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Value functions are used in sports applications to determine the optimal action players should employ. However, most literature implicitly assumes that the player can perform the prescribed action with known and fixed probability of…
With the aid of mathematical modelling (basic tool is the random walk with absorbing barriers) we derive subsequent formulas to study the effect of different versions of possible rules. For different rules the probability of winning a game,…
Individual sports competitions provide a natural setting for examining the relative importance of talent and luck/chance in achieving success. The belief that success is primarily due to individual abilities and hard work rather than…
This paper investigates the Tennis Momentum Model (TMM), which aims to enhance the understanding of match dynamics by integrating key factors such as efficiency, historical scoring probabilities, and real-time scoring data. The model is…
Current exergaming sensors and inertial systems attached to sports equipment or the human body can provide quantitative information about the movement or impact e.g. with the ball. However, the scope of these technologies is not to…
We establish a general formula for the distribution of the score in table tennis. We use this formula to derive the probability distribution (and hence the expectation and variance) of the number of rallies necessary to achieve any given…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
In this paper we analyse tiebreak results from some tennis players in order to investigate whether we are able to identify some strategy in this crucial moment of the game. We compared the observed results with a binomial distribution…
Traditional NBA player evaluation metrics are based on scoring differential or some pace-adjusted linear combination of box score statistics like points, rebounds, assists, etc. These measures treat performances with the outcome of the game…
Automated tennis stroke analysis has advanced significantly with the integration of biomechanical motion cues alongside deep learning techniques, enhancing stroke classification accuracy and player performance evaluation. Despite these…
We show that information on the first server influences the expected total number of games and margin in a tennis match under the standard assumption that each player's serve point win probability remains constant, and identify the exact…
In reinforcement learning, it is typical to use the empirically observed transitions and rewards to estimate the value of a policy via either model-based or Q-fitting approaches. Although straightforward, these techniques in general yield…
This study explores strategic considerations in professional golf's Match Play format, challenging the conventional focus on individual performance. Leveraging PGA Tour data, we investigate the impact of factoring in an adversary's…
We study how individuals trade off outcome ("what") and process ("how") utility in high-stakes strategic decisions, namely professional tennis. Using optimality conditions and the second-service rule, we derive a sufficient condition for…
This paper represents an analysis on the momentum of tennis match. And due to Generalization performance of it, it can be helpful in constructing a system to predict the result of sports game and analyze the performance of player based on…
There is a hidden energy in tennis, which cannot be seen or touched. It is the force that controls the flow of the game and is present in all types of matches. This mysterious force is Momentum. This study introduces an evaluation model…
The standard mathematical approach to fourth-down decision making in American football is to make the decision that maximizes estimated win probability. Win probability estimates arise from machine learning models fit from historical data.…
Tennis is one of the world's biggest and most popular sports. Multiple researchers have, with limited success, modeled the outcome of matches using probability modelling or machine learning approaches. The approach presented here predicts…
Wearable technology has transformed sports analytics, offering new dimensions in enhancing player experience. Yet, many solutions involve cumbersome setups that inhibit natural motion. In tennis, existing products require sensors on the…
Success in sports is a complex phenomenon that has only garnered limited research attention. In particular, we lack a deep scientific understanding of success in sports like tennis and the factors that contribute to it. Here, we study the…