A comprehensive review of plus-minus ratings for evaluating individual players in team sports

Open access

Abstract

The increasing availability of data from sports events has led to many new directions of research, and sports analytics can play a role in making better decisions both within a club and at the level of an individual player. The ability to objectively evaluate individual players in team sports is one aspect that may enable better decision making, but such evaluations are not straightforward to obtain. One class of ratings for individual players in team sports, known as plus-minus ratings, attempt to distribute credit for the performance of a team onto the players of that team. Such ratings have a long history, going back at least to the 1950s, but in recent years research on advanced versions of plus-minus ratings has increased noticeably. This paper presents a comprehensive review of contributions to plus-minus ratings in later years, pointing out some key developments and showing the richness of the mathematical models developed. One conclusion is that the literature on plus-minus ratings is quite fragmented, but that awareness of past contributions to the field should allow researchers to focus on some of the many open research questions related to the evaluation of individual players in team sports.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Awad T. (2010a). Delta with teammate adjustments – DeltaSOT. http://www.hockeyprospectus.com/puck/article.php?articleid=454 accessed 2018-09-05.

  • Awad T. (2010b). Plus-minus and Corsi have a baby. http://www.hockeyprospectus.com/puck/article.php?articleid=436 accessed 2010-10-24.

  • Barnwell B. (2009). Receiving plus/minus part I. https://www.footballoutsiders.com/stat-analysis/2009/receiving-plusminus-part-i accessed 2018-09-19.

  • Bohrmann F. (2011). Problems with an adjusted plus minus metric in football. http://www.soccerstatistically.com/blog/2011/12/28/problems-with-an-adjusted-plusminus-metric-in-football.html accessed 2018-09-13.

  • Constantinou A. & Fenton N. (2013). Determining the level of ability of football teams by dynamic ratings based on the relative discrepancies in scores between adversaries. Journal of Quantitative Analysis in Sports 9 37–50.

  • Deshpande S. & Jensen S. (2016). Estimating an NBA player’s impact on his team’s chances of winning. Journal of Quantitative Analysis in Sports 12 51–72.

  • Elo A. (1978). The Rating of Chessplayers Past and Present. New York: Arco Publishing.

  • Engelmann J. (2011). A new player evaluation technique for players of the National Basketball Association (NBA). Proceedings of the MIT Sloan Sports Analytics Conference.

  • Engelmann J. (2017). Possession-based player performance analysis in basketball (adjusted +/− and related concepts). In: Albert J. Glickman M. Swartz T. & Koning R. eds. Handbook of Statistical Methods and Analyses in Sports Boca Raton: Chapman and Hall/CRC 215–228.

  • Fearnhead P. & Taylor B. (2011). On estimating the ability of NBA players. Journal of Quantitative Analysis in Sports 7 https://doi.org/10.2202/1559-0410.1298.

  • Franks A. D’Amour A. Cervone D. & Bornn L. (2016). Meta-analytics: tools for understanding the statistical properties of sports metrics. Journal of Quantitative Analysis in Sports 12 151–165.

  • Fyffe I. & Vollman R. (2002). Improving plus-minus. http://www.hockeythink.com/research/plusmin.html accessed 2011-12-19.

  • Gramacy R. Jensen S. & Taddy M. (2013). Estimating player contribution in hockey with regularized logistic regression. Journal of Quantitative Analysis in Sports 9 97–111.

  • Gramacy R. Taddy M. & Tian S. (2017). Hockey performance via regularized logistic regression. In: Albert J. Glickman M. Swartz T. & Koning R. eds. Handbook of Statistical Methods and Analyses in Sports Boca Raton: Chapman and Hall/CRC 287–306.

  • Guryashkin I. (2012). Mayweather measures up with greats. http://www.espn.co.uk/boxing/story/_/id/7780088/floyd-mayweather-jr-measuresboxing-greats accessed 2018-09-19.

  • Hamilton H. (2014). Adjusted plus/minus in football - why it’s hard and why it’s probably useless. http://www.soccermetrics.net/player-performance/adjusted-plusminus-deep-analysis accessed 2018-09-13.

  • Hass Z. (2017). Division of credit modeling for team sports with an emphasis on NCAA volleyball. Ph.D. thesis Purdue University.

  • Hass Z. & Craig B. (2018). Exploring the potential of the plus/minus in NCAA women’s volleyball via the recovery of court presence information. Journal of Sports Analytics 4 285–295.

  • Hvattum L. & Arntzen H. (2010). Using ELO ratings for match result prediction in association football. International Journal of Forecasting 26 460–470.

  • Ilardi S. (2007). Adjusted plus-minus: An idea whose time has come. http://www.82games.com/ilardi1.htm accessed 2018-08-31.

  • Ilardi S. (2014). The next big thing: real plus-minus. http://www.espn.com/nba/story/_/id/10740818/introducing-real-plus-minus accessed 2018-09-05.

  • Ilardi S. & Barzilai A. (2008). Adjusted plus-minus ratings: new and improved for 2007-2008. http://www.82games.com/ilardi2.htm accessed 2018-08-31.

  • Kacsmar S. (2016). 2015 passing plus-minus. https://www.footballoutsiders.com/index.php?q=stat-analysis/2016/2015-passingplus-minus accessed 2018-09-19.

  • Kharrat T. Peña J. & McHale I. (2018). Plus-minus player ratings for soccer. ArXiv:1706.04943.

  • Kubatko J. Oliver D. Pelton K. & Rosenbaum D. (2007). A starting point for analyzing basketball statistics. Journal of Quantitative Analysis in Sports 3 article 1.

  • Lasek J. Szlávik Z. & Bhulai S. (2013). The predictive power of ranking systems in association football. International Journal of Applied Pattern Recognition 1 27–46.

  • Macdonald B. (2011a). A regression-based adjusted plus-minus statistic for NHL players. Journal of Quantitative Analysis in Sports 7.

  • Macdonald B. (2011b). An improved adjusted plus-minus statistic for NHL players. Proceedings of the MIT Sloan Sports Analytics Conference.

  • Macdonald B. (2012a). Adjusted plus-minus for NHL players using ridge regression with goals shots Fenwick and Corsi. Journal of Quantitative Analysis in Sports 8.

  • Macdonald B. (2012b). An expected goals model for evaluating NHL teams and players. Proceedings of the 2012 MIT Sloan Sports Analytics Conference.

  • Macdonald B. Lennon C. & Sturdivant R. (2012). Evaluating NHL goalies skaters and teams using weighted shots. ArXiv:1205.1746.

  • Matano F. Richardson L. Pospisil T. Eubanks C. & Qin J. (2018). Augmenting adjusted plus-minus in soccer with FIFA ratings. ArXiv:1810.08032v1.

  • McHale I. & Davies S. (2007). Statistical analysis of the FIFA world rankings. In: Koning R. & Albert J. eds. Statistical Thinking in Sport Boca Raton FL: Chapman and Hall 77–90.

  • McHale I. & Forrest D. (2005). The importance of recent scores in a forecasting model for professional golf tournaments. IMA Journal of Management Mathematics 16 131–140.

  • McHale I. & Morton A. (2011). A Bradley-Terry type model for forecasting tennis match results. International Journal of Forecasting 27 619–630.

  • McHale I. Scarf P. & Folker D. (2012). On the development of a soccer player performance rating system for the English Premier League. Interfaces 42 339–351.

  • Okamoto D. (2011). Stratified odds ratios for evaluating NBA players based on their plus/minus statistics. Journal of Quantitative Analysis in Sports 7 Article 5 article 5.

  • Omidiran D. (2011). A new look at adjusted plus/minus for basketball analysis. Proceedings of the 2011 MIT Sloan Sports Analytics Conference.

  • Pantuso G. (2017). The football team composition problem: a stochastic programming approach. Journal of Quantitative Analysis in Sports 13 113–129.

  • Rathke A. (2017). An examination of expected goals and shot efficiency in soccer. Journal of Human Sport and Exercise 12(2proc) S514–S529.

  • Rosenbaum D. (2004). Measuring how NBA players help their teams win. http://www.82games.com/comm30.htm accessed 2018-08-31.

  • Rosenbaum D. (2005). Defense is all about keeping the other team from scoring. http://82games.com/rosenbaum3.htm accessed 2018-09-28.

  • Sæbø O. & Hvattum L. (2015). Evaluating the efficiency of the association football transfer market using regression based player ratings. In: NIK: Norsk Informatikkonferanse Bibsys Open Journal Systems 12 pages.

  • Sæbø O. & Hvattum L. (2019). Modelling the financial contribution of soccer players to their clubs. Journal of Sports Analytics 5 23–34.

  • Schuckers M. & Curro J. (2013). Total hockey rating (THoR): a comprehensive statistical rating of National Hockey League forwards and defensemen based upon all on-ice events. Proceedings of the MIT Sloan Sports Analytics Conference.

  • Schuckers M. Lock D. Wells C. Knickerbocker C. & Lock R. (2011). National Hockey League skater ratings based upon all onice events: an adjusted minus/plus probability (AMPP) approach. http://myslu.stlawu.edu/~msch/sports/LockSchuckersProbPlusMinus113010.pdf.

  • Schultze S. & Wellbrock C. (2018). A weighted plus/minus metric for individual soccer player performance. Journal of Sports Analytics 4 121–131.

  • Sill J. (2010). Improved NBA adjusted +/− using regularization and out-of-sample testing. Proceedings of the 2010 MIT Sloan Sports Analytics Conference.

  • Sisneros R. & Van Moer M. (2013). Expanding plus-minus for visual and statistical analysis of NBA box-score data. In: Proceedings of IEEE Vis Workshop on Sports Data Visualization.

  • Sittl R. & Warnke A. (2016). Competitive balance and assortative matching in the German Bundesliga. Discussion Paper No. 16-058 ZEW Centre for European Economic Research Mannheim.

  • Smith G. (2016). A shot quality adjusted plus-minus for the NHL. Master’s thesis University of Toronto.

  • Spagnola N. (2013). The Complete Plus-Minus: A Case Study of The Columbus Blue Jackets. Master’s thesis University of South Carolina.

  • Stefani R. & Pollard R. (2007). Football rating systems for top-level competition: A critical survey. Journal of Quantitative Analysis in Sports 3 Article 3 article 3.

  • Szymanski S. (2000). A market test for discrimination in the English professional soccer leagues. Journal of Political Economy 108 590–603.

  • Thomas A. Ventura S. Jensen S. & Ma S. (2013). Competing process hazard function models for player ratings in ice hockey. The Annals of Applied Statistics 7 1497–1524.

  • Tiedemann T. Francksen T. & Latacz-Lohmann U. (2010). Assessing the performance of German Bundesliga football players: a non-parametric metafrontier approach. Central European Journal of Operations Research 19 571–587.

  • Vilain J. & Kolkovsky R. (2016). Estimating individual productivity in football. http://econ.sciences-po.fr/sites/default/files/file/jbvilain.pdf accessed 2019-08-03.

  • Warnke A. (2017). Essays on Gender Differences in Training Incentives and Creativity Survey Response and Competitive Balance and Sorting in Football. Ph.D. thesis University of Freiburg.

  • Winston W. (2009). Mathletics. Princeton New Jersey: Princeton University Press.

  • Witus E. (2008). Offensive and defensive adjusted plus/minus. http://www.countthebasket.com:80/blog/2008/06/03/offensive-and-defensive-adjustedplus-minus/ accessed 2009-03-31.

Search
Journal information
Impact Factor


CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.355
Source Normalized Impact per Paper (SNIP) 2018: 0.462

Metrics
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 451 451 148
PDF Downloads 263 263 46