Extreme Score Distributions in Countable-Outcome Round-Robin Tournaments of Equally Strong Players

We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value from a countable subset of the unit interval, and the scores of the two players in a match sum to one. The final score of each player is defined as the sum of the scores obtained in matches against all other players. We study the distribution of extreme scores, including the maximum, second maximum, and lower-order extremes. Since the exact distribution is computationally intractable even for small values of $n$, we derive asymptotic results as the number of players $n$ tends to infinity, including limiting distributions, and rates of convergence.

💡 Research Summary

This paper investigates the asymptotic behavior of extreme scores in round‑robin tournaments where all participants have identical strength and each pair of players meets exactly once. Unlike the classical binary win‑loss model, the outcome of a match is allowed to take any value from a countable subset D ⊂