Decision making inside the five-yard line

While watching Nebraska’s Quincy Ununwa score a 99-yard touchdown against Georgia’s defense in the Gator Bowl last week, and then again watching Ohio State’s safety in the Orange Bowl against Clemson, I became interested in the decision making and play calling that lead to big plays when offenses are backed up inside their own five-yard line.

There are two ways to think about this: Do defensive coordinators sell out with aggressive blitzes to try for a safety, and if so, is it because they are more risk tolerant when their opponent is near their own end zone (assuming that blitzes leave the defense susceptible to explosive plays)? Second, how often (and why) do offensive coordinators try lower-percentage, but potentially explosive plays in their own five-yard line?

While there is always some degree of risk and uncertainty in play calling regardless of field position, play calling near either end zone is particularly interesting because of the magnified risk and reward for the offense and defense. Under these conditions, there is likely an increased potential for cognitive biases to creep into a coordinator’s play calling.

My hope initially is to lay out some basic propositions from prospect theory — a theory of risky decision making — for play calling when an offense is backed up inside its own five-yard line. Then we might have some ground work to test hypotheses using drive or charting data from the 2013 season.

Prospect theory argues that decision makers will accept a higher degree of risk within the domain of losses relative to an equal decision in the domain of gains. Because a decision maker’s risk propensity is heavily influenced by the way the choice is framed, the decision might fail to maximize the potential utility outcome. The standard model of expected utility decision making instead hypothesizes that individuals evaluate potential gains and losses along a single utility curve as opposed to one each for gains and losses frames. Furthermore, the value curve for losses is steeper than for gains, meaning that the subjective pain for a loss is larger than for an equivalent gain (according to the classic example, this means that losing $100 hurts more than gaining $100 feels good). In effect, a decision maker’s attitude towards risk is heavily dependent upon whether they evaluate their current position in terms of gains or losses.

There are many, many potential applications of prospect theory in football (which Stevieyo explored in this excellent two-part look last season), but below are some thoughts for when an offense has the ball within its own five-yard line:

It’s easy to imagine that an offensive coordinator would be in a losses frame in the above situation, as he evaluates his status quo based upon field position. The offensive coordinator is likely framing his choice of play call by thinking about the 95 or more yards to go for a touchdown, the potential for a safety, and the risk of an easy pick-six. Prospect theory, then, might suggest that the offensive coordinator would be more likely to accept an unhealthy amount of risk than he would with better field position.

Defensive coordinators, then, would be within the domain of gains from pinning the opponent down inside his five-yard line. Why then would he risk giving up a long touchdown by blitzing or playing aggressive man coverage? According to this logic, the defensive coordinator would be far more likely to call defensive alignments that mitigate risk and are geared toward preventing big plays. After all, why try for the risky interception or sack when the probability of a 95 yard drive for a touchdown is low in the first place?

Alternatively, there are plenty of circumstances when offensive coordinators are conservative and risk averse, calling three straight rushing plays and accepting a punt. Conversely, some defensive coordinators are risk acceptant despite a gains frame and go for the kill of a safety or interception. I can think of several explanations for purely risk averse offensive coordinators and risk acceptant defensive coordinators (and you’re welcome to add to your own thoughts in the comments):

First, it’s possible that we don’t have a full picture of how a coordinator is constructing their frame—in other words, what criteria they consider when evaluating their reference point and status quo. An offense coordinator might be in a losses frame when thinking of how the offense has 95 yards to drive for a touchdown, but might be in a gains frame if they more heavily weight their 20 point lead. Based on what is more important to their frame - field position or the score - the coordinator’s degree of gains or loss-based decision making can change greatly. We can think of many other variables that could be at play, like injuries, past performance, or the time left on the clock.

Second, prospect theory is far more probabilistic than deterministic. Even in laboratory settings, decision makers were not always risk acceptant in a losses frame.

Finally, some individual coaches might have significantly different risk and valuation tendencies, making them much more or less risky, regardless of frame, than others. These are the coaches that are always willing to go for it on fourth down (even when that choice has a lower expected utility than a punt), or the coaches that always punt (even when there is greater utility in going for it on fourth down).

In the coming weeks we can take a look at the risk propensities of specific coaches, examine the thought process of specific risky coaching decisions, and test the hypotheses above.