More Pythagoras

Bruce Cowgill, a member of the SABR Statistical Analysis Committee was kind enough to send me another formula used to predict a team's final winning percentage given their actual winning percentage at a point during the season. I don't have the original site where it was posted (by an analyst with the name or initials DBOZ) but here is the formula:

Final W% = (0.5 x (1 - GamesPlayed / 162)^2.25) + (CurrentWin% x (1 - (1 - GamesPlayed / 162)^2.25))

I applied this formula to the data I had for 2004 and added yet another column to the two tables I posted in my previous post.

                Pyth            Actual          Pyth + Actual   DBOZ
        Avg G   AvgE  StdDev    AvgE  StdDev    AvgE  StdDev    AvgE  StdDev
10-Apr     5    18.2    11.9    25.5    18.0    18.2    12.0    11.1    6.6
15-Apr     9    15.8    14.5    17.8    14.6    15.5    14.5    11.0    6.0
30-Apr    22    11.5     9.3    12.9     7.1    11.2     9.0     8.6    6.2
30-May    49     8.0     5.6     7.3     5.6     7.5     5.0     7.2    5.1
30-Jun    76     6.7     5.0     6.5     4.8     6.3     4.5     6.6    4.8
30-Jul   102     5.1     3.3     3.8     3.0     4.0     2.7     4.1    3.1
30-Aug   130     3.6     3.0     2.3     1.8     2.2     1.8     2.3    1.8
5-Oct    162     3.1     2.8     0.0     0.0     0.0     0.0     0.0    0.0

Because this formula is a "regress to the mean" formula much like using the Pyth+Actual method, the average error ends in 0 at 162 games. It matches pretty closely with Pyth+Actual but does a better job very early in the season. In looking at the raw data, the reason is that it tends to lump everybody together, thereby reducing the standard error but reducing the correlation coefficient as well.

        AvgG  PythW%  ActualW%  Pyth+ActualW%    DBOZ
10-Apr    5   0.414    0.270      0.411         0.255
15-Apr    9   0.300    0.347      0.306         0.348
30-Apr   22   0.530    0.649      0.559         0.641
30-May   49   0.719    0.771      0.757         0.771
30-Jun   76   0.780    0.797      0.812         0.799
30-Jul  102   0.890    0.930      0.934         0.929
30-Aug  130   0.937    0.975      0.976         0.976
5-Oct   162   0.951    1.000      1.000         1.000