REF-1287 · Marchal et al., 2025 · Scientific Reports · Paper · PubMed · Free full text

Can my fitness-fatigue chart predict race-day form?

In two small elite skater datasets, a fitted model's fatigue term fit past results but did not improve forecasts of new ones. Read the chart as a record of load, not a forecast.

Main caveat: Small, short, elite and sprint. 7 and 14 skaters, 10 and 13 weeks, weekly sprint tests.
limited evidenceMeasured on elite athletes

Marchal and colleagues asked whether the classic fitness-fatigue model, in which each day's training load adds a slowly decaying "fitness" and a quickly decaying "fatigue" and performance is their weighted difference, can be estimated and can predict.

They used two datasets of elite short-track speed skaters coached by the same head coach: 2019, 7 skaters over 10 weeks with a 2-week summer break (375 training and 248 performance observations; weekly 166.68 m time trials) and 2016, 14 skaters over 13 weeks (948 training and 755 performance observations; maximal acceleration on a flying lap).

For each athlete they fitted a fitness-only model and the full fitness-fatigue model, in a frequentist way and in a Bayesian way with flat or informative priors (half-lives of about 30 days for fitness and 2 days for fatigue, set before seeing the data), and judged prediction by root mean square error on later, held-out weeks (2 folds in 2019, 3 in 2016, with a 5-day gap).

The fitness time constant could not be learned from the data: the posterior simply followed the prior, and in a grid search 6 of 7 athletes showed no best half-life between 1 and 100 days.

Fixing it or giving it an informative prior gave the lowest prediction errors, though none of these differences passed the Bonferroni-corrected threshold (uncorrected p 0.0084-0.0186 against 0.0083).

In the full model the fitness and fatigue terms traded off against each other: in 2019 only 1-4 of 10 Markov chains converged per athlete, always where the prior was densest, and in 2016 six of the 14 skaters had no converged chain; non-converged chains showed near-identical fitness and fatigue parameters.

Adding fatigue improved the fit to the training data (2019: RMSE −0.017, Cohen's d 0.585, p < 0.001) but not the prediction of new data (+0.001, d 0.022, p = 0.57; 2016: −8.8 × 10⁻⁵, d 0.006, p = 0.41), the pattern of overfitting. The fatigue term did capture the performance rise after the summer break, which the fitness-only model got wrong.

Our reading: the base already treats fitness-fatigue numbers as a description of load (SYNTH-29); this paper adds that, at least in these athletes, the fatigue part of such a model fits the past without forecasting performance, so a form or fatigue number is not a race-day forecast.

Protocol

Datasets: 2019 — 9 national elite short-track skaters recruited, 2 injured and dropped (n = 7); 10 weeks, June to September, with a 2-week full rest; 16.6 ± 2.5 h of training a week; 53.6 ± 1.6 training and 35.4 ± 2.2 performance observations per athlete; outcome the time for a 166.68 m race after a standardised warm-up (timing gates). 2016 — 15 skaters, 1 injured (n = 14); 13 weeks, July to October; 25 ± 5 h a week; 67.7 ± 5.6 training and 53.9 ± 5.4 performance observations per athlete; outcome maximal acceleration from four photocells on a weekly one-lap flying start.Two athletes are in both datasets; same head coach. Ethics approval from EuroMov, University of Montpellier; written consent.
Training load: on-ice and off-ice sessions quantified deterministically from the head coach's experience (as in the authors' earlier work), not from power or heart rate.
Models: fitness-fatigue model (FFM): performance = intercept + kG × sum of past loads decaying with time constant τG − kH × sum of past loads decaying with τH; fitness-only model (FOM) without the fatigue term. All parameters per athlete.
Priors: τG = 43.28 (fitness half-life 30 days) and τH = 2.89 (fatigue half-life 2 days), from "background knowledge" that half the fatigue of a session goes in about a weekend and half its fitness in about a month; informative gamma priors centred there, or flat gamma(1, 0.5) priors.
Fitting: frequentist minimisation (Powell, SciPy; 10 runs, bounded) or Bayesian MCMC in Stan (10 chains, 4 × 10⁴ warm-up and 1 × 10⁴ sampling iterations, thinning 10); grid searches over fitness half-life (1-100 days) and fatigue half-life (1-29 days, τG fixed).
Cross-validation: time-ordered hv-block cross-validation with an expanding window; training at least 35 days, test at least 15 days, 5-day gap; 2 folds (2019) and 3 folds (2016); RMSE on test data for prediction, residual SD on training data for fit; paired one-sided or two-sided Student comparisons.
Funding and interests: no funding statement is printed.Competing interests: "The authors declare no competing interests." Four authors, including the first and the corresponding author, list "Seenovate, Paris" as an affiliation; one (Méline, data curation and recruitment) lists the Fédération Française des Sports de Glace, Paris; the corresponding author also lists DMeM, INRAe, Univ Montpellier.The acknowledgements thank the federation, INSEP and a Perpignan laboratory for sharing data sets. Data on request from the corresponding author.

Key Results

Comparison (adding the fatigue term to the fitness-only model)Fit to training data (RMSE)Prediction of held-out data (RMSE)
2019 dataset, 7 skaters × 2 folds−0.017 (Cohen's d 0.585, p < 0.001)+0.001 (d 0.022, p = 0.57)
2016 dataset, 14 skaters × 3 folds−2.8 × 10⁻⁴ (d 0.056, p < 0.01)−8.8 × 10⁻⁵ (d 0.006, p = 0.41)
Fitness time constant (fitness-only model, 2019): with a flat prior the posterior for τG carried "no physiological sense"; with an informative prior it matched the prior almost exactly. Fixed or informed τG predicted better than free estimation; the uncorrected p-values for these differences were 0.0084 to 0.0186 against a Bonferroni threshold of 0.0083, so none passed it (the authors call them "close to significance").
Grid search for fitness half-life: no likelihood optimum between 1 and 100 days for 6 of 7 athletes (longer always fitted better); one athlete peaked at 43 days. In prediction, 4 athlete-fold combinations peaked near 30 days, one at 16 days, and 9 of 14 (64.3%) had no optimum.
Fatigue half-life (τG fixed at 43.28): each athlete's likelihood peaked between 2 and 6 days, but those peaks predicted better in only 2 athlete-folds.
Identifiability of the full model: 2019 — 1 to 4 of 10 chains converged per athlete, always in the prior's densest region; non-converged chains had near-identical τG and τH and near-identical kG and kH; for two athletes kH wandered to extreme values even in converged chains. 2016 — 6 of 14 athletes had no converged chain, the other 8 had 1-3 of 10; the fitness-only model converged in all chains for all athletes.
Summer break (2019): during the 2-week rest the fitness-only model predicted a loss of performance and the fitness-fatigue model a gain, which was closer to what happened.
Starting values: simulating up to 2 years of prior training to start from non-zero fitness and fatigue did not improve prediction for either model (data not shown).
Numbers that do not add up: the 2016 results name six athletes with no converged chain (F5, H2, H5, H6, H11, H13) and then refer to "the 5 athletes for whom no chain converged at all"; the Figure 3 legend gives the fitness half-life axis as 1 to 365 days while the text says the grid ran from 1 to 100; the two datasets are called independent though they share two athletes and the coach.

Mechanisms

Measured: the fitness and fatigue terms are driven by the same single input (the load series), and in the estimation they substitute for each other; the extra fatigue parameters reduce in-sample error without reducing out-of-sample error.
Authors' interpretation: the full model is ill-conditioned and non-identifiable, as Hellard et al. showed with parameter correlations of 0.91 (kG, kH) and 0.99 (τG, τH); a prior does not cure this; the lack of statistical relevance of the fatigue component questions its biological relevance; a fitness-only model with prior knowledge is a better starting point, though it cannot capture recovery after breaks, overtraining or maladaptation.
Inference: training-software charts of fitness, fatigue and form use the same two-exponential structure with fixed time constants (commonly about 42 and 7 days) and no fitted gains (the base's reading, not from this paper); the paper's 30-day fitness half-life corresponds to a time constant of 43.28 days, close to the usual 42 (our arithmetic).The paper did not test such charts; it shows that the fatigue half of the structure, even when fitted to the athlete, did not improve prediction of performance in these skaters.
Inference: short series of 10-13 weeks with weekly tests hold little information about a month-long decay, which is why the fitness constant could not be learned; longer series might behave better, which this paper cannot show.

Practical Application

Can my fitness-fatigue chart predict race-day form? In two small elite skater datasets, a fitted model's fatigue term fit past results but did not improve forecasts of new ones. Read the chart as a record of load, not a forecast.
Say what the chart shows, not what it predicts: a rising fitness line means the recent load has been higher than the older load; a negative form value means the last week was harder than the last six. Neither is a measured performance or a readiness verdict (the base's reading of such charts, not from this paper; the base already treats these numbers as descriptions of load, SYNTH-29).
Judge form from performance and the athlete's own signals: a repeated benchmark effort, field bests and how the athlete feels carry the information the model's fatigue term did not (not from this paper; the base's own practice). Taper decisions follow SYNTH-34.
If a long-term trend line is wanted, a slow one is the defensible part: here a fitness-only model with a roughly 30-day half-life, fixed in advance, had the lowest prediction error, though not significantly after Bonferroni correction, and only 4 of 14 athlete-folds favoured about 30 days (B, elite skaters, sprint tests).
Scope: elite short-track skaters, sprint outcomes, coach-scored load, 10-13 weeks; no endurance athletes and no power-based load were studied.

Limitations

Small, short, elite and sprint. 7 and 14 skaters, 10 and 13 weeks, weekly sprint tests; whether a fatigue term helps over a season, in endurance events or with daily performance data is untested.
Load measure. The coach's deterministic session scores; the authors note this may bias the estimates. No power, pace or heart-rate load.
Power to show a difference. The prediction comparisons rest on 14 and 42 athlete-fold pairs with tiny effect sizes; "no improvement" is the result here, not proof that a fatigue term can never help.
Overlap. The two datasets share two athletes and the head coach, so they are not fully independent.
Reporting. Six vs five athletes without convergence in 2016; a figure axis of 1-365 days against a 1-100-day grid in the text; several results shown only as figures or "data not shown".
Interests. No funding statement; no competing interests declared; four authors list Seenovate, Paris, as an affiliation (the corresponding author also INRAe, Univ Montpellier) and one the Fédération Française des Sports de Glace, which the acknowledgements thank, with INSEP and a Perpignan laboratory, for collaboration and sharing data sets.
How this entry was checked and changed
Why this level

small elite cohorts with cross-validated modelling (the rubric's B for a small cohort or elite case series), read from the full text (open access, CC BY-NC-ND 4.0). The negative result is about the model's statistics, which do not depend on the sport, but it comes from short series (10 and 13 weeks), sprint outcomes and a coach-assigned load score, and its p-values compare 14 and 42 athlete-fold pairs, so it cannot show that a fatigue term never helps

Full text (checked 2026-10-27)
The model exhibited an overfitting pattern, as adding the fatigue-related parameters did not significantly improve the model's predictive ability (p-value > 0.40) (abstract; full text)
The benefit of including a fatigue component in the model led to a reduction of 0.017 in the training set RMSE (Cohen's d = 0.585, p-value < 0.001) (full text)
The predictive ability is slightly, though not significantly, decreased when providing a fatigue component with an addition of 0.001 to the RMSE (Cohen's d = 0.022, p-value = 0.57) (full text)
2016 dataset: a reduction of 2.8 × 10− 4 in training RMSE (Cohen's d = 0.056, p-value < 0.01); the RMSE in cross-validation was reduced by 8.8 × 10− 5, not significant (Cohen's d = 0.006, p-value = 0.41) (full text)
One to four Markov chains converged out of 10 for any athlete (2019); among the 14 athletes included in the 2016 dataset, 6 did not show any convergent Markov chains for the FFM (full text)
We provided the target value of τG = 43.28 for fitness and τH = 2.89 for fatigue (half-lives of 30 and 2 days) (full text)
For the 9 other combinations of athletes and folds (i.e. 64.3% of the combinations), no optimal value was found over the studied interval (full text)
Skaters sustained a mean weekly training volume of 16.6 ± 2.5 h (2019) and 25 ± 5 h (2016) (full text)
Affiliations: Seenovate, Paris; Fédération Française des Sports de Glace, Paris; the authors declare no competing interests (full text)