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The Americans United for a Better NCAA Men's Basketball Tournament Pool Manifesto







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Since the NCAA men's basketball tournament expanded to 64 teams in 1985, office pools have become big business, and as such, they require a watchful eye to ensure that they don't run out of control.  That's where we step in.  Tired of losing in the office pool year after year, a group of perennial pool wannabes decided to do what we could to wrestle some of the power from the fat cats who get their jollies by taking our money every March.  The result was Americans United for a Better NCAA Men's Basketball Tournament Pool, the foremost watchdog group for March Madness, making sure that office pools are administered fairly and properly. 

NCAA tournament pools stink, and not just because you're out of the running an hour after you've put in your $10.  No, they're no good because they're all different and they reward different things.  Some favor the guy who's great at picking the 7-10 matchups.  Others reward someone who knows the team that will go all the way.  Rarely (perhaps never) do they consistently and fairly reward knowledge, originality, and risk taking.  And with the advent of computers that will pick the games automatically using various statistical methods, it has become even tougher to design a system that will reward the person who knows his or her basketball. 

We've looked at thousands of tournament pools across the country, and we found two problems popping up consistently.  These problems were that a) the games in each round were not scored properly and b) the weight given to the different rounds was wrong. 


Problem #1: 
Within a given round, games are all treated the same.

What's the worst tournament bracket that can be submitted?  It just might be the bracket that contains no upsets, where every higher-seeded team advances.  The problem is, all other things being equal, this strategy is not a bad one to take in most pools.  You get one point if the #4 seed wins and one point if the #13 seed wins, so why risk something that probably won't happen?  Some (only a few) pools assign what are called upset points, which are meant to reward boldness in picking winners.  These points are almost always awarded arbitrarily, and they never work the way they should because not all upsets are equal, nor are they proportional.  For instance, a #10 seed has a much, much better chance of making the Sweet 16 than a #9 seed does. 

We determined that the best way to rectify this problem was to determine the value of certain picks based on the historical likelihood of their occurrence.  As of 2003, the tournament has had 64 participants for the past 19 years.  That's not a ton of data to pull from, but it's enough to draw reasonable conclusions about the relative strength of various seeds.  We took the records for each seed in each of the rounds, noting how often it won as a percentage of the opportunities it had to win.  For instance, if you pick a 4 seed to win its opening game, the data suggests that you will be correct 81% of the time, but predicting the same team to reach the Final Four will drop the likelihood to about 9%.  The likelihood that a 13 seed will upset the 4 seed is of course 21%, and a 13 seed has never reached the Final Four.  Therefore, someone who picks a 13 seed to win and is correct is making a more difficult (and better) pick. 

So the compensation for a correct pick should vary directly with the loss frequency of that seed in that round.  Picking a 1 seed, which has never lost in the first round, to move past the 16 should be compensated with a score of zero.  Picking a 1 seed to advance to the Final Four, where 1 seeds make it 43% of the time, should be compensated with 57% of the potential value for Final Four teams (scoring for the different rounds is discussed later).  Picking a 3 seed to make the second round will be worth 17% of the first round's value, and picking it to make the Final Four will be worth 87% of the fourth round's value. 

With this type of scoring in mind, we created a table to give us the value we should assign to every possible result (e.g. a 7 seed winning a national semifinal game would be one result) in the tournament.  In the table below, rows represent seeds, and columns represent the round number of the game won.  High seeds that do well early are given very little, and low seeds that make it deep into the tournament are rewarded generously. 
 


 
1
2
3
4
5
6
1
0.000
0.132
0.289
0.566
0.776
0.855
2
0.053
0.355
0.539
0.789
0.895
0.961
3
0.171
0.539
0.776
0.868
0.921
0.974
4
0.211
0.553
0.855
0.908
0.974
0.987
5
0.316
0.658
0.947
0.961
0.974
1.000
6
0.316
0.618
0.855
0.961
0.974
0.987
7
0.408
0.842
0.947
1.000
1.000
1.000
8
0.553
0.895
0.934
0.961
0.987
0.987
9
0.447
0.974
0.987
1.000
1.000
1.000
10
0.592
0.803
0.921
1.000
1.000
1.000
11
0.684
0.868
0.961
0.987
1.000
1.000
12
0.684
0.829
0.987
1.000
1.000
1.000
13
0.789
0.961
1.000
1.000
1.000
1.000
14
0.829
0.974
1.000
1.000
1.000
1.000
15
0.947
1.000
1.000
1.000
1.000
1.000
16
1.000
1.000
1.000
1.000
1.000
1.000

This table has just a few problems that we should address.  First, we noticed that later on in the tournament the values don't increase exactly as we should expect them to.  Secondly, the 8 seed actually has a losing record against the 9, and finally, the 7 seed is given a better reward for reaching the Sweet 16 than the 10 seed.  We adjusted the numbers slightly to correct these, and here is our result:
 

 
1
2
3
4
5
6
1
0.000
0.132
0.289
0.566
0.776
0.855
2
0.053
0.355
0.539
0.789
0.895
0.961
3
0.171
0.539
0.776
0.868
0.921
0.974
4
0.211
0.553
0.855
0.908
0.974
0.987
5
0.316
0.658
0.947
0.961
0.974
1.000
6
0.316
0.658
0.947
0.961
0.974
1.000
7
0.408
0.842
0.947
1.000
1.000
1.000
8
0.500
0.895
0.947
1.000
1.000
1.000
9
0.500
0.974
0.987
1.000
1.000
1.000
10
0.592
0.842
0.987
1.000
1.000
1.000
11
0.684
0.868
0.987
1.000
1.000
1.000
12
0.684
0.829
0.987
1.000
1.000
1.000
13
0.789
0.961
1.000
1.000
1.000
1.000
14
0.829
0.974
1.000
1.000
1.000
1.000
15
0.947
1.000
1.000
1.000
1.000
1.000
16
1.000
1.000
1.000
1.000
1.000
1.000

We felt that this table would help our pool administrators in rewarding upsets, but we still had one more problem to deal with. 

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© 2003 Daniel Lauve