[BostonCard]

And because I am a statistics geek, I decided to use the probabilities given in the table to simulate what would happen if we could relive the 12 NCAA tournaments that Monty was in 10,000 times (the magic of computers!)

First, given our distribution of seeds, we slightly underperformed.  In my simulations, we win at least one national championship 45% of the time (and 8% of the time we win 2 championships, 1% we win three championships and 6/10,000 times we win 4 national championships!).  The mean number of national championships we win across the simulations is 0.57.
In an additional 23% of simulations our best performance is getting to the national championship game, and another 23% of simulations our best performance is getting to the final four at least once.

In addition, the average number of total wins across all the simulations is 21.  Monty had a 16-12 record in the tournament.  In my simulations, 14% of the time we have 16 or fewer total wins.  What this tells me is that although Monty nominally underperformed his seeding come NCAA tournament time, the deviation from what would have been expected given the probabilities, the underperformance is not beyond what might have been observed by chance.

Here's a histogram of the number of wins we have in each simulation:



The arrow points to how many wins (16) Monty had.  Worse than expected, but within reason statistically.

BC

[BostonCard]

And because I am a statistics geek, I decided to use the probabilities given in the table to simulate what would happen if we could relive the 12 NCAA tournaments that Monty was in 10,000 times (the magic of computers!)

First, given our distribution of seeds, we slightly underperformed.  In my simulations, we win at least one national championship 45% of the time (and 8% of the time we win 2 championships, 1% we win three championships and 6/10,000 times we win 4 national championships!).  The mean number of national championships we win across the simulations is 0.57.
In an additional 23% of simulations our best performance is getting to the national championship game, and another 23% of simulations our best performance is getting to the final four at least once.

In addition, the average number of total wins across all the simulations is 21.  Monty had a 16-12 record in the tournament.  In my simulations, 14% of the time we have 16 or fewer total wins.  What this tells me is that although Monty nominally underperformed his seeding come NCAA tournament time, the deviation from what would have been expected given the probabilities, the underperformance is not beyond what might have been observed by chance.

Here's a histogram of the number of wins we have in each simulation:



The arrow points to how many wins (16) Monty had.  Worse than expected, but within reason statistically.

BC