Recently, I've been examining the "passing premium," the difference in expected gain between a pass play and a run play. After correcting some of the flaws in this paper, it appears that passing yields a better average gain than running, even after accounting for incompletions, sacks, and interceptions. This would suggest that NFL teams should pass more than they currently do because balance may indicate optimization.
"We can think of passing and running as two investments, each with its own expected payoff and volatility. "
This kind of analysis is based on financial portfolio theory, a branch of math that analyzes and weighs risks and rewards. We can think of passing and running as two investments, each with its own expected payoff and volatility. When a team calls a running play it invests in a run at the price of 1 down, hoping for a payoff in yards. Running would be like buying a share of GE. Passing would be more like buying a share of a tech startup. There is more upside for rapid gain, but there is also a decent chance you'll lose the kids' college fund.
The author of this site proposes several possible applications of the Sharpe Ratio in football. The Sharpe Ratio is a financial measure of expected returns per unit of variability. Specifically, it is the ratio of average returns of an investment over a risk-free alternative to the standard deviation of the investment's value.
By comparing the Sharpe Ratio of running and passing, we can see if there is a premium of one tactic over the other accounting for each tactic's risk. We could also compare two different passing strategies, a high risk/high reward passing offense or a high percentage "dink and dunk" offense.
Consider a simple fictitious example below. Team A is the high-risk/reward passing team and Team B is the higher percentage passing team. The table lists the results of several pass attempts of each team (order is not important in the Sharpe Ratio). Both teams average the same number of yards per attempt. Team A had more incompletions and sacks, yet had more yards per completion. For the zero-risk alternative, I'll use a zero-yard "QB flop" play. Each team had one interception, a -45 yard equivalent.
|Pass||Team A||Team B|
In this example, the Sharpe Ratio is higher for Team B's high percentage offense, suggesting its rewards are more worth its risks. We would get similar results for any comparison of higher-risk tactics vs. low risk tactics, assuming the average net gain is equal.
The potential for the application of the Sharpe Ratio and all of Portfolio Theory in football strategy is vast. We might finally answer the question of whether a boom/bust running back like Barry Sanders is better than a straight-ahead pounder like Jamal Lewis. We could analyze the merits of Mike Martz's high risk/reward passing doctrine. I'm sure I'll be pursuing such applications in future research. In the meantime, however, the next post will critique a very interesting research paper that makes great strides in applying portfolio theory directly to the passing premium issue.
Continue reading part 2 of The Passing Paradox.