Discriminating between the Poisson and negative binomial distributions:an application to goal scoring in association football

Baxter, MJ; Stevenson, Richard A.

doi:10.1080/02664768800000045

Cited by 10 publications

(3 citation statements)

References 4 publications

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“…6 The Poisson distribution is also a widely accepted device to investigate the distribution of the number of goals in sports involving two competing teams (see Maher, 1982;Lee, 1997;Baxter & Stevenson, 1988;Rue & Salvesen, 2000) 7 For this reason the Poisson model is often viewed as too restrictive (see Cameron & Trivedi, 1998;Winkelmann, 2003). A natural way to proceed is to estimate a negative binomial model, which relaxes the equidispersion assumption.…”

Section: Specification and Estimationmentioning

confidence: 99%

Distance matters in away games: Evidence from the German football league

Oberhofer

Philippovich

Winner

2010

Journal of Economic Psychology

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may AbstractThis paper assesses the role of distance in professional team sports, taking the example of football (soccer). We argue that a team's performance in terms of scored and conceded goals decreases with the distance to the foreign playing venue. To test this hypothesis empirically, we investigate 6,389 away games from the German Football Premier League ('Erste Deutsche Bundesliga') between the playing seasons 1986-87 and 2006-07. We find that distance increases a guest team's propensity to concede goals and exhibits a negative but insignificant impact on the ability to score goals. The parameter estimates of the squared distance terms indicate that the effects of distance on team performance are non-monotonic. Further, focusing on the outcome of the game (i.e., win, draw or defeat) as a measure of the overall success of a football team we observe significantly negative effects of distance.JEL Codes: L25, L83, C29

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Section: Specification and Estimationmentioning

confidence: 99%

Distance matters in away games: Evidence from the German football league

Oberhofer

Philippovich

Winner

2010

Journal of Economic Psychology

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“…Letter the Editor SIR-The article by Baxter & Stevenson (1988), hereafter referred to as BS, describes a useful application of the use of several negative binomial distributions with one common parameter and also the relationship between the variance and the mean. It may be of interest to compare and contrast this with similar work in the ecological area.…”

Section: 'Aspect Invariance'mentioning

confidence: 99%

Digital Image Processing

Mardia

Hainsworth

1989

Journal of Applied Statistics

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In image analysis, the shape of an object in a 2-dimensional image is usually summarised by some suitable feature descriptors. One method is to use the image moments for which we introduce area corrections since images are only observed on a discrete lattice. In particular, moment invariants (Hu, 1962;Barton & David, 1962) are constructed which are invariant under translation, rotation and dilation of spatial variables and rescaling of response variables. We critically examine the low order moments. In particular, it is known that any function of the invariants could be used and we propose invariants which stabilise the variance. Variance stabilising transformations are derived and their behaviour is examined for pure and segmented objects. It is shown that unbiased estimates of the population size are obtained under naive thresholding when the object and background are of equal size. Our results indicate how an improved feature vector can be obtained by utilising a suitable combination of variance stabilised moment invariants and the moment invariants themselves. The synthetic examples given here are motivated by real inpa-red images containing objects of interest and background. We also examine other moments and approaches including the use of the shape space itself.

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“…Furthermore, Negative Binomial Regression has been discussed in detail in Hilbe (2007). Negative binomial distributions have been also used for fitting data on goal scoring (see Baxter & Stevenson, 1988; Lee, 2002); these studies deal with modelling scores in association with football and rugby Leagues, respectively. In the same way, a model based on an extension of the negative binomial distribution, known as Generalized Waring Regression model (GWRM), has been employed by Rodríguez‐Avi, Conde‐Sánchez, Sáez‐Castillo, Olmo‐Jiménez, and Martínez‐Rodríguez (2009) for fitting the number of goals scored in relation to several covariates in the Spanish football league.…”

Section: Introductionmentioning

confidence: 99%

Expected number of goals depending on intrinsic and extrinsic factors of a football player. An application to professional Spanish football league

Sáez-Castillo¹,

Avi²,

Sánchez³

2011

European Journal of Sport Science

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A Bayesian regression model for the number of goals scored by players in the Spanish football league during nine seasons is fitted. The model handles overdispersion in such a way that individual footballers ability for scoring may be estimated regardless of the number of minutes played, the position in the field and the team in which they play. Additionally, the posterior predictive distributions of the fitted model allow to obtain an estimation of the performance of any player in each season with reference to the number of goals scored, locating that number as a quantile in the expected distribution of the goals scored by this player in this season. The results show how the model awards the fact that defenders and midfielders score goals because it does not expect that they score many goals and evaluates a forward more strictly in relation to the expected number of goals.

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Discriminating between the Poisson and negative binomial distributions:an application to goal scoring in association football

Cited by 10 publications

References 4 publications

Distance matters in away games: Evidence from the German football league

Distance matters in away games: Evidence from the German football league

Digital Image Processing

Expected number of goals depending on intrinsic and extrinsic factors of a football player. An application to professional Spanish football league

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