3.Pass on every down: Well, maybe not. It depends on the team's ability to move the ball and wear down the defense. The average pass play in the NFL in 2008 gained 6.5 yards, while the average running play gained 4.2 yards. No team gained more yards per rush than yards per pass. In general, that would indicate that passing is more valuable than running.
However, there are the issues of talent and variance. Talent-level of all players will be needed by coaches to evaluate the inputs for the process set forth here. We make several assumptions regarding the negligible differences between things like sack yards and QB rush yards and fumbles per rush and interceptions per pass attempt. On many teams, these differences are not negligible and should be considered.
With variance, most running backs – basically with the exception of Curtis Martin – set their yards per rush averages with some negative plays, a lot of two to six yard runs and a few breakaways. Passing plays are very different. Last season, 39% of all pass attempts went for zero yards as incomplete passes, the other 61% of pass plays averaged 10.7 yards gained. For the purposes of this example, the yards lost on sacks are negated by the yards that are gained by quarterbacks who run. And, since the average difference in interceptions per pass attempt and fumbles per run is less than 1%, that falls out of this.
Long story short, there is far less volatility in the output of a running play as compared to a pass. Enter the Sharpe ratio. The Sharpe ratio is the financial world's simple answer to risk vs. reward. It is calculated by taking a stock's average net return over time and dividing it by its standard deviation (a measure of variance) over the same time period. Either factor can be weighted differently so that, when applied to football, the formula could be tweaked to account for an individual/coach's level of risk-aversion. But essentially, the higher the return the better; the lower the standard deviation the better.
At some point – probably around the same time that all officiating in every major sport is done electronically, but that is for another article – after each play, coaches will have computer-generated results of otherwise complicated formulas or simulations that will provide the probabilities of different conclusions – initial success of the individual play, scoring on the drive, winning the game, turning the ball over – based on the decision that is made for the next play call. Since that may be a few years away, football should adopt the Sharpe Ratio for decision-making. Some teams may find that passing is far more valuable than running and pass on every down. Some may find the opposite and run on every down. Others may see very similar numbers and run a balanced attack that is far more reliant on the situation.
Ultimately, I would guess that most teams should find that they should pass far more, only running when a yard or two are needed or when the situation dictates that calling a running play will very likely net a better result than an average pass.
This does not consider the type of running or passing play that would be called and how the threat of a run or pass alters the success of the other. These are items we hope teams would factor when building models for expected results.
Go to #2 Two is Better than One and Six is Better than Three or go back to the Introduction for more.
Paul Bessire is the Senior Quantitative Analyst and Content Manager for WhatIfSports.com and a member of the Pro Football Writers of America. With any comments, questions or topic suggestions, Paul can be reached at firstname.lastname@example.org. Thanks!