NCAA basketball tournament

It is collegiate spring break in March, thus, the NCAA men's basketball tournament is beginning this week. At time of this post, 1:20 PM CST, the games have begun. This post will cover just a few statistics associated with the 65 team, three week long single elimination tournament. I am playing in a bracket on ESPN.com with my coworkers. I know little about college basketball, but after my last place showing in the bracket last year this year is going to be based on the professional sportscasters' prognostications.

First, we will investigate random picking of winning teams starting at the 64 team start. If one flips a coin, the chances of landing on one side (say heads up) is 50 % or 1 in 2. Flip the coin a second time, there is still a 1 in 2 chance that coin will land heads up. Basic statistics have you multiply the results together for the odds of both coin flips being heads up, 0.25 % or 1 in 4. The simplest way to calculate the odds of every flip being heads up are 1 in 2^n, where n is the number of coin flips. We will apply this to the NCAA tournament. In the single elimination tournament with 64 teams, 63 games are played. The odds of picking every game correctly in a random fashion (50% odds per game) are 1 in 9*10^18 or 1 in 9,000,000,000,000,000,000!

Second, the tournament setup has teams in 4 regional brackets. Each bracket has teams ranked as seeds 1 to 16 according to their regular season record and strength of competition. The first round has the seeds playing against each other in this manner: 1 vs 16, 2 vs 15, 3 vs 14, 4 vs 13, 5 vs 12, 6 vs 11, 7 vs 10 and 8 vs 9. According to wikipedia since 1985 and institution of the 64 team bracket, the following odds apply during first round.

1. The #1 seed has beaten the #16 seed all 100 times (100%).
2. The #2 seed has beaten the #15 seed 96 times (96%).
3. The #3 seed has beaten the #14 seed 85 times (85%).
4. The #4 seed has beaten the #13 seed 79 times (79%).
5. The #5 seed has beaten the #12 seed 66 times (66%).
6. The #6 seed has beaten the #11 seed 69 times (69%).
7. The #7 seed has beaten the #10 seed 61 times (61%).
8. The #8 seed has beaten the #9 seed 46 times (46%).

Using these statistics by picking the highest seeded team through entering points 1 to 6 above in our statistics and assuming that rest of the tournament has 50% odds, the new odds of picking every game correctly is still the astronomically high 1 in 7*10^13 or 1 in 70,000,000,000,000.

Those people who do correctly pick every winner in the brackets are not using random choices, they are using educated guesses (statistics) with some luck to help them out.

Theft in West Campus

As a fellow Longhorn, I know word on the street says Austin, TX has a low crime rate for a city its size of about 1 million people. This website has the highest theft rates of various neighborhoods throughout the US according to statistics. Before living in Austin, I use to reside in Albuquerque, NM and the Duke City is thought to have a high crime rate for its 1/2 million residents. It turns out that none of the neighborhoods in Albuquerque made the list while Austin's West Campus west of the University of Texas was #6 on the list with the odds of being a property crime victim being 1 in 2!

Digging further into statistics, this website compiles FBI statistics and the two cities rank the same overall for property and violent crime. This is the way statistics work. Changing the bounds or limits of the included numbers within the calculations results in varying results. If these kinds of numbers put into manipulative hands, anything could be supported or not leading to what the population at large believes. What is more important though is public perception. I was told in Albuquerque that it was a really dangerous city and the opposite in Austin. This distorted my view of reality. As Mark Twain made famous, there are "lies, damn lies and statistics."