually mean that he got more easy balls.  I was wrong in saying that it did NOT mean that. Here is an easy way to prove that:  What if a player got 100 errors in a certain bucket with a 70% out rate for the average fielder, and another player got the usual 70 outs and 30 hits?  The second players got the typical distribution of hits and outs (we don’t know how many of these were routine or easy of course), and the first player got 100 easy balls!  How do we know that?  Duh!  He got 100 errors!  Well, how about 99 errors for the first player and again 70/30 (outs/hits) for the second player?  98?  97?  As long as one player has more errors than another player, he got more easy balls. Again, I just proved it by looking at an extreme situation and working backwards. 

You are digging yourself a deeper and deeper hole Guy with lots of faulty assumptions.

100 balls in 80% Range Bucket
Average Fielder
Out 75
Error 5
Hit 20

Obviously UZR of zero since he is average.  His range runs are zero and his error runs are zero.

Player A
Out 75
Error 8
Hit 17

First we figure the range runs.  Remember that errors are treated as outs for that.  We’ll assume no other fielders make outs in this bucket (since if they did, that would change the value of hits for this fielder, since he would have to share the responsibility with other another fielder or fielders).

He made 3 more outs+errors and 3 less hits (obviously) than the average fielder.  So he gets credit for 3*.2 plays or .6 plays or around .46 runs in range runs. 

Now, we have to do the error runs separately.  Simple.  He made 3 more errors, so he has -3 plays or around -2.25 error runs.

His total UZR is -1.79 runs. In plays, it is -2.4 plays, but the play is worth slightly different if it is an error or a hit, since the value of an ROE and a hit is slightly different.

Has we simply treated those 3 extra errors as hits, we would have:

Player A
Out 75
Hit 25

The average fielder would be (treating errors as hits)

Average Fielder
Out 75
Hit 25

So our player would have a UZR of zero since they both made the same number of outs.  The reason player A, using my method, is -1.79 runs, even though he made the same number of outs, is that he did indeed likely get more easy plays by virtue of the fact that he made 8 errors rather than 5.  Someone (and that someone might be you) would say, “Well, they both made the same number of outs, so clearly they had the same value.” Yes, they had the same “value” just like two pitchers who have the same ERA or RA had the same value.  But in UZR (and all evaluation metrics where we are trying to separate out some of the luck) we are taking into consideration how hard or easy balls are and not just their results.

Anyway, to once again prove my point, what about this fielder?

Player M
75 outs
25 errors

You want him to get the same credit as the average fielder (75 outs and 25 hits) and have a UZR of zero because they both allowed 25 missed balls?  What?  He made 75 outs, presumably on balls that were fairly easy to field (a few of them obviously were tough and he made the play anyway).  And then he got another 25 balls that were also easy to field and booted them.  So basically he got like 90 or 95 easy to field balls and maybe 5 tough ones (in which he made the out anyway, or maybe the OS scored an error even though it was a hard ball to field).

Our average player made 75 outs also, presumably on fairly easy balls and another 25 were hits.  Presumably these were impossible to catch for the average fielder.  So he has 75 easy balls and 25 hard ones (more or less - obviously there is some overlap).

So obviously the distribution of balls to both these fielders, the average one, and player M, were completely different.  How do we know that? I just explained that.  When a ball is an error, it was an easy play.  When a ball is caught, by definition, it was a fairly easy play.  And when a ball is a hit, it is, by definition, a pretty difficult play.  So when we know the percentages of errors, hits, and outs, it tells us the approximate distribution of batted balls in terms of difficulty.

Again, if you think those players had the same distribution of batted balls in terms of difficulty, well, I don’t have anything more to say.

Anyway…

Player B
Out 72
Error 8
Hit 20

Range runs are zero, since he makes the same number of outs+errors as the average fielder.  His error runs are -3 plays or -2.25 runs, for a total UZR of -2.25.

Player C
Out 72
Error 5
Hit 23

His range runs are -3 plays and his error runs are zero for a total of -3 plays.

My answers (in plays):
A 0
B -3
C -3

So, you got B and C right, but not A, for the reasons I articulated above. Again, using your method for A, you would have the 75 outs and 25 errors having a UZR of zero also, which is preposterous as I also explained above.

Simply ask Tango if that is correct - that is all he has to answer - whether a player with 75 outs and 25 errors in a 80% out bucket should have a UZR of zero when the average fielder is 75 outs and 25 hits or 75 outs, 20 hits, and 5 errors, in that same bucket.  I’ll wager any amount of money that you want (or don’t want) that Tango will say, “Of course that 75 out, 25 error player does not have a UZR of zero!  He happened to have had an anomalous distribution of ground balls (assuming an IF of course) in that 80% bucket.  He had 75 balls that he caught and rather than the other 25 being tough balls, as they are for the average fielder, hence 25 hits, he happened to have his “other” 25 balls hit right to him and THAT is how he amassed 25 errors!”

I don’t mean to put words in Tango’s mouth.  I am just speculating that that is what he will say or think, more or less.

And since you are SO sure of your position - at least that is what you say here - I am offering my usual BS detector, which is putting your money where your mouth is.  My guess is that you ain’t so sure once you have to do that.

My only qualifier is that if you choose to take the wager and Tango either supports your or me, that we both have the chance to show Tango the error of his ways, just in case he makes a mistake in his thinking or logic, which is always possible.

Anyway, based on what I said when I mis-spoke (I was just wrong), when I said that you were right that a player with more errors does not imply that he had easier to field balls, then your answer for player A would in fact be correct.  But your original thought, that my method assumes that a player with more errors had easier to field balls, on the average, is correct, and THAT is why your method of accounting for hits and error is wrong.  At least you did get that right (and I was wrong).

Here is another example and reason why number of errors as compared to average tells us something about the distribution of balls in a bucket that we don’t know if we don’t know anything about errors. You may not understand this concept (I don’t mean that pejoratively), but Tango certainly does.

I have a bucket that is 80% outs.  I have one fielder who gets 100 balls in that bucket and that is all we know.  We know nothing about the actual distribution of balls in that bucket. Obviously our best guess as the the actual distribution of balls in terms of hard or easy to field (including the position of the fielder on every play) is equal to the average distribution of balls in that bucket for the whole league.

Anyway, that is all we know:  Fielder A had 100 balls in that bucket.

Fielder B also has 100 balls in that bucket, but we know (we watched a randomly chosen video of one ball) that one of them was hit right to the fielder.  It is important that that one ball was randomly chosen, since obviously we kind of know that there was at least one easy ball hit to both fielders (although not for sure, which is also important).

Who had the easier distribution of balls?  Fielder B!  Every so slightly, bit he definitely did.

Same scenario, Fielder A has 100 balls hit in that zone with no errors.  Again, we know nothing about the distribution or even the number of hits and outs.  Only that he made no errors.  That could be because he fielded all easy balls clearly or he actually had no easy balls. Doesn’t matter.

Fielder B, we know nothing but that he had one error.  Who had the easier distribution of balls?  Fielder B, by virtue of the fact that we know that he had one easy ball to field.  This is exactly the same scenario as my first one because an error is a proxy for an easy to field ball (and yes, I know that the OS sometimes sometimes awards an error when a ball is NOT easy to field, but that does not matter - all we are about is that a ball was easIER to field than an average ball in that bucket, and surely an error means an easIER to field ball in that bucket, on the average, even with the occasional scorer mistake).

So, THAT is why, yes, it is true that more errors (than an average fielder) means easier distribution of balls, and THAT is why errors cannot be treated as outs, and THAT is why your player A does NOT have a zero UZR, even though allowed the same number of hits as an average fielder.

Guy, it is the same as if we had 2 groups of pitchers with an average ERA of 4.00, but we know that in one group, one of the pitchers had an FIP of 3.90.  Only one. We know nothing else about either group. Which group pitches better (in terms of luck independent pitching)?  The one with the pitcher with the FIP of 3.90 of course.

Still want to make that wager?

He made 3 more outs+errors and 3 less hits (obviously) than the average fielder.  So he gets credit for 3*.2 plays or .6 plays or around .46 runs in range runs.

This step makes no sense.  You already know he was +3 plays in in range.  Why would you multiply by .2 once you’ve already got the difference in plays?  If you want to use the .2 factor, you have to apply it to every play, not just to the difference (this is what you have done in past primers when using the out rate like this):

83 * .2 = 16.6

And then apply the -.8 to the hits, of course:

17 * -.8 = -13.6

Then you get for range a total plays above average of +3.  If you already have the difference in plays from average, then you don’t need to multiply by anything to get the difference in plays from average.

Player C

Out 72
Error 5
Hit 23

His range runs are -3 plays and his error runs are zero for a total of -3 plays.

Here, you do not add that extra step.  You take the 3 plays difference as -3 plays.  This is how you should be handling Player A’s 3 extra range plays:  he was +3 in plays for range, not +.6 plays, just as Player C is -3 in plays, not -.6.

In your own examples, you have Players B and C as both -3 plays, even though one had 3 extra errors and the other allowed 3 extra hits.  Your own explanation is treating those two as the exact same thing (at least in terms of plays, since they could have different conversions to runs).  Even if that is not what you want to be doing, you just showed that that is in fact what you are doing.  The *only* reason you don’t also match Guy for Player A is that you added that one weird step where you turned his +3 range plays to +.6 range plays for no apparent reason, even though you don’t use that step for any of the other players in the example or in the walk-throughs you’ve written in the past.  It’s not because your method counts errors any differently.

MGL post #19 - And clearly when any fielder makes an error, no matter how much range he has, on the average, it is a ball that gets caught 95% of the time.

Example post #64 -

100 balls in 80% Range Bucket
Average Fielder
Out 75
Error 5
Hit 20

I am confused.  MGL values an error at -.95 plays because he has calculated that errors are only assessed by the scorer on hit balls that would normally be fielded for an out 95% of the time. But if an average fielder commits 5 errors in a hundred plays wouldn’t that have to mean that all 100 balls were assumed to be easy plays?  And then wouldn’t the fact that 20 of those balls were hits be a contradiction of the original premise that easy balls are fielded 95% of the time?

Thanks, Kincaid.  Once you correct MGL’s miscalculation on player “A,” it’s clear that UZR does in practice treat errors and hits exactly the same.  As it should.  So the good news is we apparently don’t have to fix UZR.  The bad news is we still need to fix MGL. :>)

I may have done the computations wrong.  The .2 is for every ball, as Kinkaid says, obviously.  How UZR is computed is laid out exactly in the article.  How I say it here while watching TV and eating a sandwich is another story.

I’ll try again:

Bucket with 80% catch rate (including errors counted as outs) and assuming no other fielding position makes any outs in that bucket.

Player A
Out 75
Error 8
Hit 17

Range runs

83 outs plus errors, with each one getting .2 plays of credit.  17 hits, getting -.8 runs of credit. Pretty simply.  3 plays of credit (not .6 like I said before, of course).

Error runs

-3 plays.

A total of 0 plays.

Maybe I have lost my mind.  On the other hand, I did say a while back on this thread that once I explained that first I treat errors as outs, we might all be saying the same thing.

On the other, other hand, that puts a kink in my “errors are worse than hits” theory.

I’ll have to think about it later…

Well, two things are evident:

1) I WAS in fact treating an error the same as a hit in UZR, in a roundabout way.

2) An error is clearly not the same as a hit, in terms of fielding talent, which is what UZR is trying to estimate.

Therefore, I am undervaluing fielders like Jeter with few errors and overvaluing the ones with more errors.

One more example of why errors are not the same as hits (obviously they lead to the same thing, which is a base runner, but UZR does not care about the result, it cares about the fielding talent behind it), although it really should be obvious that they should not be treated the same.  And, for the record, I did not MEAN for them to be treated the same, but I blew it in the methodology, and I am therefore grateful that we had this discussion, which is what I have always said - the goal of any academic discussion is to get things right, not to determine who is right or wrong.

Let’s say that we use very large buckets for UZR.  Say hard hit balls from line to line is a bucket.  That is probably a 10% bucket for the SS or something like that.

Fielder A comes back with 90 hits and 10 outs in 100 BIP in that bucket.  His UZR is obviously around zero.  He likely had a pretty normal distribution of balls hit in that bucket (we don’t know for sure, and since the bucket is so large, there is a lot of uncertainty in that zero UZR for this bucket - but that does not matter).

Fielder B comes back with 90 errors and 10 hits.  Again, if hits and errors were treated the same, this guy would have a zero UZR as well.  But everyone knows that is ridiculous.  What likely happened to generate those 90 errors and 10 hits?  Well, we know that this fielder had a (major) fluke 90 balls hit near him that he booted. He obviously could not possibly have gotten anywhere near a normal distribution of hard hit balls from foul line to foul line and amassed 90 errors.

So who had the better fielding talent and thus the better UZR?  Do you want to give player B a zero UZR and call him an average fielder?  I don’t think I have to answer that question.

Anyway, same thing applied if fielder B even got one error and 89 hits.

In any case, I need to correct the UZR methodology again.  I think the correct thing is to simply do the error runs without considering an error as an out first (that is what caused the hit and error to be valued the same in the first place), but I am not sure at this point.

MGL—to follow through your logic (rather than your maths) you are saying that errors on balls in the 80% bucket should be counted in a separate 95% bucket. Or at least that is what I think you are saying. If that is right then:

Player A
Out 75
Error 8
Hit 17

Range runs

75 outs plus 3 errors, with each out getting .2 plays of credit and each error getting .05 plays = 15.4 plays

17 hits, getting -.8 runs of credit = 13.6 plays

Difference is 1.8

Error runs

-3*0.95 = -2.85 plays (you are saying that errors should be out 95% of the time)

A total of -1.05 plays

So I think that is what you should get if you use your methodology (as described in words) MGL.

So which is UZR doing? Is it treating an error in an 80% bucket as if it were in a 95% bucket or in a 80% bucket?

While we wait to learn what UZR actually does, a few quick points on whether it should place errors in a .95 bucket:

The average full-time SS makes about 10 fielding errors per season.  If these are in fact .95 balls, that would imply he faces about 200 such easy balls—this is a very high-frequency event. Yet we are only counting a very small number of these and—this is the key point—doing so in a biased manner, because we only count those which are misplayed.

(BTW, if the best UZR can do is create an 80% bucket, that means for every 100 easy balls there are also another 100 50%-60% balls in this bucket.  In other words, UZR buckets are a very imprecise measure.)

There are at least 3 reasons we might see one SS make 5 errors and another 15 errors on samples of 100 GBs that UZR thought were equally difficult:
*One player may in fact have better hands on easy plays (MGL’s approach would overvalue this player’s performance);
* One player might just happen to boot some easy plays by chance this player will be undervalued);
* One player in fact faced more easy plays, and so had more opportunities to make an error.

It seems to me that the first 2 factors overwhelm the 3rd.  Most of the difference in error rates will reflect skill and luck, with the proportion of easy plays almost certainly being the least important.  Surely we can all agree that Jeter’s low error rate is not mainly a function of facing fewer easy plays.

Once you split up the debit for hits between fielders, then hits and errors won’t end up being the exact same, since on an error, the one fielder is getting the full debit for allowing the baserunner, whereas with a hit, the debit is split up between fielders.  That is probably enough extra debit to give errors.  Going further and doing what you are talking about now is going to significantly over-weight errors.

What would you do about Colin’s and Peter’s points?  Colin is right that you don’t know that a ball was 95% or whatever it is just because it was an error, because the scorer’s estimation of the difficulty of the play is reliant on the fielder’s positioning.  If we know a fielder has more balls hit right at him, we know not just that the fielder probably had an easier distribution of balls, but also that he probably had better positioning.  A fielder who is better positioned will have more balls hit right at him.  So you can’t just look at the number of balls that look easy to a scorer and say that that is only due to an easier distribution of balls.

Once you are not looking at one huge bucket but several fairly precise buckets, the likelihood an easy play was due to a difference in positioning and not a difference in actual distribution probably increases.  Say you have a bucket of hard hit ground balls right up the middle.  Normally, these balls will not be right at someone (once they get by the pitcher, at least), but a certain percentage of these balls will be hit right at a fielder.  When a ball does go right at him, it can be because:

-he was positioned abnormally for whatever reason
-it was an extreme ball in the zone where it was right on the edge and not that hard hit, so the fielder gets in front of it easily enough that it looks like it’s right at him as far as we can tell
-the ball was misclassified

If you have one huge zone, you know it could be hit right at someone, and nothing in the data tells you that is unlikely.  When you have a more precise bucket, the chances of the ball actually being in that zone and hit right at a fielder who is positioned where a typical fielder is on average is relatively small, so most of those plays are going to be when the fielder is not positioned normally (or the ball is just misclassified).  The more precise your buckets are, whenever you see balls hit right at someone in a low out rate zone, the more likely it is you are picking up effects from positioning differences as opposed to effects from atypical distributions of batted balls within the zone.

And then there is Peter’s point.  If you observe that 5% of expected outs (including errors) are scored as errors, that does not mean that an error means the play was at least 95% for getting an out.  If errors were only scored on plays that were actually 95% or higher, and you still got errors on 5% of all expected outs, then all plays would have to be easy, and you would never get any hits.

Say that 80% of all batted balls are easy (95% for just out rate, not outs+errors).  95% of the time, those plays will be outs.  5% of the time (or less, if you ever have hits on those balls), they’ll be errors (and they can’t be errors more often then that, or else they wouldn’t be 95% outs, since at this point we have now split outs from errors).  That would give us at most 4% of all batted balls that are errors, since 5% of the easy balls (which make up 80% of all batted balls in this scenario) are errors, and we assume nothing easier than that can be an error.  Obviously, 4% is less than the 5% we started out with.  The problem will be worse in reality since far less than 80% of all batted balls are 95% outs.  There have to be errors given on more difficult balls than what you are calling easy in order for the error rate to be what it is.  You can’t just assume that if an error is given, and the error rate is 5%, that ball had to be 95%.  Some errors have to have a higher difficulty than that.

I think you’d be better off just leaving things as they are on this issue, and certainly just doing what you are talking about where you do just create a new bucket for all errors and assume 95% of them should be outs is a step backward.

This is basically how what MGL is talking about doing sounds to me:

If a player has 5 extra errors, we know those errors were easy plays, no matter what bucket they came from, so we alter this player’s distribution to give him 5 extra easy balls than we normally would for his observed distribution.  Basically, we start off with his observed distribution, without altering for errors, and we look at what we say an average fielder would have done with that distribution, which includes making x amount of errors.  Now, we see that our fielder made 5 more errors than that, so we assume that he had 5 more easy balls to field, and that in getting 5 more easy balls, he screwed up every single one of them even though they are probably close to the easiest balls we are giving him.

Without knowing exactly what MGL would choose to do, it’s impossible to interpret in detail what would be happening, but that’s the gist of what is coming across right now.

That is definitely going to overweight errors. Just like Guy says, with more errors, there are a number of things you have to assume, including that the fielder just made errors on a higher percentage of plays given the same distribution.  You can’t just put the whole thing into the distribution of batted balls.

Giving the full debit to the fielder with the error as opposed to splitting the debit for a hit with adjacent fielders is probably already covering enough to give errors enough extra weight on the distribution of batted balls factor.  Doing more is probably not necessary.

I think that leaving it as it is a a terrible mistake.  I really do.  Right now, I am treating an error exactly the same as a hit and clearly that is completely wrong no matter how you look at it. Considering everything that is being said, while an error might not be on a ball that is going to be caught 95% of the time, it is certainly 90+.  If the average bucket is 70% outs, we are shortchanging those low error guys and overrating the high error guys by .2 plays or so per error made or not made.  For 10 plays a year, that is 2 plays, or 1.5 runs.  I think that is enough to be concerned about.

I can figure out the right answer. I can always use a simualtor to reverse engineer everything.  By that, I mean I set up a somputer simulation whereby I assign everyone different true error rates and range rates, then I randomly hit balls to different parts of the field and I look at the results. That is really helpful.

As long as you are not splitting the debit between fielders when one commits an error, then it’s only exactly the same if you have a bucket where only one fielder ever fields the ball, and in that case, probably just about any ball in the bucket is capable of being scored an error, so it won’t matter.  Doing it as you are, the smaller portion of a hit the fielder gets debited with, the greater the difference between the cost of an error (where he gets full debit) and the cost of a hit (where he only gets a portion of the debit).  This is probably close to what you would want with what you are talking about, actually.  If a shortstop is responsible for 20% of the outs in a bucket and the third baseman for 80% of the outs, the lower the chance that the shortstop is getting an easy play in that bucket.  And for that bucket, if a hit and error are both -.5 plays, the shortstop would only get 20% of the debit on a hit (-.1), whereas on an error, he would get the full -.5.  This could still be over-counting errors once you introduce the interaction between fielders, but I definitely think you do not need to add more of an adjustment than the split between fielders is already doing.

....

I do not think that all errors would even be true 90%+ plays, since the scorer is just making a judgment on what happens once the ball is fielded.  If the fielder gets to the ball easily because he is better positioned or because he got a good jump or whatever, and he gets in good fielding position and then makes a mistake, then it might be that the success rate should be that high, given the fielding position the player got himself in, but that ignores the chances of another fielder getting into good fielding position on that play.  It could be 50/50 whether another fielder gets into standard fielding position, but once you do, the scorer will still usually give you an error if you boot the ball or throw it away.

Of course, there are also plays where the player might make a diving play in the hole that could be a true 10% play, and then he throws wild to first so that the runner takes second, and the scorer has no choice but to give an error even if he knows it was a play that is rarely made, because you have to account for the advance to second.  It could even be a hot shot down the line at third, where the runner would be on second 90% of the time anyway, and the fielder still gets an error once he stopped it and threw wild to first.

Just for the sake of example, though, let’s assume that all errors happen on plays that are 90% or easier (we’ll call these “easy” plays).  Every ball in every bucket has some probability of being an easy play, even if it is in a .20 bucket or some other low probability bucket.  The lower the out rate for the bucket, the lower the probability that a ball in that bucket is actually an easy play, but we still know a certain percentage of balls in that bucket will actually be easy, whether they are scored errors or not.

Let’s say that for a given bucket, we expect 20% of the balls to be easy.  We’ll assume we know a few things:

-if a play is scored an error, we know it was easy
-if a play is not scored an error, we still know it has some certain probability of being easy
-we know players have different true abilities on how often they make errors once they get easy balls

If a player has more errors than normal, then we can assume that it is likely some combination of him having more easy plays and him just being worse on the same number of easy plays.  We can’t assume that it just means he had more easy plays.  We can also assume that the more batted balls we have for a player, the less likely it is that the true distribution of his batted balls differs much from what we have measured, and the more likely it is that we are just picking up on the player’s true ability for fielding easy plays.  For a player like Jeter for whom we have several years of data saying he is good on easy plays, the chance that you are undervaluing him with the current system because he really got fewer easy plays than you’d expect is much, much lower than the chance that you are properly valuing him and that his distribution is close to what UZR measures it to be, with the difference in errors being that he is good on easy plays, not that he got fewer easy balls.

If we have a player who is above average in fielding easy plays (say, Jeter, for example), then we will still expect him to get 20 easy plays per 100 balls in this particular bucket.  What you are proposing is that we instead assume that the player is actually consistently getting fewer easy plays, no matter how much data you have that says he is actually just doing better on the same number of easy plays.  This will systematically overvalue anyone who is actually good on easy plays and systematically undervalue players who are bad on easy plays.  Over the short term, this might be fine, because you can’t tell who is truly good or bad on those easy plays, and the chances they got a distribution with more or fewer easy plays have to account for some of their observed error totals.  Over the long term, when you can better tell who is and who isn’t good on easy plays, then you will be systematically mis-valuing players.

"If the average bucket is 70% outs”

Really?  On the average BIP that becomes a fielding error, UZR would estimate—after accounting for location, speed, batter and pitcher handedness, and everything else—an out probability of 70%?  I don’t expect UZR to perform miracles, but I find that surprising.  That means UZR basically can’t distinguish between a sure out and a 50-50 ball --it just throws them together and says “70%.” And it’s not like these 95% balls are a rare species—you’re talking about 50% of the balls in a fielders’ zones! 

If this is true, it seems like figuring out whether to treat errors differently than hits is the least of UZR’s problems…

"Really?  On the average BIP that becomes a fielding error, UZR would estimate—after accounting for location, speed, batter and pitcher handedness, and everything else—an out probability of 70%?”

One, I was making up a number, and B, I was referring to an average ball in an average bucket, not a ball that becomes a fielding error. 

There is no way to come up with the “bucket out percentage” of a “ball which becomes a fielding error.”

All buckets have fielding errors.  I suppose that we could do a weighted average of buckets with fielding errors, weighted by the errors per BIP for that bucket.  That might be 75 or 80% or something like that. It has to be less than the highest “out percentage” bucket no matter what, and all buckets are going to represented.  For example, let’s say we have 3 buckets on the field:  20% 50% and 90%.  The 20% bucket might have an error rate (per ball in that bucket) of 1%. The 50% bucket 3% and the 90% bucket 6%.  That would still be a weighted average of only 71%.

Anyway, I like Kinkaid’s explantion above. I really like it.  I did not consider the fact that I AM not treating an error like a hit in buckets where there are other fielders involved which are almost all buckets, since the responsibility for a hit is shared but for an error it is not.  That is an important point.  Really important.  Secondly, while thinking about it all day, balls that are scored as errors are definitely not 95% balls even if that is the average fielding percentage for that position.  IOW, a BIP that is scored an error is not as easy as a BIP that is caught.  As Kinkaid says, some of those errors (not many, but some) are balls that only look easy because of positioning and range.  And some really easy balls that are caught are rarely an error.  We see errors all the time that are really hard to catch balls.  For example, the one and two hoppers that are made almost 100% of the time, I could make.  Those hard hit 20 hoppers that go through the legs of an IF and get scored an error, I would make maybe 25% of the time.  Plus there is some “slop” in terms of OS mistakes.  So I will say that even if you created a separate bucket for errors, it might be an 80% or 85% bucket and not a 95% bucket.  So that combined with the errors don’t split the responsibility thing, I don’t think I am giving up too much by using the method that I do.

But, I am definitely not handling it the “correct” way, and I could be doing better.  I think if nothing else I made all errors an 85% separate bucket, that would be better than what I do now, but it probably does not make much difference.

“If a player has more errors than normal, then we can assume that it is likely some combination of him having more easy plays and him just being worse on the same number of easy plays.  We can’t assume that it just means he had more easy plays.”

Of course that is true (and Guy needs to read that so he can finally realize that “more errors = more easy to field balls, regardless of the error skill of the fielder” (it also means fielder has less skill of course - as Kinkaid says, it is a combination)!

“Of course, there are also plays where the player might make a diving play in the hole that could be a true 10% play, and then he throws wild to first so that the runner takes second, and the scorer has no choice but to give an error even if he knows it was a play that is rarely made, because you have to account for the advance to second.”

We are only talking about fielding errors.  Throwing errors do not apply to this discussion, as they imply nothing about how hard or easy the ball was to field, although actually a throwing error implied that a ball was HARDER to field and/or the runner was fast and not easier, so that we should be giving more credit to the fielder on the “range runs” portion of the UZR computation.

In fact, one of the fixes to this problem is this:

On an error, whatever the bucket is, the range runs credit for a fielding error should be a little less than the bucket implies.  For example, if it is a 20% bucket, the fielder should be “credited” with maybe .4 plays rather than .8 plays for an error (and then docked 1 play for the extra error).  If it is a 85% bucket, he probably should be credited with .1 rather than .15 plays.  The lower the out rate of the bucket, the more adjustment should be made, I think.  If a player makes an error on a 20% bucket (balls in this bucket are hard to field), I am real uncomfortable assuming that on the error, he made a great play to get to the ball or he was somehow smart enough to figure out where to position himself.  More likely, he was on a semi-shift or something like that, which is not due to any skill of his own. I just don’t see how you can assume that when a player makes an error in a 20% bucket that only 20% of the time would an average fielder have gotten to that ball in which an error was recorded.  That is not possible.  I watch about 300 games a year, and I watch them intently.  Do you know how many times I saw an error and though, “Wow, if not for that fielder’s spectacular range or great positioning (on his own), he never would have gotten that error - how unfair?” Never. 

On a throwing error, we could probably give MORE credit than the bucket suggests, or at least leave it alone and treat it as I do now.

“For a player like Jeter for whom we have several years of data saying he is good on easy plays, the chance that you are undervaluing him with the current system because he really got fewer easy plays than you’d expect is much, much lower than the chance that you are properly valuing him and that his distribution is close to what UZR measures it to be, with the difference in errors being that he is good on easy plays, not that he got fewer easy balls. “

I don’t think that is true.  I understand what you are saying about sample size and the chance of a player’s distribution being abnormal, but I don’t think sample size changes the chance of a player being under or over rated because of the way that UZR accounts for the errors, but that is another story that we cannot afford (time-wise) to get into…

If a player makes an error on a 20% bucket (balls in this bucket are hard to field), I am real uncomfortable assuming that on the error, he made a great play to get to the ball or he was somehow smart enough to figure out where to position himself.  More likely, he was on a semi-shift or something like that, which is not due to any skill of his own. I just don’t see how you can assume that when a player makes an error in a 20% bucket that only 20% of the time would an average fielder have gotten to that ball in which an error was recorded.

You don’t have to say that it was a 20% ball.  We know that there will be some easy plays in that bucket, whether they get scored as an error or not, and that those easy balls are par of what goes into the overall average for the bucket.  Sometimes, the player will be shifted differently for whatever reason, and the ball will be easier than it normally would.  This happens whether the player makes an error or not.  Most of the time, he won’t, but you are only wanting to count the times an error is scored as being different.  This is the bias Guy talked about earlier.

If we expect 20% of the balls in a given bucket to be easy, then whether a player is good on errors or bad on errors (in true talent, not just observed talent), we still expect him to have 20% easy balls.  If he is good on errors, he will be systematically overvalued if you say that over the long term, we really expect him to have fewer easy balls than normal for that bucket.  If he is bad on errors, he will be systematically undervalued if you say that over the long term, we really expect him to have more easy balls than normal for that bucket.  We can say the player with more observed errors likely had more easy plays to the extent that we cannot tell just from the observed errors whether he was actually bad on errors or not.  However, as the sample increases, the more certainty we have about who is actually good or bad in errors, and we expect those two groups (at least as far as we can tell who they really are) to have the same distribution of balls.  The difference in distribution is only useful as far as we can’t tell who actually falls in those groups, so obviously the use of assuming a different distribution decreases as our sample on a fielder increases.

That’s without even considering the fact that the more batted balls we have for a fielder, the less likely the actual distribution is going to differ much from what is observed from the data, which is also a factor.  It is true that the larger the sample, the less likely the distribution is to be abnormal compared to what UZR already uses, but even without that, players will be mis-valued over large samples if you assume that differences in error rate mean differences in distribution.  That’s because we expect the low true error players and the high true error players to get the exact same distribution, because their true talent on errors has nothing to do with the distribution they end up getting.  When we see Jeter is good on errors over a huge sample, we can be very confident that he is actually a true talent low error player, and that the low observed errors is due to his talent and not due to other factors unrelated to his talent.  If you set up UZR so it splits up the likelihood of extra errors being due to different talent and the likelihood of extra errors being due to different distributions so that it works in small samples when you are not so sure who has what true talent and your certainty of the actual distribution is low, then when the samples grow and those relative likelihoods shift, then you will get systematic biases.  I think you’d be better off leaving the issues in the small sample sizes and letting the data work better as the sample grows than setting it up to work in the short term at the cost if biasing the long-term results.

Guy: My point is that your “95% bucket” is biased. ...

MGL: 100 balls in 80% Range Bucket .... whether a player with 75 outs and 25 errors in a 80% out bucket .... He happened to have had an anomalous distribution of ground balls (assuming an IF of course) in that 80% bucket.

This is perhaps the only thread on this site that I have not read in full.  My reading time is limited on the weekend, and you guys went gangbusters!

I think the issue seems to be with the premise of the “out” or “range” bucket.  Guy seems to be saying that the segregation / classification should be based on the out rates.  And so, for his purposes, when we talk about an “80% out bucket”, he means outs.  So, errors, to him, provide no additional information.

MGL’s premise starts with the “range bucket”, though sometimes he switches to calling them outs, as the quote above shows.  I haven’t read the thread carefully enough whether he makes it clear that he is always talking about range=outs+error (he does say it often enough though).  I think most of the casual readers probably are not appreciating enough the semantics of it.

You take all the batted balls, and you put them in various buckets.  And so, in Guy’s 80% bucket of 100 balls we will NOT see the same 100 balls in MGL’s 80% bucket.  Or more accurately, Guy’s 75% out bucket is not necessarily equivalent to MGL’s 80% range bucket.  It’s not necessarily the same balls.

I think that’s why I was having a hard time following this thread, as I was reading it like a casual reader, as I normally would on the weekend.  So, it’s hard for me to get involved as a casual bystander in this instance, since I really don’t see the common premise as a starting point.

Anyway, I’ll start reading the thread from the top, but I think I’ll end up creating a separate thread with some clear examples to see if there’s anything we can agree on.

Kincaid has it exactly right.  On larger samples, skill will be the main determinant of differences in error rates, and low-error players must be overrated if you assume fewer errors = fewer easy plays.  On small samples (e.g. 1 season), the role of luck will be much larger:  both luck in terms of how many easy balls were faced, but also random variation in a player’s error rate on those balls.  Perhaps an error adjustment would improve accuracy on small samples, though I’m skeptical.

We also have to consider whether adjusting only for errors, but not hits and outs, makes sense.  As MGL has acknowledged, every hit is in fact a more difficult play than UZR “thinks” it is.  And every out is a little bit easier.  So UZR must already has a tendency to exaggerate fielding differences (I don’t mean in comparison to true talent, but in comparison to what really happened on the field).  In that context, giving extra credit to low-error (high-UZR) players may not be a helpful adjustment in terms of the system’s overall accuracy.

*

“There is no way to come up with the “bucket out percentage” of a “ball which becomes a fielding error.””

Why not?  According to the primer, the UZR engine assigns an out probability to every BIP based on bucket, how hard ball was hit, and multiple other factors.  Why can’t you just take samples of 1,000 errors for each position, and calculate the average out expectancy for those BIP?  If the result is 90%, then this whole discussion is moot since UZR already knows these are easy plays.  If the answer is 70% or even 80%, then we have to decide how much of that reflects the reality that many errors are not truly 90% plays, and how much is just a limitation of the BIS data and UZR.

The fact that MGL began this discussion quite confident that UZR would expect only a 70% out rate on error balls makes me suspect that UZR is far less accurate than I had imagined it to be.  That would be just a terrible performance (unless you believe that official scorers are doing a horrifically bad job).  If that’s the case, then it’s not clear UZR is worth all the trouble.  Estimating expected outs for IFs based simply on how many GBs their pitchers allowed, with adjustments for batter handedness, would probably be just as accurate.  And once you had, say, 3 years of data, I’d have far more confidence in WOWY than UZR to rate a fielder. 

Hopefully MGL is wrong about this as well, and UZR estimates a pretty high out% for most errors.  And in that case, further adjustments are of course unnecessary.

Tango:  you are right that there were multiple meanings of “80% bucket” used in the thread.  Probably my fault, for not remembering that UZR begins by treating outs and errors both as “range outs.” But while that makes the thread unnecessarily confusing (not that it needed help!), I don’t think that’s the reason for the various disagreements. 

And if you want a shorter/clearer read, you should just read Kincaid’s comments and ignore me and MGL.  :>)

Tango - Read Guy’s post #57.  I think it is clear from the examples he gives that he does understand MGL’s concept of an 80% bucket being 20% hits plus errors.  The point of difference between Guy and MGL is that MGL believes that more errors for a player within a bucket is indicative of the player having a distribution of balls within that bucket that had more easy plays than average because the official scorer only fives errors on relatively easy plays.  Guy is saying that the errors provide no information about the distribution of plays within the bucket because they only indicate that a player performed worse on the easy plays that are normally in that bucket.

Peter:  That was my stated position, because I was really thinking about career or multi-season data.  But MGL and Kincaid have persuaded me that in a small sample, a high number of errors might mean more easy plays.  That said, we have no idea whether assuming 1 extra error = 1 extra easy play is the right relationship, or whether this would actually make a difference anyway (because we don’t know how UZR rates these error balls in the first place).

This is the way I see it as Guy says it:

According to the primer, the UZR engine assigns an out probability to every BIP based on bucket, how hard ball was hit, and multiple other factors.  Why can’t you just take samples of 1,000 errors for each position, and calculate the average out expectancy for those BIP?  If the result is 90%, then this whole discussion is moot since UZR already knows these are easy plays.  If the answer is 70% or even 80%, then we have to decide how much of that reflects the reality that many errors are not truly 90% plays, and how much is just a limitation of the BIS data and UZR.

Once you assign an out rate for each ball, based on whatever parameters you want, then the discussion is moot.

It seems that MGL doesn’t really do that.  It seems that he looks at a whole bunch of parameters EXCEPT if a fielder made an error to assign a play to a range bucket.  So, he classifies a “range play” as one where the fielder either made an out or an error. 

Note: I’m not even sure if he includes in the “range plays” a fielder’s choice where all runners are safe (why not?  clearly the scorer thinks that the batter would have been out, but the fielder didn’t make an out).

Once he tags each ball, he then splits it up into error runs.  So, range runs plus error runs equals out runs.

So, going back to Guy’s quoted passage above, and what I thought at the start of this thread when I said:

Right, it won’t make a difference, overall.  MGL partitions it so that we get a profile, but in the end, an error is a play not made.

It seems to me that this is still the case.  Anyway, I won’t say anything more until I read this thread from the top.

My eyes glaze over reading this thread, so I just wanted to make sure I understand correctly what’s going on. Guy/Kincaid, is this correct?

- Guy’s position: If a player makes an error on a ball UZR thinks should be caught 80% of the time, he should be credited with -0.8 plays.

- MGL’s position: If a player makes an error on a ball UZR thinks should be caught 80% of the time, he should be credited with -0.95 plays, because errors are plays that should just about always be made.

- What UZR actually does: If a player makes an error on a ball UZR thinks should be caught 80% of the time, he is credited with making the play in the “range” portion of UZR, giving him +0.2 plays, but is then debited with -0.95 plays in the “error” portion, for a total of -0.75.

David: 
Yes, you’ve basically stated my position correctly.  (With the small caveat that if someone does produce evidence that a high error total really does mean an easier ball distribution, then an additional adjustment would make sense).

I won’t speak to MGL’s position. 

Nor will I hazard a guess as to what UZR actually does.  Tango’s comment now makes me think errors are not really rated at all, so there is no such thing as “an error that UZR thinks should be caught 80% of the time.” And I’m not sure how we’ll even figure out what UZR does.  MGL seemed quite sure he was placing errors in a 95% bucket.  But then he wasn’t.  If he doesn’t know what UZR does, who does?

- What UZR actually does: If a player makes an error on a ball UZR thinks should be caught 80% of the time, he is credited with making the play in the “range” portion of UZR, giving him +0.2 plays, but is then debited with -0.95 plays in the “error” portion, for a total of -0.75.

For the 80% bucket, that will include hits+errors, and errors should be 5% of that, so 4% of the plays in the bucket should be errors.  That’s how you would use the .95, to find the expected number of errors for that bucket.  Then, the debit comes from that expected error rate.

On an error, the player gets +.2 plays for range, and then -.96 plays for errors (since he has one error, and the expected rate is .04; he is .96 errors worse than average on that one play).  Overall, he’ll be -.76.

Similarly, if the ball were a hit, the player would be -.8 in range runs and +.04 in errors (because he made no error on the play, which is .04 fewer errors than expected), and he still winds up -.76.

If the 80% you are talking about does not include errors, then UZR would add the expected error rate to that.  So really, it would be an 84.2% bucket, and when you work it out the same as above, you’ll end up with -.8 total plays on the error (which is the same as Guy’s position, since Guy would consider an error the same as a play not made).

In a one fielder system, they wind up the same.  When you introduce multiple fielders, then the -.76 for a hit will be split up between adjacent fielders, while the -.76 for the error won’t.

This thread would be alot easier to follow with actual data. 

MGL: if you update the event files so that every error is a hit, can you show the difference in UZR for SS and 3B for 2009?  If I’m right, the difference should be virtually zero.

Kincaid:  Using errors to assign responsibility in cases of multiple responsibility seems to make sense.  But how many plays can we be talking about?  How many GBs are such a sure thing they become an error, and yet UZR also assigns responsibility to two IFs?  I find it hard to imagine such a ball.  If UZR is telling us that a SS error should have been fielded by the 3B 30% of the time (for example), we either have a very bad scoring decision or UZR is so imprecise as to have almost no value.  (This might help on a few flyballs to the OF, but those errors are so rare it hardly matters.)

Right, an error that can possibly be charged to multiple fielders is not a good batted ball classification. 

For example, say we have an overshift, and Ryan Zimmerman is playing in the SS position, and he drops an easy play.  MGL might not know that the play was overshifted (BIS flags the big overshifts, but perhaps not small overshifts).  As far as he’s concerned, Zimmerman made an error 17 degrees from the 3B line, and so, is a clear SS zone.  MGL will treat that as a shared zone.  We know it is not.  It could not be, because the official scorer is implicitly telling us that the fielder fielded the spot he was stationed at. 

That is, fielder errors would only be noted as a fielding error if it takes less than 2 seconds to get to it… anything more, and that means it was probably a tough play and/or the batter might have been safe anyway.

Someone else noted earlier in the thread that this now introduces the idea of fielder-positioning.

***

Of those people who have been following this thread, do you get the impression that regardless of MGL or Guy’s position, that the end result is that the final UZR runs will be virtually unaffected?

Tango: 
What do you make of this statement by MGL:  “For example, if we just looked at the difficulty/out rate of the balls in which errors occurred, based on their buckets (location, speed, etc.), you would probably find a 60 or 70% (maybe 80%) out rate.” I know he’s just making a rough estimate here, but MGL has worked with this data for years and I’m inclined to trust his intuition (or at least I always was before this thread).  If plays that are so easy they get scored an error are actually rated by UZR at a 60-80% out rate (or would do so, if MGL allowed UZR to rate errors), isn’t that telling us that UZR is very crude?  I mean, SSs field 70-80% of ALL the balls in their zones.  So if UZR sees a 90-95% out BIP and just guesses “70%,” then really what good is it?

Am I setting unreasonable expectations?  Or missing something?

It will make a small difference on nearly every play, since all it takes is another fielder getting to a ball in that bucket once to split up the debit on hits, but for most errors, presumably it should only be a small difference.  Occasionally it will make a larger difference, but the larger the difference it makes, the less often it is going to occur.

For any bucket, even if the buckets are precise, there is a distribution of true difficulties for the plays in that bucket.  Even if the distribution is fairly narrow, there will still be some non-zero probability of a ball showing up in the tail of that distribution that is actually an easy play for a fielder.  For example, on a medium ground ball up the middle (that gets by the pitcher), it will be a hit some percentage of the time, it will be fielded by the shortstop some percentage of the time, and it will be fielded by the second baseman some percentage of the time.  Also, some percentage of the time, the second baseman might be shading up the middle quite a bit, or he might get a great read/jump on the ball, or it might be hit at the fringes of the bucket where it is at the right edge and particularly slow, or it may be misclassified, and the second baseman will be able to get set in front of the play.  Once this happens, he will probably be given an error if he boots the ball.  So now you have an error in a zone where the 2B is probably splitting a fair portion of the outs with the SS.  Part of that is imprecision in the buckets, part of it is the parameters of UZR and the parameters for the scorer being different (i.e. accounting for positioning differently - the scorer only looks at where the fielder was positioned on that play, whereas UZR is looking at where a fielder typically plays given its parameters for that play), and part of it could be data error or an iffy scoring decision.

The likelihood of the fielder being able to get in that kind of position on a play in a given bucket is probably going to decrease the greater the split of outs between that fielder and another fielder.  Presumably, most errors will be in buckets where the offending fielder is making most of the outs.  Some decreasing portion of the errors will also occur when you look at buckets where the offending fielder makes a decreasing percentage of the outs in that bucket.  That will happen even if you have precise zones; it will just happen less often the more precise zones you have.

For the errors where the offending fielder gets most of the outs in that bucket, it will make a relatively small difference, as you say.  For the smaller portion of the errors where the split will make a larger difference, the greater the chance that you got a ball that was in the easier tail of the distribution of difficulties for balls in that bucket, and, accordingly, the greater the adjustment (and again, the less often this should be happening).  That’s why this method might work fine for what MGL wants to do.  The adjustment makes little difference when you have a bucket that makes sense to have errors, and it makes a greater difference the less reasonable it seems for an error to occur on a typical ball in that bucket.

It is possible this is still going to mis-value errors in the long term, because you do know that somewhere in the distribution of balls in every bucket are going to be some balls in the tail that can be scored an error if misplayed, and you still expect that distribution to work out the exact same for high and low true talent error players even though this method is not going to end up giving them the same distribution, but I don’t think there’s any chance of MGL removing this part of UZR, and I don’t think it’s nearly as big an issue as whether or not he adds an additional adjustment on top of this.

Of those people who have been following this thread, do you get the impression that regardless of MGL or Guy’s position, that the end result is that the final UZR runs will be virtually unaffected?

If MGL’s position is the current UZR, then yeah.  If MGL still wants to change the methodology in a way that could distance it from Guy’s results, then there could still be a discussion to be had.

Tango:
What do you make of this statement by MGL:  “For example, if we just looked at the difficulty/out rate of the balls in which errors occurred, based on their buckets (location, speed, etc.), you would probably find a 60 or 70% (maybe 80%) out rate.”

The league DER (out rate per all balls in play) is .700.  Given that no errors can occur in the “no man’s land” plays, the league DER on plays where the fielder touches a ball before the batter reaches first base is probably .750 or .800.  I would guess therefore that on plays where errors are recorded, that the league DER is .900.

If plays that are so easy they get scored an error are actually rated by UZR at a 60-80% out rate

Is this what MGL is saying UZR does?

Is MGL using the recording of errors as an additional parameter, like batted ball location, speed of batted ball, handedness of batter, and “official scorer thought… hmmmm” (i.e., error).  So, on an otherwise 72% out rate play based on all the non-OS data, that if the official scorer (OS) calls it an error, it was probably a 92% out rate play.  Indeed, on that basis, if the official scorer calls a play an error, then the out rate play for those batted balls should be between 80% and 100%.

The ideal system would have the stringer mark EVERY play from .00 to .99 out rate (depending how you want to handle positioning).  So, on a play where UZR uses all the parameters and calls a Beltre play as a .72 out rate, that if the stringer says it was a .34 out rate, then we’d probably have to conclude it was somewhere in between the two, say .48 out rate.  And so, making an out means Beltre gets +.52 outs.

By ONLY looking at the error plays we are limiting it to those plays where the out rate was between .80 and 1.00.  AND we are limiting it to those plays where the fielder did not make an out.  And, since the OS is presuming a starting position dictated by the team, it highly depends on where the fielder is positioned (positioning not a skill).

Obviously, this is a biased sample.  The issue with biases in samples is to make sure that you know enough about the biases to account for them.  If you don’t then the bias persists.

"Is this what MGL is saying UZR does?”

He’s saying that he if we ignorned the error designation and treated those balls as hits, UZR would then say these balls had an expected out rate of between 60% and 80% (just his guess).  The question I was raising is completely separate from how to deal with the error designation, which is:  What does this tell us about UZR’s accuracy in general?  If balls which we know are in fact easy outs get rated as 70% out balls, how accurate can UZR be?  For every error, there are another 30-40 BIP (outs and hits) which UZR is assessing.  Is there a confidence interval of +-30% on each of these balls?  If so, it seems to me you could estimate a fielder’s expected outs just as well by knowing how many GBs were hit with him on the field.  Or just use WOWY and don’t have stringers at all.

The average groundball, to all positions, becomes an out 76% of the time.  So if UZR parameters judge them to be easier plays than the average groundball, they should be in the 80-85% range.

If MGL is treating them like a 95% based on the scorer’s call of an error, it still doesn’t look like much of a difference to me.  Can’t be more than a run either way at the fielder-season level.

David is more or less correct in #86.  Everything else on this thread (more or less) is garbage.  The fact that Guy keeps asking me what UZR does, when I have said exactly what UZR does multiple times, should be ignored by everyone else.  David jumped in for one post and is somehow able to say exactly what UZR does.  Either he has a copy of my computer code or he decided to actually read my comments.

Actually, David does not have it exactly correct.  The .95 or 95% means nothing.  That was just a number that I made up to indicate that an error is typically on a ball that, if not for the error, is going to be fielded a very high percentage of the time.  After thinking about it for a while, I see that is probably 85% or 90%, and not 95%.

But, I was just using that number for explanatory purposes only.  UZR does NOT use that number.

For the last time (and if anyone else says that they have read this thread and they still do not know how UZR handles errors, they need to get a new pair of glasses), here is how UZR handles errors (or I can simply cut and paste the 2 or 3 times I have said the exact same thing somewhere else in this thread):

(Also, for all of my positions, you can ignore everything else I have said, and ONLY use my comments below.)

First it assumes that an error is exactly the same as an out, and gives the player the appropriate credit.  In an 80% out bucket (for all years that UZR uses as the baseline, where the 80% also includes errors - outs + errors), the fielder first gets “credit” for .2 plays.

Now we do the error adjustment.

If this fielder had 100 balls in this bucket, then he is assigned 80 “chances” which is the number of outs+errors that an average fielder will have in that bucket given 100 balls in that bucket.

Now we see how many errors an average fielder would have in that bucket given 80 chances.  I suppose using an average fielder’s errors per balls in that bucket amounts to the same thing - so we can do it either way. 

Anyway, if the average fielder has 5 errors per 80 chances (or 100 balls) in that bucket and our fielder had 6 errors, then he made one more error.

He simply gets docked one play for that extra error.

So, ignoring the fact that an error “play” is worth slightly different than a “hit” play (so, I don’t add up error plays and hit plays - I convert them into runs and THEN add them up), his total credit/debit for that one extra error is -.8 plays. +.2 for the range and -1 for the error.  There is no .95 used anywhere.

That is what UZR does and my contention is that it is a mistake.

The reason it is a mistake is because in first crediting the fielder with .2 runs in range, it assumes that the fielder had to go exactly as far to reach the ball as he does for an out.  That is wrong.  On all outs in any bucket, sometimes the ball is hit right to the fielder, sometimes the fielder’s positioning through skill is very good (and the balls is hit right to him), and sometimes he makes a very good or a spectacular play.  On errors, that is not true.  The very good and spectacular plays are largely eliminated from the equation, so what is left is an easier play than an out.  So to give him the full .2 credit for reaching the ball is wrong.  He should get maybe .1 credit.  The error part of the equation is fine.  That simply takes away the out that we are assuming that the player would have made once he got to the ball, if not for the error.

An example which makes this concept obvious is a bucket that has an out rate of 1%.  Using the method which UZR uses and I contend is wrong, the player with the extra error would get .99 plays in range and then be docked 1 play in errors, for a total of -.01 plays, basically nothing.  To say that a player who made one more error on ANY bucket than the average fielder should get docked nothing is wrong of course.  The reason for that problem is that my method assumes that the player made a spectacular play on the average to get to the ball before he made the error, which is obviously false.  On an out, we CAN assume that he made a spectacular play on the average, or at least a much better play than on the error.  In reality, on the out (in that 1% out bucket), the player probably made some spectacular plays, some easy plays, and everything in between.  For errors, we can eliminate spectacular and very good plays, because no OS is going to award an error (at least a fielding error) on a play where the fielder made a spectacular effort - and even if 1 in 50 do, that won’t change things, obviously.

That is it. That sums up two things:  One, how UZR handles errors (please don’t ask again - Guy), and two, why I think (know) it is wrong.

How much difference it will make - I don’t know.  Probably not much.

Don’t worry, I promise not to ask.  Because I’m sure the answer will change again in a couple of hours anyway…

The biggest mistake that MGL makes with UZR is his method of handling zones where more than one player can make a play.  There is no reason for shared responsibility between a third baseman and a SS.  A SS can make a play on a ball that gets by a third baseman, but a third baseman CAN’T make a play on a ball that gets by a SS.  The way I do these plays in BZM is to not consider any ball that a third baseman touches (either fielded out, error or infield hit) as a chance for the SS.  I also eliminate any plays where the ball is fielded or touched by the catcher or pitcher.  I have mentioned this difference in methodolgy to MGL, but he seems to think his method takes care of the problem. It really doesn’t and it just doesn’t make any logical sense.  If someone fields a ball in front of you why should that hit ball have anything to do with a measure of your fielding ability?

Tango - To answer your question, no it won’t make much difference to the final UZR runs.  There are just too few fielding errors to matter much.  For SS the range is about +7 on fielding errors for the best SS to -7 for the worst.  Most SS fall within +- 3 or 4.  If I follow Kinkaid’s analysis correctly he is saying that the difference between Guy’s treating all error’s equal to hits and UZR’s current methodolgy would be a small fraction of a run.  So less than a run a SS per year.

Just for fun I looked at the Hit f/x information from April 2009.  There were 2031 balls that I have recorded that reached the shortstop position.  765 were hits or FC and 50 were ROE errors; 25 throwing and 25 fielding.  I divided the SS area (+5 degrees to -55 degrees, 0 dead center) into 5 degree segments and 3 levels of hit ball speed.  This roughly equivalent to BIS type zones, resulting in 24 buckets.  No bucket had an out rate greater than 91%.  The average out rate in the buckets in which the 25 fielding errors occurred was 67.8% and the median 70%.  The average out rate on the total 2031 hit balls was 62.4%.

"divided the SS area (+5 degrees to -55 degrees, 0 dead center) “

I think you meant -35 degrees or something.  If 0 is dead center, then -45 is 3B and +45 is 1B (90 degrees between the foul lines, naturally).

I think I use -17 as the center point for SS, so you seem to be going about 22 degrees one way to get to +5, so I guess 22 degrees the other way for -39.  Since -45 is the 3B line, I figure you meant -35, not -55.

***

Interesting about the error rates.  Good stuff.

Yes, -35.

So, ignoring the fact that an error “play” is worth slightly different than a “hit” play (so, I don’t add up error plays and hit plays - I convert them into runs and THEN add them up), his total credit/debit for that one extra error is -.8 plays. +.2 for the range and -1 for the error.  There is no .95 used anywhere.

MGL, are you saying that for that 80% bucket, where the average fielder is 75 outs/5 errors/20 hits per 100 balls, that the each error is worth -.8 plays (+.2 range and -1 errors)?  And that presumably each out that is not an error is +.2, and each hit is also -.8, and that you would apply those factors to each ball in the bucket appropriately?

It sounds like you are either saying that, or you are saying you are only applying that factor to the difference of one error, like when you messed up Player A’s calculation earlier by using the factor to diminish the difference once you already knew what the difference was.  When you say, “his total credit/debit for that one extra error...”, it is ambiguous which you are trying to do.

Or, are you trying to say something else entirely?

Kinkaid, the wording might be confusing to you, but the example is not.  Please just read the example and put it down on paper if you have to.  You can then attach any words you want to it.  The example is 100% clear and unambiguous.  I’ll even make it easy for you by cutting an pasting:

“Anyway, if the average fielder has 5 errors per 80 chances (or 100 balls) in that bucket and our fielder had 6 errors, then he made one more error.”

All errors are originally treated as hits.  No ambiguity there.

In the above example, our fielder made one more error than the average fielder would have made given 100 balls in that bucket. So he gets docked exactly 1 play.

Period.

"All errors are originally treated as hits.”

I mean “treated as outs” of course.  The faux pas should make Guy happy though, as he can now put that in one of my “different explanations” buckets to compensate for his reading comprehension issues.

Yes, clearly he is -1 play or errors.  But an error in that example is also clearly not -.8 plays, and there was no ambiguity when you also said that it was.  When you give an example that gives two explanations, and one is correct and one is wrong, that is not clear, and it is confusing.  You can’t quote just the part that was correct and say, look, there is no ambiguity, while ignoring where you also gave an incorrect explanation right next to it.

I am not asking this to be a jerk, nor because I don’t understand what is going on.  I am asking you to clarify because you are giving conflicting explanations, and I am giving you the benefit of the doubt that you are just poorly communicating rather than just assuming you truly are not understanding what you are doing.  That is why people are confused:  like Guy said, you have given multiple conflicting explanations in this thread.  Several of the things you have said in this thread are flat out wrong.  Even the example you gave in your last post gives two completely incompatible explanations (that the player with 6 errors in 100 balls when the average player has 5 is 1 play worse than average on errors, and that each error is worth a total of -.8 plays overall when you combine its range and error value).  The first is correct.  The second is not.  There is no ambiguity in that.

Really, I cannot believe you can be so condescending in this thread when the thing confusing people most is that you have so consistently mangled the explanation of your own simple process.

Jeez, MGL, you should really cut Kincaid some slack.  His role in this thread has largely been to tell the rest of us which of your statements we should believe, and which we should ignore.  Without his contributions, reading this would be like watching a foreign film without the subtitles.....

Guy, right, I appreciate his contribution.  That doesn’t mean that I am going to change the same tone I have been using for 30 years.  What the hell is the difference?  If you guys can’t separate tone from substance, that is your problem not mine.  Stop being such whiners about tone. You don’t ever see Tango complaining about someone’s “tone” because it doesn’t matter.  The only thing that matter to a discussion is what someone says, substance-wise.  As I said, whether you get your feelings hurt or whatever it is that causes you to complain about my “tone,” that is your problem and not mine.  You’ve got to accept the bad with the good in all things in life.  If you focus on the bad, and “fight it,” you will miss out on some of the good, not to mention that you are wasting your time (and others) with all your, “I don’t like your tone” talk.  But, that is just my strategy in life.  It works for me.  Maybe it doesn’t for you.  But, I am not about to change my style of communicating just to spare some feelings on a blog.  In another context I might, but not here.

Anyway, it IS -.8 plays, Kinkaid. If a player has one extra outs+errors in an 80% bucket, he gets credit for +.2 plays.  If he also happens to have one more error than an average player, then he gets deducted one play for that. Total UZR is -.2 plays.  The player would have to have 70 outs, 6 errors, and 25 hits for that to be the case, more or less.  I say more or less since that is 101 total balls, and the average fielder for 101 total balls would have slightly more than 70 outs, slightly more than 5 errors, and slightly more than 25 hits.

But, as I said, I might screw up the math, but it doesn’t matter.  You guys know how UZR including errors is done.  It is documented on FG and to some extent here in this thread.  You don’t need me to give you an examples, unless your goal is for me to screw them up so that you can say, “See, I told you he keeps changing his mind.” That is ridiculous.  Read the primer on FG.  That tells you almost everything you need to know.  What it does not tell you which I have told you 108 times now on this thread, is that all errors are counted as outs in the range runs portion of UZR.  And all errors over and above (or below) an average fielder’s errors given the same number of “chances” (see this thread for the definition of “chances") are counted as minus 1 play.  That is regardless of whether I screw up my examples or not.  If I screw up any examples, just say, “You screwed up your example,” rather than, “You are telling us another story again, MGL.” I am only telling you ONE story.  If I screw up an example, it just that - a “screwed up example.”

Here. Another screw up:

“Total UZR is -.2 plays.” That should be -.8 plays.

I’m loving this thread, because

1) it challenges me, to follow and try to understand everything, and

2) it’s kind of entertaining to see the bickering among the heavyweight posters here

Usually, Tango will step in and clarify everything in these situations, but so far he hasn’t.

I can’t recall another such advanced discussion where so much energy is being devoted/wasted on just trying to understand what each other is saying.

I hope this thread doesn’t just die out before a consensus is reached.

No, it is not -.8 plays.  As you suggested, please, just write it out on paper if you don’t see why.

Average

75 outs/5 errors/20 hits

Now say you have a player like you describe who is:

75 outs/6 errors/20 hits

If we give .2 for outs, -.8 for errors, and -.8 for hits, we get:

75*.2 - 6*.8 - 20*.8 = -5.8

Obviously, the player is not -5.8 plays.  He is -.75 plays.  Your explanation is saying he is -5.8, because you are completely ignoring the fact that on each ball, we expect .05 errors.  So an error is not -1 plays for errors, it is -.95 plays for errors, because you observe 1 error, and that is .95 plays worse than the .05 errors you expect on average.  This is the exact same thing you have to do for the range plays.  I don’t see why you don’t also see that you have to do this step for error plays.

Using the correct factors, each out is +.2 range plays and +.05 error plays, each error is +.2 range plays and -.95 error plays, and each hit is -.8 range plays and +.05 error plays:

75*.25 - 6*.75 - 20*.75 = -.75

You guys know how UZR including errors is done.  It is documented on FG and to some extent here in this thread.  You don’t need me to give you an examples, unless your goal is for me to screw them up so that you can say, “See, I told you he keeps changing his mind.”

Yes, I do know how it is done.  I don’t need you to give me examples.  I have not once asked you to give an example, only to clarify what you mean when you give a wrong example if I think it is possible you made a silly mistake that you might wish to correct or that you are just not communicating properly what you intended to say.  But if someone else comes to this thread and asks for an example (like David Gassko in #86; is he just trying to screw with you too?), and you give an incorrect explanation that is clearly going to either confuse someone or teach them how to do it wrong, since I do know how to do it, I am going to help explain it properly so people do not leave without knowing what is really going on.  Are you honestly saying that if you explain something wrong, you would rather we just ignore it and have people learn it wrong instead?  Do you really think that when we correct mistakes in your explanations so that people don’t learn this wrong that we are only doing it to screw with you? 

You didn’t even have to go through that example if you didn’t want to.  If you are so indignant that you have explained it elsewhere and you shouldn’t have to here, that’s fine.  I learned what you are doing from reading your various primers, and I do know how to do it, so I’m happy to explain it to people if you don’t want to keep doing it over again.  I gave a perfectly good explanation for how to handle his example in #88 so that you didn’t have to go through it if you didn’t want to.  Then, you chose to say that everything in the thread was garbage (presumably including my explanation), and then proceeded to give an incorrect explanation instead.  Of course I am not going to ignore that if I want David or anyone else reading this to understand this properly.  I didn’t mean to offend you in the process.

Also, the issue is not with you being a jerk.  We know you can be a jerk, we deal with it.  The issue is that you are giving conflicting and sometimes wrong information, and then your reaction to being corrected is just further confusing people as if you have no interest in whether or not anyone learns anything from this thread or not.

I’m just telling you how I do it.  If you think that is wrong, fine.  I don’t do it the way you are doing it and I think my way is right - at least as far as the what I think it is doing.  I think the methodology in UZR is wrong for treating errors, but I am just telling you how UZR does it.  UZR does not use any .95’s. It does it exactly as I said. .2 for outs and errors, -.8 for hits, in an 80% zone with no other felders having any responsibility, and then when it does the error adjustments, it does -1 for every extra error and +1 for every fewer error.

Peter, let me see if I understand what you are saying, which is intriguing.

Let’s say that we have bucket between 3rd base and SS, in the hole, and the 3B catches 20%, the SS catches 10% and 70% go for hits.

The way UZR does it, of course, is if the 3B or the SS catch it, they gets .7 plays.  If it is a hit, they split the -.3 plays, -.2 to the 3B and -.1 for the SS since the 3B makes 2/3 of the plays in that bucket (20% versus 10%).

Now, you are saying that the balls that the 3B fields should be completely ignored for the SS.  So the same bucket for the SS should be 1/8 outs for the SS and 7/8 hits (10 outs and 70 hits for every 80 balls, since we are ignoring the 20 balls that the 3B catches).  Your logic, which is intriguing and might actually be correct, is that the balls that the 3B catch could never be caught by the SS anyway, since the 3B has the first chance at a ball in the hole (which is generally true).

Now, we just go on from there, where we have different distributions for the SS and the 3B for that bucket?  The 3B of course still has a bucket where he catches 20%, the SS catches 10% and 70% are hits?  IOW, all balls count for him?

Is that right?

And you do the same if a pitcher or catcher field a ball that I might have in a bucket for any other infielder.  So basically a SS can only have balls caught by the 2B in his buckets, the 2B can only have balls caught by the SS in his buckets (can he have balls caught by the 1B?), and no other infielder can have balls caught by the catcher or pitcher in his buckets?

Makes sense, I think.  As with everything else, I am not sure it will change the overall results very much at all…

BTW, Tango, I am not ignoring your requests for data. It is just that it takes around 6 hours to run one year of regular UZR, so I can’t really generate much data for you.  I will try and recode all errors as hits and see what happens and I will try and incorporate Peter’s changes, if I got them right.

For Peter’s changes, I will ignore all outs and errors made by the pitcher and catcher since I don’t do their UZR anyway.

Then for the SS, I will ignore all outs and errors made by the 3B.

Then for the 2B, I will ignore all outs made by the 1B if Peter thinks that is correct.

MGL - Yes, you pretty much have it.  Remember in my defensive metric each infielder just has one big zone and the zones don’t overlap.  So the balls fielded by the third baseman, pitcher, and catcher are only counted if they were fielded in the one big zone assigned to the SS.

I think it does make a significant difference in runs allowed because there is a rather large variance in the rate that balls are fielded in front of a shortstop.  For instance, in 2009 Derek Jeter and Stephen Drew each had a total of 492 ground balls hit in the SS area.  But Derek Jeter had 101 balls that were fielded in front of him and Stephen Drew only 71.  Troy Tulowitzki had 133 of 638 fielded in front of him where Miguel Tejeda had 96 of 639.

Peter, what about the first and second baseman?  Should I ignore balls fielded by the first baseman for 2B buckets?  Sometimes the 1B cuts in front of the 2B but not quite like the 3B and 2B.  I am not really sure about that.

MGL - Its a little hard for me to translate the logical framework of my one non overlapping zone per fielder system to your system of shared zones, but I think ignoring the 1B fielded balls in all your zones is probably correct.  If you establish your baseline as the percentage of balls an average 2B fields in that zone of the balls that get through to him without being touched by another fielder, and then compare each 2B on that same criteria to the average 2B, I think that will give you the best measure of the 2B’s range.  Sorry, I was trying to work it out conceptually as I wrote.  The short answer to your question is yes, ignore all the 1B plays.

I like Peter’s idea about the hierarchy of plays.

MGL, no sweat on the data.

I’m just telling you how I do it.  If you think that is wrong, fine.  I don’t do it the way you are doing it and I think my way is right - at least as far as the what I think it is doing.  I think the methodology in UZR is wrong for treating errors, but I am just telling you how UZR does it.  UZR does not use any .95’s. It does it exactly as I said. .2 for outs and errors, -.8 for hits, in an 80% zone with no other felders having any responsibility, and then when it does the error adjustments, it does -1 for every extra error and +1 for every fewer error.

MGL, do you really think that if you have a bucket where average is:

75 outs/5 errors/20 hits

and you have a player who has 101 balls in that bucket that are as follows:

75 outs/6 errors/20 hits

then you are really giving him -5.8 plays?  Really?  Seriously?  That is for some reason what you insist you are doing.  If that is what you are doing, and you really do give that player -5.8 plays for being 0.75 plays worse than average, then, just say, yes, you really would give that player -5.8 runs even though it is obviously wrong (not just vaguely saying you are saying what you think you are doing, but flat out say, “Yes, UZR flat out says that player was 5.8 plays worse than average on those 101 balls,” and I will believe you, but never take UZR seriously again.

Or, admit that you are not using the method that spits out -5.8 runs for that player on those 101 balls, and that just because you can’t actually see the math that is going on does not make what you think is happening right when it is clearly spitting out blatantly wrong answers.

It does it exactly as I said. .2 for outs and errors, -.8 for hits, in an 80% zone with no other felders having any responsibility, and then when it does the error adjustments, it does -1 for every extra error and +1 for every fewer error.

Yes!  That is clearly not what your example shows!  It is what my example shows.  I do not understand why you cannot see this.  Do exactly as you said earlier, and work it out on paper, since even if I work it out plainly on here for you and show you exactly why what you think you are doing is way off, you still don’t get it.

When you compute only range runs, you use .2 and -.8 for plays made and hits.  Those are obviously not the final values for each play (in terms of plays), because you have not added in the value of the play in terms of errors yet.  On top of those values, you still have to separately take out 1 for each extra error.  For some reason, you keep ignoring that you actually need to figure out how many extra errors there are when you try to explain how to do this one ball at a time.

If 20% of the balls in the bucket are hits, and 80% are outs or errors, why do you give .2 for a play made and -.8 for a hit?  Because on the average ball in that bucket, you expect .8 plays on average, so when you observe 1 play, that is .2 plays more than average.  Guess what?  When you observe 1 error, you are expecting .05 errors on any given ball, so how many extra errors is that?  .95!  And if the player has 0 errors on the play, guess how many fewer errors that is than expected?  .05.  What is so difficult to understand about that?  You understand you have to do that for range plays.  The only way I can think of that you wouldn’t be able to see that you have to also do it for error plays, even after being explicitly shown how when you leave that step out, you get results that are blatantly wrong and clearly not what UZR is doing, is that you refuse to even think on this issue.  Or, you don’t actually care if people learn it wrong and care more about them not thinking you made a mistake.

Maybe this will make it clearer.

Average per 100 balls:
75 outs/5 errors/20 hits

which means the average per 101 balls is:
75.75 outs/5.05 errors/20.2 hits

Our player does the following in 101 balls:

75 outs/6 errors/20 hits

Clearly, that is -.75 outs +.95 errors = +.2 range plays, and -.95 errors, for a total of -.75 outs overall.  Computing the differences in aggregate instead of for each individual play is a perfectly legitimate way to compute UZR, and when you explain it that way, you have no problems showing how to do it.

Now, if you want to compute the value of each individual play and giving it a weight that combines its range and error values, which of the following is mathematically equivalent to the above:

75*.2 - 6*.8 - 20*.8

or

75*.25 - 6*.75 - 20*.75

You can run the math on that in 30 seconds and see that the first method is clearly not equivalent to computing UZR in aggregate plays.  What you are insisting you are doing is two completely different things when you try to explain it both ways.  Your answers literally cannot be right, because the two different methods you give as equivalent are mathematically incompatible.

Kinkaid, I did not read your entire 2 posts.  Where in the world are you getting -5.8 runs or plays from?

I said (twice) +.2 plays for range and -1 play for errors.  That is -.8 plays (or around -.6 runs)! 

That is for a player who allows the same number of hits as average, one more “out + error” than average, and 1 more error than average.  Did I say -5.8 plays or runs anywhere?

Ok, I see that YOU came up with -5.8 plays.  Here is what you wrote:

Average

75 outs/5 errors/20 hits

Now say you have a player like you describe who is:

75 outs/6 errors/20 hits

If we give .2 for outs, -.8 for errors, and -.8 for hits, we get:

75*.2 - 6*.8 - 20*.8 = -5.8

Well, YOU are doing it wrong!  You got some serious reading comprehension issues!  For the one millionth time (with a little exaggeration), a player in an 80% bucket, with no other players being part of that bucket, gets +.2 for a hit OR AN ERROR, and gets -.8 for a hit.

So…

This player…

75 outs/6 errors/20 hits

Gets…

75*.2 + 6*.2 - 20*.8 in range plays, and

-1 in error plays,

for a total of -.8 runs.

I have no frickin’ idea what you are doing in your equation.

You are giving me a headache!

Here is how many times in this thread I said that an error is first treated as an out and therefore the fielder gets credit for 1 minus the out rate of the bucket for an error in the “range” part of UZR, and then the fielder gets docked -1 play for every extra error he makes:

In post # 42

IOW, if an error is committed in a 20% bucket, first the fielder gets credited with an out.  He gets exactly .8 balls worth of credit, or around .65 runs.  Then when the errors calculations are done, he gets docked around .75 runs for the error, assuming that it is an “extra” error over and above the average player at that position (for that year and league).  So the net value of the error is -.1 run in that 20% bucket.

In post #64:

Player A
Out 75
Error 8
Hit 17

First we figure the range runs.  Remember that errors are treated as outs for that. We’ll assume no other fielders make outs in this bucket (since if they did, that would change the value of hits for this fielder, since he would have to share the responsibility with other another fielder or fielders).

He made 3 more outs+errors and 3 less hits (obviously) than the average fielder.  So he gets credit for 3*.2 plays or .6 plays or around .46 runs in range runs.

Now, we have to do the error runs separately.  Simple.  He made 3 MORE errors, so he has -3 plays or around -2.25 error runs.

His total UZR is -1.79 runs. In plays, it is -2.4 plays, but the play is worth slightly different if it is an error or a hit, since the value of an ROE and a hit is slightly different.

Post #69:

Bucket with 80% catch rate (including errors counted as outs) and assuming no other fielding position makes any outs in that bucket.

Player A
Out 75
Error 8
Hit 17

Range runs

83 outs plus errors, with each one getting .2 plays of credit. 17 hits, getting -.8 runs of credit. Pretty simply.  3 plays of credit (not .6 like I said before, of course).

Error runs

-3 plays (even though he made 8 errors - that is because he made 3 MORE errors than the average fielder).

A total of 0 plays.

Post #98

First it assumes that an error is exactly the same as an out, and gives the player the appropriate credit. In an 80% out bucket (for all years that UZR uses as the baseline, where the 80% also includes errors - outs + errors), the fielder first gets “credit” for .2 plays.

Now we do the error adjustment.

...

He simply gets docked one play for that extra error…

Post #105

“All errors are originally treated as hits.”

I mean “treated as outs” of course. 

Post #108

Anyway, it IS -.8 plays, Kinkaid. If a player has one extra outs+errors in an 80% bucket, he gets credit for +.2 plays. If he also happens to have one MORE error than an average player, then he gets deducted one play for that. Total UZR is -.2 plays.

Post #112:

It does it exactly as I said. .2 for outs and errors, -.8 for hits, in an 80% zone with no other fielders having any responsibility, and then when it does the error adjustments, it does -1 for every extra error and +1 for every fewer error.

So, I explained exactly the same thing in 7 different threads, then you somehow butcher what I said, and claim that this is the way I do it:

Now say you have a player like you describe who is:

75 outs/6 errors/20 hits

If we give .2 for outs, -.8 for errors, and -.8 for hits, we get:

75*.2 - 6*.8 - 20*.8 = -5.8

You somehow give the fielder -.8 plays for each error when I said 7 different times that an error gets .2 runs, the same as an out (in an 80% bucket) and then every EXTRA (you will see that in all the posts above, I clearly say EXTRA error) error gets docked -1 plays, and then you yell at me?!

I have learned a lot more about how UZR works thanks to this thread - MGL, Kincaid, Guy - thank-you.

And also this is without doubt the most comedy thread on this blog by some distance (although for you three I suspect it is the most painful).

It is abundantly clear that I understand that the error counts as an out for range plays.  That is quite clearly a part of every single example I have worked out in this thread.

So, ignoring the fact that an error “play” is worth slightly different than a “hit” play (so, I don’t add up error plays and hit plays - I convert them into runs and THEN add them up), his total credit/debit for that one extra error is -.8 plays. +.2 for the range and -1 for the error.

That is where I am getting it.  The quoted is wrong.  There is no ambiguity in that.  That is not a lack of reading comprehension on my part.  Perhaps you did not mean what you wrote and just communicated it poorly, or left out a step by mistake, but then that is why I asked you to clarify, and you insisted that it was correct and took offense that I would dare do such a thing.

And, also from you insisting that my method is wrong, even though it is mathematically equivalent to what you are doing when you compute the differences in aggregate, or when you calculate range first and then add in errors separately.  Hell, it’s even the exact same thing I was doing earlier when you said I have your methodology “exactly down pat” in this very thread.  I don’t know how many times I can ask you to just work it out on paper if you don’t understand that, because obviously you are not.  You are refusing to even think about this, because it is not a hard concept to grasp once you actually start to work out the math for yourself.

If you are dealing only with range plays, then it is +.2, and then later you will take out the cost of the error (which will work out equivalent to being +.05 for every non-error and -.95 for ever error; if you don’t believe me, work it out; 6*-.95 + 95*.05 = -.95, which is exactly the same as taking 5.05 expected erorrs - 6 total errors for the fielder).  If you are combining the range and error values of that play, like you do in the quoted passage, then it is not .2-1=-.8.  That is wrong.  When you said the total cost of an error, once you combine the the value of the range play and the value of the error, is -.8 plays, that is wrong, because you are ignoring the expected number of errors for that play on average, which is necessary to calculate how many errors you have beyond what is expected.  If you try to actually calculate UZR using -.8 as the total combined value (between range and errors) of errors and hits, and +.2 as the combined value of outs, then you will get. -5.8 for that player.  If you do it how I showed (which you for some reason insist is wrong), then you get the right answer.

You don’t use the .95 anywhere if you already have the total errors and the total expected errors, just like you don’t use the .8 or .2 for anything if you already have the total range plays and hits and expected range plays and hits.  If you want to find the value of each individual play and total them up that way, then just like you then need the .2/-.8, you would need the .05/-.95 for errors.  When you walk through a full example, you are never doing it this way, so maybe that is why when you explained how you would do it this way, you don’t realize the implications of what you said.

-1 in error plays,

for a total of -.8 runs.

Wrong (though close).  The average player is 5 errors per 100 balls, so per 101 balls, he is 5.05 errors.  That means that the player is only -.95 in errors, and -.75 overall.  Which is exactly what my method says.  So, how can my method be so surely wrong when it is giving the correct answers?

If you want to ignore what you wrote that was wrong, fine.

At this point, I’d be happy with you just trying to explain what exactly is wrong with my method when it returns the correct answer every time instead of just insisting it is wrong.

For the average player:
75 outs/5 errors/20 hits

For the player we are rating:
75 outs/6 errors/20 hits

-outs are +.2 range plays and +.05 error plays
-errors are +.2 range plays and -.95 error plays
-his are -.8 range plays and +.05 error plays

Total plays is:

75*.25 - 6*.75 - 20*.75 = -.75 plays

Ignoring that you would want to apply the different run factors to the plays first and then combine the range and error values (since that has not been a part of this discussion), why do you think that is wrong?

I see the logic in Peter’s hierarchy, but I don’t think it matters for UZR.  My understanding is that outs only count for the player making the out in UZR.  So if the 3B fields a GB that is 20-3B/10-SS/70-hit, the 3B is +.7 but the SS is not debited for failing to make that play.  So it already ignores this play for the SS, and there is no Jeter vs. Drew inequity. 

So the change in out distribution MGL poses does not fix Peter’s concern (which isn’t actually a problem anyway), and I don’t think is a good idea.  MGL is suggesting (I think) that for 3B a hit in this 20-10-70 bucket will still count as -.3, and an out as +.7.  But now for the SS a hit is -.12 and an out is .88.  I don’t get the logic for this.

"Wrong (though close).  The average player is 5 errors per 100 balls, so per 101 balls, he is 5.05 errors.  That means that the player is only -.95 in errors, and -.75 overall.  Which is exactly what my method says.  So, how can my method be so surely wrong when it is giving the correct answers?”

That is 100% correct.  I never said it was wrong.  What was wrong was you thinking that I credited a fielder with -.8 plays for every error, not for every EXTRA error. I also realize that for 101 plays, it is -.75 and not -.8, which I also said in one of my posts above.  I didn’t say “-.75:” but I said “slightly less” or “more” because of the 101 rather than the 100.  I don’t use the .95, because, as you said, I compare expected errors to actual errors based on the number of balls. I also said that 1000 times (maybe only 7 times).  So the average fielder would have 5.05 error in 101 balls, again, as you say, so the difference is only .95 errors and not 1.  That is exactly the way I do it.  Same as you.  Never said you were doing it wrong.  Never, ever, ever.  If anything, you could have said that my -.8 was wrong (which I was aware of and said so) and that the correct answer is -.75 (for the 101 balls).  Why you kept insisting (well, you did twice anyway) that I was claiming -5.8, I have no idea. That was my issue, as you can see from my post above.

Anyway, I agree that this thread has been comical from the argumentative side!

If we give .2 for outs, -.8 for errors, and -.8 for hits, we get:

75*.2 - 6*.8 - 20*.8 = -5.8

Obviously, the player is not -5.8 plays.

When you convert a sure out into a sure hit (or vice versa) the difference is .80 runs.  In this case, you are not doing that.

You have to use Linear Weights.  That would mean this:
75*.3 - 6*.5 - 20*.5 = +9.5 runs in 101 plays

Now, you need a baseline to compare that against:
75*.3 - 5*.5 - 20*.5 = +10 runs in 100 plays

And 10 in 100 is 10.1 in 101 plays.

The difference is 9.5 minus 10.1 or -0.6 runs for the extra error in this case.

Tango, we’ve been excluding conversions to runs for the purpose of this conversation and just focusing on plays.

MGL, that is exactly why I asked you to clarify what you said before I ever said anything about it, and you refused to clarify what you were talking about.  Do not get upset when someone goes out of his way to ask you to clarify before responding, and then you refuse, and then they do not interpret it how you intended.

When David asked for an explanation of the process, and I had already explained it a way you now are agreeing was correct, and then you came in saying that everything before that in the thread was garbage, and then proceed to give an explanation that can easily be interpreted in the incorrect way I was describing, that definitely has the potential to confuse people or give them the wrong understanding, and that should be clarified.  If you refuse to clarify which way is actually correct, do not get upset at someone else for doing it for you.

Also, please clarify what you mean when you say you are crediting a fielder with -.8 plays for every extra error, because that is also ambiguous and can certainly be interpreted in a way that will lead to wrong results.  For example, that can be interpreted as saying if the average fielder has 5 errors, and a fielder has 6, you are giving him -.8 plays for having 1 extra error, or that you are applying that factor to the difference when you already know what the difference in plays is.  Presumably that is not what you mean, but if someone does not know that already, they could easily think that is what you mean.

Kincaid, even if you are talking about plays, the point stands. 

For example, let’s start with the baseline:
75*.2 - 5*.8 - 20*.8 = -5 plays per 100 BIP, which is -5.05 per 101 BIP.

Your example with the extra error was at -5.8 plays per 101 BIP.

That difference is -0.75 plays.  (Which, if you multiply by 0.8, corresponds to the -0.60 runs I noted). 

The problem is that the example had presumed that 0 was the baseline, when the baseline was actually -5.  That is, it was not a good baseline that was chosen. 

So, I think when you said -5.8, it gave off the wrong impression.  Implied was -5.8 from average, when really it was -5.8 from some unknown baseline.

"Also, please clarify what you mean when you say you are crediting a fielder with -.8 plays for every extra error”

I’m reluctant to wade into the MGL-Kincaid mess, but I’ll say that talking about “extra errors” (or “extra” anything) creates “extra” confusion.  Because this could mean one additional play made by a fielder—and thus additional range credit—OR it could mean a player committed one more error on a given distribution of balls, and thus recorded one less out as well.  If people will stick to comparing various outcomes per 100 balls, and how they think these should be treated, it would clarify things.

Tango, yes, exactly.  The -5.8 would be useless in that example because you have no idea what the baseline is.  For UZR it is zero, so if someone read MGL’s comments that way and tried to do it like that, they aren’t going to work out that average if you do it that way is -5.05, not 0.  That was the whole point of clarifying that you shouldn’t do it that way.

And Guy, right.  There has been so much said that is ambiguous and could easily be interpreted by someone to mean the wrong thing, or to just have no idea what it is supposed to mean, that clarification is needed in some more concrete way.  That’s all I have been trying to do.

I should say I regret that it turned into such a mess.  All I intended was to attempt to clarify where I saw things that at least had a decent chance of being understood incorrectly, or where things could lead someone to get the wrong idea of what is happening in the math, or were ambiguous.  That’s it.

I am not sure this thread could be more entertaining even if you took the full, unedited version of it and presented it as performance art. Thanks to everyone involved.

"Also, please clarify what you mean when you say you are crediting a fielder with -.8 plays for every extra error..”

Are you seriously still asking me?  In post #122 above, I quote 7 separate posts where I say exactly how errors, hits, and outs are handled, some with explicit examples. You can’t seriously be asking me again.  You have to be giving me a hard time for some reason.  Re-read post number #122, and if you are still unclear, I’ll send you a plane ticket and we can discuss it in person, with a chalkboard like Glenn Beck does.

Seriously, I would never poke fun at a person if they did not understand even a simple concept.  That happens to me sometimes.  But, rather than saying you don’t understand something (and I know that you do), you keep asserting that I am not explaining myself and/or I am changing my story.  That is beyond preposterous - in fact, it borders on the irrational/insane - so let’s just drop it…