Multivariate internal load quantification in university basketball: principal components, mixed models and Mahalanobis-Taguchi

Authors

DOI:

https://doi.org/10.47197/retos.v82.119410

Keywords:

Multivariate analysis , Basketball, internal load, RPE, TRIMP

Abstract

Introduction: Internal load quantification constituted a fundamental element for training planning and injury prevention in team sports. Most basketball studies employed univariate approaches that failed to capture the multidimensional nature of load.

Objective: Internal load in Mexican university basketball was analyzed using an integrated multivariate approach combining principal component analysis, linear mixed models, the Mahalanobis-Taguchi system and Bland-Altman concordance, evaluating differences by playing position, game period, and match outcome.

Methodology: Seventeen male players from a university team participated, yielding 236 observations across 22 official games. Physiological load was quantified using the Training Impulse (Edwards' TRIMP) per game quarter and perceptual load with the Rating of Perceived Exertion scale. Principal component analysis, linear mixed models, the Mahalanobis-Taguchi system, and Bland-Altman concordance analysis were applied.

Results: Principal component analysis revealed a single component explaining 55.28% of variance, evidencing unidimensionality of internal load. Linear mixed models identified game period as the dominant factor, with greater demand in the second and fourth quarters. In lost games, load did not decrease in the third quarter. Perceived exertion differed between positions while Training Impulse showed no differences, evidencing perceptual-physiological dissociation. Discussion: Results were consistent with prior studies reporting unidimensionality of internal load in team sports. The sawtooth temporal pattern replicated findings from elite basketball and the positional perceptual-physiological dissociation suggested selecting monitoring indicators according to playing position.

Conclusions: The integrated multivariate approach reveals internal load patterns undetectable through conventional univariate analysis, with direct implications for individualized training load management.

References

Bates, D., Mächler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1–48. https://doi.org/10.18637/jss.v067.i01

Ben Abdelkrim, N., El Fazaa, S., & El Ati, J. (2007). Time-motion analysis and physiological data of elite under-19-year-old basketball players during competition. British Journal of Sports Medicine, 41(2), 69–75. https://doi.org/10.1136/bjsm.2006.032318

Bourdon, P. C., Cardinale, M., Murray, A., Gastin, P., Kellmann, M., Varley, M. C., Gabbett, T. J., Coutts, A. J., Burgess, D. J., Gregson, W., & Cable, N. T. (2017). Monitoring athlete training loads: Consensus statement. International Journal of Sports Physiology and Performance, 12(s2), S2-161–S2-170. https://doi.org/10.1123/IJSPP.2017-0208

Camacho-Sánchez, R., Pla, P., Serna, J., & Lavega-Burgués, P. (2023). Efecto de las tareas motrices en el comportamiento fisiológico y emocional de jugadores de baloncesto semiprofesional. Retos, 48, 1031–1039. https://doi.org/10.47197/retos.v48.96321

Capdevila, L., Guillen, J., Lalanza, J., Zamora, V., Rodas, G., & Caparrós, T. (2024). Protocolo de VFC no invasivo y nuevo índice para evaluar la carga de entrenamiento interna durante el calentamien-to de baloncesto. Retos , 54 , 169-179. https://doi.org/10.47197/retos.v54.102596

Clemente, F. M., Mendes, B., Bredt, S. da G. T., Praça, G. M., Silvério, A., Carriço, S., & Duarte, E. (2019). Perceived training load, muscle soreness, stress, fatigue, and sleep quality in professional bas-ketball: A full season study. Journal of Human Kinetics, 67, 199–207. https://doi.org/10.2478/hukin-2019-0002

Espasa-Labrador, J., Peña, J., Caparrós, T., Cook, M., & Fort-Vanmeerhaeghe, A. (2021). Relationship be-tween internal and external load in elite female youth basketball players. Apunts Sports Medi-cine, 56(211), 100357. https://doi.org/10.1016/j.apunsm.2021.100357

Espasa-Labrador, J., Fort-Vanmeerhaeghe, A., Montalvo, A. M., Carrasco-Marginet, M., Irurtia, A., & Calleja-González, J. (2023). Monitoring internal load in women’s basketball via subjective and device-based methods: A systematic review. Sensors, 23(9), 4447. https://doi.org/10.3390/s23094447

Fox, J. L., Stanton, R., & Scanlan, A. T. (2018). A comparison of training and competition demands in semiprofessional male basketball players. Research Quarterly for Exercise and Sport, 89(1), 103–111. https://doi.org/10.1080/02701367.2017.1410693

García, F., Vázquez-Guerrero, J., Castellano, J., Casals, M., & Schelling, X. (2020). Differences in physical demands between game quarters and playing positions on professional basketball players dur-ing official competition. Journal of Sports Science & Medicine, 19(2), 256–263. https://www.jssm.org/jssm-19-256.htm

Guedea-Delgado, J. C., Nájera Longoria, R. J., Zubiaur Ochoa, P., López Guillen, L. G., Carrasco Mendoza, M. M., Mar Sánchez, R., & Ramírez Félix, D. R. (2022). Percepción acerca de las funciones y el ni-vel de conocimiento general en entrenadores de basquetbol en México. Revista Mexicana de Ciencias de la Cultura Física, 1(2), 1–14. https://doi.org/10.54167/rmccf.v1i2.970

Hair, J. F., Black, W. C., Anderson, R. E., & Babin, B. J. (2019). Multivariate data analysis (8th ed.). Pear-son.

Helwig, J., Diels, J., Röll, M., Mahler, H., Gollhofer, A., Roecker, K., & Willwacher, S. (2023). Relationships between external, wearable sensor-based, and internal parameters: A systematic review. Sen-sors, 23(2), 827. https://doi.org/10.3390/s23020827

López, J. A. B., Martínez, S. G., Valero, A. F., & Cuartero, J. O. (2021). Cuantificación de la carga de entre-namiento y competición: Análisis comparativo por posiciones en un equipo de la Liga Española de Baloncesto Oro. Retos, 42, 882–890. https://doi.org/10.47197/retos.v42i0.87268

Mancha-Triguero, D., García-Rubio, J., Antúnez, A., & Ibáñez, S. J. (2020). Physical and physiological pro-files of aerobic and anaerobic capacities in young basketball players. International Journal of Environmental Research and Public Health, 17(4), 1409. https://doi.org/10.3390/ijerph17041409

Manzi, V., D’Ottavio, S., Impellizzeri, F. M., Chaouachi, A., Chamari, K., & Castagna, C. (2010). Profile of weekly training load in elite male professional basketball players. Journal of Strength and Con-ditioning Research, 24(5), 1399–1406. https://doi.org/10.1519/JSC.0b013e3181d7552a

McLaren, S. J., Macpherson, T. W., Coutts, A. J., Hurst, C., Spears, I. R., & Weston, M. (2018). The relation-ships between internal and external measures of training load and intensity in team sports: A meta-analysis. Sports Medicine, 48(3), 641–658. https://doi.org/10.1007/s40279-017-0830-z

Petway, A. J., Freitas, T. T., Calleja-González, J., Medina Leal, D., & Alcaraz, P. E. (2020). Training load and match-play demands in basketball based on competition level: A systematic review. PLoS ONE, 15(3), e0229212. https://doi.org/10.1371/journal.pone.0229212

Power, C. J., Fox, J. L., Dalbo, V. J., & Scanlan, A. T. (2022). External and internal load variables encoun-tered during training and games in female basketball players according to playing level and playing position: A systematic review. Sports Medicine - Open, 8(1), 107. https://doi.org/10.1186/s40798-022-00498-9

Russell, J. L., McLean, B. D., Stolp, S., Strack, D., & Coutts, A. J. (2021). Quantifying training and game de-mands of a National Basketball Association season. Frontiers in Psychology, 12, 793216. https://doi.org/10.3389/fpsyg.2021.793216

Sanders, G. J., Boos, B., Rhodes, J., Kollock, R. O., & Peacock, C. A. (2021). Competition-based heart rate, training load, and time played above 85% peak heart rate in NCAA Division I women’s basket-ball. Journal of Strength and Conditioning Research, 35(4), 1095–1102. https://doi.org/10.1519/JSC.0000000000002876

Scanlan, A. T., Dascombe, B. J., & Reaburn, P. R. J. (2012a). The construct and longitudinal validity of the basketball exercise simulation test. Journal of Strength and Conditioning Research, 26(2), 523–530. https://journals.lww.com/nsca-jscr/fulltext/2012/02000/the_construct_and_longitudinal_validity_of_the.28.aspx

Scanlan, A. T., Dascombe, B. J., Reaburn, P., & Dalbo, V. J. (2012b). The physiological and activity de-mands experienced by Australian female basketball players during competition. Journal of Sci-ence and Medicine in Sport, 15(4), 341–347. https://doi.org/10.1016/j.jsams.2011.12.008

Stojanović, E., Stojiljković, N., Scanlan, A. T., Dalbo, V. J., Berkelmans, D. M., & Milanović, Z. (2018). The activity demands and physiological responses encountered during basketball match-play: A systematic review. Sports Medicine, 48(1), 111–135. https://doi.org/10.1007/s40279-017-0794-z

Svilar, L., Castellano, J., Jukic, I., & Casamichana, D. (2018). Positional differences in elite basketball: Selecting appropriate training-load measures. International Journal of Sports Physiology and Performance, 13(7), 947–952. https://doi.org/10.1123/ijspp.2017-0534

Taguchi, G., & Jugulum, R. (2002). The Mahalanobis-Taguchi strategy: A pattern technology system. John Wiley & Sons.

Weaving, D., Marshall, P., Earle, K., Nevill, A., & Abt, G. (2014). Combining internal- and external-training-load measures in professional rugby league. International Journal of Sports Physiology and Performance, 9(6), 905–912. https://doi.org/10.1123/ijspp.2013-0444

Yang, K. (2024). Quarterly fluctuations in external and internal loads among professional basketball players. Frontiers in Physiology, 15, 1419097. https://doi.org/10.3389/fphys.2024.1419097

Downloads

Published

01-09-2026

Issue

Section

Original Research Article

How to Cite

Torres Correa, A., Florez Sanchez, A., Nieto Serrano, E. J., Alonso Ramos, Z. N., & Hernández Cruz, G. (2026). Multivariate internal load quantification in university basketball: principal components, mixed models and Mahalanobis-Taguchi. Retos, 82, 1068-1079. https://doi.org/10.47197/retos.v82.119410