Monday, July 14, 2008

How Not To Glean Information From Vegas Lines

What might you "learn" from this post?

Let's focus on one team, USC. USC plays 12 games this year. Their season wins line is 11, with the under being a substantial favorite; you have to lay -180 on under 11, while over 11 pays +160.

Now, using this information, and only this information, Vegas Watch calculates that USC should win 10.45 games, giving them an .871 winning percentage. How often does an .871 team go 12-0? 18.9% of the time, says the post, by simply assuming a constant winning percentage: .871^12 = .189. (This number should actually be 19.1%, but that's not germane to this discussion. I will, however, use the correct numbers from here on out.)

Using the same method, how often will an .871 win 11 games? The calculation is a little more complicated, but the probability is equal to 12*(.871^11)*(1-.871) = 33.9%.

With 19.1% 12-win seasons and 33.9% 11-win seasons, USC will go under 11 wins the remaining 47.0%. What would be fair odds on the over/under for 11 season wins? Since 11 is a push, the odds should equal the ratio of 12-win seasons to 10-and-under seasons. That's 19.1%/47.0% = +247 over, -247 under.

What happened? Somehow the fair line went from about +170/-170 to +247/-247.

I'm not sure whether .871 is really USC's true winning percentage; if it's not, that's a big reason our numbers are off. But there's another problem: the probability of winning each game is not constant. Is USC going to beat Ohio State 87.1% of the time? Are they only 87.1% favorites against East Dickhead State? Being a 7-1 favorite in every game is a lot different from being an overwhelming favorite in ten games and a slight favorite in the other two.

The lesson? Don't use short-cut math if you're putting real money down on it.

1 comment:

Garrett W. said...

He sucks at life. Lynch him.