A comparative study of scoring systems by simulations

TL;DR

This paper compares different scoring systems in sports competitions, especially Formula One, using simulations to analyze risks like early clinching and winning without top finishes, highlighting the current system's balanced performance.

Contribution

It provides a simulation-based comparison of historical and geometric scoring rules, offering insights into their tradeoffs and evolution in Formula One.

Findings

Current scoring system balances risks effectively

Geometric rules offer competitive alternatives

Historical systems are near Pareto optimal

Abstract

Scoring rules aggregate individual rankings by assigning some points to each position in each ranking such that the total sum of points provides the overall ranking of the alternatives. They are widely used in sports competitions consisting of multiple contests. We study the tradeoff between two risks in this setting: (1) the threat of early clinch when the title has been clinched before the last contest(s) of the competition take place; (2) the danger of winning the competition without finishing first in any contest. In particular, four historical points scoring systems of the Formula One World Championship are compared with the family of geometric scoring rules, recently proposed by an axiomatic approach. The schemes used in practice are found to be competitive with respect to these goals, and the current rule seems to be a reasonable compromise close to the Pareto frontier. Our results shed more light on the evolution of the Formula One points scoring systems and contribute to the issue of choosing the set of point values.