Critical speed estimated by statistically appropriate fitting procedures

Patoz, Aurélien; Spicher, Romain; Pedrani, Nicola; Malatesta, Davide; Borrani, Fabio

doi:10.1007/s00421-021-04675-8

Cited by 7 publications

(7 citation statements)

References 52 publications

(78 reference statements)

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“…In this case, exp(intercept) is an estimate of S and (slope + 1) is an estimate of E. To keep the presentation simple, we adopt this approach throughout this work. However, none of our results would change qualitatively if we used linear regression based on the fact that log(P ) is (affine) linear in the log-work log(W ) or if we used more sophisticated non-linear least-squares approaches such as those advocated for the hyperbolic model in Patoz et al (2021).…”

Section: Estimationmentioning

confidence: 75%

“…To keep the presentation simple we adopt this approach throughout this work (except for some of the panels in Figure 4). However, none of our results would change qualitatively if we used the more sophisticated non-linear weighted least-squares approaches (potentially based on the power–work relationship) advocated in Patoz et al (2021). The estimation requires data from a sufficiently large number of maximal efforts (i.e.…”

Section: Power–duration Modelsmentioning

confidence: 97%

See 1 more Smart Citation

Modelling human endurance: Power laws vs critical power

Drake

Finke²,

Ferguson³

2022

Preprint

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The power–duration relationship describes the time to exhaustion for exercise at different intensities. It is generally believed to be a "fundamental bioenergetic property of living systems" that this relationship is hyperbolic. Indeed, the hyperbolic (a.k.a. critical-power) model which formalises this belief is viewed as the "gold standard" for assessing exercise capacity, e.g. in cycling, running, rowing, and swimming. However, the hyperbolic model is now the focus of two heated debates in the literature because: (a) it unrealistically represents efforts that are short (< 2 minutes) or long (> 15 minutes); (b) it contradicts widely-used performance predictors such as the so-called functional threshold power (FTP) in cycling. We contribute to both debates by demonstrating that the power–duration relationship is more adequately represented by an alternative, power-law model. In particular, we show that the often observed good fit of the hyperbolic model between 2 and 15 minutes should not be taken as proof that the power–duration relationship is hyperbolic. Rather, in this range, a hyperbolic function just happens to approximate a power law fairly well. We also prove a mathematical result which suggests that the power-law model is a safer tool for pace selection than the hyperbolic model. Finally, we use the power-law model to shed light on popular performance predictors in cycling, running and rowing such as FTP and Jack Daniels' "VDOT" calculator.

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Section: Estimationmentioning

confidence: 75%

Section: Power–duration Modelsmentioning

confidence: 97%

Modelling human endurance: Power laws vs critical power

Drake

Finke²,

Ferguson³

2022

Preprint

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“…In this scenario, the MLSS 15-30 and MLSS 20-30 criteria discussed herein could offer valid support to select the most appropriate estimate of CP and consequently identify MMSS. This strategy, which has been previously suggested and used (3,29,30,33,(53)(54)(55), would improve the rigor of MMSS characterization.…”

Section: Discussionmentioning

confidence: 99%

Methodological Reconciliation of CP and MLSS and Their Agreement with the Maximal Metabolic Steady State

Iannetta

Ingram

Keir

et al. 2021

Medicine &Amp; Science in Sports &Amp; Exercise

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The critical power (CP) and maximal lactate steady state (MLSS) are operational surrogates of the maximal metabolic steady state (MMSS). However, their concordance and their agreement with MMSS remain variable likely because of methodological factors. Purpose: This study aimed to compare the concordance between CP and MLSS estimated by various models and criteria and their agreement with MMSS. Methods: After a ramp test, 10 recreationally active males performed four to five severe-intensity constant-power output (PO) trials to estimate CP and three to four constant-PO trials to determine MLSS and identify MMSS. CP was computed using the three-parameter hyperbolic (CP 3-hyp ), twoparameter hyperbolic (CP 2-hyp ), linear (CP lin ), and inverse of time (CP 1/Tlim ) models. In addition, the model with the lowest combined parameter error identified the "best-fit" CP (CP best-fit ). MLSS was determined as an increase in blood lactate concentration ≤1 mM during constant-PO cycling from the 5th (MLSS 5-30 ), 10th (MLSS 10-30 ), 15th (MLSS 15-30 ), 20th (MLSS 20-30 ), or 25th (MLSS 25-30 ) to 30th minute. MMSS was identified as the greatest PO associated with the highest submaximal steady-state V ˙O2 (MV ˙O2ss ). Results: Concordance between the various CP and MLSS estimates was greatest when MLSS was identified as MLSS 15-30 , MLSS 20-30 , and MLSS 25-30 . The PO at MV ˙O2ss was 243 ± 43 W. Of the various CP models and MLSS criteria, CP 2-hyp (244 ± 46 W) and CP lin (248 ± 46 W) and MLSS 15-30 and MLSS 20-30 (both 245 ± 46 W), respectively, displayed, on average, the greatest agreement with MV ˙O2ss . Nevertheless, all CP models and MLSS criteria demonstrated some degree of inaccuracies with respect to MV ˙O2ss . Conclusions: Differences between CP and MLSS can be reconciled with optimal methods of determination. When estimating MMSS, from CP the error margin of the model estimate should be considered. For MLSS, MLSS 15-30 and MLSS 20-30 demonstrated the highest degree of accuracy.

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“…Burnley and Jones 13 provide a detailed discussion of the physiological aspects of the model (3). Using laboratory data, Patoz et al 14 consider inferential aspects associated with the CV-2 model. In particular, they investigate the bias associated with various weighted least squares fitting procedures.…”

Section: The Cv-2 Modelmentioning

confidence: 99%

Bayesian approaches for critical velocity modelling of data from intermittent efforts

Peng

Clarke

Swartz

2022

International Journal of Sports Science & Coaching

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In sports science, critical power and related critical velocity models have been widely investigated, and are being increasingly applied to field-based team sports. A challenge associated with these models is that laboratory experiments that yield accurate measurements of maximal sustainable velocity are expensive. Alternatively, inexpensive field data (from training and matches) are being used to fit such models. However, the intermittent nature of efforts in field-based sports implies that the dependent variable concerning maximum sustainable velocity is reliably calibrated only for short time durations. This paper develops methods where field data based on short time durations is combined with prior knowledge to fit the three-parameter critical velocity model. This is accomplished in a Bayesian framework for which Markov chain methods are required for model fitting and inference.

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Critical speed estimated by statistically appropriate fitting procedures

Cited by 7 publications

References 52 publications

Modelling human endurance: Power laws vs critical power

Modelling human endurance: Power laws vs critical power

Methodological Reconciliation of CP and MLSS and Their Agreement with the Maximal Metabolic Steady State

Bayesian approaches for critical velocity modelling of data from intermittent efforts

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