On skill and chance in sport
Phil Scarf, Akshay Khare, and Naif Alotaibi
IMA Journal of Management Mathematics, Sep 2021
This work studies outcome uncertainty and competitive balance from a broad perspective. It considers four sports with varying scoring rates, from soccer with typically three goals per match to netball with one hundred goals per match. Within a general modelling framework for a two-competitor contest, we argue that outcome uncertainty, the extent to which the outcome of a contest is unpredictable, depends on scoring rate, on strength variation and on score dependence. Score dependence is essentially the tendency for scores to alternate because possession alternates and possession is advantageous. We regard competitive balance as lack of variation in strength or skill, so that when strength variation is large competitive balance is low and vice versa. Thus, we argue that the outcome of a contest depends on skill, scoring rate, score dependence and chance. This description of outcome is useful because it informs policy-making in sport about the design of scoring systems and the control of competitive imbalance. Broadly, we find that: soccer is relatively competitively unbalanced but outcomes are uncertain because the scoring rate is low; the Australian football league is competitively balanced and so outcomes are uncertain in spite of the high scoring rate in this sport; international rugby matches are relatively neither competitive nor uncertain so that little is left to chance; and netball matches have uncertain outcomes because scores are positively dependent.