March madness

No, I’m not talking about the credit markets– I’ll take those up in my next post, I promise. But first I need to discuss something really important, namely, the men’s college basketball tournament.

A popular American tradition is betting on the outcome of the 64-team NCAA basketball tournament (I know, I’m not counting the “play-in” game). Picking the outright winner is not a hopeless task. After all, if you simply picked a team at random, you’d have a 1 in 64 chance of being right. It’s not hard to do much better than that, since some teams are much more likely to win than others. If you trust the probability assignments of Team Rankings (which I’m supposing may be as good as any), the tournament favorite (Kansas, according to them) has a 1 in 5 chance of winning all 6 of its games.

Probability of getting all the teams that make it to indicated level correct
level

probability

winner

1 in 5

championship

1 in 13

final 4

1 in 36

elite 8

1 in 435

sweet 16

1 in 9,556

1st round win

1 in 61,218

Picking both the winner and the team that will play against them in the championship round, however, is substantially harder. Team Rankings thinks there’s almost a 1 in 3 chance Kansas will make it at least that far, and a 1 in 4 chance that Memphis (their most likely opponent) faces them. But the two events are essentially independent, so that the odds of both happening are about 1 in 13. Trying to pick all the teams to make the Final Four, you maybe have a 1 in 36 chance of getting it right. And good luck picking all the winners of each of the first 32 games– you have less than a 1 in 60,000 chance of getting that right.

Those Team Rankings probabilities are reproduced at the end of this entry. Now, if you have opinions in these matters, you will have some different probabilities from these. But whatever probabilities you may think are correct, if you multiply them out you’ll probably get something similar to the numbers in the table at the left. Even if you knew the exact true probabilities of who should beat whom, you can be essentially certain that some of your predictions will be wrong.

But that doesn’t stop us from playing. Following the inspiration of Tim Haab of Environmental Economics, I’ve set up an Econbrowser NCAA Bracket Challenge, where you can compete for the honor and/or glory of being the smartest and/or luckiest Econbrowser sports fan. Just go to the Econbrowser group at ESPN, do some minor registering to create a free ESPN account if you haven’t used that site before, and fill in your bracket. Or create more than one bracket, if you care to “diversify”. I’ve entered the Team Rankings choices as a benchmark to beat, and another doubtless even less likely outcome just for fun.

So feel free to play along, but note you must enter before Thursday.



Source: Team Rankings
Team R64 R32

R16 R8 Final 4 Champ WIN
1
North Carolina
100% 96.96% 74.68% 54.84% 39.12% 22.45% 13.06%
16
Mt St Marys
73.52% 2.77% 0.47% 0.07% 0.01% 0% 0%
16
Coppin St
26.48% 0.26% 0.01% 0% 0% 0% 0%
8
Indiana
100% 62% 16.95% 8.25% 3.77% 1.26% 0.42%
9
Arkansas
100% 38% 7.89% 3% 1.06% 0.27% 0.07%
5
Notre Dame
100% 73.85% 36.96% 12.53% 5.89% 2.04% 0.7%
12
George Mason
100% 26.15% 7.57% 1.27% 0.32% 0.05% 0.01%
4
Washington St
100% 80.45% 49.88% 19.24% 10.23% 4.04% 1.59%
13
Winthrop
100% 19.55% 5.6% 0.79% 0.18% 0.03% 0%
Team R64 R32

R16 R8 Final 4 Champ WIN
3
Louisville
100% 81.8% 55.81% 30.5% 13.19% 5.36% 2.17%
14
Boise St
100% 18.2% 5.42% 1.17% 0.18% 0.02% 0%
6
Oklahoma
100% 54.5% 21.9% 8.34% 2.44% 0.67% 0.18%
11
St Josephs
100% 45.5% 16.87% 5.87% 1.56% 0.38% 0.09%
7
Butler
100% 65.2% 29.64% 15.32% 5.65% 1.96% 0.67%
10
South Alabama
100% 34.8% 11.73% 4.42% 1.13% 0.27% 0.06%
2
Tennessee
100% 87.2% 56.03% 33.89% 15.22% 6.44% 2.71%
15
American
100% 12.8% 2.59% 0.49% 0.05% 0.01% 0%
Team R64 R32

R16 R8 Final 4 Champ WIN
1
Kansas
100% 94.2% 78.5% 63.4% 45.8% 31.04% 19.78%
16
Portland St
100% 5.8% 1.61% 0.41% 0.07% 0.01% 0%
8
UNLV
100% 47% 9% 3.98% 1.25% 0.36% 0.09%
9
Kent
100% 53% 10.89% 5.1% 1.72% 0.52% 0.14%
5
Clemson
100% 68.33% 47.53% 15.94% 7.3% 3.04% 1.12%
12
Villanova
100% 31.67% 16.57% 3.58% 1.05% 0.28% 0.06%
4
Vanderbilt
100% 66.8% 27.02% 6.37% 2.03% 0.58% 0.15%
13
Siena
100% 33.2% 8.88% 1.23% 0.25% 0.05% 0.01%
Team R64 R32

R16 R8 Final 4 Champ WIN
3
Wisconsin
100% 81.35% 53.82% 33.28% 15.62% 8.3% 3.98%
14
CS Fullerton
100% 18.65% 5.37% 1.41% 0.27% 0.06% 0.01%
6
USC
100% 60% 26.23% 12.81% 4.75% 1.95% 0.71%
11
Kansas St
100% 40% 14.58% 5.8% 1.76% 0.59% 0.17%
7
Gonzaga
100% 42.5% 17.65% 6.78% 2.12% 0.73% 0.22%
10
Davidson
100% 57.5% 27.29% 12.22% 4.45% 1.79% 0.64%
2
Georgetown
100% 84.95% 51.97% 27.19% 11.5% 5.47% 2.32%
15
Umbc
100% 15.05% 3.09% 0.52% 0.06% 0.01% 0%
Team R64 R32

R16 R8 Final 4 Champ WIN
1 Memphis 100% 96.68% 76.67% 58.75% 41.39% 25.5% 14.82%
16
Texas Arlington
100% 3.32% 0.58% 0.09% 0.01% 0% 0%
8
Mississippi St
100% 48.5% 10.83% 4.85% 1.78% 0.53% 0.14%
9
Oregon
100% 51.5% 11.92% 5.52% 2.09% 0.64% 0.18%
5
Michigan St
100% 66.8% 37.36% 12.62% 5.67% 2.09% 0.71%
12
Temple
100% 33.2% 13.09% 2.92% 0.89% 0.22% 0.05%
4
Pittsburgh
100% 69.3% 38.52% 13.01% 5.84% 2.16% 0.73%
13
Oral Roberts
100% 30.7% 11.04% 2.25% 0.64% 0.14% 0.03%
Team R64 R32

R16 R8 Final 4 Champ WIN
3
Stanford
100% 82.7% 50.88% 28.21% 12.56% 5.54% 2.26%
14
Cornell
100% 17.3% 4.29% 0.93% 0.14% 0.02% 0%
6
Marquette
100% 72.23% 36.28% 18.17% 7.27% 2.85% 1.03%
11
Kentucky
100% 27.77% 8.56% 2.53% 0.56% 0.12% 0.02%
7
Miami Fla
100% 50.5% 16.64% 5.97% 1.67% 0.45% 0.11%
10
St Marys CA
100% 49.5% 16.15% 5.73% 1.58% 0.42% 0.1%
2
Texas
100% 90.4% 65.14% 38.18% 17.9% 8.33% 3.61%
15
Austin Peay
100% 9.6% 2.07% 0.29% 0.03% 0% 0%
Team R64 R32

R16 R8 Final 4 Champ WIN
1
UCLA
100% 99.42% 75.62% 56.88% 37.44% 22.95% 13.04%
16
Miss Valley St
100% 0.58% 0.02% 0% 0% 0% 0%
8
BYU
100% 46% 10.66% 4.98% 1.81% 0.59% 0.17%
9
Texas A&M
100% 54% 13.7% 6.93% 2.76% 0.98% 0.31%
5
Drake
100% 64.8% 40.47% 14.64% 6.62% 2.69% 0.98%
12
Western KY
100% 35.2% 16.91% 4.27% 1.38% 0.4% 0.1%
4
Connecticut
100% 76.97% 37.43% 11.66% 4.59% 1.61% 0.5%
13
San Diego
100% 23.03% 5.19% 0.64% 0.11% 0.02% 0%
Team R64 R32

R16 R8 Final 4 Champ WIN
3
Xavier
100% 76.43% 45.03% 18.23% 7.28% 2.9% 1.04%
14
Georgia
100% 23.57% 6.87% 1.3% 0.24% 0.04% 0.01%
6
Purdue
100% 56% 28.19% 10.01% 3.49% 1.22% 0.38%
11
Baylor
100% 44% 19.9% 6.18% 1.89% 0.57% 0.15%
7
West Virginia
100% 51% 17.62% 9.29% 3.45% 1.28% 0.42%
10
Arizona
100% 49% 16.62% 8.6% 3.13% 1.14% 0.37%
2
Duke
100% 90.4% 63.82% 45.95% 25.76% 14.61% 7.61%
15
Belmont
100% 9.6% 1.95% 0.43% 0.06% 0.01% 0%



3 thoughts on “March madness

  1. JDH

    Ironman, I just copied the bottom table from Team Rankings, adding a little color to make it more readable. I assume that they’ll be updating their numbers as the tournament progresses. I hand’t intended to reproduce those updates here, but will give brief reports after each weekend on who’s leading among the Econbrowser pool in the quest for honor and/or glory.

    But I’ll bet you could do a much cooler job with updating and making creative use of those Team Rankings numbers than I could.

  2. Ironman

    Sadly, I cannot – sure, I could make the data in the tables dance, but I don’t have a good solution to keep up with the volume of games as the results come in. Given my limited time, anything I would do would be hopelessly out of date!

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