How to Price a Baseball Player

Over the past month or so, no question has been more important in New York City than this one: “Will the Yankees re-sign Bernie Williams?” Williams is the World Series champs’ star centerfielder, who won the American League batting crown this year while developing into one of the best all-around players in the game. Given that, and given that Williams is represented by Scott Boras, the most powerful agent in baseball, it’s not surprising he’s demanding to be paid on a par with the sport’s highest-priced players. These include, most notably Mike Piazza, whom the New York Mets recently signed to a nine-year contract worth $13 million a year.

The debate over whether Williams is worth the kind of money Piazza got has focused on whether his statistics are really as good as Piazza’s (they’re not, but they’re close), whether he’s durable enough (he’s been on the disabled list six times in his career), and whether he’s really the kind of superstar who puts fans in the seats. But in some sense these issues are all immaterial. Even if Williams’ numbers were the equal of Piazza’s and even if he never got hurt, he wouldn’t be worth as much as Piazza. And the reason why is a nice illustration of the simple power of supply and demand.

Every team needs a catcher, and every team needs a centerfielder. If the Yankees don’t re-sign Williams, then, they’re going to have go out and hire a new centerfielder, just as if the Mets had not signed Piazza, they would have had to find a catcher somewhere else. But while the demand for these positions is therefore equivalent (every team needs a starting centerfielder and every team needs a starting catcher), the supply is not. There are a lot more people out there playing the outfield than there are people behind the plate. That means that catchers’ salaries are inflated relative to other positions. It also means, more importantly, that someone who’s a mediocre or even poor offensive player is often well-paid because he’s a catcher, while a player with the very same offensive statistics wouldn’t even be able to warm the bench as an outfielder.

Even in absolute terms, remember, Piazza’s offensive statistics are better than Williams’ are. And relative to the statistics of the average catcher, Piazza’s numbers are off the charts. If the Yankees don’t pay Williams $13 million a year, they can go out and get an outfielder who will produce somewhere between 70 percent and 80 percent of Williams’ output and pay him $2 million a year, leaving them $11 million to spend on someone else. If the Mets hadn’t signed Piazza, they would have had to sign a a catcher who provided 30 percent to 40 percent of Piazza’s production (if that), and would have had to pay him $2 million a year as well.

Piazza’s replacement value, in other words, is qualitatively higher than Williams’ is. There are a lot of great-hitting outfielders in the major leagues, and there are very very few great-hitting catchers. As with everything else, it’s more valuable to be one of few than it is to be one of many. Williams should stop thinking about Piazza and start worrying about how much his outfielder peers are making. Then he might have a real case.