THE BOOK--Playing The Percentages In Baseball

Using .060 as the SD for the prior distribution gives an expected true W% of .450 for a team that goes 2-10.

From 2000-2010, there were 1255 stretches where an MLB team went 2-10 over 12 games (per Retrosheet gamelogs).  The average record of those teams in games outside that 12 game span (from the same year) is .451.  So that fits reality much better than using .050.

Great stuff Kincaid!  I’m not surprised really.  From 1961-present, the observed SD in win% is .071, where the random is .039.

sqrt(.071^2-.039^2)=.059

Hence, the reason I always use .060 in baseball.  That implies 69 games of regression that you add to each team.

Continuing, that means 2+69/2 in the numerator and 12+69 in the denominator.  Or 36.5/81 = .451 as the theoretical.  And Kincaid shows the actual as .451.

Good stuff.  I really enjoyed it.

This is a great thread, thanks to both Kincaid and Tango.  I’ve used this as the inspiration to create a google doc that compares the implied regression of 69 games and the long-form Bayesian approach.

http://bayesball.blogspot.com/2011/05/early-season-standings-and-bayes.html

My only question is to Tango—I got 66 games as the implied regression, and I’m trying to work out if I missed something or if the difference is simply a matter of rounding.  Can I ask you to share the details of your calculation?

I don’t know that I’d worry about 66 or 69, as that sounds like a rounding error, or some other tiny difference along those lines.

I made an Excel macro to make calculating Bayesian W% and regression-to-the-mean estimates for a group of teams easier. You’ll need an Excel spreadsheet with each team’s W and L totals, and then paste the linked code into Excel’s VBA environment. Read the comments embedded in the code to see what values you might have to alter.

https://docs.google.com/document/d/1xdtx4H_upEzAqkspRwWJl_OAmuqIq9to7sgpHn0Uld0/edit?hl=en_US

I can’t access that document from the office, so let me jsut ask you while you are here.

What kind of setup would you have to have in order for the Bayes estimate and the regression toward the mean estimate to be off by at least 1 win (in 162 games)?

An 0-22 team would be just over 1 win different per 162 games between regression and Bayes (using 69.4 games as the regression point instead of rounding to 69, it’s 0-21).

For a full season, a 40-122 team would show about the same difference.

Excellent.  Regression toward the mean is always a shortcut for Bayes, and it’s good to know at what extreme point it breaks down.

So, if you have a 40-122 team, that would regress to a 52-110 team, which is one win from what Bayes would suggest.