The previous post proposed an efficiency stat for interceptions that helped reduce the cause-effect conflation created by interceptions. The interception efficiency stat calculates interceptions thrown per pass attempt. Evaluating interceptions this way reduces the impact of losing teams throwing often and predictably when behind. Although this new stat does not have the retrospective explanatory power of gross interceptions on winning, I believe it is superior to gross interceptions because it better isolates the direction of causation from the independent variable (interceptions) to the dependent variable (winning).
Evaluating fumbles in the same manner may also make sense, but the issue is more complex. First, a fumble can happen on nearly any play, not just runs. At first glance, if winning teams "run out the clock" and shy away from risky passes, it follows it would be at a higher risk for fumbles due to the higher number of running plays. But fumbles can happen during sacks or completions too. Second, there is also the question of fumbles lost vs. fumbles in general (lost or recoverd)--which should be used? Can the ratio of fumbles lost to fumbles tell us anything significant? So a fumble efficiency stat might not be a better measure of a team's tendency to fumble. For now, I'm going you use offensive fumbles per run+sacks+completions. Special teams fumbles are not counted.
To be honest, I'm not sure what the answers are. But here are the correlations with wins, offensive points scored, and defensive points allowed (0.15 for 5% significance):
What does everyone think?
My own initial thoughts: It looks like Off Fumble Rate (both lost and recovered) is the best to use for a win-regression model. I'm guessing this is because which team recovers a fumble is random, but fumbles in general approximate more purely a team's propensity to caugh up the ball. Plus, a recovered fumble usually aborts a play and costs a down and perhaps a loss of a couple yards.
Also, fumbles no matter how they are measured, tend to hurt an offense more than help the opposing team. Note the strong negative correlation of offensive fumble stats to offensive points scored vs. the weak or insignificant correlation with defensive points allowed (the top 4 rows).