Loss Aversion in the N.F.L.

Football coaches are known for being extraordinarily conservative when it comes to calling a risky play, since a single bad decision, or even a good decision that doesn’t work out, can get you fired. In the jargon of behavioral economics, coaches are “loss-averse”; this concept, pioneered by Amos Tversky and Daniel Kahneman, holds that we experience more pain with a loss of x than we experience pleasure with a gain of x. Who experiences loss aversion? Well, just about everyone: day traders; capuchin monkeys; and especially football coaches.

Which is why the last play of yesterday’s Chiefs-Raiders game was so interesting. With five seconds left, Chiefs coach Dick Vermeil had a tough decision to make. His team was trailing by 3 points with the ball inside the Raiders’ 1-yard line. If the Chiefs ran a play and didn’t score, they would likely not have time for another play and would lose. If they kicked the easy field goal, the game would go to overtime — and even though the Chiefs were playing at home, the Raiders had moved the ball easily late in the game and Vermeil, as he would later admit, was scared that the Raiders would win the coin toss in overtime and promptly score, winning the game without the Chiefs ever having a chance.

In retrospect, it wasn’t all that tough of a gamble. Choosing between a) a very significant gain if his team could accomplish the relatively simple act of moving the ball two feet; or b) a shadowy outcome that seemed as likely to end in loss as in victory, Vermeil did what most of us would probably do if we didn’t have several million people peeping over our shoulders, ready to criticize us: he went for the touchdown.

Vermeil sent in a running play, and Larry Johnson dived into the end zone, and the Chiefs won. The cover headline on today’s USA Today: “Chiefs’ Bold Gamble Hits Pay Dirt at Home: Kansas City shocks Oakland with touchdown after forgoing typing field goal on last play of game.”

The fact that Vermeil’s decision became the lead story is one good indicator how rare it is for coaches to take such a risk. Here is what he later told reporters: “Wow! I was scared. I just figured I’m too old to wait. [Vermeil recently turned 69.] “If we had not made it, then you guys would have had a lot of fun with that. It was not an impulsive thing. It was the right thing for us to do.”

Congratulations to Vermeil for making a good choice that turned out well. Here’s hoping a few of his colleagues will be envious enough of the attention he gets for making this wise gamble and follow suit.


Well, one could argue that Vermeil was actually trying to regain a previous loss--the lead. KC was up with 8 min to go in the fourth. Oakland marched down the field and scored the go-ahead touchdown with 1:45 to go. Now we will never know this, but its possible Vermeil had already "incorporated" the win (we assimilate gains more quickly than losses), and was therefore defending or regaining it with that risky call at the end. I wonder if we looked at a large numebr of these types of situtations where the team acting risky had just given up the lead rather than situations when they have been behind all day if we would find risk-seeking behavior in the former while risk-averse behavior in the latter...just a thought.


Actually, Vermeil's running play was even more clever than you give him credit for. Five seconds is plenty of time to try a quick pass - if incomplete, the clock will stop and there will still be time for a field goal try. This is the strategy the T.V. announcers assumed the Chiefs were using. The Raiders were probably assuming it too. The running play would run out the clock if it failed, so it was extremely risky. But this is precisely why it worked - it took the Raiders' defense by surprise. Nobody expects an N.F.L. coach to do something so brave!


Actually, bp32, your intuition is pretty much what Kahneman/Tversky formalized - to put it simply, they argue people are risk-averse in gains, but risk-seeking in losses. It all depends on the decision-maker's reference point. (Sorry if you're already familiar.)




I agree this seems like an example of someone resisting loss aversion and experiencing a good outcome. But when I analyze it from an expected utility perspective, it doesn't quite look like loss aversion. Let 1=victory, -1=loss and 0=temporary tie. Going for the touchdown is a gamble with 40% chance of (1) and 60% chance of (-1). Going for the field goal is a two-stage gamble. Part 1 has 80% chance of 0 and 20% chance of –1. Part 2 has 30% chance of 1 and 70% chance of –1. So FG=24% chance of victory and TD=40% chance of victory.

So the EU of going for the TD is greater than the EU of going for the FG. I guess where the loss aversion comes in is that in the VERY short run (the first play) if you go for the TD, your risk of losing is greater. Most demonstrations of loss aversion don't have this temporal component. But I agree that loss aversion would lead a coach to choose the option that has the lowest p(loss) on the very next play.

My favorite example of someone resisting loss aversion and experiencing a positive outcome is the story of Aron Ralston, the hiker trapped under a boulder who was willing to accept a sure loss (amputating his arm) in order to minimize the risk of a greater loss (death). He was not “risk seeking for losses.” This is very unusual (like the coach) and probably saved his life.




Yup, sorry if I wasn't clear but yes, I was essentially arguing (following K&T) that Vermeil's reference point may have been the recovery of a loss and not the prospect of a gain...


Unfortunately, it appears that the sports media is equally loss-averse as NFL coaches. It has characterized Vermeil's decision as a "big gamble," when it is not. Kicking a field goal and going to overtime -- where your chances of a win are basically 50/50 -- is really a bigger gamble than trying to go one yard for the win. This perpetuates loss aversion.

So while Vermeil struck a blow for modernity, the media's characterization of his decision has disappointed.

ps. The Tuesday Morning Quarterback (aka, Gregg Easterbrook, Brookings fellow) has been lamenting the loss aversion of NFL coaches for many years. He is now writing (as TMQ) for NFL.com.

Ken D.

Devotees of both football and freakonmics might enjoy John T. Reed's Football Time Management; http://www.store.yahoo.com/johntreedcom-store/footclocman2.html.
He doesn't make it easy to get, but libraries or used book services should have it. He analyzes clock management and related subjects with a high degree of logical clarity. For example, there is reason to believe that he is responsible for the trend in recent years for a trailing team to call time outs on defense with substantial time left, rather than hoarding them until they get the ball.

Robert Schwartz

Yet another reason why I hate the NFL.


I'd like to suggest that aversion to loss is biologically based. I tend to remember losses more than I remember successes. Losses tend to hurt more than successes tend to heal.
In the book “Tipping Point” (sorry to cite another book) the author(s) note that a person treated with contempt is more likely to be sick, from a cold or other maladies. This suggests are biological reaction to a negative event. (This is not precisely on point, but a loss and being treated with contempt are both significantly negative). My observation is that the opposite is also true, i.e., a person that acts with contempt tends to gain strength from such conduct. For example, dominant chimpanzees tend to have a higher level of testosterone, indicating the act of domination increases help hormone levels. (I understand that there are other explanations, i.e., that dominant chimps started out with higher levels of testosterone, which allows them to be dominant).
I wonder if anyone has seen any biological evidence to support inference from my experiences.


Bob Davis

Here's hoping a few of his colleagues will be envious enough of the attention he gets for making this wise gamble and follow suit.

But if that were to happen, then it wouldn't be rare enough to merit the attention of the press, and so it would make no sense to use that strategy as a way to seek attention.


I too agree that Vermeil's decision was less risky then the ESPN talking heads would have you believe. I wish that more coaches thought like that. Risk aversion seems to be second nature to most professional coaches. Fortunately, this leaves the fans of the game frustrated and scratching their heads on a constant basis. As part of this discussion, I would like to quantify this line of thinking: whenever a QB goes way downfield, four events can happen. 1. The ball is caught by the receiver, 2. The ball is intercepted by the covering back, 3. The ball lands harmlessly on the ground or 4. There is a pass interference call. I seem to think, based upon no scientific study at all, that there is a 25 % or a 30 % shot that the team throwing downfield will get a pass interference call in their favor. If that is true, which I have every reason to believe that it is, why are SOME (not all) coaches so risk averse to throw downfield? Great postings everyone!


Larry Horse

Yeah, it seems like the right choice. If you figure that the Chiefs would probably have a 50% chance of winning in OT and say 90% chance of the field goal being successful, then they were looking at a 45% chance of winning by kicking the field goal. With a good coach who can trust his players, I'd say that the probability of moving the ball 1 yard into the end zone would be at least 50% on a given goal line play, so I wouldn't criticize his move.


It more complicated that just making the right choice. I don't have the odds, but I've watched enough football to know that Larry Horse's numbers are about right. Thus the right choice to increase Vermeils chances of winning is to go for it.

But it is interesting that the best odds to avoid humiliation in national newspapers would be to kick the field goal. Why? Kick field goal - no one would critisize. Loose the toss and Oakland wins - well bad luck. Thus the odds break down as 40-50% chance of humiliation if go for it, near 0% chance of humiliation if kick field goal.

So the interesting choice is that Vermeil chose the right choice for the team over at the expense of risk to himself. Something that is rarely done.


The study of loss aversion seems intersting. How is loss aversion tested, what are the models for understanding it? I mean, not as questions to discuss in a comments column, but any recommended further reading? Is anyone exploring rational explanations for loss aversion?

So, the "rational" evaluation is P*L (probability, loss). Loss averse individuals, what, they add some meaningful exponent to loss (so large losses are magnified a bit compared to smaller losses)?

Maybe this isn't so irrational. Perhaps we're just trying to avoid something like ruination? But while that could explain aversion to large risks, it should be accompanied by an aversion to small risks too. So why might risk averse individuals discount ruination with small risks?

It's certainly harder to contemplate going broke when you buy a 1 dollar lottery ticket; it's definitely easier when contemplating a large investment. But maybe that's no great detriment. Maybe we can temporarily ignore ruination when buying the $1 lottery ticket, because we can always modify our behavior as we approach ruination, when we have more info. With the large investment, there will be no opportunity to modify your decisions later.

This isn't thoroughly satisfying, still some hiccoughs. But, any potential here?


Don't Slog To Blog.

Chiefs win, Vermeil cries and everything is fine with the world!

King Kaufman

14. razdoctor has it right.

The conversation about risk taking and loss aversion is a little off the point. NFL coaches aren't averse to loss as much as they are averse to being blamed for loss. Gregg Easterbrook, "TMQ," cited above, has made this point often.

What makes Vermeil's move so unusual isn't that he took a gamble -- as others have pointed out, kicking the field goal would have been the riskier move, the decision less likely to result in a win -- it's that he put himself in position to be have the blame fall squarely on him if his team lost. That blame being misplaced or ill-informed would make it no less heavy.

Here are some better figures for Larry Horse's equation in 15. The chance of hitting that field goal is closer to 100 percent than 90. Last year, there were 1,103 PAT attempts -- which are two yards longer than this field goal would have been. 1,095 of them were good, 8 weren't. So the chance of winning in overtime would be .993 x .50 = .496. I'm comfortable calling that 50-50.

According to footballoutsiders.com, the leaguewide success rate on fourth-and-1 this year is 65 percent. (The play was first-and-goal at the 1, but the clock situation made it equivalent to a fourth-and-1, since it was make 1 yard or lose.) The Chiefs' success rate on third- or fourth- and 1 or 2, the closest analagous stat that has a meaningful sample size, is 68 percent. (The Chiefs are 6-for-6 this year running on fourth-and-1.) The Raiders are a below-average defense, and they were tired and on their heels at that moment, the Chiefs having just driven downfield in the no-huddle two-minute drill. Plus, they were looking for a pass, as explained above.

The Chiefs' likelihood of success by going for it was almost certainly well north of 70 percent. It would have been plum stupid to kick that field goal if you're thinking in terms of loss-aversion. If you're thinking in terms of blame-aversion, though, it would have made sense. That's why other coaches most likely won't be following Vermeil.


DonXML Demsak's All Things Techie

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"It would have been plum stupid to kick that field goal if you're thinking in terms of loss-aversion. If you're thinking in terms of blame-aversion, though, it would have made sense."

I agree. It's a stretch to apply loss aversion to the example since p(loss) is actually greater with the field goal than the touchdown attempt.

It's an excellent illustration of the fact that even though Decision Science 101 says "bad outcomes don't imply bad decisions," try telling that to grouchy Monday morning quarterbacks.

The coach chose the utility maximizing outcome instead of the blame/regret minimizing one. But you can bet your bottom dollar that if it had failed, he would have been trashed for making a "bad decision."


To be clear, and to partly respond to Thomas' question, T & K never said that loss aversion was about experiences (though they speculated). They merely said that losses LOOM larger than gains, such that people treat losses as bigger than gains of an equal magnitude when *choosing* what to do. In other words, if somebody were to offer you a 50/50 bet where you would win $25 or lose $20, few people (except economists) would take it because the -$20 would seem bigger than +$20 and even +$25. Kahneman discusses this, part of Prospect Theory, in his Nobel lecture (along with a lot of other interesting things). See: http://nobelprize.org/economics/laureates/2002/kahneman-lecture.html