Allometric exponents for scaling running economy in human samples: A systematic review and meta-analysis

Jay Lee, Zhiwen Wang, Mingjian Chen, Siqi Liu, Qian Yu, Mingzhu Hu, Zhaowei Kong, Jinlei Nie

Research output: Contribution to journalArticlepeer-review


Ratio-scaled VO2 is the widely used method for quantifying running economy (RE). However, this method should be criticized due to its theoretical defect and curvilinear relationship indicated by the allometric scaling, although no consensus has been achieved on the generally accepted exponent b value of body weight. Therefore, this study aimed to provide a quantitative synthesis of the reported exponents used to scale VO2 to body weight. Six electronic databases were searched based on related terms. Inclusion criteria involved human cardiopulmonary testing data, derived exponents, and reported precision statistics. The random-effects model was applied to statistically analyze exponent b. Subgroup and meta-regression analyses were conducted to explore the potential factors contributing to variation in b values. The probability of the true exponent being below 1 in future studies was calculated. The estimated b values were all below 1 and aligned with the 3/4 power law, except for the 95 % prediction interval of the estimated fat-free body weight exponent b. A publication bias and a slightly greater I2 and τ statistic were also observed in the fat-free body weight study cohort. The estimated probabilities of the true body weight exponent, full body weight exponent, and fat-free body weight exponent being lower than 1 were 93.8 % (likely), 95.1 % (very likely), and 94.5 % (likely) respectively. ‘Sex difference’, ‘age category’, ‘sporting background’, and ‘testing modality’ were four potential but critical variables that impacted exponent b. Overall, allometric-scaled RE should be measured by full body weight with exponent b raised to 3/4.

Original languageEnglish
Article numbere31211
Issue number10
Publication statusPublished - 30 May 2024


  • Allometric scaling
  • Fat-free body weight
  • Full body weight
  • Meta-analysis
  • Running economy

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