THE BOOK--Playing The Percentages In Baseball

I just ran the test for the OBP leaders during the past 10 years. Here’s what I got:

Top 10 Average OBP .434
Year T+1 Average: .408

Over the past 10 years, the T+1 OBP for the top 10 is about 73.3% Year T average and 26.7% League Average OBP.

I’ll run SLG/ERA if I have time later.

For HR and K, what do you suggest using for league average?

Great job Leo!  We need guys like you doing the work.  I can say this stuff til I’m blue in the face, but until the new people out there do the work, it’ll just be part of the inner club.

So, thanks for joining the fray.

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For HR, maybe do HR/AB or HR/PA for the league leaders, and treat it as you would OBP or SLG.

Top 10 Average SLG: 0.6215
Year T+1 Average: 0.5576

I am not sure how to calculate the last step.

By the way, here is a(n ugly) query that immediately gets you the top-10 players and their subsequent years from BDB.  Just modify the SLG to OBP or HR/AB or whatever you’re looking for.

Someone can probably simplify; this was brute force.

Let’s say lgSLG = .410

Then:

.558 = .662 * (x) + .410 * (1-x)

Solve for x.  So, that simplifies to:

x = (.558-.410) / (.662-.410)

x = 59%

David Pinto did it for SLG as well:
http://baseballmusings.com/?p=63091

His 10 year average in year T was .622
And in T+1 was .559

And if you did 70% of year T and 30% of league average, Pinto reports this result:
.561

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So, yes, that illustrates it rather perfectly, doesn’t it?  If he used 69% for year T and 31% for amount of regression, it would have nailed it perfectly.

This is what regression is all about.  This is why we have regression.  Because when you select on something, and you purposefully select the outlying observations, those observations are much more likely to have benefitted from good luck than bad luck.

The “true” of those particular entities is going to be somewhere between what you observed, and what the population mean is.

And that’s what we’re seeing here: the true rate is about 70% of the observed and 30% of the population mean.  Or, you regress 30% of the difference toward the population mean.

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This 70% is not fixed.  It depends on a bunch of things.  But, for what we need for illustrative purposes, 70% does the trick.  Once everyone is happy that we need regression and regression works, we can show how to figure out the “70%” for whatever metric you are using.

Regression is actually the single most important concept to understand when dealing with observed data.  Fangraphs, BPro, THT, BtB, etc, should all be taking up this challenge to show their readers that when they look at data, that part of that data is noise.  These simple examples show things plainly and simply in ways that mathematical gyrations will simply make the common person ignore this concept.

Regression, regression, regression ~= location, location, location

I remember MGL hammering this point home on the old BaseballBoards.  It took me quite a while to understand and accept it.  And really, it makes no sense to do any analysis without getting this.

Somebody just asked me to project Sidney Crosby’s points for the season yesterday.  I said you should assume that he’ll post something like a 3-2-1 weighted average of his last three seasons, and so he’s looking at something like 120 points if he doesn’t get injured.

This answer was not well-received, but I said I could not in good conscience allow anyone to make future projections without regressing

Even 3-2-1 won’t have enough regression.

Also, I presume you forecasted his remaining games, and then added his already earned points?

.558 = .662 * (x) + .410 * (1-x)

Solve for x.  So, that simplifies to:

x = (.558-.410) / (.662-.410)

x = 59%

I said .622 not .662

.5576 = .6215x + .410(1-x)
x = (.5576-.410)/(.6215-.410)
x = 69.8%

Neat! Thanks Tango.

I guessed on .410.  According to Pinto, it was .420.  Your numbers and his were similar.  So, using your numbers:
x = (.5576-.420)/(.6215-.420) = 68.3%

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Anyway, is everyone a believer of regression toward the mean?  Is there anyone NOT on the regression train?

Tango, I took you up on #1 of the challenge, but went off on a bit of a tangent to add another car (or two, when I finish the next piece) to the regression train.

Summary: 2007-2008, top 25 SLG across both leagues, 66% (and it would have been lower if not for Pujols).

http://bayesball.blogspot.com/2010/12/slugging-regression.html

Average HR/AB of league leaders: 0.0812
League Average (roughly): 0.036
Average HR/AB of leaders in T+1: 0.0681

That is 71% of Year T, and 29% league average.

I know I’m doing nothing but belaboring the point, but I just find it very cool.

Please, keep belaboring!

The only way we can go on to the next town is if everyone gets on the regression train.

ERA of top-10 ERA leaders, 2000-2009: 2.86
ERA of that group of pitchers in T+1: 3.79
Average ERA over that timespan: 4.06

Can this be highlighted in the same sort of way? Something tells me it’s different.

Ryan/15:

ERA minus league ERA in T: -1.20
ERA minus league ERA in T+1: -0.27

-1.20 * x + 0 * (1-x) = -0.27

x = 22.5%

ERA in T+1 = 22.5% of ERA in T + 77.5% of league ERA

There’s a good reason for the ERA to behave differently, however:

Average ERA over that timespan: 4.06

That can’t be right.  ERA average must be around 4.30 or so.  And, since you are limiting the pitchers to starters only, probably more like 4.40.

Oops, you are correct.  That was the average of pitchers who qualified for the ERA title.  The average of pitchers with 100IP is 4.35 and the total aggregate average is 4.40.

That would give us an x of 37%, if I didn’t botch anything else.

Regression to the SLG mean, 75+ ABs—evidence (not particularly robust, but a start) that the top hitters regress down, the weaker sluggers regress up.  Read more at
http://bayesball.blogspot.com/2010/12/slugging-regression-ii.html

Pinto looks at OBP:
http://www.baseballmusings.com/?p=63107

Year T: .434
Year T+1: .407
Lg Avg: .333

Maintain rate: 73%

I understand the numbers suggest a 30% regression towards the league mean for the top 10 players in a given category, but what about when evaluating players outside the top ten. In a larger sample you will certainly get players who performed at, or even below, their true talent levels. How do you know to what degree to modify the regression level?

You apply regression to EVERY player (the degree of which is linked to his PA). 

This does NOT mean that you will get the exact true talent level for the player, but a best estimate, of which there will be an uncertainty level.

I don’t know if this is interesting but I did a little study for my own amateur league in Germany (7 teams with only 24 games per season).

First of all I selected all players with at least 1 PA in both 2009 & 2010. I then split all players into two groups, one with all those players whose AVG. was above league average (.269) in 2009 and the other ones with an AVG. below league average.

Group 1: AVG .354 (500-1413)
Group 2: AVG .186 (272-1459)

Then I checked the AVG. for both groups in 2010.

Group 1: AVG .319 (425-1333)
Group 2: AVG .265 (384-1447)

Is this way of doing this excercise valid? If so, I guess it points to “regression towards the mean”, correct?

Thanks for a short feedback!

As long as you weight each player the same in the two pools.  Usually, we take the minimum of the two PA for each player.

Otherwise: yes!

Don’t expect the 70% to hold though.  The 70% is specific to MLB and to one season.

Cool. Thanks for the quick reply!