Wednesday, May 26, 2010

Returns to Scale in Sports

The authors of "The Wages of Wins" point out that basketball talent follows the law of diminishing returns: each additional talented player helps the team less than the player before him. Time and possessions are scarce; there is only one ball, and when one star has it, his teammates, by definition, do not. In their words:

To further illustrate this point, consider a team comprised of the top five players at each position in 1993-94. Such a team would have John Stockton (22.0 wins produced) at point guard, Nick Anderson (13.3 wins produced) at shooting guard, Scottie Pippen (20.4 wins produced) at small forward, Dennis Rodman (29.6 wins produced) at power forward, and Shaquille O’Neal (26.8 wins produced) at center. These players combined to produce 112 wins. If all these players were on the same team, though, their wins produced could not exceed the length of the regular season, or 82 victories. Hence, if we put all five players on the same team someone would have to play worse.
If you don't like the abstract concept of wins, here's an easier one: if you take the top 5 scorers in the NBA, who each average around 30 points per game, and put them on the same team, the team won't average 150 points per game. There just aren't enough shots to go around.

Similarly, adding a productive hitter to an already-talented baseball team also will decrease his productivity or that of one of his teammates. This is because top spots in the batting order are limited. Each time someone besides the No. 9 hitter makes his team's last out in a game, he and the players ahead of him end up with one more plate appearance than the players lower in the batting order. Over the course of the season, the No. 1 hitter gets about 140 more plate appearances than the No. 9 hitter. Each spot down the order gets about 15 to 20 fewer plate appearances per year than the spot preceding it (see the data for yourself). If the team's new hitter now bats sixth instead of third, as he did with his previous team, he'll get fewer opportunities to drive in runs.

Starting pitching, on the other hand, has constant returns. One star starter does not detract from another star starter. Both pitch every 5 days and, barring injury, will end up with about the same number of starts.