GH And Petey's Timberwolves Blog

Wednesday, December 28, 2005

Variance in Sports

I ranted the other day, over at SBG's place about a fourth down and one situation during the Viking's game. In essence, the Vikes needed to score and they punted the ball instead. It was a terrible call by Mike Tice for so many different reasons. For starters, you're on about the 40, so you don't gain a whole lot by punting. Second, teams tend to be much too conservative in these situations (this doesn't just apply to Mike Tice, so I'll give him a small pass on this one) but Tice should be going for this one with 14 minutes left in the first quarter.

But the biggest reason is that YOU'RE BEHIND AND IT'S LATE IN THE GAME. Who cares if you give the Ravens good field position? If you don't score you lose. It doesn't even matter if the Ravens score or not. A loss by 1 counts the same as a loss by 100.

The reason has to do with a mathematical concept called variance. Variance is a measure of how far you fall from your average. A team who outscores their opponents by 2 points on average and has a variance of 0 will win 100% of their games (all by exactly two points). On the other hand, a team who outscores their opponents by 2 points but has a variance of 100 points will have a record very close to .500.

From this simple observation it becomes clear that a winning team would prefer to play a style of basketball that has lower variance. Conversely, a losing team would prefer to play a high variance style, since although they will get completely slaughtered in some games, they will win more frequently because of it. This is part of the reason there are lots of upsets in the NCAA Final Four tournament. The underdogs tend to shoot a lot of threes (the highest variance play in basketball). You will get a lot of them that go on to lose by 20+ points, but some will get lucky and pull off an upset.

Another similar observation is that a team which is currently losing should do things to increase variance, even at the expense of point expectation. A perfect example of this is in hockey when a team pulls their goalie. This increases the scoring chances of both teams, but obviously favors the team who is still using their goalie more. Of course, if the other team gets an empty netter, it doesn't much matter in the win column.

Of course, the converse to this is also true. A team who is ahead should reduce variance as much as possible. In basketball, this is done by slowing down the pace of the game and taking shots close to the basket. The Suns did a horrible job of this against the Wolves the other night. It's just sort of a problem with the whole team. They play high octane basketball, but have trouble slowing it down. This is part of the reason nobody really expects them to succeed in the post-season.

In the Wolves game, they got a lead, but then kept pushing the ball and taking long jumpers. This is not the proper way to handle a lead and they're lucky it didn't come back to bite them in the ass. Personally, I was happy every time they launched a 3-ball. If they make a bunch of them, it doesn't much matter because we were probably going to lose anyway, but they take the risk of going on a cold streak and letting the Wolves get back in the game.