Risk and Return in Play Selection

Below is a chart describing the probability (based on a normal distribution) of gaining 10 yards in 3 plays, based on a particular play's expected gain/variance relationship (or three different plays with the same characteristics):



Chart courtesy of reader Brad Eccles.

You can muse on this for some time, but this is accounting for losses, as well. It shows the important relationship between risk and return but also demonstrates--looking at the steep slope for the results on the right hand side of the chart--that average or expected return has a huge effect, implying that higher return rather than conservative playcalling strategies are beneficial, even accounting for risks (standard deviation).

Quick caveats: This is highly abstract, and takes no account of down or distance or position on the field; what may have a low standard deviation or high return in one circumstance may not in another. Also, the standard deviation for higher returns may need to be higher than 20. I still am looking for a large enough set of data to analyze.

Lastly, and this is not a bad thing, is that the assumption of a normal distribution may be off, because I would imagine that returns for a football play are heavily skewed (i.e. in a single play it is more common to gain 30 or 40 yards than it is to lose 30 or 40 yards.). This may also work in the favor of aggressive playcalling, particularly if you can quantify turnover/field position risk.