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"Basketball Mathematical models."
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\"Learn and review math skills while also learning about the history of basketball\"-- Provided by publisher.
Book
Viral dynamics of acute SARS-CoV-2 infection and applications to diagnostic and public health strategies
SARS-CoV-2 infections are characterized by viral proliferation and clearance phases and can be followed by low-level persistent viral RNA shedding. The dynamics of viral RNA concentration, particularly in the early stages of infection, can inform clinical measures and interventions such as test-based screening. We used prospective longitudinal quantitative reverse transcription PCR testing to measure the viral RNA trajectories for 68 individuals during the resumption of the 2019–2020 National Basketball Association season. For 46 individuals with acute infections, we inferred the peak viral concentration and the duration of the viral proliferation and clearance phases. According to our mathematical model, we found that viral RNA concentrations peaked an average of 3.3 days (95% credible interval [CI] 2.5, 4.2) after first possible detectability at a cycle threshold value of 22.3 (95% CI 20.5, 23.9). The viral clearance phase lasted longer for symptomatic individuals (10.9 days [95% CI 7.9, 14.4]) than for asymptomatic individuals (7.8 days [95% CI 6.1, 9.7]). A second test within 2 days after an initial positive PCR test substantially improves certainty about a patient’s infection stage. The effective sensitivity of a test intended to identify infectious individuals declines substantially with test turnaround time. These findings indicate that SARS-CoV-2 viral concentrations peak rapidly regardless of symptoms. Sequential tests can help reveal a patient’s progress through infection stages. Frequent, rapid-turnaround testing is needed to effectively screen individuals before they become infectious.
Journal Article
Effective injury forecasting in soccer with GPS training data and machine learning
Injuries have a great impact on professional soccer, due to their large influence on team performance and the considerable costs of rehabilitation for players. Existing studies in the literature provide just a preliminary understanding of which factors mostly affect injury risk, while an evaluation of the potential of statistical models in forecasting injuries is still missing. In this paper, we propose a multi-dimensional approach to injury forecasting in professional soccer that is based on GPS measurements and machine learning. By using GPS tracking technology, we collect data describing the training workload of players in a professional soccer club during a season. We then construct an injury forecaster and show that it is both accurate and interpretable by providing a set of case studies of interest to soccer practitioners. Our approach opens a novel perspective on injury prevention, providing a set of simple and practical rules for evaluating and interpreting the complex relations between injury risk and training performance in professional soccer.
Journal Article
Research on team efficacy in CBA games based on complex network theory
Using complex network theory, we quantify the topological characteristics and anti-destruction resilience of the 12 playoff teams that contested the 2023 Chinese Basketball Association (CBA) season. By constructing similarity networks based on players’ performance indicators, this study examines various topological features, including node degree, betweenness centrality, clustering coefficient, and average path length, and assesses their robustness under random and deliberate attacks.The results indicate that the structural balance of the network exerts a significant influence on a team’s resilience. For example, the Liaoning Bensteel team exhibited high network connectivity and resilience, with an average node degree of 11, a clustering coefficient of 0.83, and an average path length of 0.72. In contrast, the Jiangsu Kendia demonstrated greater structural vulnerability when key nodes were compromised, possessing a maximum node degree of 10, but a clustering coefficient of only 0.74, leading to an increased average path length of 1.17. Furthermore, teams with high clustering coefficients, such as Shandong High-Speed, which achieved a coefficient of 0.82, exhibit close internal cooperation and efficient ball movement.Consequently, it is recommended that CBA teams enhance their resilience by improving the balance and redundancy of key nodes within their network structures, thereby providing a scientific basis for basketball tactical planning and team management. These findings offer a novel perspective on understanding and enhancing the organizational structure and competitive performance of basketball teams.
Journal Article
Modeling the formation of defensive gaps in basketball: Cutting on a teammate’s drive
Basketball is a game of simultaneous actions, and inter-player coordination is key for offensive success. One of the most challenging aspects in this regard is basket cutting on a teammate’s drive. The ability to make these cuts is considered to be an artistic skill, mastered by only a handful of players. This skill is also hard to assess, as there is no method to measure the players’ capability with respect to this quality–especially not automatically. Using SportVU data from the NBA, we created a mathematical model that identifies the openings in the defense which allow to perform a cut. Our model succeeds to generalize, as it detects these openings on average 139ms earlier than the actual cuts start and has an overall (balanced) accuracy of 0.818 on the test set. Having a tree-based gradient boosting classifier, we received a clear hierarchy of feature importance and were able to inspect the interactions between these attributes during action. This way, the model gives insights about the kind of defensive movements needed for a player to allow enough space to cut while in practical usage the analysis of the output can also help the coaching staff in designing play options and assessing player abilities. By paying more attention to the possible off ball movements during drives, offensive plays can become more versatile–benefiting the participants and the spectators alike.
Journal Article
AI and big data personalized training protocol for Chinese youth basketball
Youth basketball talent development in China faces multiple challenges—homogeneous training methods, insufficient attention to individual differences, and a lack of systematic, evidence-based decision-making. This study protocol describes the design and planned validation of an AI- and big-data-driven personalized training system aimed at testing whether integrated multidimensional data and dynamic feedback can improve talent identification and training outcomes in Chinese youth basketball. The protocol outlines the randomized effectiveness trial, process evaluation, and implementation measures that will be used to evaluate feasibility, potential efficacy, and adoption. A mixed-methods, randomized controlled pretest–posttest design will be implemented. One hundred youth basketball athletes aged 12–18 will be recruited and randomized (1:1) to an AI-driven personalized training (experimental) arm or a conventional training (control) arm. Multidimensional data (physical, technical, training-load, psychological, and game statistics) will be collected using validated field tests, wearable devices, video analysis, and standardized questionnaires. Primary quantitative analyses will compare pre–post changes between groups using intention-to-treat principles. The primary inferential approach will use ANCOVA (adjusting for baseline score, age stratum, sex, and team clustering) and linear mixed-effects models for repeated measures; effect sizes (Cohen’s d) and 95% CIs will be reported. Advanced methods (Bayesian regression, SEM) and predictive ML models will be treated as exploratory pending sample size adequacy and diagnostic checks. Qualitative interviews with coaches and participants will explore acceptability and implementation barriers guided by the Technology Acceptance Model (TAM). This study is anticipated to meet the criteria for exemption under Article 32 of the 2023 Ethical and Moral Management Measures; nevertheless, the full protocol and participant-facing materials will be submitted to the institutional Ethics Review Committee for formal confirmation (or exemption letter) and any correspondence will be archived. Study findings will be disseminated for academic, non-commercial purposes subject to ethical approvals.
Trial registration
To be registered prior to trial commencement. Registry name and registration number will be provided in the final manuscript (e.g., Chinese Clinical Trial Registry or ClinicalTrials.gov).
Journal Article
A hierarchical approach for evaluating athlete performance with an application in elite basketball
In this paper, we present the ON score for evaluating the performance of athletes and teams that includes a season-long evaluation system, a single-game evaluation, and an evaluation of an athlete’s overall contribution to their team. The approach used to calculate the ON score is based on mixed-effects regression models that take into account the hierarchical structure of the data and a principal component analysis to calculate athlete rating. We apply our methodology to a large dataset of National Basketball Association (NBA) games spanning four seasons from 2015–2016 to 2018–2019. Our model is validated using two systematic approaches, and our results demonstrate the reliability of our approach to calculate an athlete’s performance. This provides coaches, General Managers and player agents with a powerful tool to gain deeper insights into their players’ performance, make more informed decisions and ultimately improve team performance. Our methodology has several key advantages. First, by incorporating the hierarchical structure of the data, we can obtain valuable information about an athlete’s contribution within their team. Second, the use of principal component analysis allows us to calculate a single score, the ON score, that captures the overall performance of an athlete. Third, our approach is based on classical restricted likelihood methods, which makes the calculation faster than Bayesian methods typically requiring 1000 posterior samples. With our approach, coaches and managers can evaluate athletes’ performance throughout the season, compare athletes and teams over a year, and assess an athlete’s performance during a single game. Our methodology can also complement other ratings and box score metrics to provide a more comprehensive assessment of an athlete’s performance as our method uses the hierarchical nature of performance data (i.e. player nested within team over season) which is typically ignored in player rating systems. In summary, our methodology represents a significant contribution to the field of sports analytics and provides the foundation for future developments.
Journal Article
Exploratory approach to speculate on body composition models for elite teenage basketball players
The study of human body composition covers many fields, from clinical assessment to sports performance. Humans manifest different traits that set limitations in model estimation. This investigation aimed to (i) provide sport-specific densities for reducing biological variation in body composition assessment, and (ii) develop new regression models for body volume and density estimation by field applications. Thirty elite basketball players (16.84 ± 1.15 years; 188.48 ± 6.74 cm; 82.66 ± 12.23 kg) with a mean of 10.48 years of sport experience underwent anthropometric, bio-impedance (BIA) and air-displacement plethysmography (ADP) evaluations. Many models accounting for body fat percentage (BF) used the measured body mass (BM), volume (BV) and density (d) to analyse adipose and fat-free tissues. A new model payable for all players encompassed BF, with low error propagation (3.4% of BM). In addition, two new methods estimated BV by anthropometry (R
2
= 0.96, RMSE = 2.9%) or BIA (R
2
= 0.81, RMSE = 4.56%), with a high degree of precision (97.8 and 86.8%) and accuracy (100 and 99.6%). Body composition requires rigorous speculation, advanced instruments and high costs that could lead investigators to omit relevant concepts and produce estimation biases. Specific and easier methods may enhance its applicability.
Journal Article
Uncertainty in the Hot Hand Fallacy
We study a class of permutation tests of the randomness of a collection of Bernoulli sequences and their application to analyses of the human tendency to perceive streaks of consecutive successes as overly representative of positive dependence—the hot hand fallacy. In particular, we study permutation tests of the null hypothesis of randomness (i.e. that trials are i.i.d.) based on test statistics that compare the proportion of successes that directly follow k consecutive successes with either the overall proportion of successes or the proportion of successes that directly follow k consecutive failures. We characterize the asymptotic distributions of these test statistics and their permutation distributions under randomness, under a set of general stationary processes, and under a class of Markov chain alternatives, which allow us to derive their local asymptotic power. The results are applied to evaluate the empirical support for the hot hand fallacy provided by four controlled basketball shooting experiments. We establish that substantially larger data sets are required to derive an informative measurement of the deviation from randomness in basketball shooting. In one experiment, for which we were able to obtain data, multiple testing procedures reveal that one shooter exhibits a shooting pattern significantly inconsistent with randomness—supplying strong evidence that basketball shooting is not random for all shooters all of the time. However, we find that the evidence against randomness in this experiment is limited to this shooter. Our results provide a mathematical and statistical foundation for the design and validation of experiments that directly compare deviations from randomness with human beliefs about deviations from randomness and thereby constitute a direct test of the hot hand fallacy.
Journal Article
Effect of the Solid Particle Diameter on Frictional Loss and Heat Exchange in a Turbulent Slurry Flow: Experiments and Predictions in a Vertical Pipe
The study deals with experiments and predictions on turbulent flow and heat exchange in a fully developed slurry flow in a vertical upward pipe. Four slurries were considered: two with glass spheres particles with diameters of 0.125 mm and 0.240 mm, respectively, and two with sand spheres particles with diameters of 0.470 mm and 0.780 mm, respectively. The volume concentration of the particles was changed in the range of 10% to 40%. This study has indirectly demonstrated the existence of turbulence suppression to a degree dependent on the diameter of the solid particles. A mathematical model for heat transfer between slurry and pipe was developed using the two-equation turbulence model and a specially designed wall function, including particle diameter and solid concentration. The model assumed a constant wall temperature and heat flux. The study’s objective was to determine the influence of the diameter of the solid particles on the heat exchange. The Nusselt number was found to change sinusoidal, reaching a maximum for a slurry with d = 0.125 mm, and a minimum for d = 0.470 mm. The higher the solid concentration, the lower the Nusselt number. The novelty and value of this study lies in the deeper characterisation and understanding of the influence of the diameter of solid particles on heat exchange.
Journal Article