by Andrew Mooney
For a general manager of a professional sports team, dealing with legally wayward athletes can be one of the thorniest aspects of the job. How does one evaluate “character issues”—usually, past legal run-ins—objectively? Will players’ off-the-field issues serve as a distraction, detracting from the players’ production in games, or will their talent supersede all other considerations? With the recent release of Plaxico Burress from prison, this is certainly a timely topic, as teams decide whether or not they want to take the risk on this prodigiously talented, but behaviorally suspect, individual.
In effect, the question here is to determine how pronounced the influence of these mental distractions is on subsequent performance. Here, my analysis focuses on professional football: the primary questions to be explored are whether or not the arrest of an NFL player will have a significant effect on his production on the football field, and what additional factors might influence the strength of this effect.
Methods: The names of the arrested NFL players were derived from NBC Sports’ Pro Football Talk, which keeps an up-to-date record of the legal troubles of employees of all NFL teams, stretching back to February 2007. For each position, one statistical category was chosen as the measure of performance—for quarterbacks, QB rating was used; for running backs, rushing yards; for receivers and tight ends, receiving yards; and for linebackers, tackles. Thus, offensive linemen, defensive linemen, and defensive backs were omitted from my analysis, as they either had no measurable indicator of performance, in the case of offensive linemen, or no indicator of performance that was relatively stable and nonzero—sacks and interceptions—in the case of defensive linemen and defensive backs. Next, a uniform performance index had to be created that could compare performance among players of different positions—in this analysis, I did so in units of standard deviation. After noting the performance of each player across 20 games before and 8 games following his arrest, according to his respective position statistic, I recorded a mean performance statistic (in rushing yards, QB rating, etc.) and an individual-game standard deviation (“SD”) for each player. To compare the average of “several games before” to “several games after,” the estimated standard deviation of the difference between the “before” and “after” periods for each player was computed as follows:
Difference = (mean ‘before’ performance over N games) – (mean ‘after’performance over K games)
DifferenceSD = SD * sqrt((1/N) + (1/K)) (for each player, N = 20, K = 8 )
With this figure, a performance index was created as follows:
Index = ((mean of 20 ‘before’ games) – (mean of 8 ‘after’ games)) / DifferenceSD
This formula yields results that can be interpreted as the number of standard deviations that performance has changed, creating a common scale to measure variation in performance across the different positions. A number of dummy variables were also included to be regressed against this performance index to determine whether other factors could influence a player’s performance following an arrest. Specifically, a “felony” variable was added, recording whether or not the crime for which the athlete was arrested was more serious (a felony). In addition, a “married” dummy variable was included to determine whether or not being married, and presumably having a more stable home life, could affect a player’s production after an incident of legal trouble. Finally, the effect of a player’s position on the index was tested, creating three dummy variables (receiver, linebacker, and quarterback) for four positions—the fourth category, running back, was the baseline value, the effect of which is measured by the constant.
Results: The one-sample t test used to determine whether the index variable = 0 (that is, a test to determine whether there was any significant difference in performance before and after an arrest) was inconclusive. The p-value for this test was far above 0.05 (0.5419) for the alternative hypothesis that performance is different before and after arrests, so the null is unable to be rejected.
The results of the regression of the performance index against the dummy variables also yielded insignificant results. Again, none of the p-values listed are even close to 0.05. In addition, the R-squared value from the regression is 0.0191, which is incredibly weak—in other words, the three x-variables serve to explain about 2% of the variation in y, the players’ performances. Finally, the overall F-test yields a value of 0.8589, revealing that the overall model is insignificant, or that none of the dummy variables are useful in explaining the variation in “index.” The effect of position was similarly insignificant, as the p-values demonstrate (all above 0.05).
After running the regressions, it does not appear that an athlete’s arrest has a statistically significant effect on his on-field performance, and none of the dummy variables used in my regressions could help explain any change existing in performance following an arrest (p-values > 0.05). Perhaps the analysis could have been strengthened by examining data from earlier than 2007, but unfortunately, this information doesn’t seem to be readily accessible in any database like the one used in this project. It could also have been improved with more data points (i.e. a greater sample of “before” and “after” games) or the discovery of truly significant dummy variables (perhaps age or salary of players), but based on the current results, in which no category was very close to statistical significance, these alterations don’t seem like they would make much of a difference to the final conclusions. The results of the analysis seem to indicate that football players are able to put legal, off-the-field distractions out of mind during games, producing very similarly before and after an arrest. The study implies that the “character issues” alluded to earlier in the paper are not as important as many believe—players perform largely at the same level after an arrest as they did before. Assuming they can keep their handguns out of their sweatpants, of course.