Measuring the Technical Efficiency of Hockey Legends: Who is the Best NHL Player of All Time?

Vol.18,No.1(2024)

Abstract

The aim of the research is to determine the technical efficiency of legendary hockey players in the National Hockey League (NHL), to create a ranking of these players and to reveal the best NHL players of all time. The research uses statistical data on 379 players from the 1944/45 season to the 2023/24 season. The methodology is based on multi-criteria analysis, specifically the concept of data envelopment analysis (DEA). The DEA provides an objective measure of the overall playing profile of hockey players and can help supplement the information in rankings provided by sports journalists. Andersen and Petersen's model is used to evaluate the data collected, providing super efficiency scores by aggregating NHL statistics related to various aspects of the game to produce a final ranking of hockey legends. The concept of data envelopment analysis works with multiple variables and allows for greater objectivity to be incorporated into the rankings. The number of games played is chosen as one of the model's input variables. The output variables include: number of goals scored, number of assists, plus/minus, inverse of penalty minutes, points per game, number of shots, number of individual awards, and number of Stanley Cups won. The research named Wayne Gretzky, Butch Goring and Serge Savard as the best players in the NHL historically in terms of technical efficiency. Among other things, the ranking of legendary hockey players revealed that players with a high number of games played or points scored are not necessarily technically efficient.


Keywords:
sport; ice hockey; technical efficiency; National Hockey League; DEA
References

Agrawal J., & Kamakura W. A. (1995). The economic worth of celebrity endorsers: an event study analysis. Journal of Marketing, 59, 56–62. https://doi.org/10.2307/1252119

Alcaraz, J., Pastor, J. T., Del Campo, F. J., & Pastor, D. (2019). Evaluating the emergence of elite professional golfers in europe with data envelopment analysis. European Journal of Human Movement, 43, 145–166.

Alp, I. (2006). Performance evaluation of goalkeepers of the world cup. G.U. Journal of Science, 19(2), 119–125.
Ampere Sports Consumer. (2022). Sports – Consumer. Ampere Analysis. Retrieved 5 December, 2023. Available from https://www.ampereanalysis.com/products/about/sports-consumer

Andersen P., & Petersen N. C. (1993). A Procedure for Ranking Efficient Units in Data Envelopment Analysis. Management Science, 39(10), 1261–1264. https://doi.org/10.1287/mnsc.39.10.1261

Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078–1092. https://doi.org/10.1287/mnsc.30.9.1078

Banker, R. D., Charnes, A., Cooper, W. W., Swarts, J., & Thomas, D. A. (1989). An introduction to data envelopment analysis with some of its models and their uses. In J. L. Chan, & J. M. Patton (Eds.), Research in governmental and nonprofit accounting (pp. 125–163). CT: Jai Press.

Beijing Realworld Research and Consultation Company Ltd. (2024). MaxDEA X is powerful and fastest big data DEA software. Retrieved 5 January, 2024. Available from http://maxdea.com/Index_En.htm

Bharnuke, A. (2023). Top 10 Great Ice Hockey Players of All Time. fallinsports.com. Retrieved 1 December, 2023. Available from https://fallinsports.com/top-10-great-ice-hockey-players-of-all-time/

Cinca, C., & Molinero, C. M. (2004). Selecting DEA specifications and ranking units via PCA. Journal of the Operational Research Society, 55(5), 521–528. https://doi.org/10.1057/palgrave.jors.2601705

Cooper, W. W., Seiford, L. M., & Tone, K. (2007). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software (2nd ed.). Springer.

DeOliveira, E. H., & Callum, R. (2004). Who’s the Best? Data Envelopment Analysis and Ranking Players in the National Football League. In S. Butenko, J. Gil-Lafuente, & P. M. Pardalos (Eds.), Economics, Management and Optimization in Sports. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24734-0_2

Deshpande, S. K., & Jensen, S. T. (2016). Estimating an NBA player’s impact on his team’s chances of winning. Journal of Quantitative Analysis in Sports, 12(2), 51–72. https://doi.org/10.1515/jqas-2015-0027

Djordjević, D. P., Vujošević, M., & Martić, M. (2015). Measuring efficiency of football teams by multi-stage DEA model. Tehnički vjesnik, 22(3), 763–770. https://doi.org/10.17559/TV-20140306134047

Dlouhý, M., Jablonský, J., & Novosádová, I. (2007). Use of data envelopment analysis for Efficiency Evaluation of Czech Hospitals. Politická Ekonomie, 55(1), 60–71. https://doi.org/10.18267/j.polek.590

Duffett, N. (2023). 25 greatest NHL players of all time, ranked. ClutchPoints. Retrieved 15 December, 2023. Available from https://clutchpoints.com/25-greatest-nhl-players-of-all-time-ranked

Fried, H. O., Lambrinos, J., & Tyner, J. (2004). Evaluating the performance of professional golfers on the PGA, LPGA and Spga Tours. European Journal of Operational Research, 154(2), 548–561. https://doi.org/10.1016/s0377-2217(03)00188-7

Friedman, L., & Sinuany-Stern, Z. (1998). Combining ranking scales and selecting variables in the DEA context: The case of industrial branches. Computers and Operations Research, 25(9), 781–791. https://doi.org/10.1016/s0305-0548(97)00102-0

Golany, B., & Roll, Y. (1989). An application procedure for DEA. Omega, 17(3), 237–250. https://doi.org/10.1016/0305-0483(89)90029-7

Guzmán, I., & Morrow, S. (2007). Measuring efficiency and productivity in professional football teams: Evidence from the English Premier League. Central European Journal of Operations Research, 15(4), 309–328. https://doi.org/10.1007/s10100-007-0034-y

Haas, D. J. (2003). Technical efficiency in the major league soccer. Journal of Sport Economics, 4(3), 203–215. http://dx.doi.org/10.1177/1527002503252144

Halkos G., & Tzeremes N. (2012). Evaluating professional tennis players’ career performance: A Data Envelopment Analysis approach. MPRA Paper 41516. Munich: University Library of Munich.

Helfrick, E. (2024). Top 10 Best Ice Hockey Leagues. The Hockey Writers. Retrieved 5 January, 2024. Available from https://thehockeywriters.com/top-10-best-ice-hockey-leagues/

Hirotsu, N., Iguchi, Y., & Yoshimura, M. (2018). Development of Simple Indicators to Evaluate Performance of Soccer Player by Use of Data Envelopment Analysis. Juntendo Sports and Health Science Research, 9(2), 53–63.

Homburg, C. (2001). Using data envelopment analysis to benchmark activities. International Journal of Production Economics, 73(1), 51–58. https://doi.org/10.1016/s0925-5273(01)00194-3

Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429–444. https://doi.org/10.1016/0377-2217(78)90138-8

Chen, Y., Gong, Y., & Li, X. (2016). Evaluating NBA player performance using bounded integer data envelopment analysis. INFOR: Information Systems and Operational Research, 55(1), 38–51. https://doi.org/10.1080/03155986.2016.1262581

Chiu, S., Hsiao, C., & Wu, H. (2015). Measuring pitchers’ performance using data envelopment analysis with Advanced Statistics. Contemporary Management Research, 11(4), 351–384. https://doi.org/10.7903/cmr.14157

Jablonský, J. (2012). Multi-criteria approaches for ranking of efficient units in DEA models. Central European Journal of Operations Research, 20(3), 435–449. https://doi.org/10.1007/s10100-011-0223-6

Jablonský, J. (2021). Individual and team efficiency: a case of the National Hockey League. Central European Journal of Operations Research, 30(2), 479–494. https://doi.org/10.1007/s10100-021-00775-0

Jablonský, J., & Dlouhý, M. (2015). Modely hodnocení efektivnosti a alokace zdrojů. Professional Publishing.

Jablonský, J., Dlouhý, M., & Zýková, P. (2018). Analýza obalu dat. Professional Publishing.

Jenkins, L., & Anderson, M. (2003). A multivariate statistical approach to reducing the number of variables in data envelopment analysis. European Journal of Operational Research, 147(1), 51–61. https://doi.org/10.1016/s0377-2217(02)00243-6

Kapera, R. (1996). The structure of goalkeeper s offensive play in soccer – practical applications. Trening, 2, 132–137.

Kenyon, D. (2018). Ranking the Top 10 NHL Hockey Players of All Time. Bleacher Report, Inc. Retrieved 28 December, 2023. Available from https://bleacherreport.com/articles/2771078-ranking-the-top-10-nhl-hockey-players-of-all-time

Kvasnička, D. (2022). Legendy. 10 nejlepších hokejistů v historii NHL, kteří už ukončili sportovní kariéru. CZECH NEWS CENTER a.s. Retrieved 28 December, 2023. Available from https://sportrevue.isport.blesk.cz/legendy-10-nejlepsich-hokejistu-v-historii-nhl-kteri-uz-ukoncili-sportovni-karieru

Langr, M. (2019). Praha potvrdila, že NHL patří i do Evropy. NHL.com. Retrieved 12 December, 2023. Available from https://www.nhl.com/cs/news/praha-potvrdila-ze-do-ni-nhl-patri-309766478

Mazur, M. J. (1994). Evaluating the relative efficiency of baseball players. Data Envelopment Analysis: Theory, Methodology, and Applications, 369–391. https://doi.org/10.1007/978-94-011-0637-5_19

NHL. (2024). Statistics. NHL.com. Retrieved 15 October, 2023. Available from https://www.nhl.com/stats/

Nunamaker, T. R. (1985). Using data envelopment analysis to measure the efficiency of non-profit organizations: A critical evaluation. Managerial and Decision Economics, 6(1), 50–58. https://doi.org/10.1002/mde.4090060109

Pelloneová N. (2023a). Measuring the Technical Efficiency of Hockey Players: Empirical Evidence from Czech Hockey Competition. Studia Sportiva, 16(2), 229–248. https://doi.org/10.5817/sts2022-2-23

Pelloneová, N. (2023b). Evaluating hockey players using Andersen and Petersen’s super-efficiency model: Who is the best Czech hockey player in the NHL? Polish Journal of Sport and Tourism, 30(3), 23–28. https://doi.org/10.2478/pjst-2023-0016
Pelloneová, N., & Tomíček, M. (2022a). Ranking players by DEA: An analysis of Czech and Danish football. Studia Sportiva, 16(1), 76–90. https://doi.org/10.5817/sts2022-1-8

Pelloneová, N., & Tomíček, M. (2022b). Performance evaluation of goalkeepers of Slovak Football League. ACC Journal, 28(2), 96–105. https://doi.org/10.15240/tul/004/2022-2-008

Raab, R. L., & Lichty, R. W. (2002). Identifying subareas that comprise a greater metropolitan area: The criterion of county relative efficiency. Journal of Regional Science, 42(3), 579–594. https://doi.org/10.1111/1467-9787.00273

Ramanathan, R. (2003). An introduction to data envelopment analysis: A tool for performance measurement. Sage.

Ramón, N., Ruiz, J. L., & Sirvent, I. (2012). Common sets of weights as summaries of DEA profiles of weights: With an application to the ranking of professional tennis players. Expert Systems with Applications, 39(5), 4882–4889. https://doi.org/10.1016/j.eswa.2011.10.004

Ribeiro, A. S., & Lima, F. (2012). Portuguese football league efficiency and players‘ wages. Applied Economics Letters, 19(6), 599–602. https://doi.org/10.1080/13504851.2011.591719

Ruiz, J. L., Pastor, D., & Pastor, J. T. (2011). Assessing professional tennis players using data envelopment analysis (DEA). Journal of Sports Economics, 14(3), 276–302. https://doi.org/10.1177/1527002511421952

Santín, D. (2014). Measuring the technical efficiency of football legends: Who were real Madrid’s all‐time most efficient players? International Transactions in Operational Research, 21(3), 439–452. https://doi.org/10.1111/itor.12082

Tiedemann, T., Francksen, T., & Latacz-Lohmann, U. (2011). Assessing the performance of German Bundesliga football players: a non-parametric metafrontier approach. Central European Journal of Operations Research, 19(4), 571–587. https://doi.org/10.1007/s10100-010-0146-7

Tone, K. (2002). A slacks-based measure of super-efficiency in data envelopment analysis. European Journal of Operational Research, 143(1), 32–41. https://doi.org/10.1016/s0377-2217(01)00324-1

ul Haq Bhat, Z., Ahmad, N., Bhat, & Dar, Q. F. (2021). Ranking of Football Players by DEA-Super Efficiency Model: An Evidence From English Premier League 2016/17 Season. Turkish Online Journal of Qualitative Inquiry, 12(4), 2009–2019.

Vavrek, R. (2021). An analysis of usage of a multi-criteria approach in an athlete evaluation: An evidence of NHL attackers. Mathematics, 9(12), 1399. https://doi.org/10.3390/math9121399

Weeks J. (2021). Best of the Bruins: Boston‘s All-Time Great Hockey Players and Coaches. McFarland & Company, Inc.

Metrics

0

Crossref logo

0


139

Views

53

PDF views