Monday, September 30, 2013

Not All Fumbles Are Created Equal

Abstract
A fumble can be a key play in a football game, where just a single turnover can be the difference between a win and a loss. Recovering a fumble is therefore a hugely critical act. While the recovery itself is at least a mostly random event, the location of the fumble can significantly alter the odds that the defense will recover it. Fumbles behind the line of scrimmage are more likely to be recovered by the offense, while fumbles after a successful rush or pass are more likely to get scooped up by the defense.

Introduction
Nothing in football can change the momentum of a game faster than a turnover. A positive turnover differential is highly correlated with winning, so it's no wonder that teams are constantly talking about making fewer of them. While interceptions are generally directly caused by poor decision-making by the quarterback, the apparent random nature of fumbles makes them so much more exciting (and vexing, when your team is the one doing the fumbling).

Of course, fumbles aren't really random. Usually a player doesn't just accidentally drop the football, and defensive players are taught to hold offensive players up while their teammates attack the ball. However, the act of recovering a fumble is generally considered to be a random event, one that is entirely based on luck. (I'm not quite as convinced of this assertion as the sites I just linked; I've seen too many players try to pick the ball up when the should have fallen on it, or fall on it only to have the ball squirt away. But testing this is not the focus of this post so I'll leave it be for now.)

It's important to recognize that this does not mean that all fumbles have the same probability of being recovered by a certain team—you wouldn't want to use fumble recoveries as a random number generator, for instance. The more players on the defense near the fumble, the more likely one will make the recovery. Conversely, if only the fumbling player is aware that he's fumbled (such as on the quarterback-running back exchange), the offense will be more likely to recover. By this logic, a team's chance of recovering a fumble should be strongly dependent on where the fumble occurs relative to the line of scrimmage.

Data
Data come from the Armchair Analysis database, which I queried for all plays which resulted in fumbles, as well as all subsequent plays (to determine whether the fumbling team maintained possession). To avoid potential errors in this method of determining the recovering team, I excluded fumbles occurring on fourth down. To avoid biases from teams altering their strategy at the end of a half, I only used data from the first and third quarters. As usual all errors are bootstrapped.

Results
First I selected only fumbles made by offensive players—specifically QBs, RBs, and WRs (I lumped TEs in with the wide receivers). From here, computing the fraction of fumbles recovered by the defense is relatively simple, and it turns out that overall the defense recovers 54.80±1.002% of all offensive fumbles—slightly (but statistically significantly) more than half. This is not hugely surprising, given that the defense is much more focused on whoever has the ball than offensive players are.
 
Figure 1: Breakdown of fumble recovery probability as a function of position relative to the line of scrimmage. The horizontal red bar shows the overall defensive fumble recovery rate, while the bins are shaded proportionally to which offensive positions are responsible for the fumbles.

Figure 1 shows the defense's fumble recovery rate as a function of field position, split up into bins with roughly even numbers of fumbles per bin to maintain a constant signal-to-noise ratio. The histogram has also been split up into positions, showing who is responsible for the lost fumbles.

The most striking feature in Figure 1 is the clear dichotomy between fumbles that occur just behind the line of scrimmage and the ones that occur after positive yards have been gained. This makes intuitive sense: most of the fumbles behind the line of scrimmage are likely occurring in the center-quarterback or quarterback-running back exchange, which happen before the defense has had a chance to get into the backfield. (The uptick in defensive recoveries more than ~10 yards behind the line of scrimmage is almost certainly due to strip-sacks.) Once the offense gets beyond the line of scrimmage, however, most fumbles are going to be directly caused by the defense, in a region of the field where defensive players greatly outnumber the offense.

Interestingly, a fumble on a very successful play, one that gains more than 20 yards, isn't more likely to be recovered by the defense than the average play. I'm not sure exactly why that is, but it may be that a larger proportion of long plays end up near a sideline, and therefore any fumbles have a higher likelihood of going out of bounds.  Since in this analysis a fumble out of bounds counts as an offensive recovery, it could be artificially depressing the defensive recovery rate.

Discussion and Conclusions
It's clear that the location of a fumble is of significant importance, as there is a ~20% swing in a defense's chance of recovery with just a few yards' change in position. A quarterback that drops the snap from the center will generally only be responsible for a wasted down, but a receiver who catches a 5-yard quick slant and can't hold on is likely to be the direct cause of a turnover. It's no wonder that running backs who fumble rarely last very long in the NFL; most of their runs will end up right in the range where the D is most likely to come up with a recovery.

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