Original W'-balance models do not transfer to high-intensity interval training in trained adult runners: Proposal of a single-coefficient linear alternative.
6 affiliations
- 1Department of Physical Education and Sports, Faculty of Sport Sciences, Sport and Health University Research Institute (iMUDS), University of Granada, Granada, Spain.
- 2Department of Physical Education, Sport and Recreation, Universidad de La Frontera, Temuco, Chile.
- 3Department of Sport Science, University of Innsbruck, Innsbruck, Austria.
- 4Department of Physical Education and Sports, Faculty of Education, University of Cádiz, Puerto Real, Cádiz, Spain.
- 5Sport Training Laboratory, Faculty of Sport Sciences, University of Castilla-La Mancha, Toledo, Spain.
- 6Research Group in Health, Physical Activity, and Sports Technology, Faculty of Education, University of Alicante, Sant Vicent del Raspeig, Spain.
Abstract
This study evaluated the off-the-shelf predictive accuracy of four original W'-balance recovery models (Morton and Billat linear, W'BAL-INT, W'BAL-ODE and W'BAL-CAEN) and proposed a single-coefficient modified linear formulation (Linear_mod) for predicting high-intensity interval training (HIIT) performance with passive recovery in trained runners. Twenty-seven trained runners completed a 9/3-min running critical power (CP) test and two open-ended HIIT sessions to volitional exhaustion at 108% CP with a 2:1 work: rest ratio. Work intervals were individualized so that energy expenditure above CP equalled 40% (HIIT40%) or 60% (HIIT60%) of W'. The original models were applied using their published parameters. All substantially over-predicted the number of intervals completed (pooled MAE 26.4-72.4 intervals; bias +20.1 to +72.4). Linear_mod with its default recovery coefficient (R = 1) achieved a MAE of 4.85 intervals. Optimizing R at the population level (R = 1.63) reduced MAE to 2.85 intervals, while athlete-specific optimisation (R = 1.54 ± 0.29) reduced MAE to 0.55 intervals. Individual R values were stable between protocols (within-subject CV = 9.9%). Original W'-balance models did not accurately predict running HIIT performance, whereas Linear_mod provided high predictive accuracy using a single athlete-specific recovery coefficient.
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BibTeX
@article{garciapinillos2026original,
title = {{Original W'-balance models do not transfer to high-intensity interval training in trained adult runners: Proposal of a single-coefficient linear alternative.}},
author = {Felipe García-Pinillos and Diego Jaén-Carrillo and Leonardo Riquelme-Sebastián and Santiago Alejo Ruiz-Alias and Iván Fernández-Navarrete and Fernando González-Mohino and Violeta Muñoz de la Cruz and Javier Olaya-Cuartero},
journal = {Physiological reports},
year = {2026},
month = oct,
doi = {10.14814/phy2.71152},
url = {https://europepmc.org/article/MED/42902450},
note = {CC BY},
}
RIS
TY - JOUR
TI - Original W'-balance models do not transfer to high-intensity interval training in trained adult runners: Proposal of a single-coefficient linear alternative.
AU - Felipe García-Pinillos
AU - Diego Jaén-Carrillo
AU - Leonardo Riquelme-Sebastián
AU - Santiago Alejo Ruiz-Alias
AU - Iván Fernández-Navarrete
AU - Fernando González-Mohino
AU - Violeta Muñoz de la Cruz
AU - Javier Olaya-Cuartero
PY - 2026
DA - 2026/10/01
JO - Physiological reports
DO - 10.14814/phy2.71152
UR - https://europepmc.org/article/MED/42902450
AB - This study evaluated the off-the-shelf predictive accuracy of four original W'-balance recovery models (Morton and Billat linear, W'BAL-INT, W'BAL-ODE and W'BAL-CAEN) and proposed a single-coefficient modified linear formulation (Linear_mod) for predicting high-intensity interval training (HIIT) performance with passive recovery in trained runners. Twenty-seven trained runners completed a 9/3-min running critical power (CP) test and two open-ended HIIT sessions to volitional exhaustion at 108% CP with a 2:1 work: rest ratio. Work intervals were individualized so that energy expenditure above CP equalled 40% (HIIT40%) or 60% (HIIT60%) of W'. The original models were applied using their published parameters. All substantially over-predicted the number of intervals completed (pooled MAE 26.4-72.4 intervals; bias +20.1 to +72.4). Linear_mod with its default recovery coefficient (R = 1) achieved a MAE of 4.85 intervals. Optimizing R at the population level (R = 1.63) reduced MAE to 2.85 intervals, while athlete-specific optimisation (R = 1.54 ± 0.29) reduced MAE to 0.55 intervals. Individual R values were stable between protocols (within-subject CV = 9.9%). Original W'-balance models did not accurately predict running HIIT performance, whereas Linear_mod provided high predictive accuracy using a single athlete-specific recovery coefficient.
SN - 2051-817X
ER -