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With Jamarcus Russel’s recent benching, there’s been a lot of talk about when it’s time for a team to cut its losses on a failed quarterback. I don’t have hard numbers at my fingertips, but I’d be fairly certain that if a QB isn’t playing above average football or there hasn’t been steady improvement, by the end of his second year, it’s time to move on. [Edit: Here's a good look at that very question at PFR.] There’s no question teams tend to stick with struggling QBs well beyond their expiration date, even when better alternatives exist. The real question is, why?

Let’s say you’re an out-of-town Bills fan, and before the season began you were understandably optimistic about the team’s prospects. You bought prime tickets to the January 3rd game hosting the Colts, including parking and a hotel room. Altogether the bill comes to $400. In August, this feels like a great deal.

As the season wears on, it becomes clear the Bills aren’t contenders. The coach is fired, and the upcoming Colts game is not looking promising, as the Colts appear likely be playing for home field advantage in the playoffs. Everything points toward a humiliating blowout. What’s worse, as the game approaches the weather isn’t looking good. Bills fans are always the hardy type, but the foercast is beyond bad—snow, wind, freezing rain, and bitter cold. You’re not exactly excited about the prospect of going to the game.

A few days before the game, your friend invites you to watch the game at a party to inaugurate his new palacial home theater. You’d really rather do that than actually go to the game, but you’ve already sunk $400 and it’s too late to sell the tickets. Naturally, you can’t let those tickets go to waste, so you suck it up and go to the game.

But this is completely irrational. It’s called the sunk cost fallacy.

To understand your mistake, think of your options in terms of costs and benefits. We’ll call the $400 you spent a cost of -4. Actually going to the game would be a benefit of +0, since it doesn’t appeal to you. And going to the party is a benefit of +2. Here are the options for January 3rd in matrix form:

Cost-Benefit Matrix
Option Cost Benefit Net
Go to game -4 +0 -4
Go to party -4 +2 -2

Going to the party is the better option. You’ve spent the $400 already—it’s out the door no matter where you spend your Sunday. Economists would call those $400 ‘sunk’ because there is no way to retrieve them. You’re better off ignoring the money you spent and making the best of your day.

Sunk costs play tricks on our minds. People will forego alternatives belieiving that previous costs will somehow be ‘made good.’ We all have a stubborn loyalty to our past mistakes. Studies have shown that people honor sunk costs more when they believe they have responsibility for them. Other studies have shown that people become overly optimistic about a project’s outcome when they are responsible for the sunk costs.

A famous example of the sunk cost fallacy is the Concorde supersonic passenger jet. Planned and built as a joint effort between the British and French, early in its development it became obvious it could never make money. Decision-makers pushed forward in spite of the projections because they had already invested so much in the project. But those investments were irrelevant. They’re sunk costs whether the program continues or not. Only future costs and benefits matter.

Jamarcus Russel is the Concorde of the NFL. Russel was the overall #1 draft pick in 2007. For three seasons now, he has given every indication, statistical and otherwise, that he will not become a decent quarterback anytime in the near future. Russell cost the Raiders the #1 pick, over $30 million in guaranteed money, plus many millions more in base annual salary. All of these costs, except for his future base salary, are sunk. They’re already gone and they’ll never come back, no matter how good or bad Russell turns out to be.

If Bruce Gradkowski, who makes about $400,000 per year, is the better option at quarterback, then the past investment in Russell shouldn’t matter. Starting Russel is like going to the Bills game. You thought it was going to be awesome and you invested a lot, and you just can’t bear to let that investment ‘go to waste.’

Russell certainly isn’t the only top pick who was kept under center too long. Just about every team has had a similar experience in recent memory. General managers and coaches are the ones least willing to cut their losses with bad players because they’re the ones most attached to the sunk costs. The importance of responsibility is why it makes some sense to periodically replace senior management, whether at corporation, a government agency, or professional football team. New managers are not beholden to their predicessors’ sunk costs, and are freer to make rational decisions.

You don’t have to be an NFL GM to fall victim to the sunk cost fallacy. In fact, I’d bet you’re doing it right now—go take an honest look at your fantasy roster. We fall prey to sunk costs all the time in real life too, whether it’s with a crazy girlfriend, a falling stock market investment, or a dead-end career.

There are a number of theories that may explain our vulnerability to sunk costs. Our strong aversion to losses, whether in the future or the past, might be part of the cause. Another theory is that people are sometimes acting rationally when honoring sunk costs, especially in political settings. It may be better for a decision-maker in the short-run to deny making a mistake for as long as possible.

I think the most likely explanation has a psychological basis. Almost everyone perceives themselves as rational, competent decision-makers. For example, in survey after survey the vast majority of people claim to be above average drivers, which is obviously not possible. When a situation occurs that challenges our self-perception as competent, such as when we invest in a failing project, we need to somehow reconcile the difference between our perception and reality. This difference is known as cognitive dissonance, which produces stress, anxiety, and a number of other negative emotional consequences. Honoring sunk costs is a way of avoiding the admission of error and the psychologically painful reconciliation involved.

So what should we do when faced with a sunk cost situation? The best approach is to ask yourself what you would do if the asset fell to you for free. What if you those Bills tickets landed in your lap a few days before the game? You’d almost certainly not go.

Imagine that this past off-season Jamarcus Russell suddenly showed up on the roster of some other team, say a team with an unsettled QB situation. Would that team’s coach think, “We gotta find a way to make this guy our starter?” No, of course not! The coach would rightfully think, “If he’s not as good as his $5 million base salary, he’ll be cut before I can say ‘Get me Jeff Garcia’s phone number.”