Monday, September 29, 2014

The Matrix Model Reflecting Actual Win %

I've been curious all season as to how close the Matrix Model (which only takes into account wins and losses) would reflect the actual win percentages of teams at the end of the MLB regular season. With 162 games and all teams connected with very low degrees of separation, I assumed that the residuals between the output of the Matrix and each team's actual win percentage would be very small.
In the above chart, the teams are sorted by win percentage. This indicates that (overall) the Matrix suppresses the "true" win percentages of good teams and raises that of bad teams, meaning the model is biased towards .500. The largest residual (in absolute value) was 0.010, and the sum of all residuals is 0.001, indicating that they are small and centered around 0 as designed.

The aim of the Matrix Model is to adjust each team's wins and losses by the strength of their opponents, so I checked to see if this was the case by looking at the residuals of the teams with the highest and lowest strengths of schedule (basically to check if the model is consistent with itself).

SOS RankResidual
1NYY-0.002
2MIN-0.007
...
29SF0.009
30LAD0.010

Note: A negative residual indicates that the Matrix raised the team's win percentage, while a positive residual means the model lowered it. The above table indicates that a stronger SOS correlates with a higher matrix rating, which means the model is consistent.

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