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.

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## 1 comment:

He sucks at life. Lynch him.

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