Using Bradley–Terry models to analyse test match cricket

Dewart, Neil; Gillard, Jonathan

doi:10.1093/imaman/dpx013

Cited by 6 publications

(6 citation statements)

References 22 publications

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“…This paper has contributed to the quantitative modelling of sports (Haigh 2009). Whilst, increasing attention has been paid to other sports such as football (Owen 2011), cricket (Dewart and Gillard 2019), golf (Lewis 2005), athletics (Volf 2011), and tennis (Forrest and McHale 2019) until recently relatively little attention had been paid to Rugby Union (Scarf et al 2019). In extending a classical Poisson model we are able to highlight important conceptual differences between football and Rugby Union.…”

Section: Managerial Insightsmentioning

confidence: 99%

A Variance Gamma model for Rugby Union matches

Fry

Smart

Serbera

et al. 2020

Journal of Quantitative Analysis in Sports

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Amid much recent interest we discuss a Variance Gamma model for Rugby Union matches (applications to other sports are possible). Our model emerges as a special case of the recently introduced Gamma Difference distribution though there is a rich history of applied work using the Variance Gamma distribution – particularly in finance. Restricting to this special case adds analytical tractability and computational ease. Our three-dimensional model extends classical two-dimensional Poisson models for soccer. Analytical results are obtained for match outcomes, total score and the awarding of bonus points. Model calibration is demonstrated using historical results, bookmakers’ data and tournament simulations.

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Section: Managerial Insightsmentioning

confidence: 99%

A Variance Gamma model for Rugby Union matches

Fry

Smart

Serbera

et al. 2020

Journal of Quantitative Analysis in Sports

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“…. Hence, conditional on N , we obtain the Bradley-Terry model (Bradley and Terry, 1952;Dewart and Gillard, 2019;Baker and Scarf, 2020). The parameter r appears only in Pr( ) N , thus quantifying the overall scoring-rate.…”

Section: Poisson-matchmentioning

confidence: 99%

The binomial-match, outcome uncertainty, and the case of netball

Baker

Chadwick

Parma

et al. 2021

Journal of the Operational Research Society

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We introduce the binomial-match as a model for the bivariate score in a paired-contest. This model is naturally associated with sports in which the restart alternates following a goal. The model is a challenger to the Poisson-match, a pair of independent Poisson random variables whose means are related to the strengths of the competing teams. We use the binomial-match primarily to study the relationship between outcome uncertainty and scoring-rate, particularly for high values of the scoring-rate. Netball has a high scoring-rate and motivates our model development. In the binomial-match framework, we also evaluate rule-variations, and study tactical play in netball. Our analysis suggests that the binomial-match is not a better forecaster than the Poisson-match, but it is better for representing outcome uncertainty and evaluating rule-variations and tactics. In general, we find that the binomial-match implies greater outcome uncertainty than the Poisson match, for a given scoring-rate, and that an alternating-restart is a good rule for reducing the frequency of tied outcomes. For netball in particular, we show that starting the final quarter with possession in a close, balanced match may confer a significant advantage.

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“…Then, the Bradley-Terry model (Bradley and Terry, 1952), and variations of it (e.g. Glickman, 2008;Dewart and Gillard, 2019;, is a convenient quantification of outcome uncertainty. Therein, given two competitors with strengths η 1 , η 2 > 0, the probability that team 1 wins depends only on strength variation ε = η 2 /η 1 , that is, Pr(win) = η 1 /(η 1 + η 2 ) = 1/(1 + ε).…”

Section: The Poisson-matchmentioning

confidence: 99%

On skill and chance in sport

Scarf

Khare

Alotaibi

2021

IMA Journal of Management Mathematics

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This work studies outcome uncertainty and competitive balance from a broad perspective. It considers four sports with varying scoring rates, from soccer with typically three goals per match to netball with one hundred goals per match. Within a general modelling framework for a two-competitor contest, we argue that outcome uncertainty, the extent to which the outcome of a contest is unpredictable, depends on scoring rate, on strength variation and on score dependence. Score dependence is essentially the tendency for scores to alternate because possession alternates and possession is advantageous. We regard competitive balance as lack of variation in strength or skill, so that when strength variation is large competitive balance is low and vice versa. Thus, we argue that the outcome of a contest depends on skill, scoring rate, score dependence and chance. This description of outcome is useful because it informs policy-making in sport about the design of scoring systems and the control of competitive imbalance. Broadly, we find that: soccer is relatively competitively unbalanced but outcomes are uncertain because the scoring rate is low; the Australian football league is competitively balanced and so outcomes are uncertain in spite of the high scoring rate in this sport; international rugby matches are relatively neither competitive nor uncertain so that little is left to chance; and netball matches have uncertain outcomes because scores are positively dependent.

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Using Bradley–Terry models to analyse test match cricket

Cited by 6 publications

References 22 publications

A Variance Gamma model for Rugby Union matches

A Variance Gamma model for Rugby Union matches

The binomial-match, outcome uncertainty, and the case of netball

On skill and chance in sport

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