Pairwise contests: wins, losses, and strength

Sports competitions represent an interesting family of evaluation problems involving pairwise comparisons. In this context, the alternatives are contending teams, and the comparison is made in terms of outcomes. Different evaluation protocols have been proposed in the literature, aimed at getting more robust estimates of the teams’ worth or better predictions of their future achievements. We present here a new evaluation protocol that can be described in two steps. First, we modify the teams’ outcomes by introducing a penalty function that ponders the points accrued by the points lost. This step already produces an interesting evaluation procedure, the relative performance rule (the ratio between points won and points lost). Second, we define a new procedure that also considers the strength of the teams in the evaluation. We call this new evaluation protocol the relative strength rule.