Multi-Opponent James Functions

TL;DR

This paper extends the James function to scenarios where a single team or player faces multiple opponents simultaneously, providing a probabilistic framework for such multi-opponent competitions.

Contribution

It introduces a novel generalization of the James function for multi-opponent contests, expanding the applicability of the original two-team model.

Findings

Derived a new formula for multi-opponent probabilities

Validated the model with theoretical analysis

Provides insights into multi-player competitive dynamics

Abstract

The James function, also known as the "log5 method," assigns a probability to the result of a competition between two teams based on their respective winning percentages. This paper, which builds on earlier work of the authors and Steven J. Miller, explores the analogous situation where a single team or player competes simultaneously against multiple opponents.