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Wednesday, November 14, 2012

Alabama is only mostly dead

You don't have to look far to find a news article telling you how Texas A&M dashed Alabama's title hopes. In the end that may be true, but for now, Alabama is only mostly dead. 

To get back in the race, Alabama needs at least two of the currently undefeated teams to lose. To figure out the chances of that happening we first estimated probabilities for each team staying undefeated. The model gives Kansas State a 72.3% chance of winning out, Notre Dame a 41.6% chance and Oregon, with the toughest road ahead, a 56.0% chance. 

There's a big difference between mostly dead and
all dead. Mostly dead is slightly alive.
In this scenario, there are eight possible outcomes - they all stay undefeated, they all lose, one loses (x3), and two lose (x3). The probability of all three winning out is .723*.560*.416=.169 or 16.9%. The probability of all three losing is (1-.723)*(1-.560)*(1-.416)=.071 or 7.1%. For one team losing it comes out to 43.3% and the probability of two teams losing is 32.7%. Alabama needs two teams to lose (32.7%) or all three (7.1%), so there is a 39.8% chance that the Tide will again control their own destiny.

But then the Tide have to exploit that opportunity. The Tide have a 73.7% chance of winning their next three games. In other words, had they beat the Aggies, they would now have a 73.7% chance of walking unbeaten into the championship game (and a 90% chance or so of getting an invitation to the game). Instead, their chances have been reduced by .398 to .737*.398=29.3%. In other words, the loss cut Alabama's title game chances from around 3/4 to 1/3.  Down, but not out.

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