Hidden dynamics of soccer leagues: The predictive ‘power’ of partial standings

Autoři: Clive B. Beggs aff001;  Alexander J. Bond aff001;  Stacey Emmonds aff001;  Ben Jones aff001
Působiště autorů: Institute for Sport, Physical Activity and Leisure, School of Sport, Leeds Beckett University, Leeds, West Yorkshire, England, United Kingdom aff001;  Yorkshire Carnegie Rugby Union club, Leeds, England, United Kingdom aff002;  England Performance Unit, The Rugby Football League, Leeds, England, United Kingdom aff003;  Leeds Rhinos Rugby League club, Leeds, England, United Kingdom aff004;  School of Science and Technology, University of New England, Armidale, New South Wales, Australia aff005;  Division of Exercise Science and Sports Medicine, Department of Human Biology, Faculty of Health Sciences, the University of Cape Town and the Sports Science Institute of South Africa, Cape Town, South Africa aff006
Vyšlo v časopise: PLoS ONE 14(12)
Kategorie: Research Article
doi: https://doi.org/10.1371/journal.pone.0225696



Soccer leagues reflect the partial standings of the teams involved after each round of competition. However, the ability of partial league standings to predict end-of-season position has largely been ignored. Here we analyze historical partial standings from English soccer to understand the mathematics underpinning league performance and evaluate the predictive ‘power’ of partial standings.


Match data (1995–2017) from the four senior English leagues was analyzed, together with random match scores generated for hypothetical leagues of equivalent size. For each season the partial standings were computed and Kendall’s normalized tau-distance and Spearman r-values determined. Best-fit power-law and logarithmic functions were applied to the respective tau-distance and Spearman curves, with the ‘goodness-of-fit’ assessed using the R2 value. The predictive ability of the partial standings was evaluated by computing the transition probabilities between the standings at rounds 10, 20 and 30 and the final end-of-season standings for the 22 seasons. The impact of reordering match fixtures was also evaluated.


All four English leagues behaved similarly, irrespective of the teams involved, with the tau-distance conforming closely to a power law (R2>0.80) and the Spearman r-value obeying a logarithmic function (R2>0.87). The randomized leagues also conformed to a power-law, but had a different shape. In the English leagues, team position relative to end-of-season standing became ‘fixed’ much earlier in the season than was the case with the randomized leagues. In the Premier League, 76.9% of the variance in the final standings was explained by round-10, 87.0% by round-20, and 93.9% by round-30. Reordering of match fixtures appeared to alter the shape of the tau-distance curves.


All soccer leagues appear to conform to mathematical laws, which constrain the league standings as the season progresses. This means that partial standings can be used to predict end-of-season league position with reasonable accuracy.

Klíčová slova:

Curve fitting – Finance – Gambling – Games – Ranking algorithms – Sports – Team behavior – Administrative law


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