Nobuyoshi Hirotsu

Using a Markov process model of an association football match to determine the optimal timing of substitution and tactical decisions

A football match is modelled as a four-state Markov process. A log-linear model, fed by real data, is used to estimate transition probabilities by means of the maximum likelihood method. This makes it possible to estimate the probability distributions of goals scored and the expected number of league points gained, from any position in a match, for any given set of transition probabilities and hence in principle for any match. This approach is developed in order to estimate the optimal time to change tactics using dynamic programming, either by making a substitution or by some other conscious change of plan. A simple example of this approach is included as an illustration.

Determining the best strategy for changing the configuration of a football team

This paper proposes a dynamic programming (DP) approach to find the optimal substitution strategy for a football match, which maximises the probability of winning or the expected number of league points, supported by real data of the English Premier League. We use a Markov process model to evaluate the offensive and defensive strengths of teams by means of maximum likelihood estimators. We develop a DP formulation to derive quantitatively the optimal substitution strategy of a team, in relation to the number required of each type of outfield player. We demonstrate how this approach may help to determine how many of each type of player should start a match and be substituted during a match. We also show how the expected league points would increase if the optimal strategy were followed.

The Professional Foul in Football: Tactics and Deterrents

We demonstrate the use of a model calibrated using data from every 1999–2000 Premiership match to determine the circumstances under which a player ‘should’ commit a professional foul in order to benefit his team. The results are illustrated using two hypothetical matches, one between evenly balanced teams and one where one of the teams is much stronger than the other. These circumstances turn out to be wide-ranging and, in some cases, somewhat counterintuitive. The many drawbacks of the current system for punishing such fouls are discussed, and a simple remedy is proposed that would not only be much fairer to all involved but would also, at a stroke, render the professional foul virtually obsolete.

The transformation of technical-tactical behaviors for hand techniques used in attacking below the belt after the 2010 International Judo Federation rule revision

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.

Modeling a Baseball Game to Optimize Pitcher Substitution Strategies Using Dynamic Programming

The modeling of baseball games has been a topic of interest to several OR workers (Bennett 1998,Bukiet et al. 1997, D’Esopo and Lefkowitz 1977, Hi-rotsu and Wright 2003, Trueman 1976, Trueman 1977), and the task of finding optimal tactics can be assisted by the application of OR techniques. In a pre-vious paper (Hirotsu and Wright 2003), we developed a Markov chain model of a baseball game between teams consisting of non-identical players, taking into account the number of runs by which the home team leads. In the paper we proposed the formulation for obtaining the optimal pinch-hitting strategy under the designated hitter (DH) rule, for which the substitution of pitchers is not a very complex issue, since under the DH rule pitchers do not have to bat.