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.

Comparison of markerless and marker-based motion capture systems using 95% functional limits of agreement in a linear mixed-effects modelling framework.

Biomechanics analysis of human movement has been proven useful for maintenance of health, injury prevention, and rehabilitation in both sports and clinical populations. A marker-based motion capture system is considered the gold standard method of measurement for three dimensional kinematics measurements. However, the application of markers to anatomical bony points is a time consuming process and constrained by inter-, intra-tester and session reliability issues. The emergence of novel markerless motion capture systems without the use of reflective markers is a rapidly growing field in motion analysis. However an assessment of the level of agreement of a markerless system with an established gold standard marker-based system is needed to ensure the applicability of a markerless system. An extra layer of complexity is involved as the kinematics measurements are functional responses. In this paper a new approach is proposed to generate 95% functional limits of agreement (fLoA) using the linear mixed-effects modelling framework for hierarchical study designs. This approach is attractive as it will allow practitioners to extend their use of linear mixed models to assess agreement in method comparison studies in all domains where functional responses are recorded.

Modelling menstrual cycle length in athletes using state-space models.

The ability to predict an individual's menstrual cycle length to a high degree of precision could help female athletes to track their period and tailor their training and nutrition correspondingly. Such individualisation is possible and necessary, given the known inter-individual variation in cycle length. To achieve this, a hybrid predictive model was built using data on 16,524 cycles collected from a sample of 2125 women (mean age 34.38 years, range 18.00-47.10, number of menstrual cycles ranging from 4 to 53). A mixed-effect state-space model was fitted to capture the within-subject temporal correlation, incorporating a Bayesian approach for process forecasting to predict the duration (in days) of the next menstrual cycle. The modelling procedure was split into three steps (1) a time trend component using a random walk with an overdispersion parameter, (2) an autocorrelation component using an autoregressive moving-average model, and (3) a linear predictor to account for covariates (e.g. injury, stomach cramps, training intensity). The inclusion of an overdispersion parameter suggested that [Formula: see text] [Formula: see text] of cycles in the sample were overdispersed. The random walk standard deviation for a non-overdispersed cycle is [Formula: see text] [1.00, 1.09] days while under an overdispersed cycle, the menstrual cycle variance increase in 4.78 [4.57, 5.00] days. To assess the performance and prediction accuracy of the model, each woman's last observation was used as test data. The root mean square error (RMSE), concordance correlation coefficient and Pearson correlation coefficient (r) between the observed and predicted values were calculated. The model had an RMSE of 1.6412 days, a precision of 0.7361 and overall accuracy of 0.9871. In conclusion, the hybrid model presented here is a helpful approach for predicting menstrual cycle length, which in turn can be used to support female athlete wellness.