Sports Statistics

In this paper,I have found a formula using Linear Regression Techniques which find the relationship between the different statistics(points with other factors) given on a Television Screen in Football Matches.Also the relationship may give something different dependence on a certain parameter as we may not think.That is why the partial correlation clears our doubt.

Data analytics in sports is crucial to evaluate the performance of single players and the whole team. The literature proposes a number of tools for both offence and defence scenarios. Data coming from tracking location of players, in this respect, may be used to enrich the amount of useful information. In basketball, however, actions are interleaved with inactive periods. This paper describes a methodological approach to automatically identify active periods during a game and to classify them as offensive or defensive. The method is based on the application of thresholds to players kinematic parameters, whose values undergo a tuning strategy similar to Receiver Operating Characteristic curves, using a ground truth extracted from the video of the games.

Because of the advent of GPS techniques, a wide range of scientific literature on Sport Science is nowadays devoted to the analysis of players’ movement in relation to team performance in the context of big data analytics. A specific research question regards whether certain patterns of space among players affect team performance, from both an offensive and a defensive perspective. Using a time series of basketball players’ coordinates, we focus on the dynamics of the surface area of the five players on the court with a two-fold purpose: (i) to give tools allowing a detailed description and analysis of a game with respect to surface areas dynamics and (ii) to investigate its influence on the points made by both the team and the opponent. We propose a three-step procedure integrating different statistical modelling approaches. Specifically, we first employ a Markov Switching Model (MSM) to detect structural changes in the surface area. Then, we perform descriptive analyses in order t...

Achieving superior performance parameters in major competitions has highlighted a number of issues that characterize the current basketball game practiced by the best teams in the world. Depending on the height, role, importance and the effectiveness of players on their positions, specific models are to be observed in the case of senior teams [In this paper we present a comparative study regarding the parameters’ models in the men's basketball games during the World Championships in Japan - 2006, in Turkey - 2010 and in Spain - 2014. Along with data interpretation, we tried to effectively bring our scientific contribution in shaping a model significant for the international basketball games, useful for the specialists in the field. Centralization of the statistical data used in our study was useful in calculating the averages for each game parameter and the increasing value for each tournament, managing to achieve a precise statistical comparison. The values encountered in this ...

A new approach to performance analysis in team sports consists in studying movements and trajectories of players during the game. State of the art tracking systems produce spatio-temporal traces of players that have facilitated a variety of research aimed to to extract insight from trajectories. Several methods borrowed from machine learning, network and complex systems , geographic information system, computer vision and statistics have been proposed. However, the use of an effective and easy-to-use visual tool in support to these methods is of major importance. To this scope this paper suggests the use of motion charts, built by means of the open-source gvisMotionChart function in googleVis package in R, a user-friendly procedure that also allows to easily import data. A basketball case study is presented. Data refers to a match played by an italian team militant in C-gold league on March 22nd, 2016. Analyses show that motion charts give insights on different spacing structures among offensive and defensive actions, corroborating evidences from other supporting analyses.

Because of the advent of GPS techniques, a wide range of scientific literature on Sport Science is nowadays devoted to the analysis of players' movement in relation to team performance in the context of big data analyt-ics. A specific research question regards whether certain patterns of space among players affect team performance, from both an offensive and a defensive perspective. Using a time series of basketball players' coordinates, we focus on the dynamics of the surface area of the five players on the court with a twofold purpose: (i) to give tools allowing a detailed description and analysis of a game with respect to surface areas dynamics and (ii) to investigate its influence on the points made by both the team and the opponent. We propose a three-step procedure integrating different statistical modelling approaches. Specifically , we first employ a Markov Switching Model (MSM) to detect structural changes in the surface area. Then, we perform descriptive analyses in order to highlight associations between regimes and relevant game variables. Finally, we assess the relation between the regime probabilities and the scored points by means of Vector Auto Regressive (VAR) models. We carry out the proposed procedure using real data and, in the analyzed case studies, we find that structural changes are strongly associated to offensive and defensive game phases and that there is some association between the surface area dynamics and the points scored by the team and the opponent.

Sports leagues consist of conferences subdivided into divisions. Teams play a number of games within their divisions and fewer games against teams in different divisions and conferences. Usually, a league structure re-mains stable from one season to the next. However, structures change when growth or contraction occurs, and realignment of the four major professional sports leagues in North America has occurred more than twenty-five times since 1967. In this paper, we describe a method for realigning sports leagues that is flexible, adaptive, and that enables construction of schedules that min-imize travel while satisfying other criteria. We do not build schedules; we develop league structures which support the subsequent construction of ef-ficient schedules. Our initial focus is the NHL, which has an urgent need for realignment following the recent move of the Atlanta Thrashers to Win-nipeg, but our methods can be adapted to virtually any situation. We exam-ine a variety of scenario...

Big Data Analytics help team sports' managers in their decisions by processing a number of different kind of data. With the advent of Information Technologies, collecting, processing and storing big amounts of sport data in different form became possible. A problem that often arises when using sport data regards the need for automatic data cleaning procedures. In this paper we develop a data cleaning procedure for basketball which is based on players' trajectories. Starting from a data matrix that tracks the movements of the players on the court at different moments in the game, we propose an algorithm to automatically drop inactive moments making use of available sensor data. The algorithm also divides the game into sorted actions and labels them as offensive or defensive. The algorithm's parameters are validated using proper robustness checks.

Spatial tracking data are used in sport analytics to study the players' position during the game in order to evaluate game strategies, players' roles, performance, also in prospect. From the broad fields of statistics, mathematics, information science and computer science it is possible to draw theories and methods useful to produce innovative results based on speed, distance, players' separation trajectories. In basketball , spatial tracking data can be combined with play-by-play data, joining results on spatial movements to team performance. In this paper, using tracking data from basketball, we study the spatial pattern of players on the court in order to contribute to the literature of data mining methods for tracking data analysis in sports, with the final objective of suggesting new game strategies to improve team performance.

For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼eventum mechanics in the most approachable way. This is what I'm trying to do in this work. The co∼eventum mechanics is another name for the co∼event theory, i.e., for the theory of experience and chance which I axiomatized in 2016 [1, 2]. In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conict between quantum observers and quantum observations [4]. Since my theory of uncertainty satises the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the " tossing a coin ". Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the " "flipping a coin " and the " spinning a coin " to explain the co∼eventum mechanics, which describes the results of a combined experienced random experiment. I would like to resort to the usual for the probability theory " coin-based " analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance. Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual " coin-based " model that clarifies what occurs as a result of a combined experienced random experiment in which the experience of observer faces the chance of observation. I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics.

Due to the advent of GPS techniques, a wide range of scientific literature on Sport Science is nowadays devoted to the analysis of players movement
in relation to team performance in the context of big data analytics. A specific research question regards whether certain patterns of space among
players affect team performance, from both an offensive and a defensive perspective. Using a time series of basketball players coordinates, we
focus on the dynamics of the surface area of the five players on the court with a twofold purpose: (i) to give tools allowing a detailed description and
analysis of a game with respect to surface areas dynamics and (ii) to investigate its influence on the points made by both the team and the opponent.
We propose a three-step procedure integrating different statistical modelling approaches. Specifically, we first employ a Markov Switching Model
(MSM) to detect structural changes in the surface area. Then, we perform descriptive analyses in order to highlight associations between regimes
and relevant game variables. Finally, we assess the relation between the regime probabilities and the scored points by means of Vector Auto
Regressive (VAR)models. We carry out the proposed procedure using real data and, in the analyzed case studies, we find that structural changes
are strongly associated to offensive and defensive game phases and that there is some association between the surface area dynamics and the points
scored by the team and the opponent.

This dissertation uses simulation-based methods to evaluate cricket players for the Indian Premier League T20 competition prior to the 2015 season. Using techniques such as Expectation-Maximisation, Simulation and a Cumulative Probit Model for ordinal data, we consider the batting and bowling ability of a player independently, and then combine them into a metric called a WAVE (Wins Above Average) score, which is similar in concept to existing work in baseball. Data is used from the first six seasons of the tournament, and the seventh season acts as a test. We finally consider the problem of assembling a team within constraints ahead of the 2015 season and produce optimal hypothetical solutions.

You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or ``No'' with the believability that your experience tells you.

The present study verified if 10 minutes of interval in the 1RM test had been enough for recovery the total of strength and reliability of its re-test 10 minutes after application. Sample was composed by 20 health trained male without history of lesion, aging (23.5  ± 3.69), weight (73.1 kg ± 9.93) and stature (1.76 m ± 0.05). To analyze the recovery interval between 1RM tests a paired t test was used, and for the reliability analysis the intraclass correlation coefficient (ICC) was used to determine the internal consistence. Only high ICC indices were found (> 0.90, p < 0.001), reaching the reability needs. We concluded that 1RM test carried out in a same day and 10 minutes after presented a high ICC index for bench press exercise to male that are familiar to the test, showed adequate recovery interval to restore strength.

O presente estudo verificou se 10 minutos de intervalo no teste de 1RM foram suficientes para a recuperação total de força e fidedignidade de seu re-teste 10 minutos após sua aplicação. A amostra foi composta de 20 homens saudáveis e treinados, sem histórico de lesão, com média de idade (23,5 ± 3,69), peso (73,1 kg ± 9,93) e estatura (1,76 m ± 0,05). Para analisar o intervalo de recuperação entre os testes de 1RM utilizou-se um teste t pareado, já para a análise da fidedignidade utilizou-se o coeficiente de correlação intra-classe (CCI) para determinar a consistência interna. Somente foi verificado um alto índice de CCI (>0,90, p < 0,001), atingindo excelente fidedignidade. Conclui-se que o teste de 1RM realizado em um mesmo dia e 10 minutos após apresenta um alto índice de CCI para o exercício de supino em homens familiarizados ao teste, mostrando-se suficiente para o intervalo de recuperação para restabelecimento total da força.

There is a three step process in calculating the Capitalization Rate of soccer in the U.S.A. Combining Phase 2, Participation Rate, with Phase 3, Developmental Rate, and comparing to Phase 1, Target Participation Rate, reveals the capitalization rate of (youth) soccer in the U.S.A.

Moneyball was a 2011 American sports drama film that popularized the role of Statistics in baseball like never before. The film depicts the true story of a professional baseball team, the Oakland Athletics and their 2002 regular season. The team won 20 consecutive games - tying a 118 year old record for the 3rd highest winning streak in history. This was all the more surprising as this was a franchise without any notable “big name” players. More significantly, the Oakland As were ranked the third lowest in payroll in the entire league. For our particular interest, behind this winning streak was a statistical model designed by Peter Brandt a young Yale economics graduate. Going against conventional baseball logic, young Brandt proposed an assembly of an unlikely set of players, based purely on their OBP (on base percentage). OBP up until that time at the time had been an overlooked statistic. It is now believed to be one of the most effective statistics in baseball that shows the ability of a batter to hit the ball and get on a base, thus advancing the offensive aspect of the game. The model was supported and put into action by the team’s general manager Billy Beane (played by Brad Pitt in the movie). The net result was that statistical analysis in evaluating player performance and team combinations became institutionalized in modern baseball almost in span of few months.

El presente trabajo propone una nueva forma de análisis del fútbol que se fundamenta en la perspectiva de redes sociales. Tomando como objeto redes construidas en base a los partidos de la última Eurocopa, se desarrollan una serie de construcciones que combinan el ARS tanto con los fundamentos tácticos y estratégicos como con la estadística clásica de este deporte, en la búsqueda de mostrar los valiosos aportes que pueden surgir de dicha conjunción. En este marco  desplegamos, entre otras cuestiones, la posibilidad de mostrar la importancia de determinados vínculos dentro del campo de juego a partir de las propiedades de peso de los lazos, el virtual correlato entre la centralidad de determinados nodos y lo que se espera de jugadores tácticamente claves, y la interesante complementariedad que aparece entre la densidad de un componente y el porcentaje de posesión de balón que muestra un equipo.</p>            <p>Se incluyen también, una serie de aplicaciones posibles de este análisis y el detalle de su aplicación efectiva en el club Arsenal de Sarandi, dentro del periodismo deportivo como en el campo también en el de asesoría técnica, a la vez que buscamos fundamentar la incursión del ARS en el fútbol no solo por su valor metodológico, sino también por su importancia didáctica e incluso ideológica.

The book about the eventology ~ a science about events and its applications to problems of management of sets of events ~ a new direction in philosophy, mathematics and event management (see English version of the book: https://www.academia.edu/38605343/).
This book outlines ideas that inspired me while I was trying to build a new event science, eventology. Not each of these ideas was developed, but all of them inspired me in the construction of eventology, and then in the discovery of a revolutionary theory of experience and chance, co~eventum mechanics. (see, for example, https://www.academia.edu/34357251,
https://www.academia.edu/34373279,
https://www.academia.edu/34390291,
https://www.academia.edu/38368776,
https://www.academia.edu/38154263 and so on).

This article presents a Bayesian implementation of a cumulative probit model to forecast the outcomes of the UEFA Champions League matches. The argument of the normal CDF involves a cut-off point, a home vs away playing effect and the difference in strength of the two competing teams. Team strength is assumed to follow a Gaussian distribution the expectation of which is expressed as a linear regression on an external rating of the team from eg the UEFA Club Ranking (UEFACR) or the Football Club World Ranking (FCWR). Priors on these parameters are updated at the beginning of each season from their posterior distributions obtained at the end of the previous one. This allows making predictions of match results for each phase of the competition: group stage and knock-out. An application is presented for the 2013-2014 season. Adjustment based on the FCWR performs better than on UEFACR. Overall, using the former provides a net improvement of 24% and 23% in accuracy and Brier’s score over the control (zero prior expected difference between teams). A rating and ranking list of teams on their performance at this tournament and possibilities to include extra sources of information (expertise) into the model are also discussed.

Quantifying the potential market of sports licenses is key in order for National Governing Bodies of sport (NGBs) to be able to design good strategic planning. We compared the classical methods of univariate prediction and the Autoregressive Integrated Moving Average (ARIMA) methods. Reliability of the available data was verified with the Time Series Regression with ARIMA Noise, Missing and Outliers (TRAMO) method, and the existence of a trend was verified using Daniel's test. For the purposes of this study-the researches collected and analysed secondary data from a 40-year series in 45 sports in Spain covering a very long period of time in a variety of sport disciplines. The study shows that, with the available data, short-and mid-term forecasting is possible in a number of sports, but not in all of them. It also proves that Holt's classical method of exponential smoothing is the one that yields best results. Golf, Basketball, Athletics and Hunting NGB show worrying prospects of decline levels and need an immediate change in the strategic plans. Other than for forecasting the evolution of athletes in the mid-term in order to improve strategic planning in NGBs, the present findings can be useful for public authorities to define their aid policies for NGBs, and they can also help companies in the industry to anticipate market developments.

Many studies have reported the frequency and types of injuries in soccer players. However, a few have assessed the relationship of playing position, climate, psychological effects and infra structure facilities with injury. The purpose of the study is to develop a
statistical model for injuries among the soccer players in Jaffna.
The observations on the following soccer injury-related variables, age, body mass index (BMI), playing position, years of experience, training method, equipment and ground facilities, climate and psychological effect were collected from a sample of 125 soccer players from Jaffna. We have grouped the above 9 variables into 3 factors using the
factor analysis techniques. The first factor (TIF) consists of training method and infrastructure facilities; the second factor (AE) consists of age and years of experience and the third factor (BMP) consists of BMI and playing position. It is interesting to note that the three variables in the 1st factor are common for a soccer team and the variables in other
two factors are associated with individual players.

Categorical data analysis techniques revealed that years of experience, BMI and playing position were significantly associated with soccer injury. Moreover, odds ratios were calculated for the international standardized BMI groups and found that injury risk was very less in normal weight BMI group. As per the playing position, the odds of getting injury increased from back to forward direction in the soccer field.

Logistic regression analysis was used to fit a model for soccer injury for a team by considering the factor TIF and another logistic regression model was fitted for soccer injury for an individual player considering other two factors AE and BMP. Further, we have developed a sample maximum likelihood discriminant function (SMLDF) to classify a soccer player as injured or not. Using the SMLDF, based on an individual
soccer player’s observations on the above nine variables, we will be able to advice him about the risk of getting injury in future.

Keyword: Discriminant Analysis, Factor Analysis, Logistic Regression, Odds Ratio, Principal Component Analysis

The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co∼event. The theory of experience and chance is the theory of co∼events. To study the co∼events, it is not enough to study the experience and to study the chance. For this, it is necessary to study the experience and chance as a single entire, a co∼event. In other words, it is necessary to study their interaction within a co∼event. The new co∼event axiomatics and the theory of co∼events following from it were created precisely for these purposes. In this work, I am going to demonstrate the effectiveness of the new theory of co∼events in a studying the logic of uncertainty. I will do this by the example of a co∼event splitting of the logic of the Bayesian scheme, which has a long history of fierce debates between Bayesionists and frequentists. I hope the logic of the theory of experience and chance will make its modest contribution to the application of these old dual debaters.

Keywords: Eventology, event, probability, probability theory, Kolmogorov’s axiomatics, experience, chance, cause, consequence, co∼event, set of co∼events, bra-event, set of bra-events, ket-event, set of ket-events, believability, certainty, believability theory, certainty theory, theory of co∼events, theory of experience and chance, co∼event dualism, co∼event axiomatics, logic of uncertainty, logic of experience and chance, logic of cause and consequence, logic of the past and the future, Bayesian scheme.

For certain algorithms such as sorting and searching, the parameters of the input probability distribution, in addition to the size of the input, have been found to influence the complexity of the underlying algorithm. The present paper makes a statistical comparative study on parameterized complexity between linear and binary search algorithms for binomial inputs.

El objetivo del trabajo es cuantificar el grado de correlación existente entre algunos factores que a priori condicionarían los resultados de las delegaciones nacionales en las citas olímpicas, y la cantidad de medallas logradas.
Para ello nos enfocamos en la situación argentina y decidimos contrastarla con la realidad de las naciones que conforman la Unión Europea, dada la disponibilidad y facilidad de acceso en materia estadística.

Eventology of multivariate statistics
Eventology and mathematical eventology
Philosophical eventology and philosophy of probability
Practical eventology
Eventology of safety
Eventological economics and psychology
Mathematics in the humanities, socio-economic and natural sciences
Financial and actuarial mathematics
Multivariate statistical analysis
Multivariate complex analysis
Decision-making under risk and uncertainty
Risk measurement and risk models
Theory of fuzzy events and generalized theory of uncertainty
System analysis and events management

EEC'2016 ~ workshop on axiomatizing experience and chance, and Hilbert's sixth problem

With topics from quantum physics, probability and believability to economics, sociology and psychology, the workshop will be intended for an interdisciplinary discussion on mathematical theories of experience and chance. Topics of discussion include the results, thoughts and ideas on axiomatization of the eventological theory of experience and chance in the framework of the decision of Hilbert sixth problem.
Eventology of experience and chance
Beleivability theory and statistics of experience
Probability theory and statistics of chance
Axiomatizing experience and chance

Summary
    In tennis it is required the knowledge of the amount of strokes made in a match to be used as a parameter of the training loads. This study aimed to determine the amount of the types of scams used by most tennis players in a youth tournament-class on clay floor. Were analyzed 08n simple games (05 male and 03 female) tennis at Banana Bowl Tournament of the school year 2003. Data collection was performed using the quantitative analysis process of the movement described by Knudson & Morrison (2001). The shooting occurred protocol by randomly selecting one of the starting players, which was filmed exclusively and also noted the game's duration. Through a scout record the blows were transcribed and divided. The four strokes analyzed were: right-hit (forehand), left stroke (backhand), volley or smash and service. The results show that the youth tennis players have analyzed some quantitative indices lower compared with the pros data.
    Key Words: Tennis. Statistical analysis. Motor actions.

Achieving superior performance parameters in major competitions has highlighted a number of issues that characterize the current basketball game practiced by the best teams in the world. Depending on the height, role, importance and the effectiveness of players on their positions, specific models are to be observed in the case of senior teams [1]. In this paper we present a comparative study regarding the parameters' models in the men's basketball games during the World Championships in Japan-2006, in Turkey-2010 and in Spain-2014. Along with data interpretation, we tried to effectively bring our scientific contribution in shaping a model significant for the international basketball games, useful for the specialists in the field. Centralization of the statistical data used in our study was useful in calculating the averages for each game parameter and the increasing value for each tournament, managing to achieve a precise statistical comparison. The values encountered in this comparative research showed growth or regression trends for the game parameters. In conclusion, trends of progress or regress, referring to the statistical model parameters involved in the game, pragmatically showed, that in the game of basketball-training is the key to success. Rezumat Obţinerea unor performanţe la parametrii superiori în marile competiţii a scos în evidenţă o serie de aspecte ce caracterizează jocul de baschet actual, practicat de cele mai bune echipe din lume. În funcţie de statura, rolul, importanţa şi eficacitatea jucătorilor pe posturi, se pot observa modele specifice în cadrul echipelor de seniori [1]. În acestă lucrare prezentăm un studiu comparativ al parametrilor modelului de joc la Campionatele Mondiale de baschet masculin din Japonia 2006, Turcia 2010 şi Spania 2014. Odată cu interpretarea datelor, încercăm să ne aducem contribuţia într-un mod cât mai stiinţific şi eficient la profilarea unui model de joc internaţional, util specialiştilor în domeniu. Centralizarea datelor statistice utilizate în studiul nostru ne-au fost utile în calcularea mediilor pentru fiecare parametru de joc, cât şi în calcularea procentului de creştere pentru fiecare campionat în parte, reuşind asfel să realizăm o comparaţie matematico-statistică exactă. Valorile întâlnite în cadrul studiului comparativ de faţă, arată tendinţele de creştere sau regresie a valorilor indicatorilor statistici, a parametrilor modelului de joc. În concluzie, tendinţele de progres sau de regres, referindu-ne aici la statistica parametrilor modelului de joc, observaţi în cadrul studiului nostru, arată în cel mai pragmatic mod, că în jocul de baschet-pregatirea este cheia succesului.

A Copa do Mundo de Futsal FIFA - 2016 ocorreu na Colômbia. Foram realizados 52 jogos com 352 gols efetuados. A Argentina sagrou-se campeã da competição, tendo a Rússia como segunda colocada, o Irã em terceiro e Portugal ficou em quarto lugar. A amostragem foi constituída com as quatro primeiras equipes vencedoras da competição. Foram coletados os resultados da competição (quantidade de vitórias, empates e derrotas, assim como o número de gols por partida de cada equipe) disposto no site da FIFA. Com base nestes numerários, foram efetuados os cálculos de percentil, média , mediana e moda de cada uma das quatro equipes. Concluímos que a equipe campeã Argentina se diferenciou das demais, pois demonstrou a partir da quarta partida, um leve pico na quantidade de gols e, daí em diante estabilizou-se até a partida final.
The FIFA Futsal World Cup - 2016 took place in Colombia. There were 52 games with 352 goals scored. Argentina won the competition, with Russia second, Iran third and Portugal fourth. The sampling was constituted with the first four winning teams of the competition. The results of the competition (number of wins, draws and losses, as well as number of goals per team match) were collected on the FIFA website. Based on these cash, the percentile calculations were performed, mean, median and mode of each of the four teams. We concluded that the champion team Argentina was different from the others, as it demonstrated from the fourth game a slight peak in the number of goals and from then on it stabilized until the final match.

A fixed company of players observes a person selected from a fixed queue. After each observation, players are asked to bet the dollar secret from others, either on the fact that person is bald, or on what is not. A denite formula of the gain is suggested, such that every time after bets the gain of each player from a given company are completely determined by this formula. However, before bets player's gain is an uncertain value. Is it possible for a given company of players and a given queue of people before bets to build a correct mathematical model of uncertaint gain of each player within the framework of Kolmogorov's probability theory? If not, what else do you need to add to the foundations of probability theory so that before bets to be able to use this model for decision making? The paper answers these questions within the framework of the new theory of experience and of chance (the certainty theory) [1] that consists of two dual halves: the believability theory and the probability theory, and that is intended for the mathematical description of experienced-random experiments, the uncertainty in outcomes of which is generated by the observer. A xed company of players observes a person selected from a xed queue. After each observation, players are asked to bet the dollar secret from others, either on the fact that the person is bald, or on what is not. If, as a result of the bets made, the player's choice is in the minority, the player loses the bet. If, on the other hand, in the majority, the player is returned his bet plus an equal share of the loser players' bets. With a draw, the equality of the number of betting on the bald and the number of betting on the not bald, all players remain at their own: they are returned their bets 1. Every time after the bets, the gain of each player from this company is fully certain. But before the bets, the gain is an uncertain value. Is it possible for a given company of players and a given queue of persons before bets to build a correct mathematical model of uncertain gain of each player within the framework of Kolmogorov's probability theory?
c ⃝ 2016 O.Yu.Vorobyev Oleg Vorobyev (ed.), Proc. XV FAMEMS'2016, Krasnoyarsk: SFU

Performance in strength and power sports is greatly affected by a variety of anthropometric factors. The goal of performance normalization is to factor out the effects of confounding factors and compute a canonical (normalized) performance measure from the observed absolute performance. Performance normalization is applied in the ranking of elite athletes, as well as in the early stages of youth talent selection. Consequently it is crucial that the process is principled and fair. The corpus of previous work on this topic, which is significant, is uniform in the methodology adopted. Performance normalization is universally reduced to a regression task: the collected performance data is used to fit a regression function which is then used to scale future performances. The present paper demonstrates that this approach is fundamentally flawed. It inherently creates a bias which unfairly penalizes athletes with certain allometric characteristics and, by virtue of its adoption in the ranking and selection of elite athletes, propagates and strengthens this bias over time. The main flaws are shown to originate in the criteria for selecting the data used for regression, as well as in the manner in which the regression model is applied in normalization. My analysis brings into light the aforesaid methodological flaws and motivates further work on the development of principled methods, the foundations of which are also laid out in this work.

The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reections of one essence, which is called co∼event. The theory of experience and chance is the theory of co∼events. To study the co∼events, it is not enough to study the experience and to study the chance. For this, it is necessary to study the experience and chance as a single entire, a co∼event. In other words, it is necessary to study their interaction within a co∼event. The new co∼event axiomatics and the theory of co∼events following from it were created precisely for these purposes. In this work, I am going to demonstrate the effectiveness of the new theory of co∼events in a studying the logic of uncertainty. I will do this by the example of a co∼event splitting of the logic of the Bayesian scheme, which has a long history of erce debates between Bayesionists and frequentists. I hope the logic of the theory of experience and chance will make its modest contribution to the application of these old dual debaters., theory of experience and chance, co∼event dualism, co∼event axiomatics, logic of uncertainty, logic of experience and chance, logic of cause and consequence, logic of the past and the future, Bayesian scheme.

This is a further formation of the theory of experience and chance. My previous works are devoted to the elements of this new theory, which can also be called the theory of co∼events, or the certainty theory. The theory is a synthesis of two dual theories: Kolmogorov's theory of probability and the believability theory based on the axiomatics, which is a non-trivial extension of Kolmogorov's axiomatics. In my paper " Theory of dual co∼event-based means " (2016), the concepts of two dual co∼event-based means of one co∼event are introduced (the bra-mean and the ket-mean). Here I first suggest the definition of the unifying mean of one co∼event (the bra-ket-mean), and then I enter the general definition of the bra-ket-mean for a finite set of co∼events. The mean co∼event-based characteristics of co∼events play the same role in the theory of experience and chance as the mean numerical characteristics of random variables — in the probability theory, or the mean characteristics of events — in the eventological theory.

In my recent works, I propose a new theory of experience and chance, or the theory of certainties, which is a synthesis of two dual theories: Kolmogorov's theory of probabilities and a new theory of believabilities. The theory of experience and chance is based on axiomatics, adding to the Kolmogorov axiomatics of probability theory an axiom of co~event, a new concept defined as a pair of dual objects, one of which serves as a Kolmogorov event in probability space and the other - as an event in the dualistic believability space. One of my papers gives a theory of dual co~event-based means and examples of its use for processing
statistics of ``approving voting'' in elections and in forestry. In this paper, I will go into more detail in examples of processing the statistics
of ``approving voting'' in forestry, where a group of forestry experts is actually engaged in ``approving voting'' when they label the trees of the
forest, labelling those that according to their opinions must be felling. My goal is to show in these examples that the theory of experience and
chance is an effective tool for constructing co~evnts models of experts' behavior in different fields.

Measuring players&#39; performance in team sports is fundamental since managers need to evaluate players with respect to the ability to score during crucial moments of the game. Using Classification and Regression Trees (CART) and play-by-play basketball data, we estimate the probabilities to score the shot with respect to a selection of game covariates related to game pressure. We use scoring probabilities to develop a player-specific shooting performance index that takes into account for the difficulty associated to score different types of shots. By applying this procedure to a large sample of 2016–2017 Basketball Champions League (BCL) and 2017–2018 National Basketball Association (NBA) games, we compare the factors affecting shooting performance in Europe and in the United States and we evaluate a selection of players in terms of the proposed shooting performance index with the final aim of providing useful guidelines for the team strategy.