THE BOOK--Playing The Percentages In Baseball

Wednesday, January 30, 2008

Per Possession Win%

In response to a Phil-linked thread about figuring the chances of the Patriots winning if their number of possessions goes down, I said:

The win% in Brian’s data has an almost perfect match to this equation:

Wins divided by Losses
= 1.1 ^ possessions

So, if you have 12 possessions, the above equation will give you 3.14. That is, 3.14 wins per loss, which is a win% of .758. Brian’s simulator said .755.

Here’s how Brian’s simulator compares to my above equation:

9 0.714 0.702
10 0.727 0.722
11 0.740 0.740
12 0.755 0.758
13 0.765 0.775

So, a 12-possession game for the Pats has the equation at .758. If I extend back to only 6-possessions (half a game), I get a win% of .639. And that is pretty much the half-way point between .500 and .758.