Recently I've been looking at risk and reward in the NFL using financial portfolio theory, a branch of math that analyzes and optimizes various risk-reward strategies. I've been building on previous research that applied the utility function to analyze each team's run/pass balance. In the last post, I calculated what each team's risk level (α) was for the 2006 season.
Risk was calculated as a level of risk aversion (or tolerance) based on the relative expected yardage gains and volatility of a team's running plays and passing plays. This method considers not only the simple ratio between run plays and pass plays, but the variance of each as well. For example, it considers whether a passing game is a short, high-percentage game or an aggressive down field game. Positive α means a team was risk averse, and negative α means a team was risk tolerant.
But grading play callers as risk tolerant or averse is slightly more complicated. I noted that winning teams were often the more conservative teams, but that conservative play calling was likely the result of having a lead. In other words, winning leads to conservative play calling, not the other way around.
I also noticed a clearly linear relationship between team wins and risk level. Below is a graph of risk aversion vs. team wins. We can see that teams with a lot of wins generally are the teams that can afford to be conservative.
The upward sloping line is the regression best-fit line. It suggests the typical level of risk for each number of season wins. For example, a team with 12 wins should have a fairly conservative profile, an α of about 0.02. And a team with 8 wins should have been more aggressive, with an α of about 0.01.
The distance above or below the best-fit line could be considered the excess risk beyond that which is appropriate for each number of wins. This value is the "residual" of the regression. Note that I said "could be considered." Keep in mind that an 8-win team that appears "too risky" may really be a 6-win team that gambled often and got lucky. There is an unquantified part of the equation that is random luck.
Now we have a way to score teams and coaches as risk averse or risk tolerant. The table below ranks each coach in terms of his excess risk, from the most risky to the most conservative. (I excluded Atlanta from the analysis because they were severe outliers in 2006. Vick's boom and bust scrambling style defied convention. The Falcons appeared to be over 20 times more aggressive than the next riskiest team due to their relatively very high variance in their running game.)
Another way of looking at excess risk is presented in the graph below. The teams are sorted from most to fewest wins. Click to expand it.
Notice how many below-average teams were risk averse. Oakland was the only team to display a high degree of risk tolerance. But this is likely due to their incredibly inconsistent passing game and inability to protect their quarterbacks.
Also notice how many teams that are considered "pass first" teams, such as IND, STL, CIN, and NO, show up on the risk averse side. They aren't considered too risk averse because they run too much, but because their passing games were so consistent. This result suggests they should have thrown even more, or thrown deeper to riskier routes more often.
Of course we really could be talking about offensive coordinators rather than head coaches. But with few exceptions, it's the head coach that really sets his team's overall strategy. We're also only looking at one year--because it's the one year of data I have. It would be really interesting to see if some coaches consistently show the same level of risk aversion or tolerance over several seasons. But to get the data requires a play-by-play NFL database, something not readily available...yet.