If fumble recoveries are random, should defenses be credited with fumbles or fumble recoveries that result from unforced fumbles? How would a defense induce an unforced fumble, such as a muffed snap or handoff? I'm guessing it can't.
So if unforced fumbles are not under the influence of a defense, and if recoveries are random, then a defense's ability to produce fumble turnovers should be measured by forced fumbles no matter who recovers them. And to be more precise, the best measure would be forced fumbles per play (in which a forced fumble is plausible, i.e. not incomplete passes).
If this is true, the win- and points- correlations with forced fumble (FF) rate will be higher than gross FFs, fumbles, or fumble recoveries. I would expect that fumble takeaways might still have the strongest correlations, but because recoveries are random, I believe that it does not estimate future fumbles as well as forced fumbles.
Here are the correlations:
As it turns out, I was partially correct, but the forced fumble rate statistic turns out to be more powerful than anticipated. Not only does defensive forced fumbles have stronger correlations to wins and points than gross fumbles and fumbles recovered, the defensive forced fumble rate stat (FF per fumble-potential play) has the strongest correlation of all (0.41).
In summary, the data suggests I use 'defensive forced fumble rate' as the defensive fumble stat for a win-regression model. It also suggests (noted in previous posts) that I use offensive fumbles, and not offensive fumbles lost. These stats correlate relatively strongly with winning, points scored, and points allowed; they do not suffer from the random noise of fumble recovery; and, since they are 'per play' rate stats, they are not biased by the causation backflow discussed in the interception post.