In our econometrics class, we recently read an article (Pay and Performance in MLB [1]) that attempted to calculate the 'worth' of a baseball player and see how that compared to his salary. In order to determine 'worth', the authors first calculated how this one player affected the team's batting average, or, for a pitcher, the strikeout to walk ratio. (I'm very liberally summarizing here) Next, they found a relationship between the team's batting average and the number of games the team won. Again, for pitchers, the stat was the strikeout to walk ratio. Finally, they found a formula for the average revenue for a baseball team given the number of games they won. This formula relies on the assumption that as a team wins more games, more fans buy tickets to their games, and the revenue goes up. So putting all that together, the worth of a player is equal to how many games he wins for his team times the revenue of the extra tickets the team sells as a result of winning those games (People who say there's no 'he' in 'team' are clearly talking about Little League, not professional baseball). It was kind of amazing how close some of these measures of worth came to the salary that the players received, and this research was done about 30 years ago. Since then, people have spent much more time and money on analyzing the worth of baseball players. For example, the book Moneyball is about Oakland A's manager Billy Beane and how he focused on unusual statistics to find players who were worth more than they were being paid. He looked into things like on base percentage and batters who worked a high pitch count, two things that my favorite Red Sox player, Kevin Youkilis, is famous for. During Youk's first two years, his batting average was an unimpressive .270, but his on base percentage was as high as .380 - about the same level as (Judas) Damon and Ramirez, but he was making less than 1/10 as much money as they were ($400,000 compared to many millions). It goes without saying that as soon as his contract is up for renewal, his salary is going to be much higher - people are starting to catch on to these 'hidden' stats, and his performance in the post season was pretty amazing.
I love seeing economics applied to very unnerdy topics, even though I think the salaries of professional sports players are a prime example of how capitalism does a terrible job of spreading wealth. But that debate is one of opinions, not numbers, and economists don't like to talk about opinions. Fortunately, there are numbers in all sports, including football, where one economist did a study on whether or not teams should go for it on fourth down [2]. In short - they should. And one of my favorite economists in the world, Bill Belichick, has taken this advice and ran with it, all the way to 3 championships in 4 years.
So I hope this convinces some people that economics isn't all math and graphs and GDP and widgets. There are lots of strange applications of the dismal science in just about every field of study. And where there aren't - you could be the first.