Tuesday, May 10, 2011

Basketball Stats

One evil effect of the computer is that now basketball commentators can lard their broadcasts with all sorts of statistics, including some pretty lame ones (JJ shot 36% from the three point line in the regular season, but so far in the playoffs he is only 1 of 9, for 11%).  While my son and I were watching the Bulls-Hawks game tonight, one of the announcers stated with apparent surprise that the team that went ahead 3 to 2 (games) in a seven games series had an 83% chance of winning the series.

Should that surprise us?  If the teams are perfectly evenly matched, so that in the long run they should each win the same number of games, then the odds of winning an individual game are 50% for each team, and team with only 2 wins should have a win fraction of .50 x .50 = .25 and the favored team should only win 75% of the time. 

My son pointed out, though, that if the 3:2 ratio of wins faithfully reflected the odds of winning an individual game, then the weaker team had only a probability of winning .40 x .40 = .16, so the stronger team should win 84% of the time - so that 83% number based on the data is pretty darn plausible.

How about the hoary old fact that no team down 3 to zip has ever come back to win.  Well, if the teams were perfectly balanced either team has a 1/8 chance of winning the first three games, so 1/4 of the series should start out that way.  Once you are in that fix, however, you only have a 1/16 chance of winning.  In reality, of course, teams are not perfectly balanced, and the home and home system almost certainly raises the home team's winning chances.  This  can be guessed to have both positive and negative effects on the likelyhood of  3-0 starts and comebacks significantly less likely.