## Prospect Theory and football (Part 1)

Stephen Dunn

Applying behavioral economics to the game of football. (Don't worry, we'll ease into it slowly.)

Back in an April post, I made reference to a behavior economic phenomenon called Prospect Theory with regards to coaching decisions on fourth down. Prospect Theory states that people make decisions based on perceived gains and losses and not on the final outcome thereof. In that article I said coaches made the decision to go for it on fourth down given a number of factors, including: field position, distance, personnel mismatches and a number of other factors. If the perceived gains outweighed the perceived risks, coaches would elect to go for it. In all cases, success and risk are measured against the status quo or distance to go.

Because football is a sport that requires teams to stop and reset themselves after each play, we have the opportunity to examine football through the Prospect Theory lens on each individual play. Over a few articles I’ll use some of our charting data to highlight interesting examples of Prospect Theory in action in the college game from 2012.

First, I will start by saying Prospect Theory has a complete mathematical formula to calculate likely decisions, but for the sake of my sanity and yours, I’ll leave the math out of this article.

What better place to start an article on Prospect Theory than on first down? The success or failure of a first-down attempt does, in large part, determine the play-calling for the rest of the drive. If a play called on first down succeeds, coaches have the opportunity to further disguise second- and third-down play calling because the offense has a shorter distance to go to attain a new set of downs. Should a play called on first down fail, or, worse, result in negative yards, the offense must play from behind schedule, which makes the threat of a pass increasingly likely and therefore easier for defenses to scheme against.

When coaches weigh the potential positives and negatives of their first down play-calling, we see that they choose running nearly three out of every five times. So even though passing has a higher yards-per-attempt average (7.8) than running (5.2), coaches are electing to run rather than pass. For the most part, coaches determine that even a few yards of forward progress are better than risking a sack, an interception or an incomplete pass. The chart below illustrates the imbalance between running and passing on first down in all scenarios and then again on all first and ten scenarios.

 All First Down Attempts First-and-10 Run: 3,858 (57%) Run: 3,421 (56%) Pass: 2,919 (43%) Pass: 2,705 (44%)

Compare the charts above with first-down play calling for all attempts greater than 10 yards (chart below). In the charts above, running was favored because any forward progress was seen as beneficial. However, in scenarios where teams faced first-and-greater than ten, passing attempts went up. At identical rates, coaches chose passing plays in these situations; this means, of course, that in half of these situations, coaches weighed the positives and negatives of running and determined that a sack, an interception or an incomplete pass was a worthwhile risk because rushing would be unlikely to gain enough yards to provide the offense with a schematic advantage on second or third down.

 First-and->10 Run: 113 (50%) Pass: 113 (50%)

What we know about running and passing on first down, though, isn’t enough. These plays do not happen in a vacuum, and we know coaches call plays based on personal preference as well as on-field personnel. No coach will run the ball on each and every first down because opposing defenses will simply adjust to stop the run. So while information on how coaches choose to advance the ball says a great deal about the coach’s risk tolerance and level of acceptance for playing second- or third-and-long, it brings me to my next point: Coaches rely on their own set of talent.

Using Alabama and USC as examples, we see that each relied on its strengths – running at Alabama and passing at USC – to move the ball, keeping the alternative to change up the pace and force opponents to defend both the run and the pass. Below is a chart showing how each school’s first-down attempts break down by running and passing:

 Alabama: All First Downs USC: All First Downs Run: 193 (60%) Run: 96 (45%) Pass: 129 (40%) Pass: 116 (55%)

In this chart we see each coach modifying his first down play-calling based on the risk, real or perceived, given on-field situations and their own play-calling history. Even though Alabama had a punishing running game, it could not run the ball on each and every first down. Similarly, even though USC had one of the best receiving tandems in the country, Lane Kiffin could not expect to pass the ball on each and every first down and expect positive results.

The end result for these two teams – and every team for that matter – is that coaches and coordinators use a variation of this behavioral economic theory to guess if a particular play is likely to be more or less advantageous than another given the criteria available. Once the pros and cons are weighed, the coach selects a play he believes will expose his offense to the least amount of risk and the team executes.

In the next article I’ll examine another facet of Prospect Theory by looking risk aversion and the effects that has on opportunity.

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