Kyriacos Talattinis, George Kyriakides, E. Kapantai, G. Stephanides
Abstract Realizing the significant effect that misprediction has on many real-world problems, our paper is focused on the way these costs could affect the sports sector in terms of soccer outcome predictions. In our experimental analysis, we consider the potential influence of a cost-sensitive approach rather than traditional machine-learning methods. Although the measurement of prediction accuracy is a very important part of the validation of each model, we also study its economic significance. As a performance metric for our models, the Sharpe ratio metric is calculated and analyzed. Seeking to improve Sharpe ratio value, a genetic algorithm is applied. The empirical study and evaluation procedure of the paper are primarily based on English Premier League’s games, simple historical data and well-known bookmakers’ markets odds. Our research confirms that it is worthwhile to employ cost-sensitive methods for the successful predictions of soccer results and better investment opportunities.
{"title":"Forecasting Soccer Outcome Using Cost-Sensitive Models Oriented to Investment Opportunities","authors":"Kyriacos Talattinis, George Kyriakides, E. Kapantai, G. Stephanides","doi":"10.2478/ijcss-2019-0006","DOIUrl":"https://doi.org/10.2478/ijcss-2019-0006","url":null,"abstract":"Abstract Realizing the significant effect that misprediction has on many real-world problems, our paper is focused on the way these costs could affect the sports sector in terms of soccer outcome predictions. In our experimental analysis, we consider the potential influence of a cost-sensitive approach rather than traditional machine-learning methods. Although the measurement of prediction accuracy is a very important part of the validation of each model, we also study its economic significance. As a performance metric for our models, the Sharpe ratio metric is calculated and analyzed. Seeking to improve Sharpe ratio value, a genetic algorithm is applied. The empirical study and evaluation procedure of the paper are primarily based on English Premier League’s games, simple historical data and well-known bookmakers’ markets odds. Our research confirms that it is worthwhile to employ cost-sensitive methods for the successful predictions of soccer results and better investment opportunities.","PeriodicalId":38466,"journal":{"name":"International Journal of Computer Science in Sport","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47791634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The purpose of the present study was to demonstrate an inductive approach for dynamically modelling sport-related injuries with a probabilistic graphical model. Dynamic Bayesian Network (DBN), a well-known machine learning method, was employed to illustrate how sport practitioners could utilize a simulatory environment to augment the training management process. 23 University of Iowa female student-athletes (from 3 undisclosed teams) were regularly monitored with common athlete monitoring technologies, throughout the 2016 competitive season, as a part of their routine health and well-being surveillance. The presented work investigated the ability of these technologies to model injury occurrences in a dynamic, temporal dimension. To verify validity, DBN model accuracy was compared with the performance of its static counterpart. After 3 rounds of 5-fold cross-validation, resultant DBN mean accuracy surpassed naïve baseline threshold whereas static Bayesian network did not achieve baseline accuracy. Conclusive DBN suggested subjectively-reported stress two days prior, subjective internal perceived exertions one day prior, direct current potential and sympathetic tone the day of, as the most impactful towards injury manifestation.
{"title":"Decision Support System for Mitigating Athletic Injuries","authors":"Kyle D. Peterson, L. Evans","doi":"10.2478/ijcss-2019-0003","DOIUrl":"https://doi.org/10.2478/ijcss-2019-0003","url":null,"abstract":"Abstract The purpose of the present study was to demonstrate an inductive approach for dynamically modelling sport-related injuries with a probabilistic graphical model. Dynamic Bayesian Network (DBN), a well-known machine learning method, was employed to illustrate how sport practitioners could utilize a simulatory environment to augment the training management process. 23 University of Iowa female student-athletes (from 3 undisclosed teams) were regularly monitored with common athlete monitoring technologies, throughout the 2016 competitive season, as a part of their routine health and well-being surveillance. The presented work investigated the ability of these technologies to model injury occurrences in a dynamic, temporal dimension. To verify validity, DBN model accuracy was compared with the performance of its static counterpart. After 3 rounds of 5-fold cross-validation, resultant DBN mean accuracy surpassed naïve baseline threshold whereas static Bayesian network did not achieve baseline accuracy. Conclusive DBN suggested subjectively-reported stress two days prior, subjective internal perceived exertions one day prior, direct current potential and sympathetic tone the day of, as the most impactful towards injury manifestation.","PeriodicalId":38466,"journal":{"name":"International Journal of Computer Science in Sport","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48203455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In mathematical modeling by means of performance models, the Fitness-Fatigue Model (FF-Model) is a common approach in sport and exercise science to study the training performance relationship. The FF-Model uses an initial basic level of performance and two antagonistic terms (for fitness and fatigue). By model calibration, parameters are adapted to the subject’s individual physical response to training load. Although the simulation of the recorded training data in most cases shows useful results when the model is calibrated and all parameters are adjusted, this method has two major difficulties. First, a fitted value as basic performance will usually be too high. Second, without modification, the model cannot be simply used for prediction. By rewriting the FF-Model such that effects of former training history can be analyzed separately – we call those terms preload – it is possible to close the gap between a more realistic initial performance level and an athlete's actual performance level without distorting other model parameters and increase model accuracy substantially. Fitting error of the preload-extended FF-Model is less than 32% compared to the error of the FF-Model without preloads. Prediction error of the preload-extended FF-Model is around 54% of the error of the FF-Model without preloads.
{"title":"Including the Past: Performance Modeling Using a Preload Concept by Means of the Fitness-Fatigue Model","authors":"M. Ludwig, A. Asteroth, C. Rasche, M. Pfeiffer","doi":"10.2478/ijcss-2019-0007","DOIUrl":"https://doi.org/10.2478/ijcss-2019-0007","url":null,"abstract":"Abstract In mathematical modeling by means of performance models, the Fitness-Fatigue Model (FF-Model) is a common approach in sport and exercise science to study the training performance relationship. The FF-Model uses an initial basic level of performance and two antagonistic terms (for fitness and fatigue). By model calibration, parameters are adapted to the subject’s individual physical response to training load. Although the simulation of the recorded training data in most cases shows useful results when the model is calibrated and all parameters are adjusted, this method has two major difficulties. First, a fitted value as basic performance will usually be too high. Second, without modification, the model cannot be simply used for prediction. By rewriting the FF-Model such that effects of former training history can be analyzed separately – we call those terms preload – it is possible to close the gap between a more realistic initial performance level and an athlete's actual performance level without distorting other model parameters and increase model accuracy substantially. Fitting error of the preload-extended FF-Model is less than 32% compared to the error of the FF-Model without preloads. Prediction error of the preload-extended FF-Model is around 54% of the error of the FF-Model without preloads.","PeriodicalId":38466,"journal":{"name":"International Journal of Computer Science in Sport","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43450503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Christopher M. Young, Wei Luo, P. Gastin, J. Tran, J. Tran, D. Dwyer
Abstract Mathematical models that explain match outcome, based on the value of technical performance indicators (PIs), can be used to identify the most important aspects of technical performance in team field-sports. The purpose of this study was to evaluate several methodological opportunities, to enhance the accuracy of this type of modelling. Specifically, we evaluated the potential benefits of 1) modelling match outcome using an increased number of seasons and PIs compared with previous reports, 2) how to identify eras where technical performance characteristics were stable and 3) the application of a novel feature selection method. Ninety-one PIs across sixteen Australian Football (AF) League seasons were analysed. Change-point and Segmented Regression analyses were used to identify eras and they produced similar but non-identical outcomes. A feature selection ensemble method identified the most valuable 45 PIs for modelling. The use of a larger number of seasons for model development lead to improvement in the classification accuracy of the models, compared with previous studies (88.8 vs 78.9%). This study demonstrates the potential benefits of large databases when creating models of match outcome and the pitfalls of determining whether there are eras in a longitudinal database.
{"title":"Modelling Match Outcome in Australian Football: Improved accuracy with large databases","authors":"Christopher M. Young, Wei Luo, P. Gastin, J. Tran, J. Tran, D. Dwyer","doi":"10.2478/ijcss-2019-0005","DOIUrl":"https://doi.org/10.2478/ijcss-2019-0005","url":null,"abstract":"Abstract Mathematical models that explain match outcome, based on the value of technical performance indicators (PIs), can be used to identify the most important aspects of technical performance in team field-sports. The purpose of this study was to evaluate several methodological opportunities, to enhance the accuracy of this type of modelling. Specifically, we evaluated the potential benefits of 1) modelling match outcome using an increased number of seasons and PIs compared with previous reports, 2) how to identify eras where technical performance characteristics were stable and 3) the application of a novel feature selection method. Ninety-one PIs across sixteen Australian Football (AF) League seasons were analysed. Change-point and Segmented Regression analyses were used to identify eras and they produced similar but non-identical outcomes. A feature selection ensemble method identified the most valuable 45 PIs for modelling. The use of a larger number of seasons for model development lead to improvement in the classification accuracy of the models, compared with previous studies (88.8 vs 78.9%). This study demonstrates the potential benefits of large databases when creating models of match outcome and the pitfalls of determining whether there are eras in a longitudinal database.","PeriodicalId":38466,"journal":{"name":"International Journal of Computer Science in Sport","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43256876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A recent proposal for a new geometry of the penalty area for football (soccer) has been put to the test by analyzing games of the 2016 continental championships, the European and South American ones, and the 2018 FIFA World Cup which are by far the three most important nations tournaments in the sport. All matches after the first stage were analyzed and some instances were found in these critical or knockout matches in which the game and its fairness would have improved if the penalty area had been drawn according to mathematics or a measure of actual scoring chance.
{"title":"Test of a non-rectangular penalty area in the Euro 2016, Copa América 2016 and 2018 World Cup","authors":"C. A. Morales","doi":"10.2478/ijcss-2019-0008","DOIUrl":"https://doi.org/10.2478/ijcss-2019-0008","url":null,"abstract":"Abstract A recent proposal for a new geometry of the penalty area for football (soccer) has been put to the test by analyzing games of the 2016 continental championships, the European and South American ones, and the 2018 FIFA World Cup which are by far the three most important nations tournaments in the sport. All matches after the first stage were analyzed and some instances were found in these critical or knockout matches in which the game and its fairness would have improved if the penalty area had been drawn according to mathematics or a measure of actual scoring chance.","PeriodicalId":38466,"journal":{"name":"International Journal of Computer Science in Sport","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42453440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In volleyball, due to the sequential structure of the game, each outcome results from events that follow consistent consecutive patterns: pass–set–attack–outcome, serve–outcome and block–dig–set–counter attack–outcome. There are three possible outcomes: point won, point lost, and rally continuation. With the aim of quantifying the importance of volleyball skills, data of world champions of the male International Volleyball Federation tournaments for three age categories (Youth, Juniors and Men) were used to construct a transition matrix between subsequent moves and skills within the game. A Dirichlet-Multinomial Bayesian model was used to estimate the transition probabilities between the subsequent moves along with the marginal probability of success of each skill in the complex. The prior distribution of each transition probabilities between moves/skills was elicited to incorporate experts' opinion. For the final evaluation of the skills a simple Monte Carlo scheme was applied to obtain a random sample from the posterior distribution. The findings of the study indicate that the relative importance of volleyball skills is robust across world champions of different age categories. Slight variations are observed on specific skills. A new index (Quantile Mid-range Ratio) is proposed for highlighting skills that are valuable for team’s gameplay.
{"title":"Bayesian Analysis of Skills Importance in World Champions Men’s Volleyball across Ages","authors":"Sotirios Drikos, I. Ntzoufras, N. Apostolidis","doi":"10.2478/ijcss-2019-0002","DOIUrl":"https://doi.org/10.2478/ijcss-2019-0002","url":null,"abstract":"Abstract In volleyball, due to the sequential structure of the game, each outcome results from events that follow consistent consecutive patterns: pass–set–attack–outcome, serve–outcome and block–dig–set–counter attack–outcome. There are three possible outcomes: point won, point lost, and rally continuation. With the aim of quantifying the importance of volleyball skills, data of world champions of the male International Volleyball Federation tournaments for three age categories (Youth, Juniors and Men) were used to construct a transition matrix between subsequent moves and skills within the game. A Dirichlet-Multinomial Bayesian model was used to estimate the transition probabilities between the subsequent moves along with the marginal probability of success of each skill in the complex. The prior distribution of each transition probabilities between moves/skills was elicited to incorporate experts' opinion. For the final evaluation of the skills a simple Monte Carlo scheme was applied to obtain a random sample from the posterior distribution. The findings of the study indicate that the relative importance of volleyball skills is robust across world champions of different age categories. Slight variations are observed on specific skills. A new index (Quantile Mid-range Ratio) is proposed for highlighting skills that are valuable for team’s gameplay.","PeriodicalId":38466,"journal":{"name":"International Journal of Computer Science in Sport","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45931946","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The increasing availability of data from sports events has led to many new directions of research, and sports analytics can play a role in making better decisions both within a club and at the level of an individual player. The ability to objectively evaluate individual players in team sports is one aspect that may enable better decision making, but such evaluations are not straightforward to obtain. One class of ratings for individual players in team sports, known as plus-minus ratings, attempt to distribute credit for the performance of a team onto the players of that team. Such ratings have a long history, going back at least to the 1950s, but in recent years research on advanced versions of plus-minus ratings has increased noticeably. This paper presents a comprehensive review of contributions to plus-minus ratings in later years, pointing out some key developments and showing the richness of the mathematical models developed. One conclusion is that the literature on plus-minus ratings is quite fragmented, but that awareness of past contributions to the field should allow researchers to focus on some of the many open research questions related to the evaluation of individual players in team sports.
{"title":"A comprehensive review of plus-minus ratings for evaluating individual players in team sports","authors":"L. M. Hvattum","doi":"10.2478/ijcss-2019-0001","DOIUrl":"https://doi.org/10.2478/ijcss-2019-0001","url":null,"abstract":"Abstract The increasing availability of data from sports events has led to many new directions of research, and sports analytics can play a role in making better decisions both within a club and at the level of an individual player. The ability to objectively evaluate individual players in team sports is one aspect that may enable better decision making, but such evaluations are not straightforward to obtain. One class of ratings for individual players in team sports, known as plus-minus ratings, attempt to distribute credit for the performance of a team onto the players of that team. Such ratings have a long history, going back at least to the 1950s, but in recent years research on advanced versions of plus-minus ratings has increased noticeably. This paper presents a comprehensive review of contributions to plus-minus ratings in later years, pointing out some key developments and showing the richness of the mathematical models developed. One conclusion is that the literature on plus-minus ratings is quite fragmented, but that awareness of past contributions to the field should allow researchers to focus on some of the many open research questions related to the evaluation of individual players in team sports.","PeriodicalId":38466,"journal":{"name":"International Journal of Computer Science in Sport","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47647708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Peter R Browne, S. Morgan, J. Bahnisch, Samuel Robertson
Abstract In netball, analysis of the movement of players and the ball across different court locations can provide information about trends otherwise hidden. This study aimed to develop a method to discover latent passing patterns in women’s netball. Data for both pass location and playing position were collected from centre passes during selected games in the 2016 Trans-Tasman Netball Championship season and 2017 Australian National Netball League. A motif analysis was used to characterise passing-sequence observations. This revealed that the most frequent, sequential passing style from a centre pass was the “ABCD” motif in an alphabetical system, or in a positional system “Centre–Goal Attack–Wing Attack–Goal Shooter” and rarely was the ball passed back to the player it was received from. An association rule mining was used to identify frequent ball movement sequences from a centre pass play. The most confident rule flowed down the right-hand side of the court, however seven of the ten most confident rules demonstrated a preference for ball movement down the left-hand side of the court. These results can offer objective insight into passing sequences, and potentially inform team strategy and tactics. This method can also be generalised to other invasion sports.
{"title":"Discovering patterns of play in netball with network motifs and association rules","authors":"Peter R Browne, S. Morgan, J. Bahnisch, Samuel Robertson","doi":"10.2478/ijcss-2019-0004","DOIUrl":"https://doi.org/10.2478/ijcss-2019-0004","url":null,"abstract":"Abstract In netball, analysis of the movement of players and the ball across different court locations can provide information about trends otherwise hidden. This study aimed to develop a method to discover latent passing patterns in women’s netball. Data for both pass location and playing position were collected from centre passes during selected games in the 2016 Trans-Tasman Netball Championship season and 2017 Australian National Netball League. A motif analysis was used to characterise passing-sequence observations. This revealed that the most frequent, sequential passing style from a centre pass was the “ABCD” motif in an alphabetical system, or in a positional system “Centre–Goal Attack–Wing Attack–Goal Shooter” and rarely was the ball passed back to the player it was received from. An association rule mining was used to identify frequent ball movement sequences from a centre pass play. The most confident rule flowed down the right-hand side of the court, however seven of the ten most confident rules demonstrated a preference for ball movement down the left-hand side of the court. These results can offer objective insight into passing sequences, and potentially inform team strategy and tactics. This method can also be generalised to other invasion sports.","PeriodicalId":38466,"journal":{"name":"International Journal of Computer Science in Sport","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43368545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Generalized knockout tournament seedings for an arbitrary number of participants in one match are designed. Several properties of knockout tournament seedings are investigated. Enumeration results for knockout tournament seedings with different properties are obtained. Several new generalized knockout tournaments seedings are proposed and justified by a set of properties.
{"title":"Generalized Knockout Tournament Seedings","authors":"A. Karpov","doi":"10.2478/ijcss-2018-0006","DOIUrl":"https://doi.org/10.2478/ijcss-2018-0006","url":null,"abstract":"Abstract Generalized knockout tournament seedings for an arbitrary number of participants in one match are designed. Several properties of knockout tournament seedings are investigated. Enumeration results for knockout tournament seedings with different properties are obtained. Several new generalized knockout tournaments seedings are proposed and justified by a set of properties.","PeriodicalId":38466,"journal":{"name":"International Journal of Computer Science in Sport","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47020572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The players’ positions of tactical groups in soccer can be mapped to formation-patterns by means of artificial neural networks (Kohonen, 1995). This way, the hundreds of positional situations of one half of a match can be reduced to about 20 to 30 types of formations (Grunz, Perl & Memmert, 2012; Perl, 2015), the coincidences of which can be used for describing and simulating tactical processes of the teams (Memmert, Lemmink & Sampaio, 2017): Developing and changing formations in the interaction with the opponent activities can be understood as a tactical game in the success context of ball control, space control and finally generating dangerous situations. As such it can be simulated using mathematical approaches like Monte Carlo-simulation and game theory in order to generate optimal strategic patterns. However, in accordance with results from game theory it turns out that in most cases the one optimal strategy does not exist (e.g. see Durlauf & Blume, 2010). Instead, a variety of partial strategies with different frequencies were necessary – an approach that is mathematically interesting but has nothing to do with soccer reality. An alternative approach, which is developed in the following, is to interrupt the strictness of a single strategic concept by creative elements, which improves flexible response to opponent activities as well as prevents from being analyzed by the opponent team. The results of respective simulation reach from improving strategic behaviour to recognizing strategic patterns and in particular to analyzing role and meaning of creative elements.
{"title":"Formation-based modelling and simulation of success in soccer","authors":"J. Perl","doi":"10.2478/ijcss-2018-0012","DOIUrl":"https://doi.org/10.2478/ijcss-2018-0012","url":null,"abstract":"Abstract The players’ positions of tactical groups in soccer can be mapped to formation-patterns by means of artificial neural networks (Kohonen, 1995). This way, the hundreds of positional situations of one half of a match can be reduced to about 20 to 30 types of formations (Grunz, Perl & Memmert, 2012; Perl, 2015), the coincidences of which can be used for describing and simulating tactical processes of the teams (Memmert, Lemmink & Sampaio, 2017): Developing and changing formations in the interaction with the opponent activities can be understood as a tactical game in the success context of ball control, space control and finally generating dangerous situations. As such it can be simulated using mathematical approaches like Monte Carlo-simulation and game theory in order to generate optimal strategic patterns. However, in accordance with results from game theory it turns out that in most cases the one optimal strategy does not exist (e.g. see Durlauf & Blume, 2010). Instead, a variety of partial strategies with different frequencies were necessary – an approach that is mathematically interesting but has nothing to do with soccer reality. An alternative approach, which is developed in the following, is to interrupt the strictness of a single strategic concept by creative elements, which improves flexible response to opponent activities as well as prevents from being analyzed by the opponent team. The results of respective simulation reach from improving strategic behaviour to recognizing strategic patterns and in particular to analyzing role and meaning of creative elements.","PeriodicalId":38466,"journal":{"name":"International Journal of Computer Science in Sport","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42284312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：