The Most Salient Matches in the History of Premier League Football

Abstract

What are the most surprising, most impressive and most exciting matches in the history of the highest division of English football? Fans, clubs, critics and broadcasters often attempt to interpret and compare the outcomes of football matches. This can be useful as a means of building a reputation for and interest in a particular club, match or competition. However, such analysis is often subjective with fan bias, personal preference and the prize on offer influencing expectation and interpretation of the results. In this paper statistical measures are developed to identify the most surprising, most impressive and most exciting outcomes from an objective ex post point of view. To achieve this it is assumed that goal scoring in soccer can approximately be considered as a Poisson process. First, the most surprising outcomes are estimated as those with the lowest Poisson probability to occur. Second, the most impressive outcomes are identified by their so-called Skellam percentile position. This measure varies between 0 and 1 and has a close relationship with the p-value in statistical testing. Finally, the most exciting match is identified by measuring the variability in the win expectancy during a match.

Quais são os jogos mais surpreendentes, mais impressionantes e mais excitantes na história da maior das divisões do futebol inglês? Torcedores, clubes, críticos e apresentadores geralmente tentam interpretar e comparar os resultados de jogos de futebol. Isso pode ser útil como meio de construção de reputações e interesses em um clube, jogo ou competição em particular. No entanto, tal análise é em geral subjetiva, com o viés do torcedor, a preferência pessoal e o prêmio oferecido influenciando a expectativa e a interpretação dos resultados. Neste trabalho, medidas estatísticas foram desenvolvidas para identificar os resultados mais surpreendentes, mais impressionantes e mais excitantes a partir de um ponto de vista objetivo ex post. Para alcanças isso, foi assumido que marcar um gol no futebol pode ser considerado aproximadamente como um Processo de Poisson. Em primeiro lugar, os resultados mais surpreendentes são estimados como aqueles com a menor probabilidade Poisson de ocorrência. Em segundo lugar, os resultados mais impressionantes são identificados por sua posição percentual na chamada distribuição de Skellam. Essa medida varia entre 0 e 1 e tem uma relação próxima com o valor-p na testagem estatística. Finalmente, os jogos mais emocionantes são identificados pela medição da variação na expectativa de vitória durante o jogo.

¿Cuáles son los partidos más sorprendentes, más impresionantes y más emocionantes de la historia de la división superior del fútbol inglés? Aficionados, clubes, comentaristas y televisiones a menudo interpretan y comparan los resultados de los partidos de fútbol. Esto puede ser útil para alimentar la reputación y el interés por un club, un partido o una competición en concreto. No obstante, estos análisis a menudo son subjetivos y están condicionados por el sesgo, las preferencias personales y el trofeo que está en juego, que puede influir en las expectativas y en la interpretación de los resultados. En este artículo se presenta un método de análisis estadístico que permite identificar los resultados más sorprendentes, más impresionantes y más emocionantes, desde un punto de vista objetivo ex post. Para ello se parte de la premisa que en el fútbol marcar un gol se puede equiparar a un proceso Poisson. En primer lugar se identifican los resultados más sorprendentes como aquellos con una menor probabilidad Poisson de ocurrencia. A continuación se identifican los resultados más impresionantes mediante su posición percentil Skellam. Esta medida varía entre 0 y 1 y guarda una estrecha relación con el valor P en los tests estadísticos. Finalmente se identifican los partidos más emocionantes midiendo la variabilidad de las expectativas de victoria durante el encuentro.

Quels sont les matches les plus surprenants, les plus impressionnants et les plus passionnants de l'histoire de la plus haute division du football anglais ? Les fans, les clubs, les critiques et les commentateurs des media essaient souvent d'interpréter et de comparer les résultats des matches de football. Cela peut être utile pour construire une réputation et éveiller de l'intérêt pour un club, un match ou une compétition particulière. Cependant, ces analyses sont souvent partiales à cause du manque d'objectivité des fans, des préférences personnelles et des prix en jeu, qui influencent les attentes et l'interprétation des résultats. Dans cet article, des mesures statistiques sont développées pour identifier les résultats les plus surprenants, les plus impressionnants et les plus passionnants, d'un point de vue objectif, ex post. Le présupposé, pour ce faire, est que le score, au football, peut être approximativement considéré comme un processus de Poisson. Premièrement, selon la loi de Poisson, les résultats les plus surprenants sont ceux qui ont la plus faible probabilité de se produire. Deuxièmement, selon la loi de Skellam, les résultats les plus impressionnants sont identifiés par leur position selon une mesure qui varie entre 0 et 1 et qui est en étroite relation avec la valeur p dans les tests statistiques. Enfin, le match le plus passionnant est identifié en mesurant la variabilité dans les attentes de victoires au cours du match.

Was sind die überraschendsten, eindrucksvollsten und spannendsten Spiele in der Geschichte der höchsten Spielklasse des englischen Fußballs? Fans, Klubs, Kritiker und Rundfunkanstalten versuchen häufig, die Ergebnisse von Fußballspielen zu interpretieren und zu vergleichen. Dies kann als Mittel zum Aufbau einer Reputation und von Interesse für einen bestimmten Klub, ein Match oder einen Wettbewerb nützlich sein. Allerdings ist eine solche Analyse oft subjektiv: Fan-Befangenheiten, persönliche Vorlieben und das Preisangebot beeinflussen die Erwartung und Interpretation der Ergebnisse. In diesem Artikel werden statistische Maßnahmen entwickelt, die überraschendsten, beeindruckendsten und spannendsten Ergebnisse aus einer objektiven Ex-post-Perspektive aufzuzeigen. Um dies zu erreichen, wird angenommen, dass Torschüsse im Fußball annäherungsweise als Poisson-Prozess angesehen werden können. Zunächst werden die überraschendsten Ergebnisse als diejenigen mit der niedrigsten Poisson-Wahrscheinlichkeit berechnet. Zweitens werden die eindrucksvollsten Ergebnisse durch ihre so genannte Skellam-Perzentil-Position ausgemacht. Diese Messgröße variiert zwischen 0 und 1 und hat eine enge Beziehung zum p-Wert in statistischen Tests. Schließlich wird das aufregendste Match durch Messung der Variabilität in der Siegeserwartung während eines Spiels bestimmt.

什么是最高级别英格兰足球史上最令人惊讶、最令人印象深刻和最令人兴奋的比赛？球迷、俱乐部、评论家和广播常常试图去解释和比较足球比赛的结果。这可能是为特定的俱乐部、比赛或竞争建立声誉和实现其利益的一种有用的方式。然而，这种分析往往是存在球迷偏见、个人喜好和奖品提供的主观评价，因此，影响了比赛结果期望和对比赛的解释。本文旨在通过开发统计手段从客观事后的分析角度来鉴定出最令人吃惊的、最令人印象深刻、最令人兴奋的比赛结果。为了实现这一目标，本文假定足球进球可近似地看作是一个泊松过程。首先，最令人吃惊的结果预计出现在泊松概率最低的比赛。其次，最令人印象深刻的比赛结果出现在被他们称为Skellam百分率的位置。这种统计测量在0和1之间变化，且在统计检验上与假定值保持密切的关系。最后，最激动人心的比赛通过测量赢得预期的变量被鉴别出来。

英国サッカーの最高峰リーグの歴史上、最も驚きに満ちた、印象的な、あるいはエキサイティングな試合はどれだろうか。ファン、クラブ、評論家、報道陣たちはしばしば試合の結果を自ら解釈して比較しようとする。これは特定のクラブや試合あるいは大会への賛美や関心を作り上げる方法としては有効かもしれない。しかしながら、しばしばファンとしての偏向や個人的な好み、そして与えられた賞品が試合結果への期待や解釈を左右するが故に、こうした分析は主観的なものになりがちである。本稿では統計学的手法を用いて、最も驚きに満ち、最も印象的で、最もエキサイティングな結果がそれぞれどれであったかを、客観的で事後的な視点から同定する。これを行うために、サッカーにおける得点をポワゾン過程に近似のものと想定する。まず、最も驚きに満ちた結果は、ポワゾン分布から言って最も確率の低いものである。次に、最も印象的な結果は、スケラム分布の百分位によって導き出される。この数値は０から１の間で表され、統計学的検定におけるp値と緊密な関係にある。最後に、最もエキサイティングな試合は、試合中の勝利の期待値の変動を計ることで同定される。

Keywords::

• soccer scores
• Poisson distribution
• Skellam distribution
• Premier League
• Sports Leagues
• football

Acknowledgements

Special thanks to John Appleton and to two anonymous referees of this journal for valuable comments.

Notes

^1. See e.g. Ryder, “Poisson Toolbox”; and Fernández-Cantelli and Meeden, Improved Award System.

^2.Ryder, “Poisson Toolbox,” 32. See Groot, Economics, Uncertainty and European Football, especially chapter 1, section 3, for a more extensive treatment of the application of the Poisson distribution to soccer.

^3. See Ryder, “Poisson Toolbox”; and Keller, A Characterization of the Poisson.

^4. See http://en.wikipedia.org/wiki/Skellam_distribution, and for the derivation of Equation (4), see Abdulhamid and Maha, On the Poisson Difference.

^5.Maher, Modelling Association Football Scores, concluded that the independent Poisson model is reasonably accurate, although the use of a bivariate Poisson model improves the description of scoring. For the limitations of the independent Poisson distributions applied to soccer, see Karlis and Ntzoufras, Analysis of Sports Data, who have shown that the independent Poisson distribution does not accurately predict the tails of the distribution when compared to the actual distribution of goals, as well as leading to a slight underestimation of the number of draws. Other references to bivariate or independent Poisson models can be found in Dobson and GoddardThe Economics of Football, especially chapter 4.

^6.Ryder, “Poisson Toolbox,” 27–8.

^7. For example, with parameters 2 and 1, the outcomes 2-10 and 10-1 both give a GDDP score of 0.

^8. See Irwin, “The Frequency Distribution of the Difference”; Karlis and Ntzoufras, Bayesian Modeling of Football Outcomes and Differences of County Data; Skellam, “The Frequency Distribution of the Difference”; and, Strackee and van der Gon, “The Frequency Distribution of the Difference.”

^9. For example, with parameters (4,1), a win with a goal difference of 2 has a Skellam percentile position of 42.8%.

^10. The other 14-goal match was Aston Villa v. Accrington (12-2) in 1891/1892 with Poisson parameters 7.2 and 1.4, giving a rather modest GDDS score of 4.2.

^11. Limited information can be found about this match on the Internet, for instance Wikipedia reports the following: “On 5 December 1908, Sunderland beat Newcastle 9–1 at St James' Park, despite this Newcastle still won the league title that season finishing 9 points ahead of their local rivals who finished 3rd. The result remains the biggest ever win in a Tyne–Wear derby, as well as the Wearsiders' biggest ever win away from home and Newcastle's biggest ever home league defeat.”

^12.Vecer, Ichiba and Laudanovic, “On Probabilistic Excitement of Sports Games.”

^13. Note that if the last goal in this match had made the score 4-4, the length would go up to 4.05 and an additional last minute goal (to make the score either 5-4 or 4-5) would increase the length to 4.55. This shows that goals late on in the match add more to excitement, which we think is in line with the subjective experience by fans.

^14. See for an historical overview, http://www.fifa.com/classicfootball/history/the-laws/from-1863-to-present.html.

The underlying research materials for this article can be accessed at http://www.rsssf.com/engpaul/FLA/league.html, supplied by Stuart Jackson and maintained by Paul Felton for the Rec.Sport.Soccer Statistics Foundation.

Additional information

Notes on contributors

Loek Groot

Loek Groot is an associate professor of economics of the public sector at Utrecht University School of Economics. His research mainly focusses on the economics of the welfare state and the interaction with the labour market, with special attention to the proposal of a basic income. His PhD Basic Income and Unemployment (1999) was awarded cum laude. Other research interests are environmental economics and sport economics. Currently he is working on a project under the title World's public goods.

Marnix Zoutenbier

Marnix Zoutenbier, MTD CIRM, is principal consultant at CQM Eindhoven, the Netherlands.