The effects of measurement error and testing frequency on the fitness-fatigue model applied to resistance training: A simulation approach

Abstract

This study investigated the effects of measurement error and testing frequency on prediction accuracy of the standard fitness-fatigue model. A simulation-based approach was used to systematically assess measurement error and frequency inputs commonly used when monitoring the training of athletes. Two hypothetical athletes (intermediate and advanced) were developed and realistic training loads and daily ‘true’ power values were generated using the fitness-fatigue model across 16 weeks. Simulations were then completed by adding Gaussian measurement errors to true values with mean 0 and set standard deviations to recreate more and less reliable measurement practices used in real-world settings. Errors were added to the model training phase (weeks 1–8) and sampling of data was used to recreate different testing frequencies (every day to once per week) when obtaining parameter estimates. In total, 210 sets of simulations (N = 104 iterations) were completed using an iterative hill-climbing optimisation technique. Parameter estimates were then combined with training loads in the model testing phase (weeks 9–16) to quantify prediction errors. Regression analyses identified positive associations between prediction errors and the linear combination of measurement error and testing frequency ([Formula: see text]=0.87–0.94). Significant model improvements (P < 0.001) were obtained across all scenarios by including an interaction term demonstrating greater deleterious effects of measurement error at low testing frequencies.The findings of this simulation study represent a lower-bound case and indicate that in real-world settings, where a fitness-fatigue model is used to predict training response, measurement practices that generate coefficients of variation greater than [Formula: see text]4% will not provide satisfactory results.

Traditional and contemporary approaches to mathematical fitness-fatigue models in exercise science: A practical guide with resources. Part I.

“…Therefore, sport scientists considering future use of FFMs, particularly within team sport environments, may require a shift in emphasis where training data is used to predict response in terms of dimensions of physical fitness measured through common exercises (e.g. 1RM squat, vertical jump height, peak power or impulse produced during an explosive movement), rather than sporting event performance, which is likely to demonstrate complex and often confounded relationships with training loads [67]. As such, the term performance in the context of fitness-fatigue modelling can be thought of as a measurable expression of a specific dimension of physical capability that can be largely isolated.…”

“…Measurement frequency and underlying measurement error should also be considered when selecting an appropriate performance measure and the ability to obtain stable parameter estimates [22,67]. It has been highlighted that missing data may lead to non-interpretable model behaviour in iteratively updated (i.e.…”

“…As a result, the ability to accurately model and predict performance is expected to require performance tests that can be completed at a high weekly frequency (e.g. at least every 1-3 days) [67]. Consequently, it is likely that only non-fatiguing performance tests (for example, the counter-movement jump) or those without persistent learning effects may be able to meet this requirement.…”

“…Several basic steps can be taken to reduce measurement error and its influence on overfitting. These steps include selection of tests that comprise low measurement error (preferably less than 3 to 5 % coefficient of variation [67], standardisation of testing procedures and if possible taking the average of repeated independent tests [65,67].…”

“…independent as they are not directly observable in the physical world) [44]. Across previous FFM research, model ill-conditioning has been assessed by calculating between-parameter correlations across multiple participants or simulations [21,30,67]. Notably, research has shown a moderate-strong relationship between the two magnitude factors (k g , k h ) in the standard model, indicating parameter interdependence between at least two of the free-parameters in the standard formulations (eq.8) [21,30,67].…”