Monday, September 3, 2007

Model of Expected Wins Based on In-Game Performances

In the previous article, I wrote about using in-game statistics to predict the outcome of a game. The logistic regression model returns a probability that the home team has won the game based on those stats. An expected win total can be calculated from these probabilities: XWins(t) = sum_{g in games} P(won g | Sg), where Sg is simply the stat line from game g (i.e. passing, rushing efficiencies, 3rd down conversion rates, etc.).

Training on all previous years in the 1996-2006 data, I tested on each year from 1997 to 2006. The average mean absolute error was 1.2556 games. The model was only off by 1.2059 games, making it slightly more accurate than the model described here, which used season stats to estimate win totals. In the same manner as the previous model, I used the expected win totals to predict who would improve/decline the following season. With m being the mean absolute error for a given year Y, a team who won more than m games above their expected win total would be predicted to decline (not win as many games) in year Y+1. A team who won more than m games fewer than their expected win total would be predicted to improve (win more games) in Y+1. From 1997-2005, the system was 77.049% accurate at predicting teams to improve the following year and 72.727% accurate predicting teams to decline. In 2002-2005, the system was 82.143% accurate at predicting teams to improve and 80.645% accurate at predicting teams to decline. This is an improvement in both areas of accuracy over the previous model.

Here are the predicted risers and fallers for 2007 based on this model:

  • Miami Dolphins (7.7448 expected wins vs. 6 actual)
  • Pittsburgh Steelers (9.6196 vs. 8)
  • Jacksonville Jaguars (9.673 vs. 8)
  • Oakland Raiders (4.8075 vs. 2)
  • Philadelphia Eagles (12.051 vs. 10)
  • Green Bay Packers (9.6266 vs. 8)
  • Minnesota Vikings (8.1455 vs. 6)
  • Tampa Bay Buccaneers (5.5788 vs. 4)
  • Arizona Cardinals (6.4778 vs. 5)

(7.39287 out of 9 expected to be correct)


  • New England Patriots (10.028 expected wins vs. 12 actual)
  • Baltimore Ravens (11.483 vs. 13)
  • Houston Texans (4.3759 vs. 6)
  • Tennessee Titans (5.7285 vs. 8)
  • San Diego Chargers (11.176 vs. 14)
  • New York Giants (6.4395 vs. 8)
  • Chicago Bears (10.273 vs. 13)

(5.64515 out of 7 expected to be correct)

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