THE BOOK--Playing The Percentages In Baseball

So, Tango, how *did* you figure out that that worked?

See this great thread, with some results from Rob Wood:

http://www.tangotiger.net/archives/stud0098.shtml#1047

If you do x/(x+PA) for each of Rob’s data points using his Bayes sim process, then x=318 gives you a perfect match.

It was from that point onward that I started doing regression toward the mean in this manner.

Further research, such as from Jared Cross, kept pointing to the match between Bayes and regression toward the mean being equivalent.

And so, that’s what I use.

Tango/2

I sent you an email about a month or so ago where I tested how well certain regression formulas did for year to year predictions.  In there I found that using a square root rule for credibility actually performed better than the x/(x+PA) formula.  But, the difference was relatively small.

According to the link here (Actuarial Study notes, have to go to page 235 of the PDF),
http://www.casact.org/pubs/Werner_Modlin_Ratemaking.pdf

“the least squares credibility is the weighted least squares line associated with the Bayesian estimate.  In certain special mathematical situations, the Bayesian analysis estimate is equivalent to the least squares credibility estimate”