A comparative study of scoring systems by simulations.

We study the trade-off between two risks for scoring rules used in sports competitions containing multiple contests: (1) the threat of early clinch when the title is clinched before the last contest(s) of the competition take place; and (2) the danger of winning the competition without finishing first in any contest. Four historical points scoring systems of the Formula One World Championship are compared with the family of geometric scoring rules. The current scheme seems to be a reasonable compromise close to the Pareto frontier. Our results contribute to the issue of choosing an optimal set of point values. [ABSTRACT FROM AUTHOR]