## Notre Dame vs. Texas A&M : The Simulated Version

It's NCAA championship game time again, and I'm returning to a post I wrote in July of 2010, where I attempted to
model the NCAA championship game played between Connecticut and Stanford that same year.  The title of that post was "Connecticut vs. Stanford - Again and Again and Again...." and you couldn't blame anyone for thinking that this title could be recycled for the 2011 championship.

No such luck.  Not only was Stanford upset by gritty Texas A&M, but the fourth time proved to be the charm for Notre Dame as they bounced Connecticut out of a threepeat.  If the Fighting Irish win it will be their second championship.  If Texas A&M wins it will not only be their first championship but will also serve as the disproof of the Prodigy Theory of Coaching in NCAA women's basketball.

(* * *)

The idea behind the original post is a simple one:  one can simulate a game in a very mechanical way by simulating a possession.  Each team gets the same number of possessions, and each of those possessions only has one of four outcomes:  finishing with zero, one (a possession can end with a trip to the free throw line), two, or three points scored.

Start with Notre Dame.  Here's how the typical Notre Dame possession ends:

48.0 percent - no points scored
5.5 percent - one point scored
40.2 percent - two points scored
6.3 percent - three points scored

Here's how the typical Notre Dame opponent fares

63.2 percent - no points scored
4.1 percent - one point scored
26.0 percent - two points scored
6.7 percent - three points scored

As you can see, Notre Dame fares a lot better than their typical opponent.

Here's how the typical Texas A&M possession ends up:

48.1 percent - no points scored
4.7 percent - one point scored
39.0 percent - two points scored
8.2 percent - three points scored

...and the typical Aggie opponent....

61.3 percent - no points scored
4.7 percent - one point scored
27.1 percent - two points scored
6.9 percent - three points scored

The model also gives us an idea of how many possessions the team gets in a game.  Notre Dame gets about 72, Texas A&M gets about 70, so we'll split the difference and model a game where each team gets 71 possessions.  We'll grind out the probabilities above and model an entire game.  This is a little tricky to do, but I was able to do it about 25 times.  Here are the final results.

Notre Dame won 13 times.
Texas A&M won 12 times.

Notre Dame's biggest win was by 18 points, a 74-56 victory.
Texas A&M's biggest win was by 22 points, an 88-66 victory.

There were four wins out of the 25 that were by exactly one point.  Notre Dame won each one of those.
Out of these 25 games, 12 games were won by six points or less - in effect, almost half of the simulated games were decided by one or two possessions.

Even though Notre Dame won more games, the average margin of victory was in favor of Texas A&M by 1.48 points - when Texas A&M won, it won "bigger" than Notre Dame did.

Given the above, here's what I expect:  that there is no true favorite in this game, and that there's a very good chance that this game will be a nail-biter.  Will we see another Colson to White moment, another game for the ages?  Tune in Tuesday night and watch the non-simulated version.