Spatial performance analysis in basketball with CART, random forest and extremely randomized trees

Abstract

This paper proposes tools for spatial performance analysis in basketball. In detail, we aim at representing maps of the court visualizing areas with different levels of scoring probability of the analysed player or team. To do that, we propose the adoption of algorithmic modeling techniques. Firstly, following previous studies, we examine CART, highlighting strengths and weaknesses. With respect to what done in the past, here we propose the use of polar coordinates, which are more consistent with the basketball court geometry. In order to overcome CART’s drawbacks while maintaining its points of force, we propose to resort to CART-based ensemble learning algorithms, namely to Random Forest and Extremely Randomized Trees, which are shown to be able to give excellent results in terms of interpretation and robustness. Finally, an index is defined in order to measure the map’s graphical goodness, which can be used—jointly with measures of the out-of-sample error—to tune the algorithm’s parameters. The functioning of the proposed approaches is shown by the analysis of real data of the NBA regular season 2020/2021.

Quantitative analysis of professional basketball: A qualitative discussion

“…One could see reviews on sports game prediction over the past two decades in Stekler et al (2010 and Horvat andJob (2020) (2020s). Regarding analytical approaches, machine learning techniques, statistical/econometric analysis, optimization methods, game theoretical attempts, and network science techniques are summoned to address the problem; a partial list of sports forecast models includes Markov models (e.g., on game outcome ( Strumbelj and Vracar, 2012) or shoot strategy (Sandholtz and Bornn, 2020)), state-space models (e.g., on game outcome (Manner, 2016) or player's hot hand (Mews and Otting, 2021)), synergy graph models (e.g., on game outcome (Liemhetcharat and Luo, 2015)), neural networks (e.g., on game outcome (Loeffelholz et al, 2009) or physical fitness evaluation (Yuan et al, 2021)), classification trees (e.g., on performance indicators (Zuccolotto et al, 2021(Zuccolotto et al, , 2023), and statistical regression models (e.g., on performance statistics (Song et al, 2018)) etc. Over the years, game prediction has become an active playground for data scientists from various expertise.…”

“…As for modeling and analysis, given the improved granularity of these new data, studies address the spatial dimension of the game and decompose the court into different regions (e.g., Miller et al, 2014;Franks et al, 2015b;Miller and Bornn, 2017;Cervone et al, 2014Cervone et al, , 2016bSandholtz and Bornn, 2018). With the help of big data, more sophisticated models are developed, which try to quantify the latent states of the game, such that one could simulate the play in a finer view (Oh et al, 2015;Sandholtz and Bornn, 2018) and therefore study the performance of players/teams with a closer look (Skinner and Guy, 2015), for example, by partitioning the game court into different performance areas (Zuccolotto et al, 2021(Zuccolotto et al, , 2023. It is evident that optical data of basketball games serve as a good companion to traditional game statistics, and embody great potential for future research.…”

Deforestation as a catalyst for natural disaster and community suffering: A cycle in the socioecological system

“…Data analysis using the Classification and Regression Tree (CART) instrument was a follow-up analysis of Chi-square analysis to find the explanatory variables in stages through the pruning stages (Shabani 2017;Zuccolotto et al 2023). The response variable in the CART analysis was the rate of forest encroachment and wood theft (Y) by people living around the forest areas, where the explanatory variable was a natural disaster (Xn), as presented in Table 1.…”