##
**Characterizing the spatial structure of defensive skill in professional basketball.**
*(English)*
Zbl 1454.62538

Summary: Although basketball is a dualistic sport, with all players competing on both offense and defense, almost all of the sport’s conventional metrics are designed to summarize offensive play. As a result, player valuations are largely based on offensive performances and to a much lesser degree on defensive ones. Steals, blocks and defensive rebounds provide only a limited summary of defensive effectiveness, yet they persist because they summarize salient events that are easy to observe. Due to the inefficacy of traditional defensive statistics, the state of the art in defensive analytics remains qualitative, based on expert intuition and analysis that can be prone to human biases and imprecision.

Fortunately, emerging optical player tracking systems have the potential to enable a richer quantitative characterization of basketball performance, particularly defensive performance. Unfortunately, due to computational and methodological complexities, that potential remains unmet. This paper attempts to fill this void, combining spatial and spatio-temporal processes, matrix factorization techniques and hierarchical regression models with player tracking data to advance the state of defensive analytics in the NBA. Our approach detects, characterizes and quantifies multiple aspects of defensive play in basketball, supporting some common understandings of defensive effectiveness, challenging others and opening up many new insights into the defensive elements of basketball.

Fortunately, emerging optical player tracking systems have the potential to enable a richer quantitative characterization of basketball performance, particularly defensive performance. Unfortunately, due to computational and methodological complexities, that potential remains unmet. This paper attempts to fill this void, combining spatial and spatio-temporal processes, matrix factorization techniques and hierarchical regression models with player tracking data to advance the state of defensive analytics in the NBA. Our approach detects, characterizes and quantifies multiple aspects of defensive play in basketball, supporting some common understandings of defensive effectiveness, challenging others and opening up many new insights into the defensive elements of basketball.

### MSC:

62P99 | Applications of statistics |

### Keywords:

basketball; hidden Markov models; nonnegative matrix factorization; Bayesian hierarchical models
PDFBibTeX
XMLCite

\textit{A. Franks} et al., Ann. Appl. Stat. 9, No. 1, 94--121 (2015; Zbl 1454.62538)

### References:

[1] | Bishop, C. M. (2006). Pattern Recognition and Machine Learning . Springer, New York. · Zbl 1107.68072 |

[2] | Böhning, D. (1992). Multinomial logistic regression algorithm. Ann. Inst. Statist. Math. 44 197-200. · Zbl 0763.62038 · doi:10.1007/BF00048682 |

[3] | Brunet, J.-P., Tamayo, P., Golub, T. R. and Mesirov, J. P. (2004). Metagenes and molecular pattern discovery using matrix factorization. Proc. Natl. Acad. Sci. USA 101.12 4164-9. |

[4] | Cervone, D., D’Amour, A., Bornn, L. and Goldsberry, K. (2014). POINTWISE: Predicting Points and Valuing Decisions in Real Time with NBA Optical Tracking Data. |

[5] | Cressie, N. A. C. (1993). Statistics for Spatial Data . Wiley, New York. · Zbl 1347.62005 · doi:10.1002/9781119115151 |

[6] | Franks, A., Miller, A., Bornn, L. and Goldsberry, K. (2015a). Supplement to “Characterizing the spatial structure of defensive skill in professional basketball.” . |

[7] | Franks, A., Miller, A., Bornn, L. and Goldsberry, K. (2015b). Supplement to “Characterizing the spatial structure of defensive skill in professional basketball.” . |

[8] | Gelman, A. and Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statist. Sci. 7 457-472. · Zbl 1386.65060 |

[9] | Goldsberry, K. (2012). Courtvision: New visual and spatial analytics for the NBA. MIT Sloan Sports Analytics Conference. |

[10] | Goldsberry, K. (2013). The Dwight Effect: A new ensemble of interior defense analytics for the NBA. MIT Sloan Sports Analytics Conference. |

[11] | Kingman, J. F. C. (1992). Poisson Processes . Oxford Univ. Press, London. · Zbl 0771.60001 |

[12] | Kubatko, J., Oliver, D., Pelton, K. and Rosenbaum, D. T. (2007). A starting point for analyzing basketball statistics. J. Quant. Anal. Sports 3 1-22. · doi:10.2202/1559-0410.1070 |

[13] | Lee, D. D. and Seung, H. S. (1999). Learning the parts of objects by non-negative matrix factorization. Nature 401 788-791. · Zbl 1369.68285 |

[14] | Lee, D. D. and Seung, H. S. (2001). Algorithms for non-negative matrix factorization. Adv. Neural Inf. Process. Syst. 13 556-562. |

[15] | Limnios, N. and Oprisan, G. (2001). Semi-Markov Processes and Reliability . Springer, Berlin. · Zbl 0990.60004 |

[16] | Macdonald, B. (2011). A regression-based adjusted plus-minus statistic for NHL players. J. Quant. Anal. Sports 7 4. |

[17] | Maruotti, A. and Rydén, T. (2009). A semiparametric approach to hidden Markov models under longitudinal observations. Stat. Comput. 19 381-393. · doi:10.1007/s11222-008-9099-2 |

[18] | Miller, A. C., Bornn, L., Adams, R. and Goldsberry, K. (2014). Factorized Point Process Intensities: A Spatial Analysis of Professional Basketball. In Proceedings of the 31 st International Conference on Machine Learning ( ICML ). Beijing, China. |

[19] | Møller, J., Syversveen, A. R. and Waagepetersen, R. P. (1998). Log Gaussian Cox processes. Scand. J. Stat. 25 451-482. · Zbl 0931.60038 · doi:10.1111/1467-9469.00115 |

[20] | Murphy, K. (2012). Machine Learning : A Probabilistic Perspective . MIT Press, Cambridge, MA. · Zbl 1295.68003 |

[21] | National Basketball Association (2014). A Glossary of NBA Terms. Available at . |

[22] | Rosenbaum, D. T. (2004). Measuring how NBA players help their teams win. Available at ( http://www.82games.com/comm30.htm ) 4-30. |

[23] | Sill, J. (2010). Improved NBA adjusted plus-minus using regularization and out-of-sample testing. In Proceedings of the 2010 MIT Sloan Sports Analytics Conference . Boston, MA. |

[24] | Stan Development Team (2014). Stan: A C++ Library for Probability and Sampling, Version 2.2. |

[25] | Thomas, A. C., Ventura, S. L., Jensen, S. T. and Ma, S. (2013). Competing process hazard function models for player ratings in ice hockey. Ann. Appl. Stat. 7 1497-1524. · Zbl 1283.62245 · doi:10.1214/13-AOAS646 |

[26] | Yu, S.-Z. (2010). Hidden semi-Markov models. Artificial Intelligence 174 215-243. · Zbl 1344.68181 · doi:10.1016/j.artint.2009.11.011 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.