#PAGE_PARAMS# #ADS_HEAD_SCRIPTS# #MICRODATA#

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
prolekare.web.journal.doi_sk: https://doi.org/10.1371/journal.pone.0225696

Souhrn

Objectives

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.

Methods

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.

Results

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.

Conclusions

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:

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


Zdroje

1. Davis C. Premier League 2017 prize money: How much your club is in line to earn this season?. The Telegraph [Internet]. 2017 4th January 2018. http://www.telegraph.co.uk/football/2017/05/16/premier-league-2017-prize-money-much-club-line-earn-season/.

2. McCourt I. Parma relegated to Serie D after failing to find a new owner. The Guardian [Internet]. 2015. https://www.theguardian.com/football/2015/jun/22/parma-relegated-serie-d-fail-new-owner.

3. Colley WN. Colley’s bias free college football ranking method: The Colley matrix explained. Princeton University, Princeton. 2002.

4. Langville AN, Meyer CD. Who’s # 1?: the science of rating and ranking. Princeton: Princeton University Press; 2012.

5. Beggs CB, Shepherd SJ, Emmonds S, Jones B. A novel application of PageRank and user preference algorithms for assessing the relative performance of track athletes in competition. PLoS One. 2017;12(6):e0178458. doi: 10.1371/journal.pone.0178458 28575009.

6. Keener JP. The Perron-Frobenius theorem and the ranking of football teams. SIAM review. 1993;35(1):80–93.

7. Dayaratna KD, Miller SJ. The pythagorean won-loss formula and hockey. The Hockey Research Journal. 2013;2012/13:193–209.

8. Caro CA, Machtmes R. Testing the utility of the pythagorean expectation formula on division one college football: an examination and comparision to the Morey model. Journal of Business & Economic Research. 2013;11(12):537–42.

9. Bradley RA, Terry ME. Rank analysis of incomplete block designs: I. the method of paired comparisons Biometrika. 1952;39(3/4):324–45.

10. Mchale I, Morton A. A Bradley-Terry type model for forecasting tennis match results. International Journal of Forecasting. 2011;27(2):619–30.

11. Lasek J, Szlavik Z, Bhulai S. The predictive power of ranking systems in association football. International Journal of Applied Pattern Recognition. 2013;1(1):27–46.

12. Agresti A. An introduction to categorical data analysis: Wiley; 2018.

13. Van Haaren J, Davis J, editors. Predicting the final league tables of domestic football leagues. Proceedings of the 5th international conference on mathematics in sport; 2015.

14. Burer S. Robust rankings for college football. Journal of Quantitative Analysis in Sports. 2012;8(2):1–22.

15. Chartier TP, Harris J, Hutson KR, Langville AN, Martin D, Wessell CD. Reducing the Effects of Unequal Number of Games on Rankings. IMAGE-The Bulletin of the International Linear Algebra Society. 2014;52(1).

16. Govan AY, Meyer CD, editors. Ranking national football league teams using google’s pagerank. AA Markov Anniversary Meeting; 2006; Charleston: Boson Books.

17. Balreira EC, Miceli BK, Tegtmeyer T. An Oracle method to predict NFL games. Journal of Quantitative Analysis in Sports. 10(2):183–96.

18. Mease D. A penalized maximum likelihood approach for the ranking of college football teams independent of victory margins The American Statistician. 2003;57(4):241–8.

19. Tsokos A, Narayanan S, Kosmidis I, Baio G, Cucuringu M, Whitaker G, et al. Modeling outcomes of soccer matches. Machine Learning. 2018:1–19.

20. van der Zaan T. Predicting the outcome of soccer matches in order to make money with betting. Rotterdam: Erasmus University Rotterdam; 2017.

21. Heuer A, Rubner O. How does the past of a soccer match influence its future? Concepts and statistical analysis. PloS one. 2012;7(11):e47678. doi: 10.1371/journal.pone.0047678 23226200

22. Heuer A, Muller C, Rubner O. Soccer: Is scoring goals a predictable Poissonian process? Europhysics Letters. 2010;89:38007.

23. Saraiva EF, Suzuki AK, Filho CAO, Louzada F. Predicting football scores via Poisson regression model: applications to the National Football League. Communications for Statistical Applications and Methods. 2016;23(4):297–319.

24. Constantinou AC. Dolores: A model that predicts football match outcomes from all over the world. Machine Learning. 2018:1–27.

25. Razali N, Mustapha A, Yatim FA, Ab Aziz R, editors. Predicting Football Matches Results using Bayesian Networks for English Premier League (EPL). IOP Conference Series: Materials Science and Engineering; 2017: IOP Publishing.

26. Louzada F, Suzuki AK, Salasar LEB. Predicting match outcomes in the English Premier League: Which will be the final rank? Journal of Data Science. 2014;12:235–54.

27. Jurman G. Seasonal linear predictivity in national football championships. arXiv:151106262v1 [statAP] 19 Nov 2015. 2015.

28. Baker LB, Stofan JR, Hamilton AA, Horswill CA. Comparison of regional patch collection vs. whole body washdown for measuring sweat sodium and potassium loss during exercise. J Appl Physiol (1985). 2009;107(3):887–95. doi: 10.1152/japplphysiol.00197.2009 19541738.

29. Lasek J, Gagolewski M. The efficacy of league formats in ranking teams. Statistical Modelling. 2018;18(5–6):411–35.

30. Shin S, Ahnert SE, Park J. Ranking competitors using degree-neutralized random walks. PLoS One. 2014;9(12):e113685. doi: 10.1371/journal.pone.0113685 25517977.

31. opisthokonta.net. R functions for soccer league tables and result matrix. opisthokontanet [Internet]. 2012 4th January 2018. http://opisthokonta.net/?p=18.

32. Fagin R, Kumar R, Sivakumar D. Comparing top k lists. SIAM Journal on discrete mathematics. 2003;17(1):134–60.

33. Borchers HW. Pracma: practical numerical math functions. R package version. 2015;1(3).

34. Bunker RP, Thabtah F. A machine learning framework for sport result prediction. Applied Computing and Informatics. 2017.

35. Massey K. Statistical models applied to the rating of sports teams. Bluefield College. 1997.

36. World football Elo ratings [Internet]. 1997 [cited 10th March 2017]. http://www.eloratings.net/.

37. eloratings.net. World Football Elo Ratings [12th July 2019]. http://www.eloratings.net/about.

38. Lazova V, Basnarkov L. PageRank Approach to Ranking National Football Teams. arXiv preprint arXiv:150301331. 2015.

39. Suzuki K, Ohmori K. Effectiveness of FIFA/Coca-Cola World Ranking in predicting the results of FIFA World Cup finals. Football Science. 2008;5:18–25.

40. masseyratings.com. Massey Ratings [updated 12th July 2019]. https://www.masseyratings.com/index.htm.

41. Price S. How FIFA’s New Ranking System Will Change International Soccer. Forbes [Internet]. 2018 12th July 2019. https://www.forbes.com/sites/steveprice/2018/06/11/how-fifas-new-ranking-system-will-change-international-soccer/#18864e86c412.

42. BBC. Guide to the SPL split 2001 [9th June 2019]. http://news.bbc.co.uk/sport1/hi/football/scot_prem/1251646.stm.

43. Switzer A. The cost of relegation from the Premier League. The Telegraph. 2011;23.

44. Flint SW, Plumley DJ, Wilson RJ. You don’t know what you’re doing! The impact of managerial change on club performance in the English Premier League. Managing Leisure. 2014;19(6):390–9.

45. Blumrodt J, Desbordes M, Bodin D. Professional football clubs and corporate social responsibility. Sport, Business and Management: An International Journal. 2013;3(3):205–25.

46. Elias N, Dunning E. Quest for excitement: sport and leisure in the civilising process. Oxford: Blackwell; 1986.

47. Quirk J, Fort RD. Pay dirt: the business of professional team sports. Princeton, N.J.: Princeton University Press; 1992.

48. Forrest D, Simmons R. Outcome uncertainty and attendance demand in sport: the case of English soccer. Journal of the Royal Statistical Society: Series D (The Statistician). 2002;51(2):229–41.

49. Buraimo B, Simmons R. Do sports fans really value uncertainty of outcome? Evidence from the English Premier League. International Journal of Sport Finance. 2008;3(3).

50. Rumsby B. Premier League TV deal: Sky Sports break bank to dominate £5.136bn contract. The Telegraph [Internet]. 2015 4th January 2018. http://www.telegraph.co.uk/sport/football/11403761/Premier-League-TV-deal-Sky-Sports-break-bank-to-dominate-5.136bn-contract.html.

51. Johnson N. Premier League is 25 years old: Facts and figures behind the first quarter-century. BBC news [Internet]. 2017 4th January 2018. http://www.bbc.co.uk/sport/football/40704646.

52. ter Weel B. Does Manager Turnover Improve Firm Performance? Evidence from Dutch Soccer, 1986–2004. De Economist. 2011;159(3):279–303.

53. Heuer A, Muller C, Rubner O, Hagemann N, Strauss B. Usefulness of dismissing and changing the coach in professional soccer. PLoS One. 2011;6(3):e17664. doi: 10.1371/journal.pone.0017664 21445335.

54. Sumpter D. Soccermatics: mathematical adventures in the beautiful game: Bloomsbury Publishing; 2016.


Článok vyšiel v časopise

PLOS One


2019 Číslo 12
Najčítanejšie tento týždeň
Najčítanejšie v tomto čísle
Kurzy

Zvýšte si kvalifikáciu online z pohodlia domova

Aktuální možnosti diagnostiky a léčby litiáz
nový kurz
Autori: MUDr. Tomáš Ürge, PhD.

Všetky kurzy
Prihlásenie
Zabudnuté heslo

Zadajte e-mailovú adresu, s ktorou ste vytvárali účet. Budú Vám na ňu zasielané informácie k nastaveniu nového hesla.

Prihlásenie

Nemáte účet?  Registrujte sa

#ADS_BOTTOM_SCRIPTS#