The curious science of sports salaries

I once heard of an academic who used to do the rounds on the speakers’ circuit. He was enough of a big shot that people paid him to show up. This is how he negotiated his price. “I’ve got two talks,” he said. “A $1,000 talk and a $500 talk. I really recommend the $1,000 talk.”

The Gareth Bale saga made me think of him. As I write these words, he’s still under contract at Real Madrid—the deal with the Chinese club Jiangsu Suning has just fallen through. But his manager, Zinedine Zidane, wants him out and at some point Bale’s going to have to go. The problem is his contract: Bale earns £650,000 a week, more than half as much again as the highest paid player in the Premier League, Alexis Sanchez. Sanchez has scored just three goals for United in two years. The next highest paid player on the list is Mesut Özil, who started only roughly half of Arsenal’s games last season. All of which suggests that the process of measuring a player’s contributions to the cause by way of salary involves more art than science.

A lot of Premier League clubs would love to have Bale in their team, but most can only afford the $500 talk. Of course, the academic was joking, and the absurdity of the joke lies in the idea that people can change their value depending on how much they get paid. I say absurd, but it happens all the time. Part of someone’s value depends on how much they have been valued. When you buy Bale you buy not only his talent but his contract, which is supposed to reflect that value. The measurement bleeds into the thing being measured.

In many American sports, clubs are used to thinking about what they can get out of players of different standing—because their leagues cap how much each team is allowed to spend on player salaries. The point is to level the playing field so that both small and big clubs can compete against each other. To avoid, in other words, what happens in the Premier League, where (with a few remarkable exceptions like Leicester in 2016) only the richest teams have a chance at winning the league.

Besides improving competitive balance, salary caps have a lot of curious side effects that turn out to be fun. One of those side effects is to increase the share of a player’s value that depends on the value of his contract. Great clubs, in order to win, need great “great” players—but they also need great “mediocre” players, and some great “bad” players, too. Herzog in Saul Bellow’s novel tells stories to his daughter about the thinnest fat man, and the fattest thin man—if you’re going to compete in a salary-capped league you need to be good at making those distinctions.

Who’s the best worst player you can get? Sometimes, in the NBA, the hot free-agent can be a mid-range talent on a cheap deal, who can come off the bench for you and give you “non-negative-value” minutes—that’s the guy everybody wants. Whereas the aging superstar, like Bale, on a heavy salary is almost impossible to trade, unless you throw in sweeteners like a few promising prospects to make up for what teams call “the salary dump” of the big name.

And those side effects have knock-on effects. One of them is that the friendly arguments you have on the couch in front of the TV—not just about whether Bale is better than fellow superstar Harry Kane, but whether the young midfielder Harry Winks is better than another young midfielder James Ward-Prowse, and the tiny corrections and minor value-adjustments you make to justify those arguments, based on stats or analytics or whatever facts or insights or websites your obsessive attention to these millionaire athletes allows you to draw on—these arguments turn out to be almost exactly the kind that a good chief executive or manager relies on to put together a strong side within the constraints of the cap. So the gap between fan and journalist and manager shrinks a little. None of us really knows what it takes to strike a ball like Gareth Bale, but we’ve all got some experience of what it means to worry about money.