Does luck play a role in the determination of the rank positions in football leagues? A study of Europe's 'big five'

It is common wisdom that luck plays a role in sports, along with skill. However, there is no consensus among researchers on what constitutes luck. One strand of the literature studied randomness in sports, most of which did the analysis at the levels of pitch actions, or at the match level. There is no empirical study to assess the role of luck in the determination of rank positions in football (soccer) leagues. In this paper, we define X-factor as unforeseen and unaccounted factors and quantify it as the difference between actual and predicted values of performance or outcome variables. For league football, we have perceived the difference between actual and expected goal difference as the X-factor effect in performance, and the difference between actual and expected points as the X-factor effect in outcome. Further, we have ideated that a plausible role of luck cannot be ruled out if the X-factor effect on outcome is significant while that on performance is not. Conducting analyses of variance on observations from seven seasons (2014-15 to 2020-21) in the top tier leagues of England, Spain, Germany, Italy, and France, we detected the presence of a significant and systematic X-factor effect. We have studied the role of luck using Tukey's HSD test. In general, luck does not play any significant role in determining the rank positions in league football.