A couple of weeks ago, I worked up a post on fumble luck, which is simply calculated as the percentage of fumbles kept or lost. But the conversation got us thinking -- in particular, it got our resident stats guru Kirt thinking about a better way to show this stat, so he got to work on a new model, I'll let him explain.

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We know that fumble recovery is pretty much random. Teams can be better or worse at putting the ball on the ground, but once that ball is out of the ball carrier's hands, it is essentially a 50-50 proposition as to which team will come up with it. This has led to the concept of "fumble luck," with teams that experience fumble recovery rates diverging from 50 percent considered to have good or bad luck.

The problem with that is that this doesn't correspond very well to the probability of those events unfolding. Take for example a team that fumbles once, and recovers that fumble, and therefore the team has recovered 100 percent of its fumbles. However, this outcome is not that improbable. Now consider a team that fumbles 10 times, and recovers all of those fumbles. This team would also have recovered 100 percent of its fumbles, same as the first example, but this outcome is literally about a thousand of times more improbable.

This metric more accurate reflect what most people would consider "luck". Most people consider "luck" to be when chance event occurs in one's favor, and the more improbable the event, the greater we consider the "luck". Thus, in this metric, the greater the improbability, the greater the score, with bad luck getting negative values and good luck getting positive values.***** The metric is the log_{10} of the probability of a particular set of fumble outcomes occurring given a 50-50 probability of recovering any given fumble. So a score of 2 would mean that a team had a 1 in 100 chance of recovering as many fumbles as it did (10^{2}=100), and each increase of 1 indicates a 10 fold increase in the improbability of the outcome. So now our hypothetical team that fumbled once and recovered that fumble has a fumble luck score of ~0, while our hypothetical team that fumbled 10 times and recovered them all has a fumble luck of ~3.

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Below are the results. The first tab presents Kirt's fumble luck statistic, while the third tab presents straight recovery percentages (upper right is lucky, lower left is unlucky in both views). If you toggle between the views you can see that teams like Air Force and FIU have near identical defensive fumble recovery percentages (76% vs 77%), but very different defensive fumble luck scores (0.76 for AF vs 1.77 for FIU).

There is also a cluster of three teams, Kansas (22 fumbles), Georgia (16 fumbles) and Missouri (6 fumbles) that lead the nation in offensive fumble recovery percentage (each near 80%). Kansas (2.36) and Georgia (1.68) hold their outlier positions in offensive fumble luck, still first and second, while Missouri (0.43) is pulling much closer to the national average.

As for WSU? Well, they're neither lucky nor unlucky!

Lastly, to our War Eagle friends at Auburn, we're just sorry. The ball has truly not bounced your way this season on offense or defense.

** Technical description from Kirt: Statistic was calculated by taking the log_{10} of the Monte Carlo simulated probability value based on 10,000 replicates for a given chi-square value of a 1x2 contingency table of a team's fumbles recovered and fumbles lost. A chi-square p-value was used as the probability rather than a straight calculation of the probability of the occurrence as such.*

*I did this because chi-square p-values tended to be a bit more conservative, and earlier in the season when I was working on this statistic I was arriving at several teams with less than 1:1000 probability, which seems very unlikely in a system of 128 teams.*

*Monte Carlo simulated p-values were used due to the general misbehavior of 1x2 contingency tables when comparing to standard chi-square distributions, and this will also give a nice theoretical underpinning to the probability. You may notice that with 10,000 replicates there is theoretically no possibility of scores >4. If any teams come close to this value after the initial run, I can increase the replicates to make sure I am not having the statistic skewed while calculating low probability events.*

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