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Received: March 26, 2021 / Modified: May 8, 2021 / Accepted: May 10, 2021 / Published: May 13, 2021

Predicting the outcome of sporting events has always attracted the attention of various groups of people, such as club managers, coaches, betting companies and the general public. The specific nature of each game plays an important role in adapting different forecasting methods based on different mathematical and statistical models. In this paper, the general method for evaluating games has a well-defined structure and a rigorous evaluation system based on the assumption of independent and uniform distribution of points. It has been shown that such models can be improved by introducing dynamism into game models in the form of sports momentum. Formal mathematical models for performing these actions are based on conditional expectations and proposed empirical Bayesian estimates, which are finally integrated into an integrated model based on Monte Carlo simulations. . Finally, this method applied to real-life volleyball data shows a significant improvement over previous methods when it comes to predicting match results. This method can be implemented in an expert program to better understand the player’s performance in different stages of the game or to study the field conditions that may arise in the field conditions. different.

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Although predicting the outcome of sports events has always been of interest to everyone, it has become more popular with the development of the Internet and the advent of live betting. Historically, domain experts have played an important role in generating such forecasts. Based on accumulated experience, familiarity with the domain and current data, domain experts will make predictions. However, relying on human expertise and hand-generated estimates is not a scalable or cost-effective solution. In addition, domain experts are often unable to make timely forecasts. Recently, with the increase in processor power and sustained power of modern information systems and developments in the field of predictive data analysis, computers are playing a leading role in predicting the future. predict the outcome of sporting events – not only regarding the final outcome, but also regarding the various events occurring in the game.

Predictive analytics has so far been successfully applied to a variety of sports ranging from football [1, 2] and basketball [3, 4], hockey [5], cricket [6] and rugby [7]. The nature of each game greatly influences the alignment of the main methods used for prediction. Games with a strictly defined structure and strict scoring system are more suitable for this purpose because they are easier to measure as a discrete random process, such as the Markovian process [8] ]. Because of this fact, throughout this article, such games will be referred to as discrete games or Markovian games. Common examples of such sports are tennis and volleyball. Articles dealing with this approach tend to choose tennis as a model [9, 10]. In this paper, the focus will be on volleyball as it has rarely been mentioned in scientific papers so far. Despite this fact, the principles presented are generalizable and can be used in other built-in games that use the same strictly defined scoring system.

Most of the published methods focus on building models (before and after the game) based on predicting match outcomes based on historical data and standard service percentages of both teams. two teams. These values ​​are predicted first and then fed into mathematical equations based on Markov series to generate the probability that a given team will win the game or to predict the time of the game by the total number of points. will be played in the game. These models are created with the general assumption that scores in fuzzy games are uniform and independently distributed (commonly referred to as iid). This means that the average serve percentages of both teams, once calculated from historical data, will never change for every game where the outcome is predicted. The concept of independence originates from the assumption that the probability of winning a service point is not affected in any way by the outcome of previous points. The assumption that every score is equal, regardless of whether it is a negligible score at the start of the match or a critical score in the final set, is part of the iid footnote. Schutz [11] was the first to describe the tennis game as a Markov sequence with the probability of continuously transitioning between states. Pollard [12] presented an analytical method used to calculate games, setups and potential games. He also finds solutions to the mean and variance of scores played in a game, set, and game respectively. Since then, many papers have been published proposing solutions for predicting the outcome of a tennis match, be it before the match starts, pre-match models [9, 13, 14] or during the match. outcome prediction match, or match pattern [15, 16, 17, 18]. Although tennis focuses heavily on the Markovian sports model, there are also articles that focus on volleyball analysis. The History of Volleyball Analysis was published in 2004 [19], where the authors found expressions to establish the probability of success according to the Legendre polynomial. They also show the importance of knowledge of who serves first in a deciding set in volleyball. Barnet et al. [20] made the first attempt to estimate the probability of winning the set and the length of the volleyball set (in terms of the number of points played in the set) using a Markovian series model. Give them multiplication formulas to estimate those values. Ferrante and Fonseca [21] restructured the previous paper from the combinatorial point of view, and at the same time made a distinction between the two system points. The common assumption on which all these papers rest is a uniform and independent score distribution.

The assumption of an independent and uniform score distribution greatly facilitates the volleyball and tennis game model, but contradicts the most common fact in psycho-psychological dynamics [22]. . Since the late twentieth century, the existence of mental psychology has been the subject of research in the field of sport, where the term “hot hand” is used frequently. In short, “hot hand” or morale is the belief that a player has a good chance of scoring after a few successful points. Research has been done in many sports, notably basketball [23, 24, 25, 26], baseball, [27] and tennis [28, 29, 30, 31, 32, 33, 34 , 35]. The most extensive research on the existence of mental health has been done in volleyball [36, 37, 38]. It’s nearly impossible to watch a game without a sports commentator mentioning the words “hot hands” or “hot teams” at some point during the game. Considering the number of timeouts that coaches call in games after a good number of consecutive moves by the opposing team, it is clear that coaches believe in the existence of psychology. Although a very plausible idea, believed by a large group of non-professionals, in scientific research, belief in the existence of mental momentum remains divided (Bar-Eli et al. [39] rewrote an excellent idea). This paper assumes that motivation exists in volleyball and proposes a prediction method related to a short-term increase in the probability of scoring through an individual’s performance after a motivating event occurs. go out. This would be called a short-term movement. Finally, an analysis is performed on how this assumption affects the prediction of the outcome of volleyball games and the results are compared with models based on the iid assumption.

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Barnet et al.