THE BOOK--Playing The Percentages In Baseball

Earlier in this thread, I mentioned that I was writing an article for SABR’s Baseball Research Journal that is a critique of Roger Tobin’s paper.  You can download it at this link:
http://webusers.npl.illinois.edu/~a-nathan/pob/BRJ-Steroids-v3.pdf.  As you will see, I find that Roger’s conclusions logically follow from the initial assumption, namely that a 10% increase in muscle mass can result in a very large fraction increase in home run production by the elite home run hitters.

I really only talked about things I know something about, which completely excludes the question of the effect of steroids on muscle mass.  I did critically examine the rest of the analysis chain (effect of muscle mass on bat speed; effect of bat speed on hit ball speed and fly ball distance; effect of fly ball distance on home run probability).  Thanks to Roger for a critical reading of my summary and for one very helpful suggestion.

Alan, first, thanks for giving us the opportunity to respond.  A few points:

1. Didn’t I read in your collision paper that the faster the pitch, the faster it’ll bounce off the bat?  I don’t know about you, but it sure seems that there ALOT more fastball pitchers in baseball than back in the 80s.

2. I don’t like the lack of context: it’s a man v man scenario, and not a man v nature (though that plays a part in it as well).  I don’t see how you cannot bring up the pitcher.  Indeed, the word pitcher only appears once in the paper, even though half of the PED users who have been caught have been pitchers.

3. I definitely do not like the era comparisons, and the 50% thing.  It should not even be brought up.  Think of it in your studies: would you have a group of players in one study, with one set of parks, weather, opposing pitchers, types of bats and types of balls, and then in the other group have totally different players, weather, opposing pitchers, bats, balls, and maybe the same parks?

The best way to make the cross-era comparisons is to look at players who played in both pools under the same conditions.  I offer one such way to do this here:
http://www.hardballtimes.com/main/article/changes-in-home-run-rates-during-the-retrosheet-years/

I make sure it’s the same batters facing the same pitchers in the same parks, back-to-back years.  Clearly we don’t expect ALL hitters to use PED at the same time, while all pitchers don’t.  That we find huge gains in the 1992-1994 time period can be almost completely explained by something other than PED.

In the 1980s, NHL used to have 7.5 goals a game.  Now they are at 5.5 goals a game.  The context changes.

4. In short, I don’t think it’s fair to make the far-reaching conclusions you make.  I accept that in the controlled scenarios you have, that you can increase HR production by 30-70%.  But, the bat and the ball can just as well be the culprit.  Or batters swinging harder.  Pitchers can also counter that as well.  So, while you can, all other things equal, increase by 50%, the pitcher is a variable in here where he has control over whether the batter even makes contact to begin with.

TT (#79):  I am puzzled by your comments.  You state

I don’t think it’s fair to make the far-reaching conclusions you make

but then you go on to say

I accept that in the controlled scenarios you have, that you can increase HR production by 30-70%. 

But that 2nd statement *is* my conclusion.  Speaking only for myself (and not for Tobin), I am claiming nothing more.  So, I am puzzled by the first quote.  What conclusion have I made that you think is unfair.  My analysis of Tobin’s paper is very narrowly focused.  If you like, it can serve as a starting point for a much wider discussion, with a focus on the points you raise (comparing across eras, the effect of the pitcher, juiced baseball, park sizes, etc.).

In Fig. 2 of his paper, he shows that for elite home run hitters in the pre-steroid era (Aaron, Ruth, Mays, Killebrew, Robinson), HRBiP was approximately 0.10 whereas for hitters in the steroid era (Bonds, Sosa, McGwire, Griffey, Palmeiro) the number jumped to 0.15, a 50% increase.

This quote bugs the heck out of me.  I didn’t read Tobin’s paper, but I accept this is what he is saying. 

But, by reprinting what he is saying, you are not presenting the whole picture.  Aaron and Mays are not only part of the pre-steroid era, they are also part of the pre-24/26/30 team era, pre-Maddux era, pre-thinHandleBat era, pre-youNameIt era.

Also, you say the number “jumped” and a “50% increase”.  Would you compare the housing prices in England, 1965 to those of USA 2009?  Or Iowa 1993 to California 2007?  I’ll bet you’d show an “increase” and a “jump” as well.

This is my big concern here: that just because it is “MLB” doesn’t mean you have an overriding controlled environment, anymore than being a “homeowner” means anything.

There is an enormous difference in contexts between what Aaron/Mays faced and what Junior/Bonds faced.

My article I linked to a couple of times addresses this. 

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So, in a controlled environment, I accept that you can show a 50% increase.

But, it is a pure coincidence that that result matches a 50% difference in empirical data between two completely unrelated groups (other than playing rules).

There is no relationship at all between the number of HR per opp of Mays/Aaron to Bonds/Junior, unless you account for the vast differences in contexts.

TT (#81):  I don’t disagree with anything you are saying.  And it may be a pure coincidence, as you say.  But, I am not claiming otherwise.  And I don’t think Tobin is either.  What I am claiming is that HRBiP is very sensitive to small changes in batted ball speed, however those changes might arise.  One way those changes might arise is increased muscle mass.  But, small changes in the ball might do the same.  Don’t mistake this analysis for a “baseball analysis.” It is more of a physics analysis.  As I have said, the focus is very narrow.  It certainly was not the intent of either Tobin’s paper or my analysis to try to explain era differences in home run production.

I think we’re on the same page, and (may) disagree on a single issue:

I think introducing the data / quote of the two eras is misleading and really has no place at all in an otherwise very good paper.  In my opinion, that unrelated data takes away from the presentation, much the way a journalist, in wanting to be topical, takes some current anecdote, and then launches into his thesis.

TT:  Thanks for your constructive comments.  I’ll give some thought to removing the era reference before publication in BRJ.  It would be counterproductive if readers are distracted from the main message by the era reference.

It might only be me.  I’m sure the rest of the readers here can chime in with their thoughts. 

Science often begins with the observation of something interesting in the world.  A number of different measures of home run production by top sluggers went up noticeably in the 1990s after remaining relatively steady for decades, and a lot of fans found that interesting and puzzling.  The data Alan mentions are just one example.  The extraordinary performances by Sosa and McGwire in 1998 and Bonds in 2001 were the most dramatic, but there are other indicators, some of which are presented in my paper. 

Fairly or unfairly, many people asked whether those changes were caused by PEDs.  The purpose of my analysis was to ask whether the PED hypothesis is even reasonable—after all, one hasn’t seen such dramatic changes in other sports records.  No one runs the 100 m dash in 8 seconds, for example.  It turns out that PED’s COULD account for changes in HR rates of the magnitude seen. 

That doesn’t mean, and I don’t claim, that PED’s ARE the explanation.  As I say in the paper:  “The fact that present-day athletes achieve at a higher level than those of a previous generation is not unique to baseball, nor is it evidence of cheating. And there have been other changes in the game that could have affected home run rates ...  [But if]the record-breaking performances of McGwire, Sosa, and Bonds are to be attributed in part to steroid use, then steroids must be able to account for an increase of ~50% in the fraction of balls put in play that are home runs, above the levels achieved without the use of steroids.” What I argue is that that’s possible.  That’s as far as the analysis goes.

Link to the paper:  http://www.tufts.edu/~rtobin/Tobin%20AJP%20Jan%2008.pdf

I wouldn’t quarrel with using Sosa/Bonds/McGwire at a taking off point for your paper.  There’s no denying that many people suspect them of PED use, and wonder whether PED use played any role in their accomplishments.  However, I would agree with Tango that presenting their 50% increase in HR/BIP as extraordinary, without providing the context, is unintentionally misleading to your readers.  The fact is, if you compare HR/BIP in 1980-1992 to 1994-2008, the rate increased 50% for ALL players.  Moreover, almost all of that change occured over two years—1993-1994—strong evidence that PEDs played at most a minor role in this change.  In that context, a similar 50% increase by the game’s top 5 HR hitters seems much less “extraordinary.”

Also, I don’t think you can compare how “dramatic” this change is to changes in other sports using percentages.  A comparable change in swimming performance would surely not require cutting one’s time by 1/3.  In the 2008 Olympics, the last place swimmer in the men’s 200M freestyle final finished in 1:47:47, more than 5 seconds ahead of Mark Spitz’s gold record time.  Is that a bigger or smaller performance increase than that of Bonds et. al.?  I’m not sure of the answer, but you certainly can’t answer it in terms of raw percentage.

I agree that you cannot use raw percentages, for exactly the reason Guy claims.

In any case, it’s a man v man situation, and not a man v nature.  Why not compare the win% of the 2001 Mariners and 2003 Tigers as something “extraordinary”.

Even if you don’t buy it, I dispute this:

The purpose of my analysis was to ask whether the PED hypothesis is even reasonable—after all, one hasn’t seen such dramatic changes in other sports records.

Wayne Gretzky and Bobby Orr has shown more than dramatic changes at their positions.

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I will now read Tobin’s paper in post 9, and I will encourage him to read mine in post 2.

In the same boat, has anyone looked into time recovery from injuries.  Many of the pitchers stated they used steroids to come back from injuries.  Might be tough to prove as medicine has improved over the years.

Looking at Tobin’s paper, he talks about pitchers, and notes how they’d get increased velocity right around what we’ve been hearing anecdotally.  Wonderful!

But, he talks about how this is less dramatic because it gives them only a 0.5 run advantage (per 9IP).  I would think more, as my estimate is closer to 1.0 run advantage.  For evidence, I provide the difference between a pitcher’s performance as a starter and as a reliever as being 1.0 runs, and there is not a 4mph difference in how hard they throw in those two roles.

Well, hitting 50% more HR (going from 20 to 30 HR in 700 PA) gives the batter 14 more runs, which is 0.02 runs per PA, which in a 39 PA game (i.e., 9 IP) is almost 0.80 runs.

So, you get an equal benefit from both sides (say 0.75 runs per 39 PA).  And if an equal number is juicing, it cancels out (at the league level), while increasing the variance in the population.

Again, there is no need at all to discuss the empirical data of the players themselves, unless and until the varying contexts is addressed.  I’m not sure why player performances are treated less strictly than you would treat a controlled experiment in a lab.

I enjoyed Tobin’s paper (of what I could understand).