THE BOOK--Playing The Percentages In Baseball

I must admit that most of the paper is over my head, as is Tango’s brief analysis herein.  (OK, I just admitted to the world that I am not as smart as I make myself out to be sometimes - or at least as readers think I make myself out to be...).

However, I agree with Tango that the 100%/100% model is correct.  The relative “responsibilities” of the batter and pitcher in the batter/pitcher matchup is simply based on the difference in the spread of skill among batters and then again among pitchers.  If all pitchers were throwing BP fastballs down the middle, as in the HR derby, it is intuitvely obvious that all of the responsibility in the outcome can be attributed to the batter.  The reason is that the spread of talent among the pitchers is zero.

Now, we know that the spread of talent among pitchers in almost (maybe all, I don’t recall OFTOMH) all of the components (HR, K, BB, etc.) is smaller than among batters.  HR rate is a good example.  Batters’ HR rates go from around 3 a year to 40 a year (true rates).  Pitcher HR rates go from around 10 to 30 (again, true rates, not observed rates).

Anyway, when we assign 100% of the “responsiblity” to pitchers and to batters when we compile the NERV changes, the “real” relative rates of responsibility “come out in the wash” because we are always comparing or normalizing each player to the average of his group (batters or pitchers).

So in the example of the batting practice pitcher, in the long run (getting rid of random fluctuation) the sum of the NERV changes for all of the pitchers will automaitcally equal zero.  IOW, all pitchers will be league average pitchers.  If we have a league where there is some spread of pitcher skill, but not much - a lot less than batter skill - we will find that the spread of total NERV change among all the pitchers will again automatically be small - at least smaller than the spread of batter NERV change.

If I do it the traditional way, using 100% for batters and 100% for pitchers, I also get a larger spread for batters than for pitchers - IOW, the best batters will be better than the best pitchers.

So I don’t really get where these guys are coming from either, although I am pretty sure that at least one of them is smarter than I.

Maybe what we are missing is that if you use the batted ball types and characteristics (distance, speed, etc.) to determine the NERV change rather than the actual result of the play (s,d, etc.), you have to somehow use this 62/38 split or you won’t come up with the correct answer.  I am not sure.

I certainly appreciate the careful reading of our work as well as the opportunity to respond to the thoughtful criticism.

When the idea of using an expected run value calculation was first introduced, it was an elegant and balance accounting system of the events that occured during a game.  This type of system certainly has its allures and its uses, but, what I argue in the paper, is that a pure accounting system does not uncover the relative value that pitchers and hitters add to their teams.  Adding up the points earned in the system described, will not net out to zero, and when in comes to evaluting players across positions, I do not believe that that is neccesary.

First, the expected runs calculated in the paper, are just the expected runs created from the game between the hitter and the pitcher (we strip out the effects of defense and running through the use of expected outcomes of balls in play), so there is not a one to one correlation between total runs and the points that hitters and pitchers earn in this system.

Second, and on a more theoretical point, consider a pitcher/hitter game (an at bat) that results in a homerun.  It is not clear to me why the pitcher and the hitter would recieve the same number of points in a system that was concerned principally with determining the relative value of these two players.  The two have obviously different tasks and because of this, one of them may exert more control on the outcome.  What we find in the paper, is that the skill of the hitter, on average, has a greater effect on the outcome of an at bat than the skill of the pitcher.  If this result is correct, than it would seem that the hitter should be rewarded more for a homerun than a pitcher is penalized, because the hitter has more control.

Third, on MGL’s point regarding the relative variation of skill between pitchers and hitters, the model specifically controls for this, by normalizing the skill variables used.

I believe this is an interesting debate and I do hope that it will continue.

-Ben Alamar

The splitting process is one that I’ve tried, and then realized that it had holes.  Which is why I do it the way I do it.

I understand why you want to do what you do, and it sounds right.  But, it breaks down.  If you can provide your aggregate team totals for hitting,pitching,fielding (or offense, defense), I will prove to you that the splitting process is wrong.  Just something like:
NYY,+86,+21,-61
or some such, should be fine.

The guys at protrade.com just sent me the most current numbers for this season.  These numbers split NERV, but do not use the 62/38 split for pitching and hitting so I would suggest that the hitting numbers are understated and the pitching numbers are over stated.  In order they are Hitting, RUnning, Pitching, Fielding, Total. 

{List edited by Tom to round numbers to one decimal place}

team,Bat,Run,Pitch,Field,NES
White Sox,101.8,2.1,62.2,-48.6,117.4
Tigers,30.6,-8.9,69.8,6.3,97.9
Mets,93.6,0.9,-1.8,-13.0,79.7
Red Sox,53.6,-4.6,64.1,-42.6,70.6
Dodgers,114.3,-2.3,-13.3,-29.8,68.9
Yankees,54.8,1.5,24.9,-18.7,62.5
Blue Jays,41.0,-3.9,45.8,-37.2,45.8
Padres,26.9,2.9,6.8,3.2,39.8
Cardinals,64.8,-5.6,-13.5,-11.5,34.2
Rockies,-13.6,-9.2,48.5,6.8,32.4
Giants,48.1,-7.3,-14.1,5.6,32.3
Indians,76.6,-1.7,-17.5,-28.2,29.2
Rangers,-11.8,-1.3,75.5,-35.2,27.2
Twins,13.5,2.8,16.0,-7.9,24.4
Reds,50.7,2.8,-29.7,-10.5,13.4
Braves,59.7,-5.1,-45.5,-7.6,1.6
Marlins,51.3,-4.8,-16.6,-32.0,-2.1
Diamondbacks,23.2,-1.3,0.8,-30.1,-7.3
Mariners,-1.7,2.2,-12.5,-1.1,-13.1
Athletics,-38.9,2.7,5.0,14.5,-16.7
Astros,9.7,-0.9,-24.0,-3.8,-19.0
Angels,-9.6,5.9,40.8,-57.8,-20.8
Phillies,8.2,0.0,0.1,-33.2,-24.9
Brewers,22.9,1.3,-10.3,-69.8,-55.9
Nationals,45.0,-10.6,-32.7,-64.6,-62.9
Pirates,3.0,-5.0,-30.1,-39.9,-72.0
Orioles,8.4,4.7,-73.5,-11.7,-72.0
Cubs,-26.6,0.3,-67.6,16.8,-77.1
Devil Rays,-58.3,-2.1,13.3,-38.0,-85.1
Royals,-34.4,-7.3,-74.1,-24.8,-140.6

This data suggest that the numbers using the run expectancy, RE, matrix (NERV as you are calling it), as I use it.  That is, no splitting done at all.  And this makes sense.

If you do a simple runs scored minus runs allowed, you will get a distribution with a standard deviation of 60 runs.  The SD of your last column is also 60 runs.  If you were to give any side any lesser credit than the full 100%, that side will be shortchanged.

Combining your two hitting measures, you get an SD of 42, and you get an SD of 43 for your pitching+fielding.  This compares to the SD of 37 for runs scored and 40 for runs allowed.  Again, everything looks perfectly in-synch.

Your top 5 NES teams (WhiteSox, Tigers, Mets, Redsox, Dodgers) are +434, while those teams’ actual run differential is +429. 

The bottom 5 NES are -447, and their run differential is -425.

In short, trying to do any splitting will simply unalign the NES numbers which are currently in-line with runs scored and allowed numbers.

Your analysis is correct, but you are still assuming that the accounting is important.  I am not trying to create a system that actualy credits specific players with specific runs, but rather trying to determine the relative value of different players.  I could just as easily set the average of my system to 1 or 100 or 54 and not change the imformation that the system provides, which is that, relatively speaking, hitters have more control of the outcome of any specific at bat than a pitcher and that over the course of a season, a great pitcher and a great hitter add approximately the same value to their team.  Note that I said value and not runs.

Let me ask a simple question: a hitter with a “true rate” of .400 OBP faces a pitcher with a “true rate” of .300 OBP.  What’s the expected outcome?  (Use whatever league average you want.)

Now, a hitter with a “true rate” of .300 OBP faces a pitcher witha “true rate” of .400 OBP.  What’s the expected outcome.

My contention is: same thing.

By your reasoning, it seems that you would argue that the first matchup will result in a higher outcome than the second.  Is that correct?

The split that is determined in the paper does not actually depend upon the skills of the hitter and pitcher in a given matchup.  It is possible to use the same regression equations to produce this type of system that adjusts for competition faced, but we do not do that.

Instead, the results say that in a typical plate appearance, the outcome is influence more by the hitter than the pitcher.  Assuming that we acurately measured that, then we say that given the hitter’s greater influence on the outcome, he deserves a greater share of the credit/blame of the outcome than the pitcher.

In essence, we are saying that when Pujols strikes out, it is more his fault than the pitcher’s.

I’m going through this thread, and wanted to maybe come to a common point.

Ben’s last statement is correct, that when Pujols does anything, in that one PA, he is more responsible for it than the pitcher.  This is simply a function of the talent distribution for hitting being wider than the talent distribution for pitching.  That is, if you have a very very tight distribution, and you have another distribution that is very very wide, and you randomly select one player from each distribution, it’s clear that the player chosen from the wider distribution will be more responsible for that one particular outcome than the other player.

And we agree on this.

But, this does not follow that the NERV should also be split as 62/38, or 160/100, or whatever non-equal split you want to make.  I tackled this splitting issue already.

I think this is what the problem may be, that the authors linked one (variance in talent distribution) to the other (overall effect to outcome).

I read this thing, and have a few questions from my old mind:

1. They did a good job in trying to make the fielding neutral, by looking at results based on type of ball hit and location, not actual results. So I think they mean its batters 62, pitchers 38 with neutral fielding impact. So, I think that fielding is not part of the 62 or 38, they are doing batting versus pitching with no fielding. If fielding is 2/3 of pitching (24), does that make it 62 versus 62?

2. They used all types of RE data. I think that most everyone assumes they cancel each other out in a large population. There data should be better, but I’m not sure how much precision they build in here. Any idea what that might be?

3. Not sure how the 62 versus 38 is finally derived. They compute batter and pitcher rate coefficients - but are those impacted because there is a greater spread of talent in hitting than pitching?

bumping

(related discussion elsewhere on “splitting")