Snake Eyes

One basic mathematical truth about college football that I have posted about is that the Vegas line is the best overall predictor of the outcome of games, but that the variance is actually much higher than fans think. 

For a large set of games with exactly the same line, the average margin of victory for the favored team is generally equal to the Vegas line. Furthermore, I have shown that the distribution of the margins of victory follows the Gaussian / Normal distribution with a standard deviation of almost exactly 14 points.

Practically, what this means is that only about two-thirds of all games (68.3%, to be exact) will end up with a final margin of victory within 14 points of the spread. Of the remaining one-third of all games, half (about one in six) will result in the favored team covering by more than 14 points, and the other half (one in six) will result in the favored team not covering by more than 14 points.

This past weekend, MSU was favored by 13 points and wound up losing by 11 points (a swing of -24 points, well over one standard deviation)

This past weekend, UofM was favored by 3 points and wound up winning by 25 points (a swing of +22 points, also well over one standard deviation)

In other words, MSU had an anomalously bad weekend, while simultaneously, UofM had an anomalously good weekend.

As stated above, if we just consider the odds of finishing above or below 14 points from the spread is about one in six, the odds of MSU and UofM having such as bad/good weekend is no better than one in 36 or 2.8%, which is identical to the odds of rolling snake eyes with two dice in the game of craps. 

(Based on the actual numbers from the Normal Distribution, the odds of actually 2.5%, but who's counting.)

Even worse, the actual margins of victory were larger than just one standard deviation, and if I plug those numbers in the right formulas, the odds of such a miserable weekend for Spartan fans is actually much, much lower. It works out to be 5.5% x 7.7% = 0.39% or 1-in-250 or so. 

That is roughly equal to an upset where the spread is 37.5. The second biggest upset in recent history was Syracuse's 2007 upset of Louisville (-37). Based on some math that I did, an upset of this magnitude should only happen about once every 50 years.

The put things in further perspective, by some estimates, the "trouble with the snap" ending to the 2015 Michigan-Michigan State games only had about a 0.2% chance of happening. So, an outcome of the magnitude witnessed by Spartan fans or Wolverine fans who are into schadenfreude this weekend is only twice as likely as MSU's last second win in Ann Arbor in 2015.

So, if MSU fans think that the weekend was particularly unpleasant (or to any Michigan fans who this that this is all just normal), it is not likely to be repeated any time soon.

As a final bizarre tidbit, if we consider the higher odds of rolling snake eyes, that is roughly equivalent to the odds of an upset in a college football game where the spread is 27 points. The current spread of this weekend's MSU-UofM game is now right around 25 points. Let's just hope that the Spartan's luck will turn around soon.