## Wizard Recommends

Last Updated: March 17, 2022

## Introduction

This article shall look at statistics in the NCAA Division 1 Basketball Tournament, otherwise known as March Madness. The goal is to examine how far any given seed will advance. A use for such information might be to example proposition bets, but bet them at your own risk.

This page is based on the 36 seasons between the inception of the tournament in 1985 to 2022. Note that the tournament was cancelled in 2021.

## Rules

I am going to mostly assume the reader already knows the structure of the March Madness tournament, but if not, it is explained well at Wikipedia.

1. The tournament begins with 68 college basketball teams. These 68 teams are divided into four geographical regions of 17 teams each.
2. The entire tournament is single elimination. In other words, if you win, you advance, if you lose you're out.
3. The tournament starts with four games, one for each region. The losers of these games are eliminated from the tournament. After these "First Four" games, there are 64 teams left.
4. The 16 teams left in each division are ranked from strongest to weakest. The methodology for doing this will overly reward a strong team in a weak conference, so the rankings will not necessarily agree with the opinion of the betting public.
5. The best team in each region is given a seed of 1, the second best a 2, down to the 16 for the 16th ranked team.
6. The winners of the First Four games do not necessarily vie for the 16 seed spot. In 2022, for example, the First Four spots were for 11, 12, 16, and 16 seeds. The reason for this is complicated, but has to do with there being different conferences and the NCAA having conflicting interests between rewarding the best teams and inclusion of teams from the weaker conferences.
7. Within each region, the 1 seed will play the 16 seed, the 2 seed will play the 15 seed, and so on down to the 8 seed playing the 9 seed. I do not know the term for this type of tournament. If you do know, please let me know.
8. After these eight games within the four regions, there will be 32 winners and 32 losers. The 32 winners will advance to the Second Round.
9. In each region in the Second Round, four games will be set up as follows:
• The winner of the game between the 1 and 16 seeds will play against the winner of the 8 and 9 seeds.
• The winner of the game between the 5 and 12 seeds will play against the winner of the 4 and 13 seeds.
• The winner of the game between the 6 and 11 seeds will play against the winner of the 3 and 14 seeds.
• The winner of the game between the 7 and 10 seeds will play against the winner of the 2 and 15 seeds.
10. After these four games within the four regions, there will be 16 winners and 16 losers. The 16 winners will advance to the Third Round, known as the Sweet Sixteen.
11. In the Third Round, each division shall have two games, as follows:
• The winner of the 1, 16, 8 and 9 seeds will play against the winner of the 5, 12, 4, and 13 seeds.
• The winner of the 6, 11, 3, and 4 seeds will play against the winner of the 7, 10, 2, and 15 seeds.
12. After these two games within the four regions, there will be 8 winners and 8 losers. The 8 winners will advance to the Fourth Round, known as the Elite Eight
13. In the Fourth Round, each region shall play one game to determine the winner of that region.
14. The winner of the 1, 16, 8, 9, 5, 12, 4 and 13 seeds will play against the winner of the 6, 11, 3, 14, 7, 10, 2, and 15 seeds.
15. After one game within the four regions, there will be 4 winners and 4 losers. The 4 winners will advance to the Fifth Round, known as the Final Four
16. Between the four teams left, there will be two games. In 2022, the winner of the West division played the winner of the East division. Likewise, the winner of the South division played the winner of the Midwest division. I do not know if these matchups are the same every year.
17. After these two games, there will be two winners and two losers. The two winners will play against each other in the Championship Game.

## Matchups

The following table shows many face-offs there have been among all unbalanced match-ups have that happened at least once. This does not include games where teams of equal seed played against each other. The right column shows the probability the higher ranked team won.

### Unbalanced Matchup Results

Higher Seed Lower Seed Games Played Higher Seed Wins Probability
1 2 67 36 0.537313
1 3 36 22 0.611111
1 4 64 47 0.734375
1 5 48 40 0.833333
1 6 13 10 0.769231
1 7 7 6 0.857143
1 8 75 60 0.800000
1 9 71 65 0.915493
1 10 6 5 0.833333
1 11 8 4 0.500000
1 12 20 20 1.000000
1 13 4 4 1.000000
1 16 144 143 0.993056
2 3 56 34 0.607143
2 4 7 3 0.428571
2 5 5 0 0.000000
2 6 30 23 0.766667
2 7 82 57 0.695122
2 8 7 2 0.285714
2 9 1 0 0.000000
2 10 52 34 0.653846
2 11 18 15 0.833333
2 12 2 2 1.000000
2 15 144 134 0.930556
3 4 7 4 0.571429
3 5 4 2 0.500000
3 6 75 45 0.600000
3 7 15 9 0.600000
3 8 2 2 1.000000
3 9 2 2 1.000000
3 10 12 8 0.666667
3 11 49 32 0.653061
3 14 144 122 0.847222
3 15 2 2 1.000000
4 5 75 42 0.560000
4 6 4 2 0.500000
4 7 5 2 0.400000
4 8 9 4 0.444444
4 9 3 2 0.666667
4 10 2 2 1.000000
4 12 39 26 0.666667
4 13 144 113 0.784722
5 6 1 1 1.000000
5 8 3 1 0.333333
5 9 3 1 0.333333
5 10 1 1 1.000000
5 12 144 93 0.645833
5 13 19 16 0.842105
6 7 9 6 0.666667
6 8 1 0 0.000000
6 10 7 4 0.571429
6 11 144 90 0.625000
6 14 15 13 0.866667
7 8 2 1 0.500000
7 10 144 87 0.604167
7 11 3 0 0.000000
7 14 1 1 1.000000
7 15 5 3 0.600000
8 9 144 74 0.513889
8 11 1 1 1.000000
8 12 2 0 0.000000
8 13 1 1 1.000000
8 16 1 0 0.000000
9 11 1 0 0.000000
9 13 1 1 1.000000
10 11 3 1 0.333333
10 14 1 1 1.000000
10 15 5 5 1.000000
11 14 7 6 0.857143
12 13 12 9 0.750000

## Expected Wins

The following table shows the expected number of wins for each seed, both for an individual team and for the four teams combined of that seed per tournament.

### Expected Wins

Seed Average Wins per Team Average Wins per Tournament
1 3.36 13.44
2 2.35 9.39
3 1.85 7.39
4 1.51 6.06
5 1.12 4.47
6 1.08 4.33
7 0.90 3.61
8 0.73 2.92
9 0.57 2.28
10 0.62 2.47
11 0.63 2.50
12 0.52 2.08
13 0.26 1.03
14 0.17 0.67
15 0.08 0.33
16 0.01 0.03
Total 15.75 63.0000

## Power Ratings

The following table shows what I call the power rating of each seed. The purpose of these power ratings is to estimate the probability of winning any given matchup between two teams.

To use this game, consider a game between teams x and y. The probability of team x winning is equals pr(x)/((pr(x)+pr(y)), where pr(x) = power rating of team x and pr(y) = power rating of team y. For example, consider a game between a 1 seed and 2 seed. The probability of the 1 seed winning is 959.58/(959.58 + 727.24) = 56.89%.

You might say at this point that the estimated 56.89% does not agree with the 53.73% from the table of actual games above. The table of actual results has a large margin of error due to a small sample size. The power ratings below consider every game every played and smooths out the ups and downs due to small sample size variance.

### Power Ratings

Seed Power Rating
1 1000
2 727.24
3 591.33
4 494.89
5 420.10
6 358.98
7 307.31
8 262.55
9 223.07
10 187.75
11 155.81
12 126.64
13 99.81
14 74.97
15 51.84
16 7.00

## Probability of Survival

The following table shows the probability of survival for any given team by seed number to any given round. For example, it shows the probability of a 1 seed to make the Final Four (and possibly further) to be 36.6%. This table was created by random simulation of playing over 10.5 billion tournaments.

### Probability of Survival

Seed Round 2 Sweet
16
Elite
8
Final
Four
Championship
Game
Champion
1 0.993049 0.599498 0.396013 0.301289 0.187582 0.112586
2 0.933460 0.396721 0.233093 0.162991 0.089511 0.047007
3 0.887484 0.529492 0.214007 0.140150 0.070110 0.033350
4 0.832169 0.417794 0.151471 0.093071 0.042640 0.018483
5 0.768372 0.458565 0.285638 0.104375 0.043830 0.017334
6 0.697333 0.366289 0.214497 0.070895 0.027233 0.009808
7 0.620753 0.346200 0.166929 0.049700 0.017390 0.005680
8 0.540654 0.274176 0.121864 0.032481 0.010286 0.003028
9 0.459346 0.214518 0.087127 0.020606 0.005855 0.001540
10 0.379247 0.165106 0.060571 0.012559 0.003164 0.000735
11 0.302667 0.101592 0.038775 0.006936 0.001525 0.000307
12 0.231628 0.073554 0.024599 0.003712 0.000697 0.000119
13 0.167831 0.032295 0.003384 0.000846 0.000131 0.000018
14 0.112516 0.020419 0.001657 0.000333 0.000041 0.000004
15 0.066540 0.003664 0.000373 0.000055 0.000005 0.000000
16 0.006951 0.000117 0.000002 0.000000 0.000000 0.000000

## Championship Winner

The following table shows the probability that the winner of the Championship Game will be any given seed number. This table was also created by random simulation. The probabilities are four times those for in the table above for winning the championship game, because there are four teams for each seed.

### Championship Winner

Seed Probability
1 0.450345
2 0.188027
3 0.133401
4 0.073933
5 0.069334
6 0.039231
7 0.022720
8 0.012112
9 0.006158
10 0.002938
11 0.001230
12 0.000477
13 0.000074
14 0.000018
15 0.000002
16 0.000000
Total 1.000000

Please take all the above with a tablespoon of salt before using it to bet with real money. Absolutely don't use this to bet an individual game. For proposition bets, that take multiple games to resolve, please still be careful. Changes in NCAA rules allow players to change teams more easily and this may cause more parity between the seeds. Remember, my data goes back to 1985 and it may not be appropriate to consider such stale data to make bets now.

To be honest, I considered not putting up this page at all, as I'm not sure it will help players make good bets. However, I put a LOT of time into the analysis and didn't want to not produce something from it.