{"title":"Coronavirus and sports leagues: obtaining a fair ranking when the season cannot resume","authors":"László Csató","doi":"10.1093/imaman/dpab020","DOIUrl":"10.1093/imaman/dpab020","url":null,"abstract":"Many sports leagues are played in a tightly scheduled round-robin format, leaving a limited time window to postpone matches. If the season cannot resume due to an external shock such as the coronavirus pandemic in 2020, the ranking of the teams becomes non-trivial: it is necessary to account for schedule imbalances and possibly for the different number of matches played. First in the literature, we identify a set of desired axioms for ranking in these incomplete tournaments. It is verified that the generalized row sum, a parametric family of scoring rules, satisfies all of them. In particular, the well-established least-squares method maximizes the influence of the strength of opponents on the ranking. Our approach is applied for six major premier European soccer competitions, where the rankings are found to be robust concerning the weight of adjustment for the strength of the opponents. Some methodologically simpler alternative policies are also discussed.","PeriodicalId":56296,"journal":{"name":"IMA Journal of Management Mathematics","volume":"32 4","pages":"547-560"},"PeriodicalIF":1.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47728240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bayesian models for prediction of the set-difference in volleyball","authors":"Ioannis Ntzoufras;Vasilis Palaskas;Sotiris Drikos","doi":"10.1093/imaman/dpab007","DOIUrl":"10.1093/imaman/dpab007","url":null,"abstract":"We study and develop Bayesian models for the analysis of volleyball match outcomes as recorded by the set-difference. Due to the peculiarity of the outcome variable (set-difference) which takes discrete values from \u0000<tex>$-3$</tex>\u0000 to \u0000<tex>$3$</tex>\u0000, we cannot consider standard models based on the usual Poisson or binomial assumptions used for other sports such as football/soccer. Hence, the first and foremost challenge was to build models appropriate for the set-difference of each volleyball match. Here we consider two major approaches: (a) an ordered multinomial logistic regression model and (b) a model based on a truncated version of the Skellam distribution. For the first model, we consider the set-difference as an ordinal response variable within the framework of multinomial logistic regression models. Concerning the second model, we adjust the Skellam distribution to account for the volleyball rules. We fit and compare both models with the same covariate structure as in Karlis & Ntzoufras (2003). Both models are fitted, illustrated and compared within Bayesian framework using data from both the regular season and the play-offs of the season 2016/17 of the Greek national men's volleyball league A1.","PeriodicalId":56296,"journal":{"name":"IMA Journal of Management Mathematics","volume":"32 4","pages":"491-518"},"PeriodicalIF":1.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaman/dpab007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49557361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D P Semenov;A P Koldanov;P A Koldanov;P M Pardalos
{"title":"A robustness comparison of two market network models","authors":"D P Semenov;A P Koldanov;P A Koldanov;P M Pardalos","doi":"10.1093/imaman/dpab001","DOIUrl":"10.1093/imaman/dpab001","url":null,"abstract":"Two market network models are investigated. One of them is based on the classical Pearson correlation as the measure of association between stocks returns, whereas the second one is based on the sign similarity measure of association between stocks returns. We study the uncertainty of identification procedures for the following market network characteristics: distribution of weights of edges, vertex degree distribution in the market graph (MG), cliques and independent sets in the MG and the vertex degree distribution of the maximum spanning tree. We define the true network characteristics, the losses from the error of its identification by observations and the uncertainty of identification procedures as the expected value of losses. We use an elliptically contoured distribution as a model of the multivariate stocks returns distribution. It is shown that identification of statistical procedures based on the sign similarity are statistically robust in contrast to the procedures based on the classical Pearson correlation.","PeriodicalId":56296,"journal":{"name":"IMA Journal of Management Mathematics","volume":"33 1","pages":"123-137"},"PeriodicalIF":1.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaman/dpab001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47147915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Predicting play calls in the National Football League using hidden Markov models","authors":"Marius Ötting","doi":"10.1093/imaman/dpab005","DOIUrl":"10.1093/imaman/dpab005","url":null,"abstract":"In recent years, data-driven approaches have become a popular tool in a variety of sports to gain an advantage by, for example, analysing potential strategies of opponents. Whereas the availability of play-by-play or player tracking data in sports such as basketball and baseball has led to an increase of sports analytics studies, equivalent data sets for the National Football League (NFL) were not freely available for a long time. In this contribution, we consider a comprehensive play-by-play NFL dataset provided by www.kaggle.com, comprising 289,191 observations in total, to predict play calls in the NFL using hidden Markov models. The resulting out-of-sample prediction accuracy for the 2018 NFL season is 71.6%, which is similar compared to existing studies on play call predictions in the NFL. In practice, such predictions are helpful for NFL teams, especially for defense coordinators, to make adjustments in real time on the field.","PeriodicalId":56296,"journal":{"name":"IMA Journal of Management Mathematics","volume":"32 4","pages":"535-545"},"PeriodicalIF":1.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaman/dpab005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42588822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bayesian spatio-temporal modelling and prediction of areal demands for ambulance services","authors":"Vittorio Nicoletta;Alessandra Guglielmi;Angel Ruiz;Valérie Bélanger;Ettore Lanzarone","doi":"10.1093/imaman/dpaa028","DOIUrl":"10.1093/imaman/dpaa028","url":null,"abstract":"Careful planning of an ambulance service is critical to reduce response times to emergency calls and make assistance more effective. However, the demand for emergency services is highly variable, and good prediction of the number of future emergency calls, and their spatial and temporal distribution, is challenging. In this work, we propose a Bayesian approach to predict the number of emergency calls in future time periods for each zone of the served territory. The number of calls is described by a generalized linear mixed effects model, and inference, in terms of posterior predictive distributions, is obtained through Markov chain Monte Carlo simulation. Our approach is applied in a large city in Canada. The paper demonstrates that using a model for areal data provides good results in terms of predictive accuracy and allows flexibility in accounting for the main features of the dataset. Moreover, it shows the computational efficiency of the approach despite the huge dataset.","PeriodicalId":56296,"journal":{"name":"IMA Journal of Management Mathematics","volume":"33 1","pages":"101-121"},"PeriodicalIF":1.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaman/dpaa028","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48293917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modelling team performance in soccer using tactical features derived from position tracking data","authors":"F R Goes;M Kempe;J van Norel;K A P M Lemmink","doi":"10.1093/imaman/dpab006","DOIUrl":"10.1093/imaman/dpab006","url":null,"abstract":"Decision-makers in soccer routinely assess the tactical behaviour of a team and its opponents both during and after the game to optimize performance. Currently, this assessment is typically driven by notational analysis and observation. Therefore, potential high-impact decisions are often made based on limited or even biased information. With the current study, we aimed to quantitatively assess tactical performance by abstracting a set of spatiotemporal features from the general offensive principles of play in soccer using position tracking data, and to train a machine learning classifier to predict match outcome based on these features computed over the full game as well as only parts of the game. Based on the results of these analyses, we describe a proof of concept of a decision support system for coaches and managers. In an analysis of 302 professional Dutch Eredivisie matches, we were able to train a Linear Discriminant Analysis model to predict match outcome with fair to good (74.1%) accuracy with features computed over the full match, and 67.9% accuracy with features computed over only 1/4th of the match. We therefore conclude that using only position tracking data, we can provide valuable feedback to coaches about how their team is executing the various principles of play, and how these principles are contributing to overall performance.","PeriodicalId":56296,"journal":{"name":"IMA Journal of Management Mathematics","volume":"32 4","pages":"519-533"},"PeriodicalIF":1.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaman/dpab006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44023699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A mathematical analysis of fairness in shootouts","authors":"Roel Lambers;Frits C R Spieksma","doi":"10.1093/imaman/dpaa023","DOIUrl":"10.1093/imaman/dpaa023","url":null,"abstract":"A shootout is a popular mechanism to identify a winner of a match between two teams. It consists of rounds in which each team gets, sequentially, an opportunity to score a point. It has been shown empirically that shooting first or shooting second in a round has an impact on the scoring probability. This raises a fairness question: is it possible to specify a sequence such that identical teams have equal chance of winning? We show that, for a sudden death, no repetitive sequence can be fair. In addition, we show that the so-called Prohuet–Thue–Morse sequence is not fair. There is, however, an algorithm that outputs a fair sequence whenever one exists. We also analyze the popular best-of-\u0000<tex>$k$</tex>\u0000 shootouts and show that no fair sequence exists in this situation. In addition, we find explicit expressions for the degree of unfairness in a best-of-\u0000<tex>$k$</tex>\u0000 shootout; this allows sports administrators to asses the effect of the length of the shootout on the degree of unfairness.","PeriodicalId":56296,"journal":{"name":"IMA Journal of Management Mathematics","volume":"32 4","pages":"411-424"},"PeriodicalIF":1.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaman/dpaa023","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44436357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On skill and chance in sport","authors":"Phil Scarf;Akshay Khare;Naif Alotaibi","doi":"10.1093/imaman/dpab026","DOIUrl":"https://doi.org/10.1093/imaman/dpab026","url":null,"abstract":"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.","PeriodicalId":56296,"journal":{"name":"IMA Journal of Management Mathematics","volume":"33 1","pages":"53-73"},"PeriodicalIF":1.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016797/9623699/09623702.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67853753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Pricing in make-to-order firms with a lead time-dependent cost","authors":"Xiaoli Cai, Jun Li","doi":"10.1093/IMAMAN/DPAB024","DOIUrl":"https://doi.org/10.1093/IMAMAN/DPAB024","url":null,"abstract":"\u0000 The existing literature on make-to-order firms typically supposes that the unit production cost is a constant. In contrast, in this study, this cost is a variable that depends on the lead time. Under this assumption, we investigate the pricing problem for both a monopoly firm and two competing firms. Specifically, we develop a queueing-game-theoretic model to capture the interaction between customers and the firm’s manager and further solve the pricing problem. The results illustrate that, for a monopoly firm, there exists a service rate threshold, and for two homogeneous firms, there is a unique symmetric equilibrium. However, for two heterogeneous firms, the equilibrium may not exist, and if it does, it may not be unique. In this case, the equilibrium is characterized analytically if it is unique and explored numerically if not. Finally, a specific cost function is adopted to analyse the sensitivity of the optimal decisions. When the firms have this variable cost, compared with those with constant unit production cost, customers’ waiting time might be shorter, and the competition between firms might be fiercer. Also, for these firms, increasing the service rate or decreasing the cost parameter does not always help to increase their market share or profit.","PeriodicalId":56296,"journal":{"name":"IMA Journal of Management Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2021-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43802224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}