Measuring the efficiency of athletes during competition has been a subject of interest both for experts and scientists in sports for more than a hundred years. Basketball has recognized in the 1940s how important it is to analyze efficiency indicators because these procedures allow coaches to increase their knowledge. There are two basic methods – objective and subjective – for evaluating the efficiency, or real quality of basketball players. The aim of this research is to establish the level of correlation between these two methods and to identify clusters, i.e. player hierarchy based on the results of both methods of efficiency evaluation. The sample of variables consisted of 12 basketball players who participated in the 2010 FIBA World Championships in Turkey. The subjective evaluation, also called expert evaluation, was performed by coaches of seven national teams that participated in the Championship. The objective evaluation was performed using the EEF efficiency index. The data was processed using z-scoring, the Pearson coefficient, and hierarchical cluster analysis. The Pearson coefficients of linear correlation between the efficiency index and the expert evaluation is r = 0.859 with a statistical significance of p ≤ 0.01. The cluster analysis distinguished two groups of players, which were named quality and super quality. The variance analysis showed that the probability of the clusters being equal is less than p ≤ 0.00. The research has shown that the evaluation by coaches is relevant and is fully consistent with the efficiency index formula. Also, the distinction of two groups of players by clustering is not uncommon in the basketball practice and is linked with efficiency at the given time.


Basketball player Efficiency Efficiency index Expert evaluation World Championship


  1. D.J. Berri, Who is Most Valuable measuring the player's production of wins in the National Basketball Association, Mangerial and Decision Economics, 20 (1999) 411–427.
  2. М. Hughes, M. Franks, Notational analysis of sport, 2nd edition (Routledge, Taylor & Fransis, London, United Kingdom), (2004).
  3. C. Carling, A.M. Williams, T.Reilly, Handbook of soccer match analysis (Routledge, London, United Kingdom), (2005). http://dx.doi.org/10.4324/9780203448625.
  4. M. Hughes, The application of notational analysis to racket sports, In: Lees A, Maynard I, Huges M, Reilly T, editors, Science and Rocket Sports (E. and F. N. Spon, London, United Kingdom, 211–231), (1998).
  5. T. Reilly, Assessment of performance in team games, In: Roger E, Reilly T. editors, Kinanthropometry and exercise physiology labaratory manual: Test, procedures and data, Volumen 1: Antropomotry, 3rd edition (Routlge, New York, 184–196), (2009).
  6. H. Fullerton, The inside game: The science of baseball, The American Magazine, 70 (1910) 3–13.
  7. S. Simović, B. Matković, M. Mijanović, M. Kocić, M. Vojovdić, Structure of efficiency factor at XIII, XIV, XV, and XVI World Championship in basketball, Journal of Human Sport & Exercise, 7 (2012) 527–543.
  8. P.J. Fay, L.L. Messersmith, The effect of rule changes upon the distance traversed by basketball players, Research Quarterly, 9 (1938) 136–137.
  9. P.J. Fay, L.L. Messersmith, The distance traversed by college and high school basketball players and effect of rule changes upon distance traversed in college games, Athletic Journal, 18 (1938).
  10. L.L. Messersmith, A Study of the distance traveled by basketball players, Research Quarterly, 15 (1944) 29–37.
  11. L.L. Messersmith, C.C. Bucher, The distance traversed by Big Ten basketball players, Research Quarterly, 10 (1939) 61–62.
  12. L.L. Messersmith, S. Corey, The distance traversed by a basketball player, Research Quarterly, 2 (1931) 57–60.
  13. L.L. Messersmith, J. Laurence, K. Randels, A Study of distances traversed by college men and women in playing the game of basketball, Research Quarterly, 9 (1940) 30–31.
  14. R. Blake, The distance traversed by basketball players in different types of defense, Athletic Journal, 21 (1941) 18–20.
  15. N. Miner, P. Hodgson, A. Espenschade, Study of distance traversed and time spent in active play in women's basketball, Research Quarterly, 9 (1940) 95–101.
  16. E.R. Elbel, F. Allen, F, Evaluating team and individual performance in basketball, Research Quartely, 12 (1941), 538–557.
  17. G. Celeux, V. Robert, Towards an objective team efficiency rate in basketball, Journal de la Société Française de Statistique, 156 (215), 51–68.
  18. V. Blanco, R. Salmerón, S. Gómez-Haro, A multiplication selection system based on player performance: Case study – The Spanish ACB Basketball League, arXiv:1802.07039 [math.OC], 27 (2018) 1029– 1046. http://dx.doi.org/10.1007/s10726018-9593- 9.
  19. D. Dizdar, Evaluation of a set of methods for assessing the actual quality of basketball players, PhD [dissertation], University of Zagreb: Faculty of Kinesiology, (2002).
  20. D. Dizdar, Application of the AHP method for the assessment of the actual quality of athletes in team sports, In: Maleš B, editor, 2nd International Conference "Contemporary Kinesiology", (Split, Croatia, 2007, 19–32), (2007).
  21. J.A. Martinez, A review of the basketball player evaluation metrics (I): A description of the existing methods, Revista Internacional de Derecho y Gestión del Deporte, 10 (2010) 37– 77.
  22. H. Kay, A statistical analysis of the profile technique for the evaluation of competitive basketball performance, MsC [thesis], University Of Alberta, (1966).
  23. J. Gomez, J.A. Moll, Technique practice and team leadership (Augusto E.P. Teleña, Madrid, Espain), (1980).
  24. S. Garba, Performance evaluation of the players and teams in basketball, Trener, 9 (1981) 426–427.
  25. D. Bradshaw, Motivation through basketball statistics, Coaching Review, 7 (1984) 52–54.
  26. D. Heeren, Basketball abstracts (Prentice Hall, Upper Saddle River, NJ), (1988).
  27. D. Heeren, Basketball abstract, (Prentice Hall, Upper Saddle River, NJ), (1990).
  28. D. Heeren, Basketball abstract, (Prentice Hall, Upper Saddle River, NJ), (1994).
  29. D. Brown, Scouting and statistics, (Dale Brown Enterprises, New York, NY). http://dx.doi.org/10.1214/aos/1176347985.
  30. K.L. Swalgin, Relationship of the basketball evaluation system (BES) to criterion measure of performance in men's division I college basketball, The Applied Research in Coaching and Athletics Annual, 8 (1993) 226–245.
  31. K.L. Swalgin, The basketball evaluation system: A scientific approach to player evaluation, In: Krausse J, editor, Coaching baskteball (Master Press, Indianopolis, IN, 40–43), (1994).
  32. K.L. Swalgin, D. Knjaz, Euro-basketball evaluation system: A computerized seamless model to evaluate player performance, In: Katz L, editor, 6th International Symposium on Computer Science in Sport (Univerzity of Calgary, Canada, 292–299), (2007).
  33. J.F. Gréhaigne, D. Bouthier, P. Godbout, Performance assessment in team sports, Journal of Teaching in Physical Education, 16 (1997) 500–516.
  34. S. Trninić, A. Perica, D. Dizdar, Set of criteria for the actual quality evaluation of the elite basketball players, Collegium antropologicum, 23 (2000) 707–721.
  35. D. Telmes, Basketball Evaluation Formulas Historical Revision, Retrived Janiary 28, 2017 from Source: http://www.ebastats.com/form/table_revis.htm.
  36. D.J Berri, A simple measure of Worker productivity in the National Basketball Association, In: Humphreys B, Howard D, editors, The Business of Sport (Praeger, Westport, CT, 1–40), (2008).
  37. D. Hwang, Forecasting NBA player performance using a Weibull-Gamma Statistical Timing Model (MIT Sloan Sports Analytics Conference, March 2-3. Boston, MA. Retrived from http://www.sloansportscon...formance_Doug lasHwang.pdf.
  38. J.A. Martinez, L. Martinez, L, A stakeholder assessment of basketball player evaluation metrics, Journal of Human Sport & Exercise, 6 (2011) 153–183. http://dx.doi.org/10.4100/jhse.2011.61.17.
  39. J. Sindik, I. Jukić, M. Adžija, Latent structure of situational efficiency parameters at Croatian top basketball players, SportLogia, 8 (2012) 132–141. https://dx.doi.org/10.5550/sgia.120802.en.132S.
  40. L. Aizemberg, M.C. Roboredo, T.G. Ramos, J.C.C.S. de Mello, L.A. Meza, A.M. Alves, Measuring the NBA teams’ cross-efficiency by DEA Game, American Journal of Operations Research, 4 (2014) 101. http://dx.doi.org/10.4236/ajor.2014.43010.
  41. B.L. Lee, A.C. Worthington, A note on the ‘Linsanity’ of measuring the relative efficiency of National Basketball Association Guards, Applied Economics, 45 (2013), 4193– 4202.
  42. P. Moreno, S. Lozano, A network DEA assessment of team efficiency in the NBA, Annals of Operations Research, 214 (2014) 99–124.
  43. S. Radovanović, M. Radojčić, G. Savić, (2014). Two-phased DEA-MLA approach for predicting efficiency of NBA players, Yugoslav Jurnal of Operations Research, 24 (2014) 347-358. http://dx.doi.org/10.2298/YJOR140430030R.
  44. S. Trninić, D. Dizdar, System of the performance evaluation criteria weighted per positions in the basketball game, Collegium antropologicum, 24 (2000) 217–234.
  45. E. Sorka, Quantitative Assessment of Basketball Players’ Performance, Sportska praksa, 2 (1980) 22-25.
  46. M.A. Brooks, L.W. Bolech, J.L. Mayhew, Relationship of specific and nonspecific variables to successful basketball performance among High School players, Perception and Motor Skills, 46 (1987) 823-827. http://dx.doi.org/10.2466/pms.1987.64.3.82 3.
  47. B. Dežman, Expert system - A model for the prediction of the success of players in basketball. In: Rychtecký A, Svoboda B, Tilinger P, editors, 6th ICHPER European Congress (Faculty of Physical Education and Sports, Charles University, Pargue, Czech Republic 111–117), (1992).
  48. F. Erčulj, Comparison of different efficiency criteria in basketball. Kineziologija, 29 (1997) 42–48.
  49. S. Trninić, D. Dizdar, B. Dežman, Pragmatic validity of the combined model of expert system for assessment and analysis of the actual quality overall structure of basketball players, Collegium antropologicum, 26 (2002) 199–210.
  50. S. Jakovljević, M. Karalejić, I. Radovanović, Relations between two ways of evaluation of actual individual qualities of basketball players as a criterion of their successfulness, Fizička kultura, 61 (2007) 34–42.
  51. J.A. Martinez, Factors determining production (FDP) in basketball, Economics and Business Letters, 1 (2012), 21–29.
  52. J.F. Grehaigen, P. Godbout, Tactical knowledge in team sports – from a constructivist and cognitivist perspective, Quest, 47 (1995) 490–550. http://dx.doi.org/10.1080/00336297.1995.10484171.
  53. S. Trninić, D. Dizdar, B. Dežman, Empirical verification of the weighted system of criteria for the elite basketball players quality evaluation, Collegium antropologicum, 24 (2000) 431–442.
  54. P. Riley, The winner within – a life plan for team players, (Putnam's Sons, New York, NY), (1993).
  55. S. Trninić, D. Milanović, D. Dizdar, Discriminant Analysis of Winning and Defeated teams in Area of Standard Indicators of Situational Efficiency in Basketball Game, Leistungs sport, 27 (1997) 29–34.
  56. S. Trninić, N. Viskić-Štalec, J. Štalec, D. Dizdar, Ž. Birkić, Ž. Latent Structure of Standard Indicators of Situational Efficiency in Basketball Game, Kineziologija, 27 (1995) 27- 37.
  57. S. Trninić, V. Papić, V. Trninić, D. Vukičević, Player selection procedures in team sport games, Acta Kinesiologica, 2 (2008) 24–28.
  58. K.L. Swalgin, Basketball evaluation system: A computerized factor weighted model with measures of validity, Kineziologija, 30 (1998) 30–36.
  59. P. Fearnhead, B.M. Taylor, On estimating the ability of NBA players, Journal of Quantitative Analysis in Sports, 7 (2011), 11. http://dx.doi.org/10.2202/1559-0410.1298.
  60. L.G. Page, Using box-score to determine a position’s contribution to winning basketball games, PhD [dissertation], Brigham Young University, (2005).
  61. L.G. Page, B.J. Barney, A.T. McGuire, Effect of position, usage rate, and per game minutes played on NBA player production curves, Journal of Quantitative Analysis in Sports, 9 (2013) 337–345.
  62. T.L. Saaty, L.G. Vargas, The Analytic Hierarchy Process, (Kluwer, London, United Kingdom), (1996).