Abstract
We analyse the distribution of results that leads to the lowest level of concentration of within-season points, as measured by the Herfindahl-Hirschman index, in sports leagues where individual matches cannot result in ties. Typically, the minimum concentration level is considered to be when teams have equal shares of points, but this may not always be feasible. We develop appropriate expressions for the minimum concentration measure in such scenarios and evaluate the accuracy of using the equal distribution assumption. The error involved in using this assumption is a decreasing function of the number of teams in the league and increases the closer the level of competition is to perfect balance. Use of the incorrect minimum concentration can lead to substantial overestimation of the normalized concentration index.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.