Drawing on the golf-related example of regression to the mean as presented by Kahneman in his best-selling book, Thinking Fast and Slow, this study shows how the regression-to-the-mean phenomenon is revealed in first- and second-round scoring in 11 different golfer populations, ranging from golfers with the highest level of skill (professional golfers on the PGA TOUR) to amateur groups of much lower skill. Using the mathematics of truncated normal distributions, the study introduces a new method for estimating the mix between variation in scoring due to differences in player skill and that due to luck. Estimates of the skill/luck mix are very close to those obtained using the regression-based methodology of Morrison and are nearly identical to those implied by fixed effects regression models where fixed player and round effects are estimated simultaneously. The study also sheds light on the “paradox of skill,” originally suggested by Gould and developed further by Mauboussin, as it relates to golf by showing that luck plays a more important role in determining player scores in higher-skilled golfer groups compared with lower-skilled groups.

中文翻译：

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11个不同高尔夫球手群体中技能和运气的相对作用

以卡尼曼在其畅销书《思考的快与慢》中提出的高尔夫相关的均值回归示例为例，该研究显示了如何在第一轮和第二轮中揭示均值回归现象从11个不同的高尔夫球手群体中得分，从技能水平最高的高尔夫球手（PGA TOUR上的专业高尔夫球手）到技能水平低得多的业余组。利用截断正态分布的数学方法，该研究引入了一种新的方法来估算由于球员技能差异和运气差异导致得分变化之间的混合。技能/运气组合的估计非常接近使用基于Morrison的基于回归的方法获得的估计，并且与固定效应回归模型所隐含的估计几乎相同，在固定效应回归模型中，固定参与者和回合效应同时被估计。这项研究还揭示了最初由Gould提出并由Mauboussin进一步发展的“技能悖论”，因为它与高尔夫有关，表明运气在确定高技能高尔夫球手组中的得分上比在低技能高尔夫球手中更重要。技能的小组。