A multiplicative approach to decathlon scoring based on efficient frontiers

Abstract

The decathlon consists of ten events with scores which are then aggregated to determine the final ranking. We develop a decathlon scoring method which is far simpler than the existing standard (IAAF1984) tables, as there are only 9 parameters instead of 30 which have an impact on the overall rank. We first identify athletes who are on the Pareto-efficient frontier i.e. those who are not dominated by anyone else. We then remove these frontier athletes and again pick all non-dominated athletes to obtain a second dominating group/Pareto frontier and iterate this procedure for the decathlon data from 1986 to 2020. Each of these groups are then characterized by their set of ten median performances. Improving from the last to the top group can then be seen as a path of progress, leading from the lowest to the highest set of median performances. Every event should have the same importance, so we normalize the data such that the path of progress follows as much as possible a space diagonal of a ten dimensional hypercube. Furthermore, any adjustment of a benchmark does not change any actual decathlon performance, hence there cannot be any unwanted rank reversals. This allows a smooth adjustment of these tables in the future, if for instance a new type of javelin needs to be introduced to reduce the range. We normalize such that current performances between 7000 and 9000 points still fall into the same range with our point tables.