Every March in the U.S. marks the beginning of the Men’s NCAA Division I basketball tournament. Dubbed March Madness, the modern version of the first round of the tournament consists of 64 teams in a single elimination bracket format. Office pools and Internet contests challenge fans to correctly guess the outcomes of all 63 games in the tournament. This is no small undertaking. In the first round of the tournament alone there are 2^{32} = 4,294,967,296 possible brackets that could result.

Statistics and probability can be used to knock this number of over four trillion down to a somewhat more manageable size. Each team is assigned a ranking or seed from #1 to #16 based upon a number of criteria. The first round of the tournament always follows the same format, featuring four games each of the following types:

- #1 seed vs. #16 seed
- #2 seed vs. #15 seed
- #3 seed vs. #14 seed
- #4 seed vs. #13 seed
- #5 seed vs. #12 seed
- #6 seed vs. #11 seed
- #7 seed vs. #10 seed
- #8 seed vs. #9 seed

### Making Predictions

Predicting the winner of each game is a complicated process that involves comparing several different variables from each team. To simplify matters, results from previous tournaments can be helpful to make predictions for the current year’s tournament bracket. The tournament has had the same 64-team structure since 1985, so there is a wealth of data to analyze.

A prediction strategy using this idea looks at all instances where a #1 seed played a #16 seed. The results from these prior outcomes give a probability that can be used to make a prediction in the present tournament.

### Historical Results

Such a strategy of picking the winner based on previous seed results is limited. However, there are some interesting patterns that start to emerge when examining the results from the first round of the tournament. For example, a #1 seed has never lost against a #16 seed. Despite a higher ranking, #8 seeds lose more often than not against #9 seeds.

The following percentages are based on 27 years of March Madness with four of the same types of matchups in each tournament.

- #1 seed vs. #16 seed – The #1 seed has won 100% of the time against the #16 seed.
- #2 seed vs. #15 seed – The #2 seed has won 96% of the time against the #15 seed.
- #3 seed vs. #14 seed – The #3 seed has won 85% of the time against the #14 seed.
- #4 seed vs. #13 seed – The #4 seed has won 79% of the time against the #13 seed.
- #5 seed vs. #12 seed – The #5 seed has won 67% of the time against the #12 seed.
- #6 seed vs. #11 seed – The #6 seed has won 67% of the time against the #11 seed.
- #7 seed vs. #10 seed – The #7 seed has won 60% of the time against the #10 seed.
- #8 seed vs. #9 seed – The #8 seed has won 47% of the time against the #9 seed.

### Other Statistics

In addition to the above, there are other interesting facts pertaining to the NCAA tournament. Since the 1985 tournament:

- Only once (4% of the time) has all four #1 seeds made it to the Final Four.
- Three times (12% of the time) no #1 seeds have made it to the Final Four.
- 14 times (52% of the time) a #1 seed has won the entire tournament.
- The lowest seed to win the tournament is a #8 seed.
- The lowest seed to make it to the Final Four is a #11 seed.

Use the above statistics at your own discretion. As the saying goes, "Past performance is not an indicator of future success." You never know when a #16 team will score an upset.