Randomness, Uncertainty, and the Optimal College Football Championship Tournament Size

Every year, there is a popular debate over how many teams should take part in the NCAA’s FBS-level college football championship tournament, and especially whether it should be expanded from 4 teams to 8 or even 12. The inherent tradeoff is that the larger the tournament, the higher the probability that the true best team is included (“validity”), but the lower the probability that the true best team will avoid being upset and win the tournament (“effectiveness”). Using simulation based on empiricially-derived estimates of the ability to measure true team quality and the amount of randomness inherent in each game, we show that the effect of expanding the tournament to 8 teams could be very small, an effectiveness decrease of only 2-3% while increasing validity by 1-4%, while a 7-team tournament provides slightly better tradeoffs. A 12-team tournament would decrease effectiveness by 5-6%.