Was Alabama's Blowout of Notre Dame Really Unexpected?

Minitab Blog Editor 18 January, 2013

Crimson TideIn this year's BCS Championship game, Alabama dominated Notre Dame 42-14 in a game that was never really even close. While many people felt Alabama would win the game, most expected a defensive battle. Few predicted it would have been so lopsided (and only a small percentage of those would have actually bet money on a blowout).

But should we really be surprised?  I mean, Alabama clearly outperformed expectations—but did they do so in a truly unusual manner?

How Can Data Reveal If a Victory Was Unusual?

To investigate how expected or unexpected this game's 28-point margin of victory was, we really need to know two things: what was the expected margin of victory, and what is the typical distribution of results around the expected margin of victory? 

For the expected margin, I'm going to use the final Las Vegas betting spread on the game, which was 10 points. Contrary to popular belief, the spread is not set by casinos to predict the most likely outcome but instead is meant to estimate where they can get 50% of bettors to take one team and 50% to take the other. But it turns out there is usually little difference between the two.

How accurate is the spread?  The web site http://www.thepredictiontracker.com/ncaaresults.php tracks results all season for many different statistical models, as well as the spread (or "line"), and the closing spread (called "Line (updated)" on the site) ranks near the top*.

* While this may at first appear to be an indictment of statistical ranking systems, keep in mind that the spread has the benefit of taking into account injured players, coaching changes, weather, off-field issues, and other factors. Virtually every statistical model simply uses who the home team is and the score, with some only using who won and who lost. It is remarkable that they still perform as well or almost as well as a spread that can account for all of the other factors.

An Unusual Margin of Victory?

Past results indicate the the difference between the spreads and the final margin of victory is normally distributed, and from the site we see that MSE for the spread is 237.353.  Taking the square root of that, we get a standard deviation of 15.4.  That number is much, much larger than most people would have guessed. Think of it in these terms: if two teams had a spread of 0 (meaning it is a toss-up for who would even win the game), and one of the teams won by two touchdowns, then that result is not even a single standard deviation away from the expectation. In fact, this Distribution Plot illustrates that in that scenario there is over a 36% chance that one team will win by at least two touchdowns:

Odds of 2-Touchdown Victory

So exceeding the spread by two touchdown is not a very unusual occurrence at all—in fact, it likely happens multiple times each Saturday, typically with analysts having strong changed of opinion about the quality of each team. 

But Alabama beat Notre Dame by 28 points, with a 10-point spread, so to answer our original question we have to look at how unusual either team beating the spread by 18 points would be. To do so, we'll simply use Minitab Statistical Software make a new Distribution Plot:

Odds of an 18-point Difference

So the odds of either team beating the spread by 18 points are a little over 24%, meaning the result we saw in the BCS Championship Game isn't that unexpected...it would be expected to happen about 1 in 4 games! 

Now you COULD have wanted to know only the odds of an Alabama blowout by 28 points or more, and not cared about an equally unexpected performance from Notre Dame, in which case of course the odds are about 12%, or 1 in 8 games.  Still, I think it makes clear that the result of the game was not nearly as unexpected as most commentators make it out to be.

Does Bowl Game Data Reveal Any Surprises?

Since we've now established that Alabama-Notre Dame was not the most surprising result, I think it's worth seeing the distribution of results from all bowl games to see if any were truly unexpected:

Boxplot of All Bowl Games

See that outlier waaaaayyyy out on the right there?  That occurred in the Hawaii Bowl between Southern Methodist and Fresno State.  Perhaps after consuming too much at a luau the night before, the Frenso State Bulldogs—a 13-point favorite—were defeated 43-10. 

The odds of either team in a game beating the spread by 46 points is less than 0.3%.  Now that's unexpected!