Sour Grapes

Friend of The Pickle Justin King called my attention to this column, by Joe Posnanski, which is an oldie but goodie: the Yankees buy championships.

One of his main points is that baseball is better at hiding competitive imbalance than are other sports. Whereas in football it’s not uncommon for a great team to win more than 90% of its games, and in basketball a great team can win over 80% of the time, the best baseball teams only win around 65%. The best winning percentages in the last 100 years of pro football, basketball, and baseball are, respectively, 100%, 88%, and 72%.

Which naturally made me wonder why, and I developed a little theory that I think isn’t bad, and perhaps is of some interest: The outcome of a baseball game is determined by fewer events.

Each of the three sports can be thought of as a sequence of zero-sum events, in which each team is doing to try to do something to help it win the game, and that better teams are better at doing. In football, the event is a play from scrimmage. In basketball, it’s an offensive possession, and, ultimately in most cases, a shot. In baseball, it’s a plate-appearance.

When two evenly-matched teams play each other in any sport, what we mean by “evenly-matched” is that, on average, each team will prevail in each of those individual events roughly an even number of times. Perfect example: The 2008 Wimbledon Final, in which Nadal won 209 points, and Federer won 204. The greater the disparity between the two teams, the greater the probability that the better team will prevail in any given trial.

And here’s the rub: For a given probability that the better team will prevail in any given trial, the probability that team will win the whole game is higher the greater the number of trials. And there are fewer trials in baseball than there are in other sports.

In football, each team runs about 70 plays from scrimmage. In basketball, each team has the ball about 100 times. But in baseball, the average game sees each team send about 40 players to the plate.

It’s just a shorter game. There are fewer random trials of an event with probability p. And that means that it’s less unusual for a bad team to beat a good one.

That, and the fact that there are Zach Greinkes on Kansas City Royalses. And I hate the Yankees. And thank you, Peter, for taking me to my first ever world series game.