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This is my first post on math.stackexchange. I am wondering how many possible seedings there could be in a seeded NCAA March Madness tournament. As a user suggests here, the number of outcomes of an already seeded bracket is

$2^{32}\times 2^{16}\times 2^8\times 2^4\times 2^2\times 2^1$.

But does this include the number of ways to seed the bracket? It seems as though $2^{32}$ is counting the number of outcomes of the first round, which is already seeded. I have done a search and nobody has seemed to address the seeding (or explicitly said it.)

Is it just $\frac{64!}{2^{64}}$? The $64!$ comes from the number of ways to order the teams, and the $2^{64}$ comes from symmetry in the arrangements? That is a vs b is the same as b vs a.

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  • You don't seed brackets, you seed teams, and place teams in brackets so as to keep the better teams from clashing early on, It is not a purely random placement. – true blue anil Oct 19 '15 at 03:52

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Seedings are supposed to represent the relative strength of the teams.

Different organizations have different ways of determining seedings, e.g. at Wimbledon, they don't just go by the ATP ranking, but incorporate (in an opaque way) performance of the players on grass also.

I have no knowledge of how seedings are determined for this particular tournament.

The brackets, of course, are organized in a manner that the better seeds are kept apart, e.g. typically, #1 would be in the topmost bracket, while #2 would be in the lowermost bracket, and so on, so that if they maintained form, you would expect a titanic clash between the two "best" teams in the final.

true blue anil
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