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.

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?