Thursday, January 11, 2007

I noticed something interesting in Pomeroy's predictions (warning: geeky)

First for a slightly geeky intro to the topic:

If you have slightly weighted a coin so that it lands on heads 60% of the time and tails 40% of the time, and you have to predict how many heads you will get if you toss the coin 10 times, what will you say? Obviously, the best guess is 6. However, if I ask you to predict which side the coin will land on each toss, you'll predict heads every time. So even though heads is "favored" on each individual toss, the aggregate prediction should not be 10, it should be 6.

When it comes to basketball (and other sports), people mess up this principle all the time. They look at a schedule and think, "Hmmm... we'll be favored in 12 games and underdogs in 4 games, so I predict we'll finish 12-4." But if a team is a slight favorite in 12 games, it makes no sense to predict that they'll win all 12.

Ken Pomeroy's site has a great feature where he uses his stats to give a percentage chance of victory for each team in each game, and then also provides an overall prediction for how many games a team will win. And he does the overall prediction the smart way - not just adding up the individual predictions, but looking at the percentage chance of victory in aggregate.

I just looked at it and he predicts that Indiana will end up with a 13-3 B10 record (after the Purdue game is factored in). That seems like a pretty reasonable prediction, perhaps a little more optimistic than me, but reasonable.

But here's what interesting: I then looked at the remaining B10 games and our percentage chance of victory in our remaining games. According to Pomeroy, Indiana is favored to win ALL of our remaining B10 games. EVERY one of them. According to the predictions, our toughest remaining B10 games are at Illinois (64% chance of winning), at MSU (58% chance of winning), and home against Wisconsin (61% chance of winning).

Pretty cool.

No comments: