Talk:Single-elimination tournament

From Wikipedia, the free encyclopedia

Does anyone know how the word "seed" cam to be used in this context?

This is in analogy to placing seeds in a seedbed. Here, some players are carefully placed into the "tournament tree". Aragorn2 21:28, 20 June 2006 (UTC)

[edit] Rationale for seeding

Maybe it would be interesting to note that the loser of the finals is not necessarily the second-best player (likewise for lower ranks), even if, for simplicity, it is assumed that "betterness" in this respect is constant over time and a transitive relation (that is, if A will win over B, and B will win over C, then A will win over C). This is one of the reasons why (re-)seeding is performed, of course, but it is not explicitely stated in the article. Worst-case example with 8 players/teams, where numbers indicate the assumed skill ranking:

First round (competing pairs in parentheses): (1 2) (3 4) (5 6) (7 8)

Second round: (1 3) (5 7) (2, 4, 6 and 8 were eliminated)

Third round: (1 5)

Best player wins (as expected) but fifth-best undeservedly ranks second.

A seeding approach, on the other hand, would ideally look like this:
First round: (1 5) (3 7) (2 6) (4 8)

Second round: (1 3) (2 4)

Third round: (1 2)

So the second-best player would score second (as desired). Good seeding thus requires that the approximate skill level of the contestants is known beforehand. The principal problem arises because only log₂n rank "comparisons" (that is matches) are performed, where n is the number of contestants, and this is not enough to determine any rank for sure other than the first. (See Sorting.)

Of course, in the real world, "betterness" is not strictly transitive, let alone constant over time, but this only aggravates this tournament ranking problem. Aragorn2 21:47, 20 June 2006 (UTC)

[edit] formula for amount of byes

In case you wanted this;

the formula for figuring out the number of teams recieving first round by is: b=x-[(x-y)*2) b-number of teams reciving first round bye x- number of teams in tournament y-next closest number to x that is lower than x and a power of 2

[edit] Number of opening round games

number of opening round games formula is n=(x-y)*2 n- number of first round games x- number of teams in tournamenst y- next closest number to number of teams in tournament that is a factor of two and lower than the amount of temas.