THE BOOK--Playing The Percentages In Baseball

Am I mistaken, or can you build lwts from the bottom up simply by adjusting the value of the out?  I also prefer to start out at zero and build upward (and then apply replacement level if necessary), but I thought lwts could do that if you used an appropriate out value.  Am I mistaken?

I think the conversion of Bill James is now officially a lost cause.

Sal - that’s exactly how it works with Estimated Runs Produced (which James himself published, not realizing that it is, in fact, a form of linear weights). I think Extrapolated Runs does the same thing. The only thing that changes is the out value.

James is confusing one thing - Palmer’s specific linear weights implementation - with the concept of linear weights themselves. The funny thing is that it’s all presentational; so long as you are clear and explicit as to what your baseline is, it doesn’t matter if you use runs above average, runs above replacement or “absolute” runs.

By the same token, you can use Runs Created in an “absolute,” replacement or average framework. This is just for illustration purposes, so excuse the use of basic RC - it keeps everything simple and means I don’t have to do any coding. OBP * SLG * AB. My example player, Ryan Theriot, hitting .315/.392/.374.

Ryan Theriot, Basic RC: .392 * .374 * 425 = 62 RC
NL Average: .329 * .412 * 425 = 58 RC

62 - 58 = 4 RCAA. Horror of horrors, I’ve just done subtraction totally contrary to the nature of baseball!

Isn’t RC by definition what a team would produce if that player batted in all 9 slots of a batting order?

Doesn’t that mean that is has no practical value whatsoever other than to compare one player to another?  I always hated RC and that is why (if what I said is true).  Why would we want to know how many runs a team of Bonds’ or of Ausmus’ would produce?

Isn’t lwts a perfect estimate of a player’s offense if we don’t know anything about his lineup slot and the team he plays for?

And if we do know a player’s lineup slot and/or what team he plays for, we could change the lwts values and make it once again a perfect metric.

That’s been James’ complaint about linear weights from the beginning.

Isn’t RC by definition what a team would produce if that player batted in all 9 slots of a batting order?

Not the most recent versions.

Certainly, you can create a good offensive estimator starting from zero, instead of average.

But, I don’t think you can do that for fielding (say, UZR and PZR).

Studes is referring, I think, to theoretical team Runs Created.

What’s the first link that comes up in Google for that term?

http://www.baseballthinkfactory.org/btf/scholars/furtado/articles/NewRC.html

Furtado breaks down the math behind TTRC and finds… a linear weights formula! I’m still trying to process this, to be honest.

Patriot has done similar things on his site, like so:
http://gosu02.tripod.com/id76.html

Click on Runs Created, and Theoretical Team.

I assume that if there is a new version of RC that is not what a team of 9 players would produce, that it is simply lwts added to average rpg!

Lwts is by definition, the number of runs a player would add to an unknown team.  You can’t do any better than that.

Using a different value for the out is the same exact thing as using regular lwts and then simply adding in some fraction of league average rpg.  If a team in the NL scored 4.6 rpg and I have a player who is zero lwts, then I can call it 4.6 runs if I want to scale it the same as RC.  Or I can call it zero plus 4.6 divided by 9 or divided by 8 (or 8.6 or whatever), or whatever I want to do.

I don’t see the argument here. Lwts is the perfect measurement for offense, by definition.  The old RC was “cute” (because it gave us a number that looked like runs per game per team, and because people liked to know, “What would my team score if all my players were like Bonds?"), but it was terrible except, as I say, to compare players.  In addition, I think it would be possible to have to players where one was higher than the other in RC but lower than the other in lwts (because of the interactive effect in RC).  No?  Or maybe RC does not really capture that interactive effect.  I don’t know.  I have never paid any attention to RC whatsoever.  I still don’t see why anyone should.

MGL, That presumes that the only point of a dynamic run estimator is to apply it to an individual hitter. When you use it for things like pitchers or teams, it works fine (with the caveat that BaseRuns is better). Component ERA is really just another expression of Runs Created, so far as I can tell.

And thanks for the link, Tom. Although I believe some of that’s been supplanted by Patriot’s recent series on BaseRuns, right?

TT can be applied to BsR too, which I’ve discussed on my site and also recently on my blog.  But it’s nothing new--David did was the first to do TT BsR.

Because of the way the math works out, TT RC is equal to 8/9 of the linear RC plus 1/9 of the regular A*B/C RC. 

To address MGL’s point, Linear Weights is our estimate of what the player would produce if he was on an average team, and as he says, it’s the “right” answer for that question.  But we also recognize that the player will have an impact on the other players on the team, and the LWTS for will change.  The TT attempts to capture this effect, and when used with a good dynamic estimator like BsR, presumably does a good job.

However, the difference between TT BsR and LWTS is not that great, and you have to keep in mind that if you let the player change the run environment, you have to use a custom runs-to-win converter if you want to convert to wins.  And once you do that, most of the difference between the two approaches washes out.  So while I like the TT concept a lot, I think the easiest course of action is to stick with LWTS for player evaluation.

I disagree with James’ basic “start from zero” and build up.

A guy gets a walk.. what is that worth?  Well, it’s worth whatever you expect the rest of the batters in that inning to do.  And what do you expect them to do?  Well, average, more or less.

The reason that the guy who gets a leadoff walk will score 40% of the time is exactly because of what the rest of the batters are expected to do.

So, there’s no such that as starting from zero.  You always start based on whatever you expect your environment to provide.  The fallacy is really in the way James is presenting the argument, and not in linear weights.

James’s old opinion was that there is interaction between getting on base and driving in runs, and that it is multiplicative (sp?) and not additive. That basically is why he didnt like linear weights.

Yes, lwts only works for individual players on an average team or you don’t know the team.

It does not work for pitchers and it does not work for teams.  It is pretty darn close, though, for teams and for pitchers, as long as the components are not extreme.

And Tango is right. Staring from zero and working your way up makes no sense for individual batters without a run environment. Unless you are assuming that everyone in the lineup is the same as the player you are evaluating, and then you are back to RC.

And while I don;t work with it, I think that BaseRuns is perfect for a team or for pitchers, no?  Wouldn’t it also be perfect for computing what a lineup full of a certain player would score as well (IOW, it is the perfect RC formula)?

What is TT?

Tango, #14, you nailed it.

I wish someone would respond to my post #7. Tango’s point about a BB being worth what it is because of the avg context it (presumably) occurs in, reaches a greater level of reality in UZR/PZR. It’s all based on what the avg fielder does. Has anyone ever tried to convert UZR into an absolute runs per out framework. I suppose it could be done, but still, you have to start from the avg with UZR, because of the interaction between the pitcher and fielder on a BIP.

TT is theoretical team, ie how many runs a player contributes in a lineup with eight average hitters (other than himself).

And right, BaseRuns should work great for pitchers - if for presentational or aescetic or lack-of-desire-to-argue reasons you want ERA instead of RA you need to add in an unearned runs adjustment, of course.

This may not be the most appropriate place to post this, but I think some people use the TT with a given batter to generate a set of ‘plus-1’ weights, and then apply these to the individual batters.

This seems wrong. If a 1b to an avg team is worth .48 runs, and .50 on a team with Bonds, you can’t simply apply that .50 to Bonds’ singles. You also have to apply an extra .02 runs for the 1b of all the other batters to Bonds. So, you simply have to do the ‘classic’ TT calculation.

If anything, I think it’d be the other way around - you’d use Bonds’ production to figure out LWTS for everyone on the team BUT Bonds. The value of all of his batting events is determined by the other eight guys in the lineup.

If you apply the +1 method to TT, and use those weights for the individual, you will get the same results as if you just applied TT directly. 

If you ran TT for the other players on the team, they would all still have average event values.  So all of Bonds’ interaction effects have been credited to Bonds already.

Perhaps I’m misunderstanding the practice that David is referring to.

I don’t think that adding a non-average player to a team of average players changes anything.  Let’s say that we have a player who is 1 single better per 500 PA than the average player.  By, definition doesn’t he add .48 runs to that lineup per 500 PA?  Isn’t that how the lwts value are calculated in the first place - by “adding” an extra single in the middle of an average “lineup” and seeing, in average how it changes the RE’s?

If you add a player who never makes out and say walks every time or hits a HR every time, doesn’t he simply add .31 runs per PA or 1.41 runs per PA, or whatever the lwts value of a BB or HR is?  It is not like RC where we have to use RC per out.  For lwts, we use runs per PA and not per out because the fact that a good player generates more PA for the other players is already included in the lwts values, isn’t it?

David, as far as creating a fielding estimator from zero, I don’t think so, but I’d have to think about what that even means…

Once you add a non-average player to an average lineup, it is no longer an average lineup.  So LWTS can be viewed as the player’s value assuming that the lineup he is in is average with his presence included.

It is not entirely clear that this is the incorrect way to view it, since the average player plays for a .500 team with his contributions already included.  But if you assume that you are adding the player to a lineup of 8 average players, it makes a difference.

Here’s a relevant article:
http://tangotiger.net/reconcile.html

Where it shows that even though someone “creates” a certain number, you don’t necessarily give it all to that guy.  There are implied runs created.

----"If you apply the +1 method to TT,....you will get the same results as if you applied TT directly.

I don’t think so. In fact, I just tried an example. I added a player who hits 600 HR in 600 PA to a TT. Doing it directly, the team scored 793 more runs. Figuring the +1 value of a HR to this TT and applying it to the batter, I get only 755 runs.

Are you saying that you found the +1 value for the TT before adding the player to it?  If so, then yes, you will get a different result, and as I thought might be the case in #20, I misunderstood what you meant.

I was talking about adding the player to the team, then going back and finding the new weights for the team with the player included.  I guess it’s confusion between the use of the TT term to refer to the 8 other players or to refer to the new 9 player team.  You mean the former and I meant the latter.

No, I used the plus 1 value of the TT with the player. Try it yourself, using the 600 HR in 600 PA player I used.

There’s still a terminology problem here, and it’s my fault.  I have never actually used the +1 method for the TT, but I have used the derivative method (which the +1 is an approximation for unless you really want to know what exactly one additional event will do for you).  In the linked post, you can see that ARod’s TT BsR using long-term and 2007 AL weights respectivley were 145.1 and 145.2 (first chart).  The last chart shows the weights for each of those cases, then applies those directly to his stats, and yields 145.1 and 145.2.

The formula for that is

LW = ((B + C + (F + G)*PA)*((A + E*PA)*(b + F*p) + (B + F*PA)*(a + E*p)) - (A + E*PA)*(B + F*PA)*(b + c + F*p + G*p))/((B + C + (F + G)*PA)^2) + d - I*p + H*p

where p = 1 for a PA event, 0 for a non PA event
E = reference team (A/PA)*8, F = (B/PA)*8, G = (C/PA)*8, H = (D/PA)*8

So it’s a pain in the butt.  But it does work--it has to, mathematically.

Let me give the numbers I used, so you can show me where I’m wrong (if I indeed am).

Avg player= 550 AB, 50 BB, 146 H, 234 TB, 16 HR

A team of 8 of those players scores 600 runs, according to the BsR version I used.

Adding in a player with 600 PA and 600 HR, I get 1393 runs for the team The difference is 1393-600, or 793 runs.

Using the plus 1 method and adding in an extra HR, I get a value of 1.2578. Multiplying by 600 gives only 755 runs.

Just staying on the sidelines a bit here, and coming in for the 3rd and long situations.  Using Markov:
http://tangotiger.net/markov.html

I get using David’s batting line (34D, 3T, 100K): 4.797 runs scored per game (BaseRuns says 4.859)

A (Markov) game is 27 batting outs.  So, David’s line has 404 batting outs times 8 equals 119.7 games, or 574 runs scored. 

If you make it 8/9ths David’s batting line, plus 1/9th 600 HR in 600 PA, you get:
11.656 : Runs Scored per Game (BaseRuns says 11.406)

The new line has 359.1 batting outs times 9 equals the exact same 119.7 games or 1395 runs scored.

So, our player has “created” 821 runs.

***

Now, this goes to the heart of the “reconcile” page I posted a few posts ago.

While David’s plus one method may in fact have 1.25 for the HR, this gives you the direct runs.  It ignores the indirect runs that all those HR created.  By having a run environment where you have more HR, the value of the hits and walks increase.  But, in the traditional sense, this great HR hitter gets no extra value for creating such an environment.

There is an indirect payoff, to which he deserves credit for.  While he doesn’t get it in the plus 1 method here, he does obviously deserve it.  (And the extreme example of that article I wrote makes it quite clear.)

Anyway, his 600 HR created 821 runs, or 1.37 runs per HR.

The average player in this team will create 574 runs / 8 players / 600 PA = .12 runs per PA.  So, the marginal effect of the HR is +1.40 runs, plus he gets a standard +.12 runs per PA for a net effect of 1.52 runs per HR.

Going back therefore, if everyone gets +.12 runs per PA, reverse engineering our HR hero from 1.37 gets +1.25 runs per HR, plus the +.12 runs per PA.

***

Sounds like we might be saying the same thing?

It seems to me all James was saying in his original response was what he long ago said about Pete Palmer’s original use of LW: average level MLB performance is not replacement level MLB performance, or to put it another way, a substantial portion of an MLB player’s value to his team (as reflected, for example, in the salary a team will be willing to pay) is in the portion of his performance from replacement level up to average level.

To “balance” an above average performance one day with an equally below average performance the next day and call that player a “zero” based on these two above-replacement level performances is a mistake.  Instead you need to “add” the above-replacement level value of each day (or month or year or whatever) together to get the player’s total value.  If you want to then figure how many of a team’s limited resources (outs on offense, for example) it took a player to achieve that total value, you can divide the player’s accumulated value by resources used (RC/27 Outs, for example). But, James insists, whatever you do don’t subtract the below average value from the above average value because that will not give you an accurate picture of player value.  I really think that’s all Bill was getting at.

You can read it that way if you like.  But, that’s not at all what he was saying.

He is talking about the nature of baseball. 

The nature of baseball is not to start at zero and build up.  It is to leverage the context you find yourself in.  That is not only the nature of baseball, it is the nature of sport, and the nature of life.

----"Sounds like we are saying the same thing?”

I think so (assuming that comment is directed to me). In #29 you wrote, “By having a run environment where you have more HR, the value of all the hits and walks goes up.”.

That’s pretty similar to what I wrote in my post #18.

BTW, I love your post #31.

David, you were right.

I got 609.9 runs without the player, 1424.7 with him for a difference of 814.8 runs (the BsR version I was using overvalues extra base hits, so it was a little more robust for this team than whatever better version you used).  +1 gave 1.278 for the homer weight, which is about what you got.

So you were right, and I was wrong.

But the derivative method I posted in #27 works for the TT, as it must.  It yields a homer value of 1.358, which times 600 is 814.8.

"That’s pretty similar to what I wrote in my post #18. “

You are right, that’s exactly the same thing.

As for 31: cool, thanks!

***

Patriot: good, looks like all three of us seem to be in agreement here.

As to #31, if you want to be philosophical I agree that we all live and work within a context and not in a vacuum, but it is also true that no society or organization can subsist merely on the contributions of its above-average performers (well maybe just Lake Woebegone); merely average (and below average) performers contribute in a positive sense as well.  That’s why one needs to “start out at zero and build up” instead of “starting everybody out in the middle and moving players up and down”.  This seems to me one of the most important general observations in all of Bill J.’s work, and misreading it would be unfortunate.

Read this please:
http://tangotiger.net/scales.html

Especially this part:

An average player is worth 4 million$. Therefore, even a slightly below average player still has alot of worth. A .490 player, or a -2 runs / 600 PA player is essentially the same thing, but expressed with a different scale.

You could choose to describe that -2 runs / 600 PA player as a 78 RC / 600 PA player, given that the league is 80 RC / 600 PA. It’s really irrelevant, since you are describing the same thing. 0 Celsius is 270 Kelvin. They both describe the same thing, but in different scales.

In short, I reject the idea that is being presented about positive and negative.

And we’ve said many times you can convert LWTS into RC by simply doing
RC = .12*PA + LWTS

or

LWTS = RC - .12*PA

(Where .12 is the number of runs per PA for the year in question.)

WAR = LWTS/10 + PA/300

Or the same thing as:

WAR
= (RC-.12*PA)/10 + PA/300
= RC/10 - PA/115

And WAR, as we know, has a 1:1 relationship with dollar value.

The entire issue hinges on presenting one number (RC or LWTS) without also presenting PA. It’s really that simple.

***

Note that this RC is the real RC, without the implied runs due to extra or fewer outs, as described earlier in this thread.

A hitter plays his first 5 games in the majors and has one single and four outs in five PAs in each of those five games.  RC tells us usefully that this hitter has created one run (5TB * .200 OBP+ 1)in his first 5 games.  This statement is accurate and intuitive—in the context of baseball as we know it, this hitter’s five hits will, on average, have resulted in one more run scored by his team than if he had had no hits at all.  If we also want to know how this one RC in 20 PAs compares to a replacement level hitter, or an average level hitter, or a HOF level hitter,we can figure how many RCs a replacement level, average level or HOF level hitter would have created in 20 PAs. 

In contrast LWTS, as I understand it, would tell us that this hitter created minus something over his first five games—his 16 outs reduced the run probability of his team’s scoring more than his 5 hits increased it.  LWTS fails to start us the simple initial fact that this hitter did in fact create a run for his team.  Yes, we can do a calculation to get there by giving back to this hitter the negative value of each PA that LWTS has subtracted, and you’ll end up back at one RC.  But then if you are going to give anyone credit for their below-average but above-replacement contributions, you have to keep making this adjustment over and over, and if you ever fail to do so, as Pete Palmer did, you end up with repeated errors in valuing players.  This is true because LWTS starts with assigning an average, not a replacement level, run probability to each event, so players are constantly falling into negative territory despite creating actual runs (maybe fewer than average in a particular time sequence but still creating them)for their team along the way,so to get back to a baseline to compare Why not just stick with RC in the first place?

LWTS assigns a value to player contributions that has an average performance level already embedded in it, and you have to rigorously umanipulate it to get that average level assumption out.  RC creates a raw number that you can then play with to compare to all sorts of performance level assumptions.

This is what I understand James to be saying.

In the second sentence of the previous post my equal sign came was mistyped as a plus sign. The phrase should read “(5 TB * .200 OBP = 1 RC)”.

"In contrast LWTS, as I understand it,”

LWTS is telling you that this player created 2 less runs than an average hitter would have created.  An average hitter would have created 3 runs.

The long and short of it is that you simply need two dimensions, not one.  To say that RC=1 (without knowing the PA or games) is a better thing to know than LWTS=-2 (without knowing the PA or games) is just plain wrong.  When you present the single dimension, both tell you half the story.

HOWEVER, with LWTS=-2, you at very least know that his performance in his PA space was below average.  You have no idea what RC=1 means in relation to anyone else.

Regardless, you need that second dimension (PA) so that you can properly evaluate the result of either LWTS or RC.  I already discussed what value is.  It’s WAR.  And to figure WAR, you need EITHER LWTS or RC, PLUS PA.

For anyone to quote LWTS and discuss value, without also talking about PA is simply not telling the whole story.

You are telling the better story, but I disagree with the “effort” part of what is needed.

***

And it’s simply storytelling on your part to ascribe what you are saying to what James is intending to mean.

And James is a fantastic writer who makes things quite clear. James is and has been quite clear on his stance toward Linear Weights.

I don’t see why average shouldn’t be the “natural” baseline for baseball analysis rather than .000/.000/.000. Baseball is a zero-sum team game, and any hit is also a hit allowed. In the context of one game, by runs scored, a below average team will lose, an above average team will win; by the components of the runs, a below average team will generally lose and an above average team will generally win. Over the course of the season, teams will have wins and losses, but throughout the season we don’t focus on how many wins a team has but rather on how many games they have won relative to .500. Why should players be different? Why is it better to point out that a team won 79 games than to point out it was -2 wins? We know that a player has to be good to be on the team to start with, so I’d rather know the net contribution to winning or losing than the gross contribution to the team. The latter treats a baseball team not as an entity attempting to maximize its winning percentage but as an accounting apparatus. If the batter has “created” one run by going .200/.200/.200 in 25 PA, then how many runs have been “created” respectively by the pitcher and the defense? The significance of a batting event in baseball is not that an otherwise scoreless game has suddenly been gifted with a run, it is that, among the many possible outcomes (each of which has a specific probability that bears relation to the overall frequency of those outcomes in the league) one outcome occurred in that specific plate appearance and that outcome should be viewed in terms of its value relative to the other possible outcomes weighted by their frequency. We know that bad pitchers “create” runs for the opposing team; what is the .000/.000/.000 baseline for pitchers? Gassko’s Pitching Runs Created work back from the league average because there simply is not an easily-conceived floor as there is for hitters.

I just don’t see the logic of saying that the same runs were created both by the batter (credited as RC) and by the pitcher (credited simply as runs). Baseball is about the *the relation* between the defense and the offense, not about the creation of runs.

One risk of using average as a base line is that it may give you a distorted view of accumulated value.  A hitter who plays every day all season long and contributes an average number of RCs would be assigned a number “zero” for run creation that season if you use average as a baseline.  A hitter called up in September who plays only in the last game of the year and goes four for four gets an above-zero number for run creation for the season.  Which of these two players created more offensive value for their team for the season, and by what margin?  Of course the player who created an average number of runs runs over a full season’s worth of PAs created more value for the team, by an enormous margin.  RC will tell you that at a glance, LWTS will not.  If you think nobody would be silly enough to use LWTS this way, check Pete Palmer’s orignal use of LWTS, and how it rightly drove Bill James crazy.  And for a more recent example, look at fangraphs for attempts to use WPA cumulations as the basis for judging most valuable players, which make the same mistake.

Let’s suppose you have a player with 15 Runs Created, birtelcom. How valuable is he?

You don’t know, because you don’t know how much playing time he’s had. A player with 15 RC in 162 games isn’t very valuable; a player with 15 RC in a week’s worth of games is extremely valuable.

You need to know playing time for either RC or LWTS to be useful across the entire spectrum of players, and that’s whether or not you denomenate by average or “from zero.”

And again - you can do Runs Created Above Average or linear weights above zero. Easily. Very easily. They’re the same thing. Which is more accurate - the temperature in Kelvin or the temperature in Celsius? The price of gold in dollars or in Euros? The distance between Paris and Rome in miles or kilometers?

They’re the same thing.

Birtelcom/43:  In that sense, it’s also a mistake to use Runs Created, unless you believe that final value should be stated over zero.  Only the final figure of runs above [your chosen baseline] would be acceptable. 

And in defense of Pete Palmer, when he published The Hidden Game, replacement level was not in vogue as it is now.  James used it, but he didn’t use it as a baseline to get a +/- figure, he used it in his “.350 chance” methodology.  Using average was reasonable for the time.

By the time Palmer’s later works came out, replacement level was in vogue, but no one agreed exactly on what it is (although there is now something resembling a consensus).  I don’t think it’s inappropriate for the editor of an encyclopedia to state his ratings against an obvious baseline like .500 that is instantly understandable to anyone.

It all depends on what you’re looking for, Colin.  An example of a context in which you want to know raw RCs, not playing time, may be in a salary context. Most baseball salaries (except for incentive based contracts) are paid in season terms, not playing time terms.  Did Moises Alou earn his salary with the Mets last season?  His LWTS number last season was very good.  His raw RC number was not so good, because he was injured much of the season.  Raw LWTS tells us correctly that Moises is a talented player. RCs per PA would tell us the same.  But raw RCs would tell us accurately that the Mets didn’t do so well paying him a high salary.  Salary is paid for production (i.e., production above replacement value) over a whole team season not for unused talent.  Similarly if you take Moises’ raw LWTS for 2007 and add it to his previous raw LWTS accumulated in previous seasons, it looks like he had a fine additional year of performance that should significantly enhance his standing for the Hall of Fame or whatever your favorite collection of all-time greats might be.  But if you look at raw RCs you get the more accurate sense that 2007 should add only a limited enhancement to his career credentials, because his actual production, his actual contribution in helping his team score runs and win games, was limited. 

You and Tango point out correctly that a raw RC number with no context of time at all is of no use, whereas at least a raw LWTS number tells you something about a player’s performance compared to average.  But we rarely experience baseball numbers without any time context at all—when we have a baseball stat in front of us we are generally looking at the stat in the context of a game, or a month, or a season, or a career.  All of these time contexts reflect what we might think of as “team time” rather than “playing time”.  Playing time is how much a player played, but team time is how many games a player’s team played duirng which it either had the player producing or, if not, then a replacement player in his stead.  Raw RCs give us an immediate sense (if we know the “team time” that has passed, as we almost always will when taking about a particular stat) of the value contribution of that player to his team during the game, the month, the season, the career.  LWTS can’t do that without additional information. 

In this respect raw RCs are similar to other raw, cumulating numbers.  Knowing that in 1996 a hitter hit six more homers than the average player would have hit over the same playing time is interesting but doesn’t tell me much without knowing exactly how much playing time he had.  Knowing a player had 54 homers in 1996, or only 2 homers tells me a lot about what he accomplished in 1996, without even knowing anything about playing time, though of course knowing about his playing time will add some useful additional information about his talent level.

birtelecom/43: Why is it a given that the player with more playing time is of more value *to the team*? The way I see it, the goal of the TEAM is to win the games; the goal of the FRANCHISE is to maximize the value of its resources, which is the point of replacement level. Baseball is a TEAM game, and your argument (that a below average hitter given a full season’s opportunity is valuable) assumes a FRANCHISE perspective.

I would define value relative to the entity:
TEAM: Value is how much a player contributes in terms of beating the competition (Linear weights relative to average)
FRANCHISE: Value is how much a player contributes beyond what the franchise could be expected to place in its stead (Linear weights relative to replacement level)
(??): Value is how much a player contributes beyond what a player incapable of reaching base or moving runners over could contribute (Linear weights relative to absolute zero, or Runs Created)

Is baseball fundamentally a team sport or a franchise sport? I think analytically we should start with the teams and then move on to the franchise level. So linear weights - with an adjustment for a replacement level that is specific to whatever analysis is at hands - seems to capture the phenomenon most correctly.

What phenomenon are runs created really measuring, since we know that by the rules of the game a run MUST be created prior to the end of the game? The very fact that it is a baseball game that cannot end until a run has been scored means that if the theoretical baseline of runs created is a 0-0 game, the theoretical baseline refers to an incomplete game rather than to baseball. An infinite perfect game is NOT baseball, so what is it doing in an argument about how to model baseball?

Now, in reality the baseline for Runs Created is not actually a .000/.000/.000 hitter, but all that means is that the theoretical construct of the runs being “created” is illusory. Runs created, just like win shares, is just an accounting trick that uses the things we know about actual baseball games (the frequency with which a runner will reach base, score, etc., which is related to the overall frequency of k,bb,hbp,1b,2b,3b,roe,out,sb,cs, etc.) and scales them to the number of runs that a performance corresponds to. Runs created, which breaks down at the extremes, inevitably depends on context. And that very context is not a context in which runs can be created at a rate of zero or infinity. So why should we even contemplate a zero or an infinity in constructing the model? Why not start with what we know to be true, that every event is zero-SUM (rather than is the sum ABOVE zero) and helps one team at the expense of another?

So the complaint in 43 seems completely without merit, as linear weights is about the relationship between the TEAM and the LEAGUE, and that relationship benefits from the hitter who is +2 in 4 PA more than it benefits from the hitter who is +/- 0 in 650 PA. Viewed in the context of the FRANCHISE in its quest to put together the TEAM, the 650 neutral PA are of more value. (Knowing nothing else, we’d put the value at about +22 runs relative to replacement using Tango’s WAR calculations.) And the “value” of runs created relative to absolute zero exists for nobody.

birt/43: yes, of course if someone uses LWTS (or RC) but doesn’t also consider PA, they only get half the story.  That’s not LWTS (or RC)’s fault.

If you look at seasonal stats, and ONLY look at RC rankings, you will probably get a good ranking of value from top to bottom (fielding position notwithstanding).  It’s hard for someone with 100 RC to not have created good value, and it’s hard for someone with 20 RC to have created good value.  The guy with 100 RC probably had at least 500 PA.  The guy with 20 RC probably had at most 250 PA.  So, there’s some inference you can derive from gross RC to get to PA. 

If you do the same with ONLY LWTS (or WPA or any metric where average is zero), then you won’t be as lucky.  A guy with +20 runs above average probably means someone with a good number of PA, but someone with -5 runs relative to average?  Could be anything.

So, RC does have the (slightly larger) potential to tell you the “game space” it was accumulated in.

That said, you need, absolutely need, the TWO dimensions (RC or LWTS, plus PA).  If you have RC or LWTS, that same source will most definitely have PA.  There’s no reason to argue is it better to have the half cake with chocolate icing or the half cake with vanilla icing.  You need the other half of the cake.

And just because Palmer didn’t use it well-enough doesn’t mean the whole thing is useless, which really is exactly what James is saying:

This is totally contrary to the nature of baseball, which is that you start out at zero and build up.  All of their other malfunctions stem from this central failing.

James is dead wrong on this issue.  There is no central failing at all with LWTS.

The peripheral failing is with people who look at LWTS without looking at PA.

At this point birtel, you are better off continuing your arguments without trying to figure out what James might have meant.  We know what he meant, and he said it exactly.  Any time you tell me that this is what James probably meant, I’ll simply tell you “no, that’s not at all what he meant”.  If you want to retort that “James did say that exactly, but he meant something else”, fine.  But, that’s taking a position on extremely shaky grounds.

In this respect raw RCs are similar to other raw, cumulating numbers.  Knowing that in 1996 a hitter hit six more homers than the average player would have hit over the same playing time is interesting but doesn’t tell me much without knowing exactly how much playing time he had.  Knowing a player had 54 homers in 1996, or only 2 homers tells me a lot about what he accomplished in 1996, without even knowing anything about playing time, though of course knowing about his playing time will add some useful additional information about his talent level.

Let’s make the comparison fair.  If you want to say 6 more HR than an average player in the same playing time, then we are talking about either a good who hit 9 HR in 125 PA, or a guy who hit 12 HR in 250 PA or a guy who hit 18 HR in 500 PA or 23 HR in 700 PA.

So, you have to say “player X hit 12 raw HR”.  Well, I have no idea if that’s good or not.  If he did it in 250 PA, that’s great.  If he did it in 700 PA, not so great.  Still ok.

If someone hit 6 more HR than the average player in the same playing time, well, that’s pretty good.

Let’s be fair then with your examples.  Don’t say “+6 HR” for one guy and then saw “raw 54 HR” for another guy.  One is super extreme and the other isn’t.

In any case, like I said, use the second dimension.  Don’t argue about which half of the book is better.

Tango, I agree entirely that arguing about what James meant is fruitless.  As to the LWTS vs. RC, I find a raw RC number over a game, a week, a month, a season or a career to be quite useful (though of course hardly complete for all purposes) to gather what a player contributed during that period.  A measure like LWTS that is constantly being measured above and below average, over the same sorts of time periods I find leaves me with a big gap. 

fifth (#47), I don’t really understand the team/franchise distinction.  All I’m really talking about here is the relatively elementary observation that a player who performs above replacement value but below average contributes postitive value to his team’s chances to win a game, a pennant race, or a series of pennant races.  A stat that purports to summarize a player’s contribution to his team’s ability to win games should recognize the cumulation of that value, including the possibility that with enough cumulated above-replacement, but below average, performance a player’s value can exceed that of another player who contributes above average performance but only a little bit of it.  Raw RC meets that test, raw LWTS doesn’t.

The theoretical point that a baseball game can’t end 0-0 doesn’t suggest to me that we have to use an RC of 1 instead of 0 as a sort of baseline.  A 0-0 game can theoretically last an infinite number of innings, with hitters recording an infinite number of outs, and thus the RC (defined rudimentarily as TB * OBP) at the end of such a game can be a vanishingly small fraction of one, the equivalent of zero for computational purposes.  A more serious concern in some contexts is that 1 RC over say 500 PAs is not replacement level, yet raw RC still treats it as “1”, not as zero and not as a negative number.  I agree that below replacement level performance needs extra adjustments to turn RC into an accurate value number—fortunately a player who performs below replacement level for long tends to be, well, replaced.

"All I’m really talking about here is the relatively elementary observation that a player who performs above replacement value but below average contributes postitive value to his team’s chances to win a game”

What does “postitive” mean, then? The player will contribute hits in some games the team wins. The player will contribute outs in some games the team loses.  The player contributes some things that are positive but in the aggregate the contribution is a net negative. If the team had a player who could MATCH the competition, that player does not hurt. If the team had a player who could EXCEED the competition, that would help. If the player NEARLY matches the competition, that is hurting the club relative to the competition, is it not? A FRANCHISE, in evaluating its assets (players), understands that there are not enough above average players to go around, so it must balance players of different ability on its own roster. So it attaches value to players who are above replacement level and on the major league roster and playing regularly. But the franchise is also attaching value to players on the 40-man roster, in the minor leagues, on the DL, and so forth. It is because they all have value to the organization/franchise that controls them. If we think of the TEAM as simply that entity that is charged with winning the game, then those players that exceed the competition are the ones who are positive and the players who don’t measure up have negative value. This isn’t a track and field match; the positive value of every event is visited upon the opponent in negative value.

To bring up replacement level as having something to do with Runs Created’s theoretical baseline I just don’t understand. I am fine with using replacement level - as I said, you start with lwts and then can alter the baseline depending on the analysis. But a) Replacement level has no relation to an absolute zero construct/baseline and b) There is no way to establish replacement level without knowing the average. If all the players on the Angels, Yankees, and Red Sox disappear suddenly and are replaced by Willie Bloomquist, replacement level gets “lower,” the average gets “lower,” and there is no effect on the zero-baseline. RL bears no relation to a 20-inning 0-0 tie; it bears relation to who the available players are. You figure out replacement level by examining the entire population, and the essential tool for that is not the contribution of those players to wins alone but their net contribution to wins and losses. It always comes back to balancing the win with the loss, since the pitcher and the batter are in balance (actually defense and offense). Indeed, the “positive value” you cite is due in no small part to fielding a position; if the point is that a below average player has value by playing a lot, then the reason for that is in part because they are in the field What does that have to do with the value of the player’s hitting, which is what both lwts and RC purport to measure? We’re not talking about the player (something the FRANCHISE has under contract because of their value in putting together a team), we are talking about the hitting (something a player does to help their TEAM beat the opposing team)!

The average player is the stand-in that lwts uses to approximate the competition. A player who is better than average is essentially a player who is better than the competition. Average players exist. They are in baseball. The 0-0 tie is a theoretical construct, and a valid one at that. But it is not the theoretical construct that is germane to placing a value on hitters’ contributions. The theoretical construct of the average player is strong enough to yield robust models; the absolute zero is not.

RC has never been an “accurate value number.” Plain and simple, RC is an accounting tool; how do we account for the number of runs that have been scored? Bonds created 10, Sosa 9, et cetera. It talks about the creation of things that, in the baseball reality that exists before us, are not CREATED whole from cloth but rather that come forth from the range of possibilities and probabilities that start each PA and that are seized upon or excluded by the pitcher, hitter, fielders, park, and so forth. The PA does not begin with nothingness and end with creation: it offers opportunities, and the outcome is one of many potential outcomes that are determined by a multiplicity of factors. To isolate HITTING, we hold the other things constant and see how much better or worse the hitter was than we would expect knowing everything else we know. Runs created looks at the world at hand and tries to describe it relative to a theoretical construct that is not internal to the game. It doesn’t do so for a scientific reason but rather an aesthetic reason.

The theoretical construct of the infinite 0-0 perfect game tie is useful in analyzing the game, but not significantly more useful than the infinite “None of my pitchers can record an out” game where the game never gets out of the top of the first. We don’t use the latter as a baseline for anything. But if the logic of RC is that we should be giving credit for all value above zero (it is the Nature of the game), then why mustn’t we also measure pitchers against the standard of giving up infinite runs? The obvious answer is that it is a ridiculous baseline and essentially can’t be calculated from. Well, RC has some issues anywhere very near its actual baseline or anywhere very far away from it, so it’s not about absolute zero being easy to model. It’s about it being easy to conceive of. We can conceive of the long-lasting perfect game because outs are much more plentiful in the league we watch. That just makes it easier to conceive, it doesn’t mean that we should treat the zero as the natural state of baseball. James’ claim about the nature of the game only makes sense, IMO, if you see the entire game from the perspective of the hitter. The purpose of the statistics we use to look at the game should not be to replicate the perspective of the hitter.

I think that aesthetics is more or less birtelecom’s argument anyway, since the contention is that when you LOOK at the stats RC will tell you something that lwts won’t. That is an argument about the correspondence of the statistic to our subjective experience of it. Ultimately, I think we should be researching our claims about which statistics affect the readers more or less rather than making assertions about them ("Batting average is so much more intuitive than OBP and always will be!"). Runs created may serve for some to overcome difficulties in the conceptualization of lwts that is immanent to their individual minds, and for that reason I have no problem with its existence. Indeed, it may even be that the bulk of baseball spectators could not, even with reasonable efforts to teach about lwts, really benefit from having a player’s lwts and playing time instead of RC alone. But we’re not trying to come up with the most palatable statistic to insert into the status quo, we are looking for the statistic that best models the reality. As a standard term for numerical or mathematical descriptions of the game, I don’t see how RC can be superior to lwts, which is simply a better model and more true to the realities of the game of baseball.

Now, if you want to say that every player who has any success has “positive value” any time two teams play, then that is a different argument entirely. It is a fair point to say, essentially, we are all winners and we should all get credit for being here, and the point of a statistic is not to denigrate good players in a great league but to celebrate all. For those purposes, feel free to Runs Created and the like. In terms of studying the systemic dynamics of baseball, however, it is just not a very useful approach. If what we are trying to do is to have metrics that accurately model baseball with a sound theoretical basis, then a model that starts with the zero-sum nature of the one victory per game system is requisite and linear weights are where it’s at.

Which one tells us more:
a) on base percentage (.400, but you don’t know the PA)
b) times on base (125, but you don’t know the PA)
c) times on base relative to average (+19, but you don’t know the PA)

This is the argument we’re having.  They are all equivalent.

You can create different scenarios where a is preferred, and another where b is preferred and another where c is preferred.

***

I also find it unappealing that birtel is saying that he knows the time frame (week, month, etc) and says that has value for RC but not LWTS.  If he can surmise that his player played 20 games in a month, and so can figure out that his 15 RC was accumulated in 20 games, then I can also surmise that his +5 runs was accumulated in 85 PA.  And therefore, LWTS and not RC is the one that tells you more.  Because with RC, you don’t know what average is.  And with LWTS, since you know three things (performance over average, average, and PA), that’s all you need to figure out value.

I think James is only half wrong when he says that baseball games start at zero and build up.

He is correct that, in physical reality, that’s what happens on the field.

Where he’s wrong is the assumption that this means that the ANALYSIS of baseball should/must also start from zero and build up.

Because of that assumption, he misses out on robust methods such as UZR and WPA. These systems are happy to start out from average, because that’s where the ‘gold’ is.