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Correlation Update

More Stats and Their Correlation to Winning Percentage

Just a table update in this post. The first table is based on substats from various phases of the game while the second table is composed of margin stats. The margins were broken out because they will clearly correlate better to winning. Points stats are still included for informational purposes only, further complaints that it's already obvious that scoring more points and allowing fewer will lead to more wins will be roundly ridiculed. Some comments after the tables, which are initially sorted by strength of correlation. As always, adjusted stats were used for the analysis.

Statistic Side Unit WPCT Corr Abs(Corr)
Points Scored per Play Offense Play 0.833 0.833
Points Scored per Game Offense Game 0.816 0.816
Points Allowed per Game Defense Game -0.811 0.811
Points Allowed per Possession Defense Possession -0.810 0.810
Points Allowed per Play Defense Play -0.803 0.803
Points Scored per Possession Offense Possession 0.789 0.789
Rushing Yards Allowed per Game Defense Game -0.767 0.767
Total Rushing Yards Allowed per Game Defense Game -0.751 0.751
Passing Efficiency Against Defense Play -0.721 0.721
Rushing Yards Allowed per Carry Defense Play -0.707 0.707
Yards Allowed per Play Defense Play -0.696 0.696
Yards Allowed per Game Defense Game -0.694 0.694
Total Passing yards Allowed per Attempt Defense Play -0.681 0.681
Passing Efficiency For Offense Play 0.670 0.670
Passing Yards Gained per Attempt Offense Play 0.664 0.664
Total Passing Yards Gained per Attempt Offense Play 0.663 0.663
Yards Gained per Play Offense Play 0.649 0.649
Passing Yards Allowed per Attempt Defense Play -0.630 0.630
Total Rushing Yards Allowed per Carry Defense Play -0.619 0.619
Touchdown Passes per Attempt Offense Play 0.612 0.612
Yards Gained per Game Offense Game 0.610 0.610
Sacks per Game Defense Game 0.610 0.610
Turnovers Forced per Play Defense Play 0.543 0.543
Interceptions Received per Game Defense Game 0.536 0.536
Turnovers Forced per Game Defense Game 0.506 0.506
Rushing Yards Gained per Carry Offense Play 0.504 0.504
Red Zone Percentage For Offense Play 0.486 0.486
Rushing Yards Gained per Game Offense Game 0.485 0.485
Total Rushing Yards Gained per Game Offense Game 0.472 0.472
Net Kickoff Average Special Play 0.467 0.467
Sacks per Attempt Defense Play 0.464 0.464
Turnovers Lost per Play Offense Play -0.455 0.455
Completions per Attempt Offense Play 0.448 0.448
Punt Return Average Special Play 0.437 0.437
Red Zone Percentage Against Defense Play -0.435 0.435
Total Rushing Yards Gained per Carry Offense Play 0.434 0.434
Interceptions Received per Attempt Defense Play 0.426 0.426
Turnovers Lost per Game Offense Game -0.411 0.411
Interceptions Thrown per Game Offense Game -0.408 0.408
Times Sacked per Game Offense Game -0.386 0.386
Fourth Down Percentage Against Defense Play -0.380 0.380
Interceptions Thrown per Attempt Offense Play -0.331 0.331
Fourth Down Percentage For Offense Play 0.329 0.329
Fumbles Forced per Carry Defense Play 0.318 0.318
Field Goals Made per Game Special Game 0.313 0.313
Time of Possession per Game Team Game -0.303 0.303
Net Punting Average Special Play 0.299 0.299
Total Passing Yards Gained per Game Offense Game 0.270 0.270
Kickoff Return Average Special Play 0.268 0.268
Field Goal Percentage Special Play 0.259 0.259
Fumbles per Carry Offense Play -0.241 0.241
Passing Yards Gained per Game Offense Game 0.238 0.238
Times Sacked per Attempt Offense Play -0.226 0.226
Total Passing yards Allowed per Game Defense Game -0.225 0.225
Third Down Percentage For Offense Play 0.157 0.157
Time per Offensive Play Offense Play -0.149 0.149
Fumbles Forced per Game Defense Game 0.147 0.147
Third Down Percentage Against Defense Play -0.136 0.136
Passing Yards Allowed per Game Defense Game -0.134 0.134
Fumbles per Game Offense Game -0.092 0.092
Penalties Against per Game Team Game -0.086 0.086
Penalty Yards Against per Game Team Game -0.043 0.043
Plays per Game Team Game 0.032 0.032

Statistic Side Unit WPCT Corr Abs(Corr)
Point Margin per Possession Team Possession 0.936 0.936
Point Margin per Game Team Game 0.935 0.935
Point Margin per Play Team Play 0.918 0.918
Yard Margin per Play Team Play 0.847 0.847
Passing Efficiency Margin Team Play 0.843 0.843
Yard Margin per Game Team Game 0.839 0.839
Total Passing Margin per Attempt Team Play 0.829 0.829
Passing Margin per Attempt Team Play 0.805 0.805
Rushing Margin per Carry Team Play 0.742 0.742
Rushing Margin per Game Team Game 0.719 0.719
Total Rushing Margin per Game Team Game 0.704 0.704
Total Rushing Margin per Carry Team Play 0.675 0.675
Turnover Margin per Play Team Play 0.484 0.484
Turnover Margin per Game Team Game 0.425 0.425
Total Passing Margin per Game Team Game 0.354 0.354
Passing Margin per Game Team Game 0.285 0.285

  1. For those that are familiar with correlation, based on our population size of 120 a correlation strength of 0.180 or greater is required to drive the P-value under 5%, 0.235 for 1%, 0.255 for 0.5%, and 0.297 for 0.1% - not sure what the best confidence interval to use here is given the heavy interaction between football stats.
  2. Time of possession has a negative correlation to winning percentage and it's statistically significant. From an overall perspective, this makes sense. As I've argued before, "keeping their offense off the field" also keeps your offense off the field in terms of number of possessions. This makes sense as a strategy for a weaker team moreso than a stronger team. Furthermore, powerful offenses tend to score more quickly than less powerful offenses overall.
  3. The top non-points stat is still rushing yards allowed per game, but as previously discussed that is at least as much an effect of winning as it is a cause of winning. If you're losing then your opponent will be more likely to run the ball than if you're winning.
  4. Rushing Defense vs. Passing Defense - The normal rushing and passing per play stats make run defense look more important than pass defense. However, simply moving sack totals to pass defense (Total Rushing and Total Passing) flips that relationship.
  5. Run The Damn Ball is not as important as Pass The Damn Ball. Obviously being better able to run the ball is correlated with winning, but not as much as being better able to sling the rock.
  6. Passing efficiency rates more highly than total passing per attempt, but this is somewhat misleading as the efficiency formula includes touchdowns per attempt. Adding a measure of scoring to a more basic stat should strengthen its correlation with winning. When running a regression, for example, adding more correlated stats to the dependent variables selection will continue to increase the R-squared value of the regression as a whole.
  7. Completion percentage isn't really that important, relatively speaking. I've run some regressions on improving the pass efficiency formula and am tempted to leave it completely out. As part of the regression using that stat along with yards per attempt, interceptions per attempt, and touchdowns per attempt against points per possession as the dependent variable, completion percentage's component p-value is 0.892 when forcing the constant to zero and 0.220 when not. It's insignificant either way. I think a lot of that has to do with the fact that completion percentage is really a subcomponent of yards per attempt, which is merely the product of completion percentage and yards per completion.

The next task is to attack from the top down. We know that scoring margin is what correlates best to winning and that it's made up of scoring points and not allowing them. What substats correlate best to those two factors?