On game theory and college football

Like many OTE posters and contributors, I am an academic by profession. As someone trained in both history and political science, I had some exposure to game theory, which is a way of using mathematical modeling to predict human behavior under various sets of circumstances and with varying degrees of information.

At the heart of game theory is the notion of risk versus reward. Social scientists use the fancy phrase “expected subjective utility,” which is an overly complicated way of saying, “What is your expected outcome if you act X in situation Y?” »

The best-known game theory contest is the so-called “prisoner’s dilemma”. The premise of the prisoner’s dilemma is that each of the two players is a suspected criminal who has been detained for questioning by the police. The police have enough evidence to convict both players of a minor charge (which will result in a short prison sentence for both). But to convict the most serious accusation, the police need at least one of the players to confess – find his partner in the hope of being pardoned. If the two suspects remain silent, they each receive a short prison sentence. If one of the suspects confesses, while the other remains silent, the one who confesses is free, while the one who remains silent receives a long prison sentence. Whether both the suspects confess, then both serve a prison sentence, but a shorter sentence than they would have served if only one of them had confessed.

Cooperate = “keep silent”, betray = “confess”

In a unique version of the prisoner’s dilemma, the logical choice for each player is always to “defect” – to confess to the police. This is because the result for this player is still better if he confesses, regardless of what the other player is doing.

However, if these interactions are repeated (we call these “iterated” or multi-round contests, because social scientists never use simple words when complicated words will), they are influenced by what is called “the shadow of the future”. My favorite study of game theory is Robert Axelrod’s 1984 book The evolution of cooperation. Even though he was working at the University of Michigan when he wrote it. Axelrod points out that in a situation where players expect to have say again interactions, cooperative patterns can emerge, as the overall outcome for both players will be better than what either would receive if they repeatedly stab each other. One of the case studies he uses to illustrate this is the emergence of a series of informal, yet highly effective, localized truces between German and Allied soldiers in the trenches of World War I. It’s a fascinating chapter, and I highly recommend it. to anyone interested.

The Christmas Truce of 1914

German and British soldiers chat and exchange gifts on Christmas Day 1914. Before they go back to trying to kill each other like civilized people.

So what the hell is this post doing on a college football fan site? Am I lost? Am I drunk?

No, and unfortunately no. There is a point to this, I promise.

Watching football as a fan offers many opportunities to observe the decision-making processes of individuals in both competitive and, oddly, cooperative situations. It’s a great opportunity to observe how well coaches manage complex tasks such as balancing risk and reward or, in the case of explosive games, steering themselves through a version. iteration of the prisoner’s dilemma.

They are two slightly different things. And, my friends, I must point out that, in the humble opinion of this writer, college football coaches, even those considered to be among the best in the business, are not very good at either other.

Let me offer two illustrations, and I’ll start by choosing my own team. During the fourth quarter of the Wisconsin game, after Wisconsin scored a touchdown to cut Ohio State leading at 45-14, Ryan Day fired CJ Stroud and the entire OSU first-string offense to the field. The result was a precise and methodical walk, culminating in a touchdown pass from Stroud to Emeka Egbuka. From a purely clinical and technical point of view, it was a beauty.

As an Ohio State fan, I didn’t enjoy this drive as much as I should have, because with each shot I held my breath, staring at the screen, anticipating that when the play was over, one of OSU’s important offensive cogs would be lying on the ground clutching one end in pain. When Ohio State scored, my emotional reaction was not happiness, but rather relief.

This is because this reader, in my opinion, showed a very poor risk-reward calculation. The value of scoring one more touchdown against an already battered Badger team was outweighed by the risk of player injury that OSU will need to be 100% healthy later in the season. When the CFP committee meets to do the playoff seeding, it will make no difference to them if the score for that game was 45-14, 45-21 or 52-21. A moment comes when the point has been made.

So Ryan Day has work to do here.

But his risk and reward shortcomings mean nothing when paired with those of Greg Schiano. Since his return to Rutgers at the start of the 2020 COVID season, Greg Schiano committed enough flagrant violations of the basic assumptions of game theory to get him thrown out of a freshman political science seminar.

Greg Schiano

Never studied game theory.

Football competitions between very different teams are, in many ways, a wonderful example of an iterative prisoner’s dilemma competition, because, however strange it may seem at first, the interests of the two teams overlap in a way who should make cooperation possible. The favored team want to build up a sufficient lead to impress the pollsters, knock their rookies out of the game and provide their substitutes with useful experience. The underdog would like to not get hammered in a mud puddle, so he can focus his limited resources on the games he has a real chance of winning.

The informal, unspoken gentleman’s agreement in such games usually goes something like this: Both teams do their best early. But when the superior team’s talent has had a chance to show itself, and they’ve built an insurmountable lead, they pull their horns, pull their chokes, and don’t unnecessarily rub the nose of the weaker team in mud. That doesn’t mean they’ve stopped trying. If your backup quarterback throws a touchdown, or your third-string running back breaks up a big winner, so be it. But most fans can tell when a favorite has taken their foot off the gas pedal.

In return, the weaker team does nothing to embarrass the team that shows them mercy. Again, that doesn’t mean they’ve stopped trying. It might even be acceptable to leave your entries against the favorite’s saves. But you don’t dive deep into the bag of tricks to try and get some cheap scores, because a) It could mean the next time you play against that favorite team, they are determined to grind you to stick, and b) Because it’s really, really dumb from a game theory perspective.

This is where Greg Schiano’s disrespect for the teachings of game theory becomes apparent. He has a well-deserved reputation for storing plenty of clever plays, some of which are actually quite clever (some less so, like whatever play he attempted against Michigan in the first half of the 2021 game.) . But he has an equally well-developed track record of picking bad times to execute them.

Draining your sleight of hand arsenal in a match against a huge favorite is, from a risk-reward standpoint, a bad idea, especially when you’re already way behind. Why? Because even if each of them works perfectly, the result is that the underdog loses by four touchdowns, rather than six.

But what if, instead, the underdog keeps those plays secret until the right situation to use them emerges in a match against a team closer to their weight class? A well-timed sleight of hand that catches an opponent off guard when the underdog team is trailing in a close game could be the difference between victory and defeat. And every win the underdog coach can pick up brings him closer to his next contract and allows him to continue Sisyphus’ work of building a winning program at Rutgers (or, you know, anywhere).

I will therefore conclude this treatise with an appeal to fans of all programs, titans and lowly underdogs. If you’re a fan of an underdog program, send your coach a copy of The evolution of cooperation, and urge him to familiarize himself with the concept of the iterated prisoner’s dilemma. If you’re a fan of a power program, implore your coach to wrestle with the vital concepts of risk vs. reward, and know when the time is right to swaddle your vital first-team players in bubble wrap and wrap them. stow away safely on the bench where they belong, especially in the fourth quarter blowouts.

Unless, of course, it’s your most hated rival you’re blowing. Because nothing is more fun than running over these guys. This is also part of our sport.

Sharon D. Cole