THE BOOK--Playing The Percentages In Baseball

This book is just a good all-round read.  Plenty of different issues to look at and to keep everyone happy.

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Let me talk about studes’ NET WIN SHARES VALUE on page 131.

I love that he shows the various $ per win at each level.  It is alot of hard work to compile whether a guy is in the 3-4 year arb-class, or in the 4-5 year class, etc.  One interesting thing is that he shows us the free agent cost is 4.5 MM per win, which is not terribly different than the 4.0 MM I’ve been using.  Who knows, if he repeats the study next year, he may show that teams paid 5.0 MM per win in 2007, and so, maybe that’s the figure my calculator should be using (5, not 4) for the 2006 off-season.  It may better explain the Soriano and Ramirez deals (though the Carlos Lee deal is unexplainable).  I’m working on making my calculator open-source, and easy-to-use.

Anyway, on to something I always talk about: SP v RP.

Studes shows us the Win Shares Above Bench, and the pitchers, as a group, come in at 40.6%.  I have them at 43%.  So, we’re a little off.  He has SP as 67.4% of all pitchers, while I have it as 69%.

These differences are acceptable.  In order for my numbers to come out, I use the following baselines:
.380 nonpitchers
.380 starters
.470 relievers

Studes effectively uses:
.376 nonpitchers
.386 starters
.473 relievers

That’s called quibbling, but it shows the great care studes took to try to rectify the Win Shares issue with starting pitchers.

One puzzling thing is how studes did go to the trouble of separating the different service years for arb players, but then just used a single multiplier for them.

What also seems pretty clear is that teams don’t know how to forecast, and that the free agent multiplier should be broken into two: first year of free agency, and future years of free agency.  Maybe we’ll find that teams pay 4 MM for the first year of free agency, and 6 or 8 MM for each future year.

For example, if we use my salary calculator, for a players that is 4 WAR, declining at 0.5 wins per year, and salaries rising at 10% per year, this is how much he should be getting paid in “those year’s dollars”:
2007 16.0
2008 15.4
2009 14.5
2010 13.3
2011 11.7

That’s a 5 year 71 MM contract, or 14.2 per year.  But, I would say that we should consider as if he’s been paid 16.0 in his first year of free agency.  So, by the time 2011 rolls around, we count 11.7, and not 14.2, against that year. 

If I use studes’ own data, rather than the flat 4.5 MM per win, I get 4.3 MM per win for the first year of free agency, 4.51 for the second year, 4.63 for the third, and 4.68 for 4th and subsequent. This would go with what I’m saying above.  That is I “overallocate” some of the free agent salaries upfront (show that he’s being paid 16.0 instead of 14.2, etc), that perhaps I’ll find that the first chart on page 133 will have a “Net WS Value” of zero for each entry.

I think the evidence available to us clearly indicates the value division between pitchers and non-pitchers is much closer to 50-50 than 40-60.  We can see this in two ways: observed performance of replacement level (RL) players, and the discount teams must demand for the volatility in pitcher performance (relative to hitters). 

Replacement:  Woolner’s original study found that RL/bench hitters were about .80 in run creation, or 20% worse than average at their position.  You seem to accept that as a reasonable estimate.  We also know from the work of Nate Silver that RL players provide league average defense. So the cumulative off/fldg run value of non-pitchers is about 20%.  Woolner found that replacement pitchers were also about 120% in runs allowed.  I don’t agree with his decision to set the same RL for starters and relievers, but the overall 120% figure seems reasonable. I don’t know of any study that has made a convincing case it should be lower.

It is of course true that the variance in hitting performance is higher than for pitchers, creating the illusion they must create more value. But that would only be true if hitting and fielding were independent, which they decidedly are not.  Good hitters tend to be bad fielders and vice versa.  there are -30 run hitters, but they are all Cs and MIs with defensive value.  (Also, because the reliever advantage goes mainly to inferior pitchers, the observed variance in pitcher performance is narrower than the true variance in talent.)

Secondly, pitcher performance is far less predictable than hitter performance, as documented in the who’s-better-than-a-monkey thread.  If MLB teams are at all rational, they should demand a substantial discount when buying pitchers.  Teams have relatively short time horizons, say 1 to 5 years depending on the franchise.  They don’t care that they’ll eventually get their money’s worth out of pitchers over a 20- or 30-year period.  The much higher risk of a bad short-term return should reduce the price of pitching.  Similarly, the difficulty in projecting pitchers makes it rational to settle for some inexpensive pitchers and hope they overperform.  (Any fantasy baseball player who has won with a $50 pitching, $210 hitting team has experience with this).

So, we have to conclude either that there is no risk premium in baseball—although the difference between J.D. Drew’s and Soriano’s contract clearly shows risk does affect contracts—or that pitchers are worth considerably more than 40%.  I think it’s clearly the latter.

And I’ll have to counter that the talent spread in offense and in defense must be exactly 50/50.  Since defense is made up of pitching and fielding, there’s no way that pitching can therefore be 50% of pitching+nonpitching.

I have two “Spread in Talent” threads here:
http://www.insidethebook.com/ee/index.php/weblog/C12/

We know exactly how much the spread in talent is in offense and in defense.  We have a pretty good idea of the spread between pitching and fielding. 

If offense and fielding were independent, the spread would be 60/40 nonpitchers/pitchers.  My current analysis makes it 57/43.

I think that’s the best estimate, regardless of how MLB perceives it.  MLB teams are a bunch of p-ssies for overpaying for starters.  That doesn’t mean they understand the landscape.

I should also say that if offense and fielding were completely dependent, and:
- directly proportional, nonpitchers to pitchers would be 66/33
- inverseley proportional (best hitters = worst fielders), nonpitchers to pitchers would be 33/66

If they are completely independent, it’s 60/40.

The level of inverse proportionality is important to establish.  This should be easy enough to establish, comparing the OPS to the Fans’ Scouting Report. 

My guess is that it’ll come in at 57/43.  However, Guy may certainly be right that it’ll be 50/50.  I just don’t believe it, at the moment.

Maybe this belongs on a different thread, but I take issue with using Rally’s projection system comparison as evidence of the unpredictability of pitcher projection, as Guy does in the post above.

As noted on that thread, the comparison of ERA to OPS already distorts the difference; ERC to OPS (or lwts/PA) would be more appropriate. Moreover, the 100 IP cutoff for pitchers is quite a different cutoff than the 400 PA cutoff for hitters.

It’s taken me a while to actually notice it, but I think the difference in projective accuracy between hitters and pitchers is much smaller than generally believed. I think it should be studied more in depth before making the arguments Guy does, IMO.

The main issue, I think, is that pitcher injuries are a) more common, b) more closely related to the ability to pitch than are position players’ injuries to the ability to hit, and c) more likely to be poorly handled when teams decide who to pitch/play. I think the standard deviation in ERC for healthy pitchers is probably quite close to the standard deviation in lwts for healthy hitters.

I also think I’m not up to the task of adequately researching that issue. Whoops.

100 IP is around 425 PA.

However, if a pool of players has a smaller standard deviation to begin with, of course the correlation coefficient will be smaller!  Imagine if you will that the true standard deviation was almost zero.  Now, try forecasting a SAMPLE.  Your mean for all the pitchers will be close to 4.50 ERA, but the actual (sample) data will be all over the place, and all due to random noise.  Your correlation coefficient will be almost zero.

In fact, the reason that your correlation coefficient can be so high is evidence that the true spread in talent is so much larger to begin with.  Or, it’s easier to forecast.  It can go either way.

The best way to do it is the way I have it done in the “Spread In Talent” series.

If I use studes’ own data, rather than the flat 4.5 MM per win, I get 4.3 MM per win for the first year of free agency, 4.51 for the second year, 4.63 for the third, and 4.68 for 4th and subsequent. This would go with what I’m saying above.  That is I “overallocate” some of the free agent salaries upfront (show that he’s being paid 16.0 instead of 14.2, etc), that perhaps I’ll find that the first chart on page 133 will have a “Net WS Value” of zero for each entry.

My copy of the THT annual hasn’t arrived yet but I can’t wait to get it, for sure.

Tango—for the above FA$ per MW do you assume that they are all in terms of first year money or have you carried a 10% annual multiplier all the way through? If the latter then in today’s terms the second year FA$ per MW would be $4.1M (at 10% escalation), which would indicate that a decline has been assumed.

One other question. Is there any research that looks at how much the FA$ per MW changes over time? Does it follow the general 10% salary inflation rule that we see (if true this would mean that FA$ per MW was $2.8M in 2001)? I guess it is probably fairly close but I’m mindful of Studes’ recent THT article about marginal win values where he concluded that an exceptionally strong pre-arb class of players may be distorting the FA market this year.

(Note: I tried to look at Studes’ article on the same subject for the previous two years and although that indicated a 10% inflation between 2005 & 2006, the 2004 number was similar to 2005. However, there are a few methodology changes that may have had an impact so I am not sure if this is a real comparison)

Thanks, Tango.  The reason I haven’t used specific arbitration years is sample size but that’s probably not really an issue in this case.  I’ll reconsider that next year.

The idea of looking at the first year of free agency vs. other years is interesting, too.  I will take a look at that, but the data also shows that players do give up salary for longer term contracts.  I’m not sure how to rectify the two points.

I have to admit that I don’t follow your replacement level logic, or how you derived your replacement levels from WSAB.  I’ve read your other talent distribution threads, but they only partly fill in what I’m looking for.  Is there a comprehensive thread or post where you’ve discussed this?

The idea of looking at the first year of free agency vs. other years is interesting, too.  I will take a look at that, but the data also shows that players do give up salary for longer term contracts.  I’m not sure how to rectify the two points.

Isn’t the right way to do this compare contracts of similar lengths together. You could do all 5 year contracts, then all 6 year contracts etc. but sample size could be an issue. Perhaps creating some buckets eg, 1-3 years, 4-5 years, 6 years+ could extract the effect. The other option is to run a regression analysis with a variable for length of contract to see if there is an inverse correlation between length of contract and $ per marginal win.

Of course there is more variance for position players.  For them we are considering two talents—offense and fielding—while for pitchers we care only about one talent.  So we get catchers who hit below the generic replacement level, and first baseman whose fielding ability is far worse than that of freely available minor leaguers.  But that just means that many non-pitchers have negative value as fielders, and some have negative value as hitters. 

The fact remains that at every position, replacement players can be found who are about -18 runs on offense and avg on defense.  As long as that’s true, then by definition the avg. value above replacement of these players is 18 runs. 

One way to think about this is to look at offensive variance at each position, rather than across all positions.  At any one position, I’d guess it’s close to the variance for pitchers. 

Suppose that first base was suddenly populated by players who were +60 runs on offense (50 above avg for 1B) but also -50 on defense.  This would greatly increase ‘value’ under your analysis, but in fact these would still be +18 players compared to replacement.

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“The level of inverse proportionality is important to establish.  This should be easy enough to establish, comparing the OPS to the Fans’ Scouting Report.”

I think you also need to account for the underlying defensive value of the position. So, maybe a -5 catcher is +15 generically, while a +5 1B should be considered -10, or something like that.  But if you do that, then I think you’ll find a huge negative correlation between hitting and fielding.

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Tom:  I agree that projecting rate-based performance and PT are somewhat separate issues.  But my point was only that the ability to project total value—such as RAR—is less for pitchers.  I think that’s pretty clearly true, even if you’re right that injury risk is the largest factor at work here.  And given that, teams should—and I believe do—pay less for an equal amount of mean expected value. In fact, since it’s downside risk the investor cares about (we don’t complain about upside volatility), then the much higher risk of injury should definitely depress pitcher salaries. 

* *

A question on Marcel:  do you regress to league average for non-pitchers, or to position-specific averages?  And if it’s the former, do you think that regressing to position-specific averages might improve accuracy?

Re: free agent prices

I would say that what we should do is to incorporate my salary model with studes’ data.  While it won’t work as nicely for young studs like Beltran and ARod, it works pretty well for most cases.  So, convert Soriano’s actually contract signed into a series of 8-yr contracts as my calculator lays out.

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Re: repl level

I can accept that each position, on its own, is around 2 wins below average, per 162 GP.  I think this number is still much more extreme than for a pitcher.

I have the starting pitcher repl level as .380, compared to the average starting pitcher being .490.  That’s +.110 wins per 9 IP.  Assuming 198 IP per starter, that’s 2.42 wins below average.

HOWEVER, let’s not forget relievers.  I have the repl level for them at .470, compared to the averag of .520.  That’s .050 wins per 9 IP.  Assuming 81 IP per relievers, that’s .45 wins below average.

In totality, for all pitchers, the repl level is two thirds of .380 and one-third of .470, for a repl level of .410, or .090 wins from average, per 9 IP.  Multiply by 162, and that gives us 14.6 wins below average. 

For position players, I have the repl level as .380, or .120 wins below average, per GP of position play.  Multiply by 162, and we have 19.4 wins below average.

So, the total is 14.6+19.4 = 34 wins below average, of which 43% is pitching.

I think the key here is the relievers.  While starters undoubtedly provide GREAT value, relievers… not so much. 

In fact, if we just look at starters (+.110 wins per 9 IP x 162 x 6 IP per season), they have +12 wins above repl, which is 35% of the whole team value.

Doesn’t that seem right, that we have 57% for the 8 or 9 full-time position players, 35% for the 5 full-time starters, and 8% for the 6 full-time relievers?

Proportionately, we get 6 or 7% for the position players, 7% for the starters, and 1.3% for the relievers.

To give pitchers 50% of the value must mean that you want to give the starters 40% and the relievers 10%.  That seems out of line.

I like my setup better.

Actually, I think an easier way to deal with correlation of offensive and defensive value is to just look at each position sepaarately.  At each position, look at the spread of total value compared to the mean for that position, essentially UZR + position-adjusted linear weight.  I’d guess that the negative correlation of UZR and hitting is such that the spread at each position looks a lot like the spread for pitchers.

Guy,

I was thinking the same thing.  You’d need a few years of data of course.  My guess is that it’ll follow the 57/43 rule.

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As for Marcel, I regress everyone to the same league average.  If you check out my archives, I give the exact methodology.  It’s as easy as it reads.

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I am now looking at the wonderful Batted Ball data from studes.  This is what sabermetrics is all about, and this should become a staple of all analyst sites, like Fangraphs. 

It’s an enormous disappointment that a site of the resource capabilities of BP and B-R.com don’t do this already.  (Though my guess is that Sean would come on board, if he’d look at studes’ data.) Sites like Fangraphs and THT take in so little money, and yet they put all of it into enormous R&D. 

Anyway, a huge no-no to studes for eschewing Linear Weights (runs relative to average) in favor of Runs Created (absolute runs) in presenting the run values on the first page of that chapter.  To give a run value of .3 for a walk and -.1 for a K is unforgivable.  At the very least, it should have been accompanied with the number of outs per event.  The IBB would stay at .1 run, while the groundball would quickly drop away from anything close to that.

I understand why he does it, and if all you read was Bill James, and I didn’t have such high hopes, I’d let it go. 

Without question whatsoever, the run value of the out must always be presented as something close to -.30 runs.  To do otherwise is to have a hole in your analysis.

Note: I tried to look at Studes’ article on the same subject for the previous two years and although that indicated a 10% inflation between 2005 & 2006, the 2004 number was similar to 2005.

Unfortunately, I’ve changed the methodology a bit each year, so year-to-year comparisons don’t work.  I think the overall result is better, though.

I could go back and re-run previous years, but it would be a ton of work.

The other option is to run a regression analysis with a variable for length of contract to see if there is an inverse correlation between length of contract and $ per marginal win.

An academic paper in the 2/02 issue of Journal of Sports Economics found that players do give up salary in exchange for longer-term contracts, and my own regression analysis has found the same thing.

Specifically, I ran salary and contract length against free agent player performance and found a better fit than salary alone.  What’s more, the coefficient for salary length was positive and statistically significant.

Anyway, a huge no-no to studes for eschewing Linear Weights (runs relative to average) in favor of Runs Created (absolute runs) in presenting the run values on the first page of that chapter.

Yeah, I knew you wouldn’t like it.  The problem is that a lot of people just plain didn’t understand or misinterpreted the original table.  I think James’s notion of communicating run values that add up to absolute runs scored instead of average is right in that it’s easier for people to understand.

David pointed out to me that I should have used outs as the denominator in my player rankings instead of plate appearances and he’s right.

I’m not sure if players give up $ for years.  It may simply look like that, if you take a look at my salary calculator.  That calculator is purely a function of decline in production and inflation.  Each year is measured on its own, with no further discounting. 

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Right, data should be presented as:
- runs relative to average, per PA
OR
- absolute runs, per out

The first is preferable.

I know people have a hard time with it, but so what.  They’re wrong, you’re right.  It just means you’ve gotta work that much harder.

Nonetheless, the Batted Ball data is one of the greatest presentations in sabermetrics ever.  It not only gives you scouting-type information, but gives you performance data tied to it.  Can’t ask for more.

Gawsh, now I’m blushing.

One thing about your salary table, Tango, is that you didn’t include rising salaries for higher performance.  Since the best players are the ones who get the longer contracts, you might be missing the overall impact.

Still, that’s only a partial answer at best.  I hope to find time after the holidays to look at this.

Right, at the moment, it’s a linear model.  I’m not really sure I’m missing anything though.  Perhaps I should have used 4.5 MM or 5.0 MM per win, instead of 4.0.

Imagine Pujols’ expected contract if I made it 3 MM for the first win, 4 for the 2nd, 5 for the 3rd, 6 for the 4th ... 9 for the 7th!

But, some of you guys are postulating that players offer discount for extra years.

I just like the idea of my simple linear model, with the inflation and decline in performance.

I just like the idea of my simple linear model, with the inflation and decline in performance.

I understand.  It’s simple and it works pretty well.  But I wouldn’t use that as proof that it captures reality.  Based on my research, I don’t think there’s much doubt that top players are paid more per win, nor do I doubt that players give up salary for length.

Using Pujols as an example doesn’t really prove anything, because he would push the boundaries beyond where owners are willing to go, I think.

Of course, my comments are based on what happened the last several years.  This year may be an entirely different beast.

This comment could go here or in the Odds Ratio thread, but I’ll throw it in here.  I think there’s a problem with the Burnson piece in the annual purporting to show that hitters have more influence than pitchers on the outcome of PAs.  He uses regression to predict outcomes with a formula of A + B*Hitter + C*Pitcher.  This is a problem, because without working off the mean you can’t predict the outcome using just the H and P rates.  For example, if a hitter is .300 BA and pitcher is .300 BAA, any version of the regression equation will predict .300, when the right answer is more like .330. He needs to use difference from the mean, so the hitter is +.030 and the pitcher is -.030.

Also, I think the regression is mostly telling us that there is more variance among hitters than pitchers, so the hitter rates have to be weighted more heavily.  That doesn’t mean, given any given hitter’s and pitcher’s true talent, the hitter’s true talent matters more in determining the outcome.  (And most of the evidence seems to suggest this isn’t true.).

Right, it’s the same issue that you get from that Protrade piece I linked to a while ago.

There’s no question at all that a .300 OBP pitcher facing a .400 OBP hitter will result in the same matchup as a .400 OBP pitcher facing a .300 OBP hitter.

However, all these regression-based analysis will tell you otherwise.  And the reason this happens is simply because there is less variance among the pitchers in their pool than the hitters.  If the variance among the hitters was exactly zero, then guess what?  The predicted matchup would be based all on the pitcher and zero on the hitter.

I can’t stand the use of regression in 90% of the cases, and this is simply another one to add to the list.

I’d put it at maybe 80%, but generally agree.

BTW, Tango, when are you going to take the blog off daylight savings time?  Looks like you’ve travelled to the future to write your comments....

I haven’t mastered the software about the DST yet.  For whatever reason, every time I create a new blog entry, the software puts everything back 1 hour.  But then, in an hour, it resets everything back to the system time.

I guess all I can say at the moment is to look at the time as being Candian Maritime time.

Ok, I made a change.  Hopefully that fixes it.  We’ll see in an hour.

Thanks for the criticism. Lesson learned. I will re-examine the numbers. Do you have a suggestion for getting rid of the effect of the variance?

Guy, Regarding the case of a .300 hitter vs. a .300 pitcher: A linear regression of match-ups *should* find a match-up BA over .300 [assuming that the data support this finding, and they should]. If the ML average is X, then a match-up of {Y, Y} should yield Y if Y>X. So (picturing this in three dimensions), a linear regression would give a line that starts at {Y,Y,Y} where Y>X. Do you agree?

This is a point that I did not appreciate, and I am grateful for your enlightenment. This doesn’t dilute your wider point about the variances.

John:  I’m not totally following your logic on the regression, but you could be right.  The way I look at it is that we know each additional point of BA or BAA should increase the expected matchup by one point.  So your coefficients should be one.  In fact, the regression should give you Matchup = 1*H + 1*P - C, where C is the league mean (leaving aside the hitter vs pitcher variance problem).  I don’t have the THT book in front of me, but from what I recall your result wasn’t anything like that.  But my memory is definitely deteriorating.....

As for dealing with the variance problem, I think you’d want to look at sets of matchups between good pitchers/bad hitters and bad pitchers/good hitters, and see if the collective outcome varied from the expected H + P - Mean.  If it consistently came out closer to the H’s rates (or P’s), you’d have something.  But before you go to the trouble, I think maybe Tom et.al. already did this in The Book?

BTW, H + P - Mean is a simplified version of (H-mean) + (P-mean) + Mean.  Basically, you’re just adding each player’s +/- to the league mean.

Right, you’ll pretty much find that as a shortcut, the H+P-L construction works well enough.  Or, H*P/L also works fine.  The best way is the Odds Ratio method, which will give you a result in between these two.

In the case of the .400 v .300 (regardless if the batter is the .400 or the .300), in a .340 league, the differential gives you .360 matchup, the multiplicative gives you .353, and the Odds Ratio gives you .357.

There is of course no reason that the “success” is on base per PA, since it could very well be outs per PA (if you look at it from the pitcher’s viewpoint).  The differential and Odds Ratio method will of course give you the exact same result either way.  However, for the multiplicative method, that now becomes .6*.7/.66=.636 outs per PA, or .364 safe per PA.

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These “multiplicative” adjustments rear their ugly heads when you are close to “1.000”, like say for error rates or zone rating.  For example, a ZR of .950 in a park of .850: what’s the ZR in a park of .900?  Multiplicative gives you:.95/.85*.9=1.01.  But, you could have done multiplicative the other way: .05/.15*.10=.03, which becomes .97.  Differential gives you 1.00.  Odds Ratio says: .968.

Hey John,

I believe that you could simply use the beta coefficients in your regression (most statistical programs provide them automatically). Beta coefficients correct for differing variances.