Single elimination outrounds

Single elimination outrounds are debate outrounds in which competitors are eliminated as soon as they lose. The outrounds thus form a straight bracket structure: half the teams in each round lose and are eliminated, until only one remains. The ultimate winner will be undefeated throughout outrounds.

The outrounds at all official NCFCA tournaments, and most Stoa tournaments, are single-elimination.

Determining opponents
Typically, each team is assigned a "seed" based on their performance in prelims. Teams are then power-protected: the highest seed debates the lowest seed, the second-highest seed debates the second-lowest seed, and so on. Ideally, this arrangement means that the best team (with the highest seed) has the greatest chance of progressing to the next outround.

A simple formula for determining which two teams meet in any elimination round is the "magic number" shortcut. The magic number is the total number of teams debating in the round, plus one. For an octofinal round, the magic number is 17; for a quarterfinals, 9, etc.

Subtract any team's seed from the magic number and the result will be the team's opponent. For a quarterfinal, the magic number is nine, so the third seed debates nine minus three, the sixth seed.

For the purpose of this shortcut, a team defeating a higher seed takes on the higher seed's number for subsequent rounds. If, in a double-octofinal round, the thirtieth seed defeats the third seed, then in the octos, the thirtieth seed effectively becomes the third seed and debates the fourteenth seed in the octofinals.