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Figures
- Fig. 1.
How individual quality masks functional trade-offs. The double-headed arrow connecting a true and counterfactual individual represents the ‘intra-individual functional trade-off’ (Wilson et al., 2014b). The double headed arrow between true individual A and true individual B represents the ‘inter-individual variation’ in quality (Q effect) that masks the intra-individual trade-off. For simplicity, the trade-off is determined by a single underlying morpho-physiological (M-P) trait that has opposite effects on the two performances (M effect). A counterfactual individual is one that is like the real individual in every way except for a change in the underlying M-P trait and the consequent changes in both performances. Individuals A and B do not differ in their M-P trait but individual B is better at both performances because of a difference in exposure to some extrinsic quality variable. This quality might result from something like differences in training or health status (for example, individual A might have a respiratory infection that both narrows respiratory tubes and decreases muscle contractility or motor unit recruitment).
- Fig. 2.
Heat map depicting the sign and magnitude of the Pearson product-moment correlations among the 10 decathlon events for the 611 NCAA athletes. The map shows that all correlations in this matrix are positive and of moderate to large value. Events: 1500 m speed, 400 m speed, 100 m speed, 110 m hurdles speed, pole vault (PV), long jump (LJ), high jump (HJ), javelin (J), shot put (SP) and discus (D).
- Fig. 3.
Heat maps depicting the sign and magnitude of the quality-adjusted correlations among the 10 decathlon events for the 611 NCAA athletes. Positive correlations are blue, negative correlations are red, color intensity reflects the magnitude of the correlation (see legend in Fig. 2). (A) Partial correlations conditional on all additional performance variables. (B) Regression residual correlations computed using the residuals of each performance trait regressed on the first principal component (PC1) scores. (C) Wright's uncorrected correlations. The values are equivalent to the covariances of the regression residuals used in B. (D) Wright's bias-corrected correlations. Note that the running performances are in units of speed and not duration. Event abbreviations as in Fig. 2.
- Fig. 4.
The distribution of the errors estimated by Monte Carlo simulation of the NCAA decathlon data. (A) Box plots with the median, and 50% and 95% intervals represented by the horizontal line, the box and the tips of the whiskers. PCOR partial correlations conditional on all other events; RR, regression residual correlation; WUC, Wright's uncorrected correlations; and WBC, Wright's bias-corrected correlations. (B) True quality-free correlation as a function of the Wright's bias-corrected estimated correlation. The blue lines are the 2.5%, 50% and 97.5% quantile regressions used to compute the 95% confidence intervals in Table 1.
- Fig. 5.
Heat maps depicting the sign and magnitude of the quality-adjusted correlations among the five performances measured for 28 soccer players. Positive correlations are blue, negative correlations are red, color intensity reflects the magnitude of the correlation (see legend in Fig. 2). (A) Pearson product-moment correlations. (B) Partial correlations conditional on all additional performance variables. (C) Regression residual correlations computed using the residuals of each performance trait regressed on the PC1 scores. (D) Wright's bias-corrected correlations.
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