Sharpe Ratio - Part III

3rd Down and Broader Applications

I saved this section for a separate post because it is intended to show some potential for wide application. First a few notes:

When we build gameplans, and specifically the playcall sheet, it is broken up into situations or versus various defensive tactics. In each category we have 2, 3, 4, or 5 or so calls that we are comfortable with. In the heat of the battle you try to pick the one that you think will work best. I read an article with Norm Chow where he said he had 4 or 5 calls that he was comfortable with in a 3rd and 3 or 4 situation and the NFL guy he was talking to had two. Besides purely decades of experience, how can you help yourself narrow down these choices, particularly vs. evolving defenses and new opponents? The Sharpe ratio can augment this decision, by quantifying the risk return relationship--specifically for situations and vs various tactics.

Second, up until now we have looked only at yards gained on a given play. This served fine for 1st and 2nd down. However, on 3rd and 10 there is a big difference between 9 and 10 yards, whereas relatively little between 8 and 9. In order to reflect this instead of using the yardage values we use simplified values to indicate success or failure. A successful conversion gets a 1, failure to get a first down gets a 0. A negative play (sack) gets a -1 value, to reflect the loss of field position, and a turnover is -2. In the statistical literature these are known as "dummy variables."

To summarize:

1 - Successful conversion
0 - Failure to convert
-1 - Negative yards
-2 - Turnover

For our benchmark value we use zero. The theory behind this is that at any time we could call a draw (or a quick 3rd down kick) and not take the negative play or turnover and just punt.

Thus we can calculate the Sharpe ratio for a given 3rd down play using these values. Below is another made up example for a particular play for a 3rd and long (7+).



As you can see the Sharpe ratio is .11734. Comparing the various Sharpe's you calculate has a lot of interesting applications. For example, if the Sharpe ratios of low risk (draw plays, quick screens, quick passes) is not much different than higher risk strategies (dropback passes) that may indicate that it is not really worth it to take on the high risk strategies too much. However, if the riskier strategies have relatively higher Sharpe ratios, then it may indicate that you shouldn't be too conservative and can safely take more risks on 3rd and long.

From this example I hope you can see that the Sharpe ratio has many, many interesting applications. You can analyze success/failure in everything from 3rd and 4th downs to 2 points, to certain red zone metrics, or beating the blitz, etc. By expanding beyond simple yardage and becoming increasingly specific to situation and circumstance you can expand the power of the tool.

Later I will discuss a few caveats and some conclusions to the use of the metric and gathering appropriate data.