A comparative study of scoring systems by simulations

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 that have favourable axiomatic properties. The formers are found to be competitive or even better. The current scheme seems to be a reasonable compromise in optimising the above goals. 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.