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.

中文翻译：

---

关于运动中的技巧和机会

这项工作从广泛的角度研究结果的不确定性和竞争平衡。它考虑了四项得分率不同的运动，从通常每场比赛打进三球的足球到每场比赛打进一百球的无挡板篮球。在两人比赛的一般建模框架内，我们认为结果的不确定性，即比赛结果的不可预测程度，取决于得分率、力量变化和得分依赖性。得分依赖本质上是得分交替的趋势，因为控球交替和控球是有利的。我们将竞技平衡视为力量或技能缺乏变化，因此当力量变化较大时，竞技平衡较低，反之亦然。因此，我们认为比赛的结果取决于技巧、得分率、分数依赖和机会。这种对结果的描述是有用的，因为它为体育决策制定计分系统和控制竞争不平衡提供了信息。从广义上讲，我们发现： 足球的竞争相对不平衡，但结果不确定，因为得分率低；澳大利亚足球联赛竞争平衡，因此尽管这项运动的得分率很高，但结果仍不确定；国际橄榄球比赛相对来说既没有竞争力也没有不确定性，因此几乎没有机会；和投球比赛的结果不确定，因为分数是正相关的。足球的竞争相对不平衡，但由于得分率低，结果不确定；澳大利亚足球联赛竞争平衡，因此尽管这项运动的得分率很高，但结果仍不确定；国际橄榄球比赛相对来说既没有竞争力也没有不确定性，因此几乎没有机会；和投球比赛的结果不确定，因为分数是正相关的。足球的竞争相对不平衡，但由于得分率低，结果不确定；澳大利亚足球联赛竞争平衡，因此尽管这项运动的得分率很高，但结果仍不确定；国际橄榄球比赛相对来说既没有竞争力也没有不确定性，因此几乎没有机会；和投球比赛的结果不确定，因为分数是正相关的。