Sharpe Ratio - Part IV - Further Thoughts

For the first three articles in the series see: One, Two, Three.

Expect more to come with charts and discussion as well and some more applications and discussion of the Sharpe ratio in the coming weeks. I've gotten some great feedback so far. First, I'd like to ask if anyone out there has some of your team data, play results, etc, please let me know. I would like to compile some large samples of data, and I'll even do some of the computations for you. I have some different ideas and the more data I can get the better. Whatever level you are--youth, high school, etc. (Hey, even if you're an NFL guy I'll look at your stuff, but if you're an NFL guy I might charge, haha.)

Anyway, here are some further thoughts:

Benchmark values:
When using benchmarks in the earlier discussion I mostly used a "risk-free" play, such as a quarterback sneak. First, it is important to emphasize that any time you are comparing Sharpes they should all have used the same benchmark value. So using different benchmarks when calculating Sharpe ratios for runs and passes is fine if you aren't comparing the two, but if you are, then you must standardize them.

Second, without going into too much detail an interesting point was raised. What if the average gain of the play is less than the yards it would take to get a first down? For example, on 3rd and 10 if you (for whatever reason) could only choose between two plays, both with an average gain of 5 yards. If the first had a Sharpe of 5 (standard deviation of one yard) and the other had a Sharpe of .5 (average 5, standard deviation 10 yards) then the first play has the higher Sharpe, so we say it'd be better.

But you can also be sure of one thing if you choose the first play: you won't be getting the first down. Conversely, play #2 will get a first down about 30% of the time (1-P(Z) where X = 10, mean is 5 and StD is 10). Now this discussion ignores negative plays (the high volatility of the play, especially with the relatively low average imply there might be a lot of them) which may not be worth it, but does bring up an interesting point, which I'll work on in more detail in a later article.

For now though, I make two recommendations. First, is that the appropriate benchmark for plays may be 3.4 yards (or 3.5 for simplicity) since that is the average you need to get a first down in 3 plays. This shouldn't so much affect the results as it affects how you look at them.

When and How to Use the Sharpe - Situational Football
This change, coupled with my recommendation that standard Sharpes (avg yards over the volatility of those results) be limited to your base offense of plays between the 20s and 1st and 2nd down. Football is a situational game but this still affects the majority of your playcalls and the majority of your offense.

For 3rd down, the red zone, and special situations I suggest a quasi-binary approach based on success/failure as discussed in article III.

Note: Only use relevant data when computing Sharpes. If you are calculating Sharpe ratios for your base offense, do not include results from 3rd and 1, backed up on your goal line, etc. The same applies otherwise. If you are evaluating third down plays, the fact that a play gained 12 yards on first down is not relevant.

Data and Play Incidents

There are a few data and input factors that can affect the usefulness of the Sharpe ratio.

Historical Data

Commonly when the Sharpe is discussed for investment there is a distinction made between using historical data (like the past average result of a play) and some kind of predictive value, such as an expected return or expected average for a play's usage. At present I know of no good method or model to predict the result of a play, other than some kind of offhand estimation which is what much of this discussion is meant to replace or augment, so I will stick with historical data.

Since it is historical data, though, there are potential caveats. Most obviously, just because something worked in the past doesn't mean it will in the future, this is something we all learn in football. Things go in trends, personnel changes, defenses change, and we must adapt. Retroactive statistics are never quite able to capture this. I do not think this says "throw out all your statistics" but we all know that things can change, which I think calls for--along with careful analysis and seasoned experience--a continual review of the statistics, tendencies, etc.

Independence

Using data like this (and almost all data in sports) assumes that all plays are independent. Essentially, this just means that everyone in the stadium has no short term memory, so what happened the last play, or what you called, does not affect the next play. This is a helpful assumption when making our computations but is not reality. If two teams were equally proficient at running the draw play, we would expect the passing team to average more yards when they call it than a running team; the defense reacts differently to the two teams. This kind of effect is something I constantly emphasize (see packaging plays), but is lost when using this particular metric.

Closing Notes

Again, I hope there is more to come on the Sharpe as well as other metrics and methods, the response I've gotten has been great. These are just some concerns and thoughts as you begin to expand your usage of the ratio and apply it to different circumstances. As with any statistic, it speaks more to relationships and correlations than to their causes, which is where humans come in. Nevertheless, this can be a very valuable and potent tool.