Sunday, August 26, 2007

NFL Totals and skewness

I was looking over NFL totals information today and found something interesting. In reviewing NFL regular season and playoff games from 1989 to 2006, this is what I found:

The average total was 40.23
The average game score was 41.1

Number of Overs: 2183
Number of Unders: 2254

So the average game score was higher than the average betting total, but there were more unders than overs. How is this explained?

The reason for this result is that games can go over the total by a lot more than they can go under. Let's say the total on a game is 40. The lowest possible scoring NFL game is 0-0 (a tie played through overtime). The highest possible scoring NFL game is boundless. So when a game goes over by a lot, it can have a bigger impact on the average than when it goes under a lot. A term for this is skewness. describes skewnewss as

See the link for a much deeper mathematical explanation of skewness in a probability distribution.

The lesson here is that looking at averages for betting purposes can sometimes be misleading. Remember, for straight wagers, we don't care how much we win or lose by, we just care if we win or lose. Winning by a half point is just as profitable as winning by 25 points.