TAMU over N.Iowa in Overtime!

Even as one of the proudest members of the Fighting Texas Aggie Class of 2004, I have become accustomed to losing.  If you followed Aggie Sports from 2000-2004, you know what I mean.  I still have faith in our boys, but giving up on Texas A&M when they were trailing Northern Iowa by 12 with 44 seconds left in the fight for a Sweet 16 berth was nothing unusual for me.  However, what followed in the last 44 seconds was beyond unusual:  here's a screenshot courtesy of the guys over at fivethirtyeight.com, that I borrowed from the CBS summary of the game.

Writers often describe such comebacks as "Miraculous", and they were quick to do so again here.   Such events are so improbable that they surely do seem impossible.  But how many times, upon seeing a particularly spectacular comeback, have you rhetorically waxed: "Holy shit, what are the odds?" Well, it's difficult to say with certainty in extreme cases, but let's assume the worst case of estimates I've seen: 99.99% for N.Iowa or a 0.01% chance of victory for the Aggies*.  So, perhaps it's roughly 1:10000, or a one in 10000 chance.  Yet, through a series of unlikely events, a comeback happened.  And as an Aggie Fan, I thank God it did.

While I am a spiritual person (even when not watching sports), I know as a mathematician that observing such a comeback is not as miraculous as one might think.  Seeing such a comeback in the NCAA tournament is an inherent part of the wonderful misery that is "March Madness".  There are entire books on the topic, but let me attempt to convince you that observing a 1:10000 chance in the history of the NCAA tournament is more probable than you might think.

The magic (or miracle) is in the law of large numbers.  By the end of this year, there will have been a lot of NCAA tournament games.  By complement logic (Total teams - Total Champs), I believe there will be 3048 games played since 1939.  That's a lot of games!  A one in 5000 chance corresponds to 0.0001 probability.  According to the solution to this standard probability problem, the probability that a 1:10000 comeback like this NEVER happens from 1939 through 2016 would be 73.7%, so the odds of at least one would be 26.3%, better than a 1 in 4 chance!  However, the fact that it happened to my Texas Aggies still feels like a wink from God.

*Note:  If instead go with Ken Pomeroy's models, his 0.03% chance or 1:3333 corresponds to a 40% chance of observing such an improbable outcome at least once in NCAA tournament history.