THE BOOK--Playing The Percentages In Baseball

OK now given this data, is it possible to add in a bunch of columns for aspects of the pitching style?  For example, dichotomous variables for knuckleballer, lefty, etc.  As well as spectrum variables, like avg fastball speed, % likelihood of pitch being a changeup, etc?  I guess this is something that would have to be hand-coded (and may be quite inaccurate given things like the loss in velocity as pitchers age or get injured)… but it would seem like the last step in “solving” how pitchers are able to demonstrate the skill of easier-to-field balls.

Also - shouldn’t about 5% of the players be outside 2 standard deviations?  I count 333, which accounts for 11.8% of the pitchers.  143 of these pitchers are beyond 2 SD worse than average (5%) where you’d expect a little under 2.5% I think.  Is there some reason that this should be a non-normal distrubution, skewed with an excess of very good and very bad talent?

If BABIP were some random metric (i.e., pitchers had no influence on its outcome), we’d expect 16% of the pitchers at 1SD or worse at both ends of the tail.  We find 22% on the “good” side and 21% on the “bad” side.  That’s fairly symmetrical.

At 2SD or worse, where we expect to find 2.4% on each tail, we get 7.3% on the good side and 5.5% on the bad side.  Not as symmetrical as we like, but don’t forget we put in a condition of at least 500 BIP, which presumably would knock off alot of bad pitchers who weren’t able to reach to that level.  Furthermore, since we are selecting the right tail of all able-bodied pitchers in the world to play in MLB, we expect to have some sort of skew.

As for your main point, since BABIP is in fact not random, you shouldn’t expect to find 68% within one SD of the mean.  Remember, the “one SD” is the random standard deviation, and not the standard deviation of the population.

As to the other point, I’ve only got the hand of the pitcher.

When I look at lefty/righty (27% of pitchers are lefties), the average gap (difference between player’s BABIP and teammates’ BABIP) is larger for lefties, by 3 points.

The % of RHP at the 1 SD tails: 25%/19%
LHP: 16%/27%

That is, 25% of RHP have a BABIP that is at least 1 SD better than their teammates.

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When I repeated the study for (K-BB)/PA, there is a decidedly unsymmetrical skew: 21% of pitchers were at the “good” 2 SD level or better, while 31% were at the bad 2 SD level or worse.  This makes sense when you consider that only the right-tail of able-bodied pitchers pitch in MLB.  There wasn’t much of a difference between LHP and RHP in this metric: the LHP were slightly better than the RHP.

As you can see by the 52% (21+31) of pitchers at 2 SD or greater (far far higher than the 4.8% that random would have told us), there is a very real skill that can be gleaned from K minus BB per PA.

In fact, the PA point where r=.50 is PA=300.  You learn far more about a pitcher on his K minus BB rate than his BABIP.

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Btw, from 1920-1994, LHP have a win% of .501 (RHP are .499).  Since 1995, LHP are at .511 (RHP at .496).  This is some evidence that teams don’t have enough LHP.  If everythign was in balance, all groups should be at .500 (be it by hand, race, or whatnot).

Since 1995, the win% of American-born pitchers is .501, and it’s .492 from the Dominican Republic (showing perhaps a bit too much reliance on pitchers there).  Mexico is .485 and PR is .475.

"This means that if you have a pitcher with 3700 BIP, you regress his sample BABIP 50% towards his teammates’ BABIP.  If you have 1850 BIP, you regress two-thirds toward your teammates’ BABIP.  With 7400 BIP, you regress one-third toward your teammates’ BABIP.  For your typical pitcher with 500 BIP in a season, the regression amount is 88% (i.e., r=.12, rSquared=.01).  It’s on this basis that you will often hear that pitchers have little influence.  What’s really true is that one-season’s worth of stats is hardly indicative of his skill.”

Poetry, Tango.  It surprises me a little that it takes 4 typical starting pitcher seasons to reach the 50% regression tipping point.  Intuitively, I figured that it was 2-3 seasons.

Great post.  Thanks for the awesome data!  It’s good to see in one place and to get more of a historical handle on which DIPS deviations are really meaningful.  The fact that it takes at least 4 years before less than 50% is regressed is a real eye-opener.

Do you know if anyone has done analysis like this a real “null hypothesis”.  The one I always think about is Run Support.  Each year you see two SP on the same team with about a 2+ gap in RS/G, the kind of gap that if the average fan saw in ERA they would be sure was due to true talent.  So, do you guys know if anyone has done a Run Support vs. Teammates study like this one to test how closely the distribution mirrors the bell curve.  Of course it should, but if it didn’t (beyond the occasional great hitting NL pitcher), that would be a fascinating and very puzzling result.

Remember, this is 3700 BIP, not 3700 PA.  That makes it over 5 years, and for guys with lots of K, 6 years.

Yeah, the recent threads about regression made me dig this one up. Can you explain how you derived the 3700 figure? I understand that it’s when the correlation is .50, but I’m not sure what you’re correlating the career numbers against.

You are comparing the observed hits per ball in play (the standard deviation of that), to the standard deviation you’d expect if there was no skill in it at all.

The observed standard deviation is 1.35 times as big as luck alone would expect.  That is, it is spread out more than luck itself would suggest.  And that extra spreading out is caused by the talent.

The only reason we could get such a decent number like 1.35, is that we had such a huge number of trials per player.

I thik he wants to know how you got that specific regression equation (with 3700 in it).

Oic.  I just explained this on another site, so I’ll repeat with the appropriate numbers:

The spread is 1.35 times the random, which was based on an average of 3000 BIP per pitcher.

So, your correlation, r, is equal to 1 - (1/1.35)^2, or r=.45

Now, solve for this:
r = 3000 / (3000 + x) = .45
In this case, x = 3700

Your general equation becomes:
r = BIP / (BIP + 3700)

If you had a player with 3000 BIP, your correlation is r=.45, meaning that you regress 1-r = 55%. That is, you regress his actual performance 55% toward the mean.

If you had 3700 BIP for your player, you’d regress half way toward the league mean.

For a typical season, with 500 BIP, your r=.12, which means regressing 88% toward the mean.

This is why we say that pitcher’s haev little influence on balls in play.  What it ACTUALLY means is that the *metric* hits per ball in play explains very little, if you only have 500 balls in play.  If you had 37,000 BIP, it would explain almost everything.  The problem is that no pitcher is involved with 37,000 BIP in his career.

Brilliant! Thanks.

And if you want a shorthand, this:
r = 3000 / (3000 + x) = .45

Is the same as:
3000/x = .45/(1-.45)

And therefore implies
x=3000*(1-.45)/.45

So, if ever you want to know when does r=.50, just take the average number of PA, IP, G, BIP or whatever, and multiply it by:
(1-r)/r

When you look at year-to-year correlation of say a hitter’s OBP, where the average number of PA will be say around 500, you’ll probably find a correlation of around r=.70.

And 500*.3/.7=214

That makes r=.50 when PA=214, and your correlation equation is:
PA/(PA+214)

(I don’t know what the actual number is, but it’s close to 200.)

Some help would be appreciated:

If a pitcher has a BABIP .010 better than his teammates after 13,000 BIP, than we can regress the 15% or so needed and still conclude that he had real BABIP skill.

What if his BABIP is only .002 better than teammates after 13,000 BIP?  Is he close enough to his mates that regressing the 15% or whatever isn’t needed and just ignore the .002 difference as random variance? Or do we conclude his BABIP skill (only .002 better than mates) is real but small and give him credit as having slight BABIP skill?

Looking at the linked list, is it safe to say that we can conclude that anyone with 1 SD over/under their mates is showing true BABIP “skill”?

Thanks!