blowing a 17-point lead against the Texans early in the season, Hall appointed himself as his own defensive coordinator. He appeared to make good on his promise a few weeks later against the Bears when he reeled in four interceptions, good for a total of 0.99 +WPA. His gambles paid off, and he essentially won the game single-handedly.
The Redskins had several players at the top or near the top of the regular season +WPA rankings for defensive positions, Hall being one of them. But as I mentioned when I introduced defensive +WPA for individual defenders, gamblers--guys who roll the dice to make a play rather than adhere to their responsibilities--are most likely to be rewarded disproportionately. The problem is that +WPA doesn't capture all the instances when a gamble goes bad, only the times when it works out.
We can't (currently) measure a defender's -WPA, the degree to which a his failures affect game outcomes, because play-by-play descriptions never say things like "DeAngelo Hall bit hard on a double-move, Andre Johnson 67-yard reception for a touchdown." So although we can't attribute defensive failures to individual players, we can measure them on a team level.
One note before I continue: On the team level, -WPA is good for a defense. But on a player level, I defined +WPA as good for the defense, which I believed would be less confusing than the term -WPA. But the terminology is inconsistent, and I apologize for any confusion. The two graphs below illustrate team defense, so negative numbers are better.
First, it's worth looking at how -WPA correlates with net WPA at the team level. As expected, it comprises a good deal of the variance of overall WPA, with a correlation coefficient of 0.52. The relationship is illustrated below for all regular season team defenses from 2000 through 2010.
The next graph focuses on the defenses of 2010 to illustrate the relationship between -WPA and +WPA. The blue bars show the component of 2010 regular season team defense WPA that is -WPA, i.e. successful plays for the defense. The green bars show the component of team defense WPA that is +WPA, i.e. unsuccessful plays for the defense. The red bars show the net WPA for each defense.
Notice the spread between -WPA and +WPA for each team. The total with of the blue and green bars indicates the degree of variance in the outcomes for each team. Teams like SD had very low variances, playing relatively safe and consistent defense. But teams like WAS had very high variances with a wide spread between total +WPA and -WPA.
In fact, WAS had the most -WPA for any defense, but they were far from the best. I wondered if there was any correlation between high-variance defenses and net performance. If the Redskins had such a wide variance but a poor net WPA, there might be a systematic relationship between gambling-type defenses and overall success.
It appears that there may be 'types' of defenses in terms of their -WPA/+WPA spread. Based on team defense data from the 2000 through 2010 regular seasons, the correlation between defensive -WPA and +WPA is -0.37. This means there is an inverse relationship: the bigger a team's -WPA, the bigger its +WPA will be. I don't mean to imply that this is proof that teams intentionally choose either low or high variance base strategies. It could be that game situations or a team's offensive strengths dictate a certain risk profile on defense. It could be that poor defenses are just on the field for more plays, giving them more opportunities for both positive and negative outcomes. Much more research would be needed to understand what's going on. But whatever the causal relationship is, there is a relationship.
Further, the wider a team's spread between -WPA and +WPA, the worse the defense does on net. There is a weak but significant correlation of 0.09 between the spread and net WPA. Keep in mind that higher WPA numbers are bad on defense, so the worse defenses have higher variances.
One possible interpretation of these relationships is that defenses are too far on the risky side of of the risk-reward spectrum. They may be gambling too often.
An immediate implication is that +WPA for individual players might benefit from an adjustment that reflects their team's net WPA. For example, a guy like DeAngelo Hall who has a very high +WPA but whose team has a relatively poor net WPA could be penalized. If the Redskins defense has mediocre 2 WPA, and Hall's plays account for 15% of his team's +WPA, perhaps he should be assigned 15% of his team's 2 net WPA, for an adjusted +WPA of 0.30.
Nothing here is conclusive. There are some interesting relationships that suggest more research may be warranted.