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Developing an Optimal Scoring System with a Special Emphasis on Volleyball

Taylor & Francis
Research Quarterly for Exercise and Sport
Authors:
Gilbert W Fellingham at Brigham Young University
Gilbert W Fellingham
Bruce Jay Collings
Bruce Jay Collings
Bruce Jay Collings
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Carl M. McGown
Carl M. McGown
Carl M. McGown
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Abstract

Scoring systems for two-team (two-person) net games are typically evaluated for accuracy, efficiency, and variability. This evaluation may be difficult if many points are involved, the probability of winning a point changes with service, and/or points are not scored every rally. A computer program that may be used to evaluate general scoring systems for accuracy, efficiency, variability, and expected score difference is presented. Four scoring systems, side-out, quick, side-out point, and bonus point, are analyzed. A list of items to consider when developing an optimal scoring system is suggested. An optimal scoring system for volleyball is introduced.
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Developing an optimal scoring system with a special emphasis on volleyball.
Fellingham, G W;Collings, B J;McGown, C M
Research Quarterly for Exercise and Sport; Sep 1994; 65, 3; ProQuest
pg. 237
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
... This score can include factors such as whether the team is serving or receiving, whether it is too early or too late in the match to distinguish the first rallies of the set from the last ones, etc. Thus, in volleyball, the model can be improved easily if it is taken into account that the scoring probability in a rally (SP) depends on the game situation of the team, Ferrante and Fonseca (2014); Kovacs (2009) ;Fellingham, Collings, and McGown (1994). The SP is p s if team A is serving. ...
... However, there are some studies that suggest that the independence assumption is compatible with the actual game experience, Schilling (1994); Gilovich, Vallone, and Tversky (1985), Avugos et al. (2013). Markovian models for volleyball matches have been successfully used to determine the average duration of a game, the effect and efficiency of the score system, the strategies to serve or receive, etc. Ferrante and Fonseca (2014); Kovacs (2009);Fellingham et al. (1994); Pfeifer and Deutsch (1981). A quite general and detailed model for beach volleyball can be found in Hoffmeister and Rambau (2017);Hoffmeister (2019). ...
... Let p s and p r be the SP for team A if it starts the rally serving or receiving, respectively. In elite male volleyball matches, p s and p r are around 0.35 and 0.75, respectively, Ferrante and Fonseca (2014); Kovacs (2009);Fellingham et al. (1994). Analogously for team B, q r = 1 − p s and q s = 1 − p r . ...
Generalized model for scores in volleyball matches
Article
Full-text available
  • Jan 2020
We propose a Markovian model to calculate the winning probability of a set in a volleyball match. Traditional models take into account that the scoring probability in a rally (SP) depends on whether the team starts the rally serving or receiving. The proposed model takes into account that the different rotations of a team have different SPs. The model also takes into consideration that the SP of a given rotation complex 1 ( K1 ) depends on the players directly involved in that complex. Our results help to design general game strategies and, potentially, more efficient training routines. In particular, we used the model to study several game properties, such as the importance of having serve receivers with homogeneous performance, the effect of the players’ initial positions on score evolution, etc. Finally, the proposed model is used to diagnose the performance of the female Colombian U23 team (U23 CT).
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... system has led to little variability in match duration and greater balance in scores, in both volleyball (Fellingham et al., 2009) and beach volleyball (Giatsis, 2003). To sign television agreements, little time variability is crucial (Fellingham et al., 1994;Giatsis, 2003). In addition, the International Volleyball Federation (FIVB) has introduced new GR changes in the game structure (the number of points played per sets and the number of sets played per match) at under-23 world championships in the last years (Stankovic et al., 2017), presumably to render volleyball more attractive to larger audiences. ...
... In addition, the International Volleyball Federation (FIVB) has introduced new GR changes in the game structure (the number of points played per sets and the number of sets played per match) at under-23 world championships in the last years (Stankovic et al., 2017), presumably to render volleyball more attractive to larger audiences. Thus, effective GR features should be accurate and give the way to little variability in terms of minimum score differences between teams at the end of a game (Fellingham et al., 1994). However, no studies have been found on the impact of rule changes on team performance and coaching implications, or which may raise interest or increase uncertainty and excitement in an audience. ...
... Thus, systems such as S15 or S21 may reduce match length and variability, which in turn leads to greater control over time and more highly structured games in tune with media requirements. Although rally-point systems reduce time variability (Fellingham et al., 1994;Kovacs, 2009), recent game structures (S21 and S15) pose a step forward in controlling match duration more effectively (less time variability). Moreover, a reduction in match duration leads to less predictable matches as suggested by Fellingham et al. (1994). ...
In Search For Volleyball Entertainment: Impact of New Game Rules on Score and Time-Related Variables
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  • Dec 2019
The aim of this research was to analyse the impact of various game structures on score and time-related variables in elite volleyball. A total of 114 male matches and 76 female matches (38 matches for each tournament) were analysed in under-23 world championships. An observational design was implemented to measure match duration, points scored per match and set, set point differences, tournament phase, match balance, and set tendencies in various game structures (set to 21, to 25 or to 15 points) in male and female categories. Standardised differences in mean values showed that a 15-point set game structure led to shortest matches and smallest time variability in match duration, the largest number of points per match, and greatest equality in terms of set score differences in both the male and the female category. The use of various game structures in training may be useful to coaches and conditioning specialists when planning training schemes and sessions, by introducing different game structures to manage volume and intensity in training more effectively. These results may also be useful to local and/or national volleyball federations willing to attract new young players, to promote learning and to render volleyball a fun activity, by implementing S15 at initial stages. In addition, they could be useful to international federations or committees, so as to attract larger audiences and sponsors interested in more appealing matches with high levels of competitiveness and entertainment.
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... The first team to win three sets wins the match 23 . The length of a match obviously depends on its parts, including the scoring system, rally length (work time during the game), rest time (time between rallies, substitutions, sanctions, technical and team time-outs, time between sets, injuries, and other technical aspects), and the players' skill 24,25 . The average duration of a volleyball match is around 100 min [26][27][28] . ...
Anthropometric but not motor characteristics of young volleyball players were improved after a one-week-long intense training sports camp
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  • Jan 2025
This study aimed to examine potential changes in the anthropometric and motor characteristics of volleyball players aged 17.98 ± 0.51 years after participation in a week-long sports camp. Potential changes in anthropometric characteristics were determined by bioelectrical impedance, and the players’ motor characteristics were assessed in a reaction time test, grip strength test, 5 × 20 s interval test on a rowing ergometer, and vertical, approach and standing long jump tests. A decrease was observed in body fat mass (difference (Δ) of 1.0 kg, p = 0.015), percent body fat (Δ of 1.16%, p = 0.008), and the waist-to-hip ratio (Δ of 0.02, p = 0.001). An increase was noted in total body water (Δ of 1.0 L, p = 0.002), proteins (Δ of 0.33 kg, p = 0.001), minerals (Δ of 0.12 kg, p = 0.003), fat-free mass (Δ of 1.46 kg, p = 0.001), and skeletal muscle mass (Δ of 0.9 kg, p = 0.001). In the group of motor abilities, a significant increase was observed only in the grip strength of the left hand. In conclusion, week-long sport camps can significantly affect the body composition characteristics of young volleyball players, but they do not induce significant changes in motor abilities.
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... Scoring application is designed so that the game can run effectively and efficiently Fellingham, G. W (1994). Perkembangan ilmu pengetahuan dan teknologi harus menjadi acuan pada praktisi olahraga dalam menciptakan suatu perubahan demi kemajuan olahraga itu sendiri. ...
KARATE SCORING SYSTEM: Aplikasi Skoring Berbasis Android
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  • Jan 2021
Perkembangan ilmu pengetahuan dan teknologi menuntut para penyelenggara kegiatan olahraga untuk melakukan inovasi dalam menghadirkan suatu pertandingan yang efektif dan efisien. WKF (World Karate Federation) telah mengeluarkan peraturan terbaru untuk sistem penilaian nomor “kata” dalam pertandingan karate. Dengan demikian penulis menciptakan sebuah inovasi berupa aplikasi berbasis android untuk pencatat skor pertandingan. Metode yang digunakan dalam penelitian ini adalah RD dengan menempuh beberapa langkah hingga aplikasi ini tervalidasi dan dikembangkan hingga menghasilkan produk. Dalam penelitian digunakan sampel sebanyak sepuluh atlet nomor “kata” dalam cabang olahraga karate. Hasil penelitian menunjukan bahwa penggunaan teknologi aplikasi Karate Scoring System efektif digunakan sebagai alat penilaian dan evaluasi pertandingan karate nomor “kata”. Hasil tersebut diperoleh dari validasi application test sebesar 0.955 dengan nilai Sig 0.000 0.05. Reliabilitas untuk application test sebesar 1.000 dengan nilai Sig 0.000 0.05. dengan demikian dapat disimpulkan bahwa aplikasi scoring system memiliki validasi yang tinggi untuk digunakan dalam pertandingan. Dengan menggunakan aplikasi karate scoring system waktu dalam satu rangkaian pertandingan “kata” menjadi efektif dengan tingkat perbedaan sebesar 40% dibandingkan menggunakan lembar penilaian manual. Namun dalam pelaksanaan uji coba produk ditemukan kesulitan dalam hal koneksifitas jaringan internet dengan prangkat yang digunakan. KARATE SCORING SYSTEM: Floating Android-Based Scoring Application AbstractThe development of science and technology requires the sports organizers to innovate in presenting an effective and efficient competition. WKF (World Karate Federation) issued the latest regulations for the "KATA" number rating system in karate matches. Thus, the author creates an android-based application for recording match scores as one method to calculate the scores. The method used in this research was RD by taking several steps until the application was validated and developed into a product. Ten athletes of "KATA" were joint as participants. The results showed that the use of the Karate Scoring System application was effectively used to calculate the "KATA" scoring in karate. The results were obtained from the application test validation of 0.955 with a Sig value of 0.000 0.05. Reliability for the application test was 1,000 with a Sig value of 0,000 0.05. Thus, it can be concluded that the scoring system application has high validation to be used in matches. The karate scoring application produces 40% time more effective compared to the manual scoring sheet. However, internet network connectivity in the device may become an issue for this trial application.
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... Egidi and Ntzoufras (2020) sought to find a unified model for predicting the outcomes of volleyball games, while Gabrio (2021) used Bayesian hierarchical models as a method to predict volleyball games. Both Fellingham, Collings, and McGown (1994) and Ferrante and Fonseca (2014) studied the various scoring systems used in volleyball and their impact on set length. An extensive study of player development in Brazil can be found in the work of Mendes et al. (2018). ...
Evaluating the performance of elite level volleyball players
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  • Feb 2022
Evaluation of individuals in a team sport setting is inherently difficult. The level of play of one individual is fundamentally tied to the level of play of the teammates. One way to think about evaluation of individuals is to ‘insert’ the posterior distribution of the parameter that measures individual play into an ‘average’ team, and see how the probability of success (or failure) changes. Using a Bayesian hierarchical logistic model, we can estimate both the average contribution to success of various positions, and the individual contribution of all the players in that position. In this paper, we use data from the 2018 World Championships in Volleyball to model both the position played and the players within each position. Using both the posterior distributions for the mean performance of the different positions, and the posterior distributions for the individual players, we can then estimate the change in the number of points scored for a team with a change from an average player to the individual under consideration. We compute both the points scored above average per set (PAAPS) and the points scored above average per 100 touches (PP100) for 168 men and 168 women playing five different positions. Contributions of the various position groups and of individual players within each position are evaluated and compared.
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... Unlike other sports, the number of attempts for modelling volleyball match outcomes is rather limited. One of the early works on the analysis of volleyball data is the article by Fellingham, Collings & McGown (1994). In this work, four different scoring systems designed for volleyball were compared and evaluated. ...
Bayesian models for prediction of the set-difference in volleyball
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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 −3-3 to 3, 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.
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... Unlike other sports, the number of attempts for modelling volleyball match outcomes is rather limited. One of the early works on the analysis of volleyball data is the article by Fellingham, Collings & McGown (1994). In this work, four different scoring systems designed for volleyball were compared and evaluated. ...
Bayesian Models for Prediction of Volleyball Set Differences
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  • Oct 2020
The aim of this paper is to study and develop Bayesian models for the analysis of the volleyball game outcomes as recorded by the difference of the winning sets. Due to the peculiarity of the outcome variable (set difference) which takes discrete values from 􀀀3 to 3, 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 differences of each volleyball game. Here we consider two major approaches: a) an ordinal 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 in order 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 regular season and play-offs games of the season 2016/17 of the Greek national men’s volleyball league A1.
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... The rally is the basic unit of one point, the time when a team can score a point. It is differentiated from the other parts of the game, which are considered rest time (Fellingham, Collings, & McGown, 1994). ...
Effects of Tested Rules on Work-Rest Time in Volleyball
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The aim of this study was to determine the influence of new rules tested at the inaugural Men’s Under 23 (U23) World Championship (set to 21 points and 15 seconds between the end of a point and the new serve) on all aspects of time in volleyball matches. The study sample comprised 36 matches partially segmented into 123 sets and 4583 points played. Applying one-way ANOVA, it was shown that the active part of the set and the whole match last slightly more than one third of the total time. The most frequent rally duration was 5 to 10 seconds (43.5% of points). As sets became more unpredictable and approached the end, rest time between points was longer. Time analysis of volleyball matches is important as it helps with proper development of physical preparation for players, gives coaches insight into appropriate match flow and provides a clear time frame of each part of a volleyball match for organisers of competitive events, pools, championships and tournaments.
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Side-out success and ways that points are obtained in women’s college volleyball
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Journal of Sports Analytics. Abstract: The purpose of this study was to assess side-out success and ways that points are obtained in relation to the result of the game in women’s college volleyball. A total of 2,435 rallies from 48 sets of the Missouri Valley Conference (NCAA Division I) were analyzed. The variables studied were: game phase, phase efficacy, reason for the success or error, number of times that the ball went over the net, result of the game, attack tempo, reception efficacy, and type of set. The findings provide reference values to guide the analysis of the volleyball team and understand the way winning teams score and build their side-out in the women’s college population. The results show the importance of side-out phase efficacy as a variable to monitor team performance in competition and the individual actions that correlate most with side-out phase success. The action that best differentiates winning and losing teams was the attack after reception. The results show the contribution of different ways to build the side-out. The actions with greater contribution were the ones that increased the setter’s possibilities to build the offense and accelerate the game, such as through the reception efficacy and the use of the jump set.
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A mathematical model for evaluating scoring systems with specific reference to tennis
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The purpose of this investigation was twofold: (a) to examine the feasibility of using mathematical probability models to evaluate scoring systems; and (b) to actually examine, by use of the model, the relative merits of various tennis scoring systems. The hypothesized model was a Markov chain with stationary transition probabilities, the total chain being divided into an initial process and a random walk. By assessing a constant probability p that player A would win a point against his opponent B, and applying probability theory to the initial Markov process and the random walks, the probability that A would win the match was calculated. This was done for each of the various scoring systems. Under the assumption that the “best” player was the one with the highest probability of winning a point, the scoring method which would most frequently result in this best player being declared the winner was ascertained. Further analysis yielded the expected number of points that would be played in a match, thus giving an indication of the efficiency of the scoring system. Data from the 1967 professional tennis tour for 14 matches (350 games) between Rod Laver and Andres Gimeno were applied to the model and yielded results agreeing very closely with the hypothesized outcomes.
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Using Markov chains and mixture distributions to evaluate scoring systems for net games
  • B J Collings
  • G W Fellingham