Limits of PageRank-based ranking methods in sports data

TL;DR

This paper critically evaluates the effectiveness of PageRank-based ranking methods in sports, showing their limitations and proposing a new variant that performs better under various conditions.

Contribution

The paper demonstrates the limited applicability of PageRank in sports ranking and introduces a new variant that outperforms traditional PageRank in multiple scenarios.

Findings

PageRank outperforms simple rankings only with few games played.

Increased randomness diminishes PageRank's advantage.

A new PageRank variant outperforms the original in all tested settings.

Abstract

While PageRank has been extensively used to rank sport tournament participants (teams or individuals), its superiority over simpler ranking methods has been never clearly demonstrated. We use sports results from 18 major leagues to calibrate a state-of-art model for synthetic sports results. Model data are then used to assess the ranking performance of PageRank in a controlled setting. We find that PageRank outperforms the benchmark ranking by the number of wins only when a small fraction of all games have been played. Increased randomness in the data, such as intrinsic randomness of outcomes or advantage of home teams, further reduces the range of PageRank's superiority. We propose a new PageRank variant which outperforms PageRank in all evaluated settings, yet shares its sensitivity to increased randomness in the data. Our main findings are confirmed by evaluating the ranking algorithms on real data. Our work demonstrates the danger of using novel metrics and algorithms without considering their limits of applicability.