Cross Country Rank-Sum Cycle Visualization
The following visualization demonstrates both independence and intransitivity violations that can occur in rank-sum scoring, which is used at the NCAA cross country tournament. Each bar can be clicked to remove or add the team to the tournament. Notice when the independence option is displayed (default) that with team Z, team Y wins and without team Z, team X win. When the intransitivity label is pressed, team X beats team Y, team Y beats team Z, and team Z beats team X, causing a cycle when the teams are considered in pairs. This was featured in Justin Ehrlich’s talk at the 2016 Midwest Sports Analytics Meeting in Pella, Iowa: