Maps of Tournaments: Distances, Experiments, and Data

TL;DR

This paper introduces a method to visualize and analyze tournaments using a 2D map framework, comparing distance measures, generating random tournaments, and applying visualization to experimental and knockout tournament data.

Contribution

It adapts the map framework from election theory to tournaments, identifying useful distance measures and demonstrating their application in visualizing tournament data.

Findings

Identified effective distance measures for tournaments

Compared random tournament generation methods with real data

Showed how maps aid in visualizing experimental results

Abstract

We form a "map of tournaments" by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no ties allowed). A map is a set of tournaments represented as points on a 2D plane, so that their Euclidean distances resemble the distances computed according to a given measure. We identify useful distance measures, discuss ways of generating random tournaments (and compare them to several real-life ones), and show how the maps are helpful in visualizing experimental results (also for knockout tournaments).