Spatial roles in hockey special teams

Jonathan Arsenault; Margaret Cunniff; Eric Tulsky; James Richard Forbes

doi:10.1515/jqas-2023-0019

Article

Spatial roles in hockey special teams

Jonathan Arsenault , Margaret Cunniff , Eric Tulsky and James Richard Forbes

Published/Copyright: April 4, 2024

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information

From the journal Journal of Quantitative Analysis in Sports Volume 20 Issue 3

Abstract

Special teams (i.e. power play and penalty kill) situations play an outsized role in determining the outcome of ice hockey games. Yet, quantitative methods for characterizing special teams tactics are limited. This work focuses on team structure and player deployment during in-zone special teams possessions. Leveraging player and puck tracking data from the National Hockey League (NHL), a framework is developed for describing player positioning during 5-on-4 power play and 4-on-5 penalty kill possessions. More specifically, player roles are defined directly from the player tracking data using non-negative matrix factorization, and every player is allocated a unique role at every frame of tracking data by solving a linear assignment problem. Team formations naturally arise through the combination of roles occupied in a frame. Roles that vary on a per-frame basis allow for a fine-grained analysis of team structure. This property of the roles-based representation is used to group together similar power play possessions using latent Dirichlet allocation, a topic modelling technique. The concept of assignments, which remain constant over an entire possession, is also introduced. Assignments provide a more stable measure of player positioning, which may be preferable when assessing deployment over longer periods of time.

Keywords: hockey; player tracking; non-negative matrix factorization; topic modelling

Corresponding author: Jonathan Arsenault, Department of Mechanical Engineering, McGill University, Montreal, Canada, E-mail: jonathan.arsenault@mail.mcgill.ca

Funding source: Carolina Hurricanes

Acknowledgments

The authors would like to thank the National Hockey League for providing access to the data. Additional acknowledgement is extended to the developers of scikit-learn which was used to implement several of the presented models.

Research ethics: Not applicable.
Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Competing interests: The authors state no conflict of interest.
Research funding: This research has been funded by the Carolina Hurricanes.
Data availability: Not applicable.

Appendix A: Gaussian blurring of player occupancy matrices

Let O ( n ) ∈ R + L x × L y be the raw player occupancy matrix for player n, where L _x and L _y are the number of bins in the x and y directions, respectively. An example of the raw player occupancy matrix for a sample player is shown in Figure 14A. These occupancy matrices are smoothed using Gaussian blurring to reduce the impact of noise and the arbitrary binning of the ice surface. A two-dimensional Gaussian filter is convolved with O ⁽ⁿ⁾ to yield a smoothed player occupancy matrix, O ̃ ( n ) . The Gaussian filter is a 5 × 5 matrix, denoted G, approximating a two-dimensional Gaussian distribution with standard deviation σ = 0.5. Each element of O ̃ ( n ) is computed as

(11) O ̃ ( n ) [ i , j ] = ∑ k = − 2 2 ∑ ℓ = − 2 2 G [ k , ℓ ] O ( n ) [ i + k , j + ℓ ] ,

where i = 1, …, L _x and j = 1, …, L _y. The scipy.ndimage.gaussian_filter Python function is used to implement this, where the default parameters are used. The smoothed player occupancy matrix is shown in Figure 14B. The difference between the raw and smoothed player occupancy matrices is shown in Figure 14C.

$Figure 14: Raw and smoothed player occupancy matrices for a sample player. Applying a Gaussian blur to the raw player occupancy matrix diminishes the impact of the small sample size and the arbitrary binning of the ice surface. The difference between the raw and smoothed player occupancy matrices is shown in (C). (A) Raw matrix O (n). (B) Smoothed matrix O ̃ ( n ) ${\tilde {\mathbf{O}}}^{\left(n\right)}$ . (C) Difference, O (n) − O ̃ ( n ) ${\tilde {\mathbf{O}}}^{\left(n\right)}$ .$

Figure 14:

Raw and smoothed player occupancy matrices for a sample player. Applying a Gaussian blur to the raw player occupancy matrix diminishes the impact of the small sample size and the arbitrary binning of the ice surface. The difference between the raw and smoothed player occupancy matrices is shown in (C). (A) Raw matrix O ⁽ⁿ⁾. (B) Smoothed matrix O ̃ ( n ) . (C) Difference, O ⁽ⁿ⁾ − O ̃ ( n ) .

Appendix B: Additional formations

The 8 most frequently observed formations on the PP and PK are shown in Figures 15 and 16, respectively.

Figure 15:

Eight most frequently observed PP formations.

Figure 16:

Eight most frequently observed PK formations.

References

Anzer, G. and Bauer, P. (2022). Expected passes: determining the difficulty of a pass in football (soccer) using spatio-temporal data. Data Min. Knowl. Discov. 36: 295–317, https://doi.org/10.1007/s10618-021-00810-3.Search in Google Scholar

Askari, F., Ramaprasad, R., Clark, J.J., and Levine, M.D. (2022). Interaction classification with key actor detection in multi-person sports videos. In: IEEE/CVF conference on computer vision and pattern recognition workshops (CVPRW). IEEE, New Orleans, LA, USA. https://doi.org/10.1109/CVPRW56347.2022.00402.Search in Google Scholar

Bialkowski, A., Lucey, P., Carr, P., Yue, Y., and Matthews, I. (2014) “Win at home and draw away”: automatic formation analysis highlighting the differences in home and away team behaviors. In: MIT sloan sports analytics conference, Boston, MA, USA.Search in Google Scholar

Bialkowski, A., Lucey, P., Carr, P., Matthews, I., Sridharan, S., and Fookes, C. (2016). Discovering team structures in soccer from spatiotemporal data. IEEE Trans. Knowl. Data Eng. 28: 2596–2605, https://doi.org/10.1109/TKDE.2016.2581158.Search in Google Scholar

Blei, D.M., Ng, A.Y., and Jordan, M.I. (2003). Latent dirichlet allocation. J. Mach. Learn. Res. 3: 993–1022.Search in Google Scholar

Cane, M. (2017a). Measuring the importance of structure on the power play. Hockey Graphs, Available at: https://hockey-graphs.com/2017/02/14/measuring-the-importanceof-structure-on-the-power-play/ (Accessed 13 April 2021).Search in Google Scholar

Cane, M. (2017b). Second units and zone entries: why teams should go all-in on the 4 forward power play. Hockey Graphs, Available at: https://hockey-graphs.com/2017/03/07/second-units-and-zone-entries-why-teams-should-go-all-in-on-the-4-forward-powerplay/ (Accessed 15 April 2021).Search in Google Scholar

Cervone, D., D’Amour, A., Bornn, L., and Goldsberry, K. (2016). A multiresolution stochastic process model for predicting basketball possession outcomes. J. Am. Stat. Assoc. 111: 585–599, https://doi.org/10.1080/01621459.2016.1141685.10.1080/01621459.2016.1141685Search in Google Scholar

Chu, D., Thomson, J., Reyers, M., and Wu, L. (2020). Route identification in the national football league. J. Quant. Anal. Sports 16: 121–132, https://doi.org/10.1515/jqas-2019-0047.Search in Google Scholar

Dutta, R., Yurko, R., and Ventura, S.L. (2020). Unsupervised methods for identifying pass coverage among defensive backs with NFL player tracking data. J. Quant. Anal. Sports 16: 143–161, https://doi.org/10.1515/jqas-2020-0017.arXiv:1906.11373.10.1515/jqas-2020-0017Search in Google Scholar

Fani, M., Neher, H., Clausi, D.A., Wong, A., and Zelek, J. (2017) Hockey action recognition via integrated stacked hourglass network. In: IEEE conference on computer vision and pattern recognition workshops (CVPRW), Honolulu, HI, USA, July.10.1109/CVPRW.2017.17Search in Google Scholar

Fernández, J., Bornn, L., and Cervone, D. (2021). A framework for the fine-grained evaluation of the instantaneous expected value of soccer possessions. Mach. Learn. 110: 1389–1427, https://doi.org/10.1007/s10994-021-05989-6.Search in Google Scholar PubMed PubMed Central

Gregory, S. (2019) Ready player run: off-ball run identification and classification. In: Barça sports analytics summit, Barcelona, Spain, Available at: https://static.capa.biliaserver.com/frontend/clients/barca/wp_prod/wp-content/uploads/2020/01/40ba07f4-ready-player-run-barcelona.pdf (Accessed 21 February 2023).Search in Google Scholar

Gudmundsson, J. and Horton, M. (2017). Spatio-temporal analysis of team sports. ACM Comput. Surv. 50, https://doi.org/10.1145/3054132.Search in Google Scholar

Hochstedler, J. and Gagnon, P.T. (2017) American football route identification using supervised machine learning. In: 2017 MIT sloan sports analytics conference, Boston, MA, USA.Search in Google Scholar

Kasan, S. (2008). Off-ice officials are a fourth team at every game. NHL, Available at: https://www.nhl.com/news/off-ice-officials-are-a-fourth-team-at-every-game/c-388400 (Accessed 31 March 2020).Search in Google Scholar

Kovalchik, S.A. (2023). Player tracking data in sports. Annu. Rev. Stat. Appl. 10: 677–697, https://doi.org/10.1146/annurevstatistics-033021-110117.Search in Google Scholar

Kovalchik, S.A. and Albert, J. (2022). A statistical model of serve return impact Patterns in professional tennis, arXiv:2202.00583, February, arXiv: 2202. 00583 [stat] (Accessed 14 November 2023).Search in Google Scholar

Kuhn, H.W. (1955). The Hungarian method for the assignment problem. Nav. Res. Logist. Q. 2: 83–97, https://doi.org/10.1002/nav.3800020109.Search in Google Scholar

Lee, D.D. and Seung, H.S. (2000). Algorithms for non-negative matrix factorization. Adv. Neural Inf. Process. Syst. 13: 556–562, https://doi.org/10.1142/S1793005715400013.Search in Google Scholar

Liu, G. and Schulte, O. (2018) Deep reinforcement learning in ice hockey for context- aware player evaluation. In: International joint conference on artificial intelligence.10.24963/ijcai.2018/478Search in Google Scholar

Lucey, P., Bialkowski, A., Carr, P., Morgan, S., Matthews, I., and Sheikh, Y. (2013) Representing and discovering adversarial team behaviors using player roles. In: IEEE conference on computer vision and pattern recognition (CVPR).10.1109/CVPR.2013.349Search in Google Scholar

Lucey, P., Bialkowski, A., Carr, P., Yue, Y., and Matthews, I. (2014) “How to get an open shot”: analyzing team movement in basketball using tracking data. In: MIT sloan sports analytics conference.Search in Google Scholar

Macdonald, B. (2012). Adjusted plus-minus for NHL players using ridge regression with goals, shots, fenwick, and corsi. J. Quant. Anal. Sports 8: 1–24, https://doi.org/10.1515/1559-0410.1447.Search in Google Scholar

McCurdy, M.B. (2022). The magnus prediction model, version 6. HockeyViz, Available at: https://hockeyviz.com/txt/magnus6ST (Accessed 10 January 2023).Search in Google Scholar

Miller, A.C. and Bornn, L. (2017) Possession sketches: mapping NBA strategies. In: 2017 MIT sloan sports analytics conference, Boston, MA, USA.Search in Google Scholar

Miller, A., Bornn, L., Adams, R., and Goldsberry, K. (2014) Factorized point process intensities: a spatial analysis of professional basketball. In: International conference on machine learning, Beijing, China, pp. 398–414.Search in Google Scholar

Nandakumar, N. and Jensen, S.T. (2019). Historical perspectives and current directions in hockey analytics. Annu. Rev. Stat. Appl. 6: 19–36, https://doi.org/10.1146/annurev-statistics-030718-105202.Search in Google Scholar

Parnass, A. (2016a). How can we quantify power play performance in formation? Hockey-Graphs, Available at: https://hockey-graphs.com/2016/04/25/how-can-we-quantify-power-play-performance-in-formation/ (Accessed 7 June 2022).Search in Google Scholar

Parnass, A. (2016b). ZEFR rate: a new and better way to evaluate power plays. Hockey Graphs, Available at: https://hockey-graphs.com/2016/04/18/zefr-rate-a-new-and-betterway-to-evaluate-power-plays/ (Accessed 13 April 2021).Search in Google Scholar

Radke, D., Radke, D., Brecht, T., and Pawelczyk, A. (2021) Passing and pressure metrics in ice hockey. In: Artificial intelligence for sports analytics (AISA) workshop at IJCAI ’21, Montreal, QC, Canada.Search in Google Scholar

Radke, D., Brecht, T., and Radke, D. (2022). Identifying completed pass types and improving passing lane models. In: Linköping hockey analytics conference. LINHAC, Linköping, Sweden.10.3384/ecp191008Search in Google Scholar

Ritchie, R., Harell, A., and Shreeves, P. (2022) Pass evaluation in women’s Olympic ice hockey. In: International ACM workshop on multimedia content analysis in sports, Lisbon, Portugal (Accessed 26 October 2022).10.1145/3552437.3555702Search in Google Scholar

Schulte, O., Zhao, Z., Javan, M., and Desaulniers, P. (2017) Apples-to-Apples: clustering and ranking NHL players using location information and scoring impact. In: MIT sloan sports analytics conference.Search in Google Scholar

Shaw, L. and Glickman, M. (2019) Dynamic analysis of team strategy in professional football. In: Barça sports analytics summit, Barcelona, Spain, Available at: https://static.capabiliaserver.com/frontend/clients/barca/wpprod/wp-content/uploads/2020/01/56ce723e-barca-conference-paper-laurie-shaw.pdf.Search in Google Scholar

Tora, M.R., Chen, J., and Little, J.J. (2017) Classification of puck possession events in ice hockey. In: IEEE/CVF conf. on computer vision and pattern recognition workshops (CVPRW), Honolulu, HI, USA.10.1109/CVPRW.2017.24Search in Google Scholar

Vats, K., Fani, M., Clausi, D.A., and Zelek, J. (2021) Puck localization and multi-task event recognition in broadcast hockey videos. In: IEEE/CVF conference on computer vision and pattern recognition workshops (CVPRW), Nashville, TN, USA.10.1109/CVPRW53098.2021.00514Search in Google Scholar

Vats, K., Walters, P., Fani, M., Clausi, D.A., and Zelek, J.S. (2023) Player tracking and identification in ice hockey. In: Expert systems with applications, p. 213.10.1016/j.eswa.2022.119250Search in Google Scholar

Wei, X., Sha, L., Lucey, P., Morgan, S., and Sridharan, S. (2013) Large-scale analysis of formations in soccer. In: International conference on digital image computing: techniques and applications (DICTA), Hobart, TAS, Australia.10.1109/DICTA.2013.6691503Search in Google Scholar

Yurko, R., Matano, F., Richardson, L.F., Granered, N., Pospisil, T., Pelechrinis, K., and Ventura, S.L. (2020). Going deep: models for continuous-time within-play valuation of game outcomes in American football with tracking data. J. Quant. Anal. Sports 16: 163–182, https://doi.org/10.1515/jqas-2019-0056.Search in Google Scholar

Received: 2023-02-28

Accepted: 2024-03-01

Published Online: 2024-04-04

Published in Print: 2024-09-25

You are currently not able to access this content.

Articles in the same Issue

https://doi.org/10.1515/jqas-2023-0019

Keywords for this article

hockey; player tracking; non-negative matrix factorization; topic modelling