I got to thinking about how often games come down to luck. Obviously, defining luck in some strict sense is hard to do, but it's commonly accepted in this field of studying sports to label close games and overtime games as lucky. Teams that win a lot of close games aren't usually the great teams, nor are they usually the bad teams or the average teams. They fit no pattern. They often don't repeat the performance from one season to the next either. Winning close games appears to be luck.
If we define luck as winning close games and going into overtime, we then have to define a close game. Is it one decided by three points, as the NBA News does? Is it two points, like last night's game? Or is it one point? Since I can't go through all the games and determine which ones were determined at the buzzer, I have to define some cutoff and I have decided that games decided by one point will be called lucky games. This isn't always true because a final three at the buzzer by the losing team to get it to a one point difference isn't really all that lucky. But it happens less for one point wins than for two or three point wins.
The reason I defined one point to be the cutoff, however, comes down to explaining an effect I mentioned in the Los Angeles Clippers comment of the Basketball Hoopla. There, I noted that, if you apply the using all the winning scores vs. all the losing scores, you don't find an expected winning percentage of 100%, which is, of course, what you get when you compare winning scores with losing scores. You actually find something like 90%. At the time, I dismissed the result as a fluke you get by applying a method incorrectly. I still think it is applying the method incorrectly, but one might look at it as a way to determine how much luck is in the game.
Since I have begun to move toward replacing the Pythagorean Method with the Method, I am going to apply it towards this problem. If we look at all the winning scores and losing scores of the NBA season thus far (454 games), we find an expected winning percentage of 91.5%. (The calculations are here. ) This means that looking at just the scores of the winners and losers over the course of the NBA season and applying them directly into the Correlated Gaussian Method underpredicts the 100% winning percentage by 8.5%. This implies that 8.5% of games are decided by luck.
Does this make sense just by looking at close games and overtime games? Actually, yes. Up through games of last night, 1/8/96, there have been 20 games decided by one point. There have been 27 (or 30 because I have two sets of numbers here) overtime games. If we say there have been 47 lucky games, then this corresponds to 10.4% of games decided by luck. This is pretty close to our 8.5% figure above and strongly indicates that between eight to ten percent of all NBA games come down to luck.
This result surprised me a bit. The fact that one out of every 10 or 12 games is decided principally upon luck seems remarkable. I wouldn't think that it would be this high for football, for instance. For a team playing 82 games in a season, this means 7 or 8 games every year that they just got lucky to win.