This study aimed to classify the movements of female soccer players during matches using raw data measured by inertial measurement units (IMUs). Twelve collegiate female soccer players were equipped with IMUs (100 Hz), and raw triaxial acceleration data from eight official matches were analyzed. The measurement data were separated every 3 s, and a Fast Fourier Transform (FFT) was performed. After FFT, the Euclidean distances between the data when the players were in the stationary state and other states were calculated to classify the movements of the players using the k-means method. The data of the clustering numbers classified as the stationary state were eliminated after analyzing the movements of players by video filming the matches. After classification, the average Euclidean distances between the stationary state and other movements were calculated. Consequently, the results showed that the upward and downward directions of the raw data affected the classification. Using the methods of this study, it was also shown that the distribution of Euclidean distances differed from player to player. Our findings indicate that the method used in this study can be used to classify and characterize the movements of female collegiate soccer players.

Accepted by: Phil Scarf We model tactical changes in association football as a Markov game. The pitch is discretized into nine zones and the states of the Markov game are defined according to the zone in which the ball is located in-play, the team in possession and the score. We first model tactical changes in a Markov decision process framework, wherein one team maximizes their probability of winning. Then, we model tactical changes in a two-person zero-sum Markov game framework, wherein both teams maximize their probability of winning. Fundamental to our modelling is the notion that tactical changes impact upon transition rates. We verify the models using data from matches in a season of the Japan Professional Football League. We define a change in transition rates that can be realized by changes in tactics, and illustrate an example of optimal tactical changes when both teams can vary their tactics. The models we develop in the paper can support managers who are considering important decisions about substitutions and changes to formation, for example, when a match is in-play.

This study models soccer as a Markov process. We discretize the pitch into nine zones, and define the states of the Markov process according to the zone of the pitch in which the ball is located, the team in possession and the score. Log-linear models are used to represent state transitions. Using the log-linear models, we estimate team strengths not only with respect to scoring or conceding, but also with respect to gaining or losing possession, while considering the discretized zones in which the ball is located. We use play-by-play data from Japan League Division 1 games in the 2015 season to illustrate our approach, and characterize the strengths of teams in this league. Sanfrecce Hiroshima is used as a particular example. We determine the goodness-of-fit of the log-linear models. Additionally, we introduce random effects into the log-linear models and discuss the complexity of the state transition process. We demonstrate that our Markov model, at the nine-zone level, provides estimates of teams’ strengths to a good approximation.

We use a Markov decision process to model the value of the sacrifice bunt. Specifically, we consider a nine-inning baseball game with non-identical batters and compute the degree to which sacrificing increases the probability of winning the game. We populate our model using data covering the National League of Major League Baseball, and demonstrate the importance of using the probability of winning the game when analyzing the value of the sacrifice bunt. We show how and why the criterion of maximizing the probability of winning is superior to that of maximizing the expected number of runs scored or the probability of scoring at least one run in the half inning Our model enables us to investigate situations that are not possible to investigate using earlier models, and find that the sacrifice bunt is more beneficial than previously thought. We also discuss the effect sizes of individual sacrifice bunts, and the effect of model simplifications on runner advancement or ignoring double plays.

The third World Baseball Classic (WBC) was held in March 2013. In this tournament, 16 teams play in Round 1 under a round-robin (RR) format and 8 teams which advanced to Round 2 play under a modified double-elimination (MDE) format. This 2013 WBC format is compared with the formats such as the past two WBCs held in 2006 and 2009, from the aspect of the probability of winning the tournament and the probability distribution of the number of games played by the same teams. We make the comparison by changing the relative strength of teams, and demonstrate the difference between the tournament formats.

In this paper, we propose a method for calculating probability of scores for men's team competition in artistic gymnastics. We here assume each gymnast's score as a normal distribution and provide a mathematical formulation for 6-5-4 format in the team competition. By setting the different mean and standard deviation (SD) of the normal distribution, we calculate the distributions of the team score, and obtain the relationship between the mean and SD of each gymnast and the expected number of the team score. We demonstrate an application of this method in the selection of five gymnasts to compete in each event.

Amateur baseball contests, particularly those involving young players, often feature a run limit, which establishes a maximum number of runs that may be scored in a half-inning of play. Although conventional wisdom can be used for designing the batting order under standard baseball rules, the composition of the optimal lineup under run limit is still unclear, and the best batting order could differ significantly from the traditional ordering. In this paper, we consider the impact of run limits on the design of the optimal batting order, by developing a Markov chain model for calculating the expected number of runs scored (ENRS) under 3- and 5-run limits. We apply this model to both a high-quality and a lower-quality team, using the data from the 2011 Little League World Series, and illustrate the effect of run limit on the ENRS and the optimal batting order.

Objective: "Mind reading" is the ability to understand another individual's mental states. In particular, individuals with developmental disorders, such as autism spectrum disorders, have a deficit in mind reading abilities. Similarly, individual differences in mind reading also exist among the healthy population and are often the cause of misunderstandings. Although the Empathizing and Systemizing Theory (E-S theory) has been used to explain individual developmental differences, its applicability to mind reading among Japanese adolescents has not been investigated. Therefore, the purpose of this study was to examine whether the E-S theory explains individual differences in mind reading among Japanese adolescents.Participants: Participants were 240 Japanese university students (M=20.58, SD=0.51).Methods: We administered questionnaires based on Japanese versions of the Empathy and Systemizing Quotients, and the Reading the Mind in the Eyes Test.Results: Empathizing, but not systemizing, was found to be related to mind reading. Additionally, relative differences in empathizing and systemizing, rather than its combination, were associated with mind reading.Conclusion: Since relative differences in empathizing and systemizing affect mind reading, we concluded that the E-S theory explains individual differences in mind reading among Japanese adolescents.

Background Due to a 2010 rule revision, attack with the arms or hands below the belt is prohibited, with the penalty being hansoku-make for the first offense. This strict rule must have affected competitors’ technical-tactical behaviors with regards to using hands and arms below the belt in contests. The purpose of the present study is transformation of technical-tactical behaviors for hand techniques attacking below the belt in men’s contests before and after the 2010 rule revision. Material & Methods: 436 men’s contests from the 2009 Grand Slam Tokyo and the 2010 Grand Slam Paris were examined. DVDs of the Federation of All Japan Judo were used. Five hand techniques used in below the belt maneuvers as referenced in the Kodokan manual were investigated. The analysts unanimously decided if the techniques performed by competitors could be categorized within one of the five hand techniques studied. Results: Use of kibisu-gaeshi significantly decreased (p<0.05). Use of sukui-nage used in countering an opponent’s crossguard grab significantly increased (p<0.05). Use of kata-guruma not utilizing below the belt hand or arm grabbing significantly increased (p<0.01). German, English, and Japanese contestants significantly decreased in their use of hand techniques below the belt (p<0.01, p <0.05, p<0.05, respectively). Conclusions: Sukui-nage was increasingly used to counter the opponent’s use of the cross-guard grab; the kata-guruma technique underwent a style transformation. On the other hand, kibisu-gaeshi could not be used effectively with the rule revision.

In previous studies for analyzing the batting order of baseball games, the order is evaluated by its expected number of runs scored in a game, under the Markov chain model on the D'Esopo and Lefkowitz runner advancement model. However, the order to maximize the expected number of runs may not be the best order in the sense that it may not get more than 0.5 in probability of winning the game against other possible batting orders. In this sense, the best batting order is reconsidered, and it is tried to find better orders than the order which maximizes the expected number of runs. In this paper, the existence of such orders and the difference between the best orders and the order to maximize the expected number of runs are concretely shown by taking into account of not only the expected number of runs but also the standard deviation of runs, based on the data of Major League teams.

This study aimed to evaluate individual and team judo strengths using an analytic hierarchy process (AHP). The source of the decision was based only upon the international regulation values assigned to each of the decisive technique: 10 points for an ippon, 7 for a waza-ari and 5 for yuko(s). The data were obtained from Japan's interscholastic athletic competition for men's judo (high school teams) in 2005. Our AHP technique demonstrated an ability to predict judo strengths of individual players, and to detect potential players regardless of unsuccessful team results. There was a significant but small correlation between the actual team rankings and predicted team strengths. The predicted team strengths, however, may be more informative and appropriate to evaluate judo strengths than the tournament results, as they were based on the content of each individual match, rather than just win/lose results. Coaches or talent scouts should consider the estimated individual or team strengths as well as competition results to make more accurate decisions when selecting players or teams.

In this paper, we analyze tactical conflicts between attacking formations and blocking formations in the phase of reception attack in volleyball, using a zerosum game model. In this model, we categorize the attacking formations into 9 patterns which consist of 3 moving patterns of forward players and 3 positions (right, center and left) from which the ball can be spiked. We also categorize the blocking formations into 3 formations: “spread”, “bunch” and “dedicate”. The conflicts are formulated as a zero-sum game by tabulating these formations, and analyzed by calculating the equilibrium points together with the value of the game. Following this formulation we have developed a game analysis system with Visual Basic programming code for solving the game. The solution gives us minimax strategies with the ratio of successful blocks. Here, we try an application of game theoretic analysis, using the empirical data taken from an intercollegiate women’s league in 2004. We estimate the values of the game in the matches, and illustrate a possible improvement in terms of the allocation of attacking and blocking formations used in the matches from the macro-view of game theoretic analysis. This approach could hopefully provide a new standpoint of the analysis of real volleyball matches. KEYWORDS, GAME THEORY, TACTICS, RECEPTION ATTACK, VOLLEYBALL

In football leagues, a won match produces three points (all for the winner) whereas a drawn match produces only two (one for each team). Here, the total resource from the viewpoint of league points is not constant and the gain of the match for both teams changes depending on the result of the match. To cater for this situation, we propose a formulation for modelling tactical changes of formation in an association football match as a non-zero-sum game using game theory. In this paper, we focus on two well-known teams in the J. League and analyse their offensive and defensive strengths based on their formation, i.e., a combination of the number of each type of outfield player on the pitch. Using these estimated offensive and defensive strengths, we develop the mathematical formulation for analyzing tactical changes of these teams' formations from the viewpoint to increase their expected number of league points gained in a match, and quantitatively demonstrate not only the effect of the introduction of the league point system on the tactical change, but also the effect of cooperation between managers which could make both teams benefit in terms of the expected number of league points gained in a match.

This paper addresses a problem of how to calculate the probabilities of winning for the sports contest under the assumption that the strength among contestants can be described by a linearly ordered set. The general formulae for calculating the probabilities of winning are given. Applying the general formulae, we give the probabilities of winning the Asian Qualifiers for 2006 FIFA World Cup.

Although tactical decisions made by managers during a match of team sports are very important, there have been few quantitative analyses which include the effect of interaction between both teams' decisions, because of the complexity of the problem where one team's decision will affect the other team's. A game theoretic approach can be useful for tackling this type of problem.This paper proposes a game theoretic approach to modeling tactical changes of formation in an association football match. We assume probabilities of scoring and conceding a goal follow Poisson distributions and use a regression model to evaluate the means of the distributions. These means represent the offensive strength for scoring a goal and defensive propensity to concede a goal in terms of a team's formation, i.e. a combination of the number of each type of outfield player on the pitch, and are estimated by means of the maximum likelihood method. We then develop a mathematical formulation with which we can calculate the probability of the home team winning the match, and use it to analyse tactical changes of the teams' formations, modeling the football match as a zero-sum game, in which the gain in probability of one team winning is equal to the loss in probability of the other team winning. We demonstrate how the managers' decisions affect the probability of winning the match using real data of the Japan professional football league, by showing four cases of the quality of both managers' decisions, depending on whether they each use their best or worst strategies.There still remains some uncertainty and longer observational studies will be required for a complete analysis, but this method can help to evaluate quantitatively the quality of tactical decisions made by managers.

This paper proposes a method for identifying the optimal strategy for substituting players in a baseball game, taking into consideration the handedness of players, which is one of the main factors in terms of managerial decision-making for substitution. Using a Markov chain model, we incorporate the effect of the handedness of players by introducing the concept of the defensive earned run average ...

This paper proposes a method for identifying the optimal strategy for substituting pitchers in a baseball game played not under the Designated Hitter rule. Using a Markov Chain model we incorporate the effect of the defensive ability of pitchers using Earned Run Average (ERA) as a measure, and develop a dynamic programming formulation to evaluate the effect of pitcher substitution. The method is illustrated using a match based on the real line-ups of the Colorado Rockies and the San Francisco Giants in the National League of Major League Baseball. We show how this approach may help to determine when to make a substitution and how much the probability of winning increases if the optimal strategy is followed.