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In professional beach volleyball, the belief in “never give up” is deeply ingrained, but its strategic implications remain underexplored. This study employs a mixed-methods approach, combining sport psychology and sport informatics, to assess the perception of set-winning probabilities (SWPs) in beach volleyball, as this is a crucial factor for strategic in-game decisions and improved performance. We examined cognitive biases and adaptive strategies influencing SWP estimations in scenarios of substantial trailing or leading. Forty-three members of the German beach volleyball national team estimated SWPs for 60 scores, responded to questions on game tactics, and completed questionnaires measuring optimism, pessimism, confirmation bias, and the sunk cost fallacy. Empirical SWPs were calculated from a dataset of 6,571 matches. Results revealed that participants significantly overestimated SWPs when trailing and underestimated them when leading. Optimism and confirmation bias significantly shaped these estimations. Notably, confirmation bias had a dual role: in trailing scenarios, it amplified overestimation, causing players to underestimate their disadvantage, while in leading scenarios, it improved accuracy by focusing on the likelihood of victory. Players were more likely to recall situations reinforcing the belief that “We (can still) win”. These findings highlight the psychological and strategic complexities of SWP estimations in competitive beach volleyball.

Background The technical and tactical diagnosis of table tennis is extremely important in the preparation for competition which is complicated by an apparent nonlinear relationship between athletes’ performance and their sports quality. The neural network model provides a high nonlinear dynamic processing ability and fitting accuracy that may assist in the diagnosis of table tennis players’ technical and tactical skill. The main purpose of this study was to establish a technical and tactical diagnosis model of table tennis matches based on a neural network to analyze the influence of athletes’ techniques and tactics on the competition results. Methods A three-layer Back Propagation (BP) neural network model for table tennis match diagnosis were established. A Double Three-Phase evaluation method produced 30 indices that were closely related to winning table tennis matches. A data sample of 100 table tennis matches was used to establish the diagnostic model ( n  = 70) and evaluate the predictive ability of the model ( n  = 30). Results The technical and tactical diagnosis model of table tennis matches based on BP neural network had a high-level of prediction accuracy (up to 99.997%) and highly efficient in fitting ( R 2  = 0.99). Specifically, the technical and tactical diagnosis results indicated that the scoring rate of the fourth stroke of Harimoto had the greatest influence on the winning probability. Conclusion The technical and tactical diagnosis model of table tennis matches based on BP neural network was highly accurate and efficiently fit. It appears that the use of the model can calculate athletes’ technical and tactical indices and their influence on the probability of winning table tennis matches. This, in turn, can provide a valuable tool for formulating player’s targeted training plans.

Schools with the highest average student performance are often the smallest schools; localities with the highest rates of some cancers are frequently small; and the effects observed in clinical trials are likely to be largest for the smallest numbers of subjects. Informal explanations of this “small-schools phenomenon” point to the fact that the sample means of smaller samples have higher variances. But this cannot be a complete explanation: If we draw two samples from a diffuse distribution that is symmetric about some point, then the chance that the smaller sample has larger mean is 50%. A particular consequence of results proved below is that if one draws three or more samples of different sizes from the same normal distribution, then the sample mean of the smallest sample is most likely to be highest, the sample mean of the second smallest sample is second most likely to be highest, and so on; this is true even though for any pair of samples, each one of the pair is equally likely to have the larger sample mean. The same effect explains why heteroscedasticity can result in misleadingly small nominal p-values in nonparametric tests of association. Our conclusions are relevant to certain stochastic choice models, including the following generalization of Thurstone’s Law of Comparative Judgment. There are n items. Item i is preferred to item j if Zi < Zj , where Z is a random n-vector of preference scores. Suppose ℙ {Zi = Zj }= 0 for i ≠ j, so there are no ties. Item k is the favorite if Zk < min i ≠ k Zi . Let pi denote the chance that item i is the favorite. We characterize a large class of distributions for Z for which p₁ > p₂ > · · · > pn . Our results are most surprising when ℙ{Zi < Zj }= ℙ{Zi > Zj }= ½ for i ≠ j, so neither of any two items is likely to be preferred over the other in a pairwise comparison. Then, under suitable assumptions, p₁ > p₂ > ···> pn when the variability of Zi decreases with i in an appropriate sense. Our conclusions echo the proverb “Fortune favors the bold.”

We analyze the traditional board game the Game of the Goose. We are particularly interested in the probabilities of the different players winning, and we show that we can determine these probabilities exactly for up to six players and using simulation for any number of players. Our original motivation to investigate this game came from progress in stochastic process theories, which prompted the question of whether such methods are capable of dealing with well-known probabilistic games. As these games have large state spaces, this is not trivial. As a side effect we find that some common wisdom about the game is not true.

There is a growing interest in applying machine learning algorithms to real-world examples by explicitly deriving models based on probabilistic reasoning. Sports analytics, being favoured mostly by the statistics community and less discussed in the machine learning community, becomes our focus in this paper. Specifically, we model two-team sports for the sake of one-match-ahead forecasting. We present a pioneering modeling approach based on stacked Bayesian regressions, in a way that winning probability can be calculated analytically. Benefiting from regression flexibility and high standard of performance, Sparse Spectrum Gaussian Process Regression (SSGPR) – an improved algorithm for the standard Gaussian Process Regression (GPR), was used to solve Bayesian regression tasks, resulting in a novel predictive model called TLGProb. For evaluation, TLGProb was applied to a popular sports event – National Basketball Association (NBA). Finally, 85.28% of the matches in NBA 2014/2015 regular season were correctly predicted by TLGProb, surpassing the existing predictive models for NBA.

The procurement process is one of the most important phases in any project life cycle, particularly when it comes to selecting the right contractor for the job. Awarding the contract to the best bid proposal is a critical step to ensure the greatest value. BIM has been recognized as not only a geometric modelling of buildings, but also, it facilitates the different stages in management of construction projects. The purpose of this paper is to study the impact of using Building Information Modeling (BIM) in the tendering process from the contractor’s perspective, based on a probability model able to predict winning probability, regardless of relative weight. The main objective of this research is to measure the likelihood of winning a tender in the case of implementing BIM strategy, compared with contractors who do not use BIM. The research uses a literature review, surveys, and interviews with experts to develop a model that predicts the probability of winning a contract; this is determined by measuring the BIM impact on each selection criterion in a multicriteria selection process using the Analytical Hierarchy Process (AHP) to develop a probability-based model. The results of the survey and the interview show that BIM strategy has a variant influence on the score the contractor could have on each of them raising the probability of winning the tender. The main result of this paper is the property-based model, which is able to predict BIM winning probability regardless of relative weight, which can be applied in any country. Nonetheless, the Saudi case study shows that utilizing BIM when proposing could increase the winning probability by up to 9.42% in the case of Quality-Based Selection (QBS), and to 5.5% in the case of Cost-Based Selection (CBS).

Esta investigación muestra que el convencionalismo tan extendido en la cultura popular deportiva “entrenador nuevo, victoria segura” tiene una base empírica. Obviamente, el tópico no se cumple siempre, pero la evidencia que se deriva del análisis de la historia de cambios de entrenador en la NBA revela que, a nivel general, es más probable que este dicho se haga realidad. A través del análisis de modelos logit, se compara la probabilidad de victoria de los equipos que cambiaron de entrenador en el partido anterior y posterior al cambio. Así, sobre un “partido tipo”, la probabilidad de victoria para el nuevo entrenador es más de 2 veces superior al último partido jugado por el equipo. Diversas implicaciones relacionadas con variables como el factor cancha o la calidad de los equipos son discutidas.

The comparison of independent random variables can be modeled by a set of dice and a reciprocal relation expressing the winning probability of one dice over another. It is well known that dice transitivity is a necessary 3-cycle condition for a reciprocal relation to be dice representable, i.e. to be the winning probability relation of a set of dice. Although this 3-cycle condition is sufficient for a rational-valued reciprocal relation on a set of three elements to be dice representable, it has been shown that this is no longer the case for sets consisting of four or more elements. In this contribution, we provide a necessary 4-cycle condition for dice representability of reciprocal relations. Moreover, we show that our condition is sufficient in the sense that a given rational-weighted 4-cycle and reciprocally weighted inverse cycle, both fulfilling the 4-cycle condition, can be extended to a winning probability graph representing a dice-representable reciprocal relation on four elements.

Suppose that both you and your friend toss an unfair coin n times, for which the probability of heads is equal to α. What is the probability that you obtain at least d more heads than your friend if you make r additional tosses? We obtain asymptotic and monotonicity/convexity properties for this competing probability as a function of n, and demonstrate surprising phase transition phenomenon as the parameters d, r, and α vary. Our main tools are integral representations based on Fourier analysis.

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 score. We use these findings to investigate the dependence of these quantities on the different parameters involved (number of points needed to win a set, number of consecutive serves, etc.), with particular focus on the rule change imposed in 2001 by the International Table Tennis Federation (ITTF). Finally, we briefly indicate how our results can lead to more efficient estimation techniques of individual players' abilities.