In the last post we could see that turnovers were most strongly correlated with wins, followed in order by pass offense, pass defense, and run offense. Run defense still was not statistically significant but it at least had a negative sign, that is it implied a better run defense helps teams win, even if only slightly.
Below is a graph of how the various phases of the game correlate with season win totals. The table under the graph are the actual Pearson coefficients. This is not a regression, just a simple 2 variable correlation. The critical value for 5% significance is 0.37 for individual years (n=32) and 0.17 for the average of the 4 years (n=128).
The first thing that struck me is how steady the correlation of wins to turnovers and to offensive passing were. They also seem systematically related (which suggests there may be collinearity problems in a regression model). This makes sense intuitively because skilled passing offenses are less likely to throw interceptions. My hunch is that fumbles tend to be random and chaotic--not dependent on a team's running ability. But interceptions are likely tied to passing ability. Also notice that passing defense is apparently related loosely to both passing offense and turnovers. As passing offense and turnovers increase in importance, so does passing defense.
But the main point is the relative steadiness of each factor. Running, on both offense and defense, are unimportant in comparison to turnovers and passing offense. Offensive passing and turnovers can't really be any better correlated than they are at .70 and .55 respectively. Offensive points per game correlated at .71 and points allowed per game correlated at .70 (link). And even Dan Fouts can tell us how important points are in winning football games.
