Friday, March 25, 2016

Round of 16: What's Sweet about It?

The Statistics Department is running a March Madness contest, and I couldn't resist entering.
It is organized a little differently than the usual bracket picking, which made it more fun to
prepare an entry.  You are given a budget of 100 units,  and you must pick a subset of teams
as many as you want subject to the budget constraint:  Teams seeded 1 cost 25, 2 cost 19, ...
16 seeds cost 1.  I simulated 10,000 brackets, and recorded the survival probabilities as in
the earlier survival plot on this blog, and then computed the expected number of wins for
each team, normalized by their cost, ordered the teams and produced the following list of
teams.  The winner is the entry whose teams accumulate the largest number of wins.

                 EWins Seeds Cost      Bang CumCost CumEWins
Gonzaga         1.1619    11    4 0.2904750       4   1.1619
Pittsburgh      0.9041    10    4 0.2260250       8   2.0660
Cincinnati      1.0757     9    5 0.2151400      13   3.1417
Iowa            1.6385     7    8 0.2048125      21   4.7802
Syracuse        0.8112    10    4 0.2028000      25   5.5914
VA Commonwealth 0.7855    10    4 0.1963750      29   6.3769
West Virginia   2.4625     3   13 0.1894231      42   8.8394
Duke            2.2013     4   12 0.1834417      54  11.0407
Purdue          1.9888     5   11 0.1808000      65  13.0295
Connecticut     0.9040     9    5 0.1808000      70  13.9335
Butler          0.8602     9    5 0.1720400      75  14.7937
Indiana         1.8908     5   11 0.1718909      86  16.6845

Texas A&M       1.8507     3   13 0.1423615      99  18.5352


Actually, several teams: MSU, Oklahoma, USC, and Kentucky came after IU but before Texas 
A&M but I couldn't afford them, so I went with the Aggies, which gave me a list of 13 teams.
Until yesterday this list served me reasonably well, I had 14 wins after the round of 32, but now
barring a miracle there is no way my remaining teams:  Gonzaga, Syracuse, and Indiana
are going to get me anywhere near my anticipated 18.5 wins.  Last year Xiaofeng Shao
won with 6 teams and 21 wins, I think that he is well on the way again this year.

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