Wednesday, March 4, 2009

A hypothetical worst case debate math scenario...

One other little bit of tournament math... Imagine this hypothetical team, call it team uno, the best team at a tournament, in a tournament using the traditional high-low power-matching system. First and second round are random, so it's possible team uno might hit the worst and second worst teams at the tournament in rounds 1 and 2. These two awful teams go on to a 0-6 win-loss record. Then, team uno, being 2-0 with the best speaker points, will hit the worst 2-0 with the lowest speaker points, which could conceivably lose all its remaining rounds and finish 2-4. The same for the next round, hitting the worst 3-0, which could finish 3-3, and all the way through. It is possible in this way for the top team to face six opponents with a combined record of only 14 wins in six rounds. This averages to just slightly better than a 2-4 record/opponent. (Of course, it will likely be better, but it could even be worse if there are an uneven number of teams in each bracket and the top team receives a "pull-up" and debates an opponent with a one-loss worse record in one or more "power-matched" round.) Now, I think the ideal is for the best team at the tournament to face excellent opponents (this is what power-matching systems, like the Swiss system, are supposed to do!) perhaps averaging 4-2 or 5-1 records, for combined opponent wins in the range of 24-30. A far cry from 14 -- which could easily results from pairings that the current algorithm does create and is powerless to flag or rectify.

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