Original W'-balance models do not transfer to high-intensity interval training in trained adult runners: Proposal of a single-coefficient linear alternative.
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.
Key Findings
Results
All four original W'-balance recovery models, applied with their published parameters, substantially over-predicted the number of intervals trained runners completed in HIIT.
Models tested were Morton and Billat linear, W'BAL-INT, W'BAL-ODE and W'BAL-CAEN.
Pooled MAE ranged from 26.4 to 72.4 intervals, with bias from +20.1 to +72.4 intervals.
Twenty-seven trained runners completed a 9/3-min running CP test and two open-ended HIIT sessions to volitional exhaustion at 108% CP with a 2:1 work:rest ratio and passive recovery.
Work intervals were individualized so that energy expenditure above CP equalled 40% (HIIT40%) or 60% (HIIT60%) of W'.
Results
A single-coefficient modified linear model (Linear_mod) with its default recovery coefficient (R = 1) predicted the number of intervals far more accurately than the original models.
Linear_mod with default R = 1 achieved a MAE of 4.85 intervals.
This compares with pooled MAEs of 26.4-72.4 intervals for the original models.
The model uses one recovery coefficient (R).
Results
Optimizing the recovery coefficient at the population level improved Linear_mod accuracy.
Population-level optimal R = 1.63.
MAE fell from 4.85 to 2.85 intervals.
Results
Athlete-specific optimization of the recovery coefficient yielded the highest predictive accuracy.
Individual R was 1.54 ± 0.29.
MAE was reduced to 0.55 intervals.
Results
Individual recovery coefficients were stable across the two HIIT protocols.
Within-subject CV of R between HIIT40% and HIIT60% was 9.9%.
This suggests R behaves as a consistent athlete-specific characteristic.
What This Means
This study tested whether existing mathematical models that track how much of a runner's finite 'above-threshold' energy reserve (W') is used and restored during rest could predict how many hard intervals a runner can complete. Twenty-seven trained runners did a critical power test and then two interval sessions to exhaustion at 108% of critical power, with rest periods half as long as the work periods. Intervals were set so each one used either 40% or 60% of the runner's W'.
When the four widely cited models were applied with their published settings, they all greatly overestimated the number of intervals the runners could complete, by roughly 20 to 72 intervals on average. A simple modified linear model with one recovery coefficient did much better. Even with its default setting it was off by about 5 intervals on average. Tuning the coefficient for the group reduced the error to under 3 intervals, and tuning it for each athlete reduced it to about half an interval. Each runner's coefficient was fairly consistent across the two sessions.
This research suggests that existing W'-balance models may not be reliable for planning or monitoring running interval sessions with passive recovery, and that a simple athlete-specific recovery coefficient could offer a more accurate approach. The findings come from 27 trained runners in one specific protocol, so they may not apply to other workouts, recovery types or populations.
Check Your Own Numbers
Upload your bloodwork. We'll cross-reference your results against this study and 4,700 others.
García-Pinillos F, Jaén-Carrillo D, Riquelme-Sebastián L, Ruiz-Alias S, Fernández-Navarrete I, González-Mohino F, et al.. (2026). Original W'-balance models do not transfer to high-intensity interval training in trained adult runners: Proposal of a single-coefficient linear alternative.. Physiological reports. https://doi.org/10.14814/phy2.71152