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.