## Coaches and Risk

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.)

 Team Coach Wins Risk Excess Risk Fisher 8 -0.013 -0.0232 Cowher 8 -0.011 -0.0206 Shanahan 9 -0.001 -0.0137 Smith 13 0.008 -0.0131 Shell 2 -0.016 -0.0122 Holmgren 9 0.002 -0.0101 Coughlin 8 0.002 -0.0075 Nolan 7 0.002 -0.0059 Jauron 7 0.003 -0.0046 Reed 10 0.011 -0.0040 McCarthy 8 0.006 -0.0037 Fox 8 0.007 -0.0034 Billick 13 0.020 -0.0016 Del Rio 8 0.009 -0.0013 Gruden 4 0.000 -0.0006 Mangini 10 0.016 0.0015 Childress 6 0.008 0.0030 Edwards 9 0.016 0.0039 Shottenheimer 14 0.029 0.0049 Kubiak 6 0.011 0.0057 Saban 6 0.011 0.0059 Crennel 4 0.008 0.0068 Dungy 12 0.026 0.0071 Parcells 9 0.019 0.0072 Linehan 8 0.018 0.0077 Gibbs 5 0.011 0.0078 Lewis 8 0.019 0.0090 Green 5 0.013 0.0094 Marinelli 3 0.009 0.0107 Payton 10 0.030 0.0151 Belichick 12 0.039 0.0197 Mora 7 -0.438 na

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.

### 3 Responses to “Coaches and Risk”

1. Dismal Numbers says:

Some people have play by play databases. You just need a crowbar to get it from them (which I don't blame them mind you but at least give me a price!). Football Outsiders will sell you some recent seasons but any analysis has to be posted there first. You can spider it I think from various websites but I don't have the PC skills to make it easy. Zeus clearly has a database as well.

http://www.pigskinrevolution.com/index.html
http://www.idsnews.com/news/story.aspx?id=35696&comview=1

2. Dismal Numbers says:

Great post, I agree, a year by year analysis would be interesting to see who is being too conservative or not. I believe both Lewis and Crennel are too conservative Palmer, TJ, and Oche Cinco! go for it! :-) Still, I can't prove it but this analysis may shed some light on it. I will read the previous analysis as it contains the meat of your analysis and maybe comment more. Maybe an analysis by quarter could add some insight?

3. Brian Burke says:

Thanks for the links. I had visited the ZUES site a while back. I wonder if they've actually been able to sell their system anywhere.

I like the other article too. I might make a post out of it.