Some Thoughts on Success in College Basketball (with Niels Boar in mind)

[Fan701]

What does the probability distribution of success in college basketball look like?  Is it distributed like heights around some sort of mean like 5'9" in men? No, it doesn't appear to be normally distributed at all.  It appears to follow a power law with a handful of schools winning most of the national championships and going to most of the final fours.  The statistical mode for championships or final four appearances for D-I schools is, unsurprisingly, 0, but UCLA has 11 championships, Kentucky 8.  North Carolina has 20 final four appearances, Kentucky and UCLA each have 17, Duke 16, Kansas 14.  It's a world in which walking down the street you wouldn't expect to see most men be around 5'9" tall, some a bit above, some a bit below.  Instead you'd see lots and lots of people about a foot tall, a few 10 feet or 20 feet tall people, and a handful of 100 feet tall people (the Kentuckys, Dukes, North Carolinas).  What does that mean for us, for Arkansas?  Arkansas has 6 final four appearances, and a national championship.  That would make us one of the 10 or 20 feet tall people on my imaginary street.  Success seems to be autocorrelated, that is, schools that have been successful in the past will tend to be successful in the future.  It's as if the data in the time series has a memory and remembers that, say, Kentucky has been successful in the past, so they're more likely to be successful in the future, too.  This should favor us, too, to a lesser degree since we do have a history of success, though much more modest than Kentucky. 

I just posted this because I thought we all might need something else to think about rather than last night's game.