Physical Sciences and Mathematics Commons^™

Efficiency Of Competitions, E. Ben-Naim, N.W. Hengartner

Eli Ben-Naim

League competition is investigated using random processes and scaling techniques. In our model, a weak team can upset a strong team with a fixed probability. Teams play an equal number of head-to-head matches and the team with the largest number of wins is declared to be the champion. The total number of games needed for the best team to win the championship with high certainty, T, grows as the cube of the number of teams, N, i.e., T ~ N^3. This number can be substantially reduced using preliminary rounds where teams play a small number of games and subsequently, only …