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Determinants of 800-m and 1500-m Running Performance Using Allometric Models


Medicine & Science in Sports & Exercise: February 2008 - Volume 40 - Issue 2 - p 345-350
doi: 10.1249/mss.0b013e31815a83dc
APPLIED SCIENCES: Physical Fitness and Performance

Purpose: To identify the optimal aerobic determinants of elite, middle-distance running (MDR) performance, using proportional allometric models.

Methods: Sixty-two national and international male and female 800-m and 1500-m runners undertook an incremental exercise test to volitional exhaustion. Mean submaximal running economy (ECON), speed at lactate threshold (speedLT), maximum oxygen uptake (V˙O2max), and speed associated with V˙O2max (speedV˙O2max) were paired with best performance times recorded within 30 d. The data were analyzed using a proportional power-function ANCOVA model.

Results: The analysis identified significant differences in running speeds with main effects for sex and distance, with V˙O2max and ECON as the covariate predictors (P < 0.0001). The results suggest a proportional curvilinear association between running speed and the ratio (V˙O2max·ECON−0.71)0.35 explaining 95.9% of the variance in performance. The model was cross-validated with a further group of highly trained MDR, demonstrating strong agreement (95% limits, 0.05 ± 0.29 m·s−1) between predicted and actual performance speeds (R 2 = 93.6%). The model indicates that for a male 1500-m runner with a V˙O2max of 3.81 L·min−1 and ECON of 15 L·km−1 to improve from 250 to 240 s, it would require a change in V˙O2max from 3.81 to 4.28 L·min−1, an increase of Δ0.47 L·min−1. However, improving by the same margin of 10 s from 225 to 215 s would require a much greater increase in V˙O2max, from 5.14 to 5.85 L·min−1 an increase of Δ0.71 L·min−1 (where ECON remains constant).

Conclusion: A proportional curvilinear ratio of V˙O2max divided by ECON explains 95.9% of the variance in MDR performance.

1English Institute of Sport, Loughborough University, Loughborough, Leicestershire, UNITED KINGDOM; 2Research Institute for Sport and Exercise Science, Liverpool John Moores University, Henry Cotton Campus, Truman Road, Liverpool, UNITED KINGDOM; 3English Institute of Sport, St. Mary's College, Twickenham, UNITED KINGDOM; and 4Department of Sports Studies, University of Wolverhampton, Walsall Campus, Walsall, UNITED KINGDOM

Address for correspondence: Stephen A. Ingham, Ph.D., English Institute of Sport, Loughborough University, Loughborough, Leicestershire, United Kingdom; E-mail:

Submitted for publication May 2007.

Accepted for publication August 2007.

Several studies have demonstrated a strong relationship between 800-m and 1500-m performance and maximal aerobic abilities such as maximum oxygen uptake (V˙O2max) (6) and the velocity associated with V˙O2max (17,29). The relationship between submaximal physiological indices such as lactate threshold (LT) and running economy (ECON) with longer-distance running is strong, but for middle-distance running (MDR), results are contradictory (1,17,18,31). Furthermore, some studies contend that among homogenous or elite performance groups, physiological variables do not discriminate among running standards (8,15,30). Attempts have been made to generate a model of MDR performance. Deason et al. (10) have presented a model that included sprint performances with V˙O2max, body fat percentage, and ECON to explain 89% of the variance in 800-m performance. Further, Yoshida et al. (31) have identified submaximal blood lactate measures as the primary determinants of 1500-m performance. The authors note a diminished contribution of lactate measures for 800-m performance in the presence of an increased importance of anaerobic indices.

Nevill et al. (21) present proportional models for 5-km running performance, where V˙O2max (mL·kg−1·min−1) was found to be the best predictor. Moreover, predictor variables of oxygen consumption have been related to cycling performance by use of a curvilinear mass exponent of about one third, purported to be related to the role of air resistance, resulting in an increasing energy cost of cycling (23). The notion of a proportional model to account for "diminishing performance returns" with increasing physiological demand has not been previously explored in elite running. Accordingly, the purpose of this study was to identify the physiological determinants of MDR in national and international athletes, using proportional modeling.

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After ethics approval from the regional committee, 62 national or international 800-m and 1500-m specialist athletes provided written informed consent to participate in the study. According to sex and event class, the participants' demographic data were 15 male 800-m runners (M800: age, 21.4 ± 2.9 yr; height, 182.5 ± 4.8 cm; mass, 70.6 ± 5.6 kg), 15 male 1500-m runners (M1500: age, 21.2 ± 2.2 yr; height, 181.0 ± 6.2 cm; mass, 67.9 ± 3.9 kg), 16 female 800-m runners (F800: age, 22.1 ± 4.6 yr; height, 168.1 ± 4.1 cm; 53.7 ± 2.1 kg), and 16 female 1500-m runners (F1500: age, 22.8 ± 5.1 yr; height, 167.2 ± 3.6 cm; mass, 54.8 ± 3.0 kg).

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Body composition.

Stature and body mass were measured using a stadiometer and balance-beam scales (Avery Berkel, Walsall, UK), respectively. Estimated body fat percentage was calculated using the sum of four skinfold sites (12,27), with precalibrated calipers (John Bull, British Indicators Ltd.).

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Exercise testing.

All evaluations were performed on a motorized treadmill (HP Cosmos Saturn, Traunstein, Germany). A 7 × 3-min submaximal incremental running test was performed, with 30 s of rest between stages. The intensity of the initial stage was designed (on the basis of previous exercise tests) such that each subject would undertake three stages below, one at, and two to three above LT, with an intended final intensity of approximately 95% V˙O2max. Exercise intensity was increased by 1 km·h−1 for each stage. After a 15-min rest period, athletes ran at an intensity 2 km·h−1 slower than the final treadmill running speed attained during the submaximal incremental test. Every minute, the treadmill gradient was increased by 1% to volitional exhaustion (end exercise = 5-8%).

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Pulmonary gas exchange.

Pulmonary gas exchange was assessed breath-by-breath. Subjects breathed through a low-dead space (47 mL) mask (Hans Rudolph, Kansas City, MO). Air was sampled through a 2-m capillary line of small bore (0.5 mm) at 60 mL·min−1 and was analyzed for O2, by a differential paramagnetic analyzer and CO2 concentrations, by a side-stream infrared analyzer (Oxycon Pro, Viasys, UK), which were calibrated with gases of known concentration. Expiratory volumes were determined using a precalibrated precision-engineered turbine volume transducer (Viasys, UK). Volume and concentration signals were integrated, and gas-exchange variables were calculated as the mean for the final full minute of each intensity. V˙O2max was determined as the highest 30-s mean achieved during the maximum portion of the test (coefficient of variation for this laboratory = 5.5%). Oxygen cost of movement (ECON) was assessed by calculating the mean oxygen uptake per unit of distance covered (L·km−1) of the six or seven submaximal stages (coefficient of variation = 7.5%). Solving the regression equation describing V˙O2 and speed for the six or seven incremental intensities calculated the speed associated with V˙O2max (speedV˙O2max). Oxygen-uptake data were recorded as absolute values for ECON (L·km−1) and V˙O2max (L·min−1) and relative to body-mass ECON per kilogram (mL·kg−1·km−1) and V˙O2max per kilogram (mL·kg−1·min−1).

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Blood lactate.

Capillary blood was sampled at the end of each stage from the earlobe and assayed for blood lactate concentration ([HLa]) (Analox GM7, London, UK). Inspection of plots of [HLa] and V˙O2 and log-log equivalents against speed, by two independent reviewers, established the speed at LT (speedLT), defined as the point at which a nonlinear increase in blood lactate occurred (coefficient of variation for this laboratory = 3.5%).

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The best performance time recorded during outdoor 800-m or 1500-m track competition ± 30 d of laboratory testing was converted to performance speed (m·s−1) and used as the criterion performance variable. Performance was paired with physiological profiles.

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Statistical methods.

As an exploratory tool, Pearson's product-moment correlation was used to examine the relationship between individual physiological variables and performance speed by event- and sex-specific group. We anticipated that a number of associations between variables and performance speed would be common to male and female and 800-m and 1500-m subgroups; thus, we felt the need to extend the investigation with the application of a model generic to a collective group of all subgroups.

Because 800-m and 1500-m running speeds are thought to increase in proportion to the energy expended by an athlete but also be limited by air resistance (which is also thought to increase proportionally with running speed), we used the following proportional (curvilinear) allometric or power-function models, which have been adopted previously (20,21), to identify the optimal determinants of 800-m and 1500-m running speeds,

where a is a constant; k 1, k 2, k 3, and k 4 are the exponents likely to provide the best predictor of running speed; ε is the multiplicative error ratio; and m is the subject's mass.

The model can be linearized with a log-transformation, and multiple linear regression can be used to estimate unknown parameters a, k 1, k 2, k 3, and k 4. The log-transformed model becomes,

Note that the parameter a will be allowed to vary between groups (e.g., sex and distances), thus conducting a form of analysis of covariance (ANCOVA).

To assess the validity of the derived power-function models, we cross-validated the derived model for performance speed (developed on the 62 athletes) using a new, independent group of national standard middle-distance runners (male: N = 8, 21 ± 1.7 yr, 69.5 ± 6.6 kg, 183.1 ± 8.5 cm; female: N = 6, 19 ± 2.3 yr, 55.7 ± 3.9 kg, 169.6 ± 4.6 cm). This was achieved by predicting the performance speeds of the independent group, using the model derived from the original 62 athletes. The success of cross-validation was assessed by comparing actual speeds with predicted speeds of the independent group, using limits of agreement (3), coefficients of variation, and correlations.

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M800 running was between 3.9 and 11.5%, and F800 was between 3.7 and 16.6% of the British record (1:41.73 and 1:56.41), respectively. M800 was 15% quicker than F800 (male vs female British record difference = 14%). M1500 speed was between 1.1 and 11.0%, and F1500 was between 0.9 and 16.0% of the British record (3:29.67 and 3:57.90, respectively). M1500 speed was 12% faster than F1500 (male vs female British record difference = 13%). Physiological differences between groups are shown in Table 1.



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Relationships between running performance and selected physiological variables.

Table 2 presents correlation coefficients for all measured variables and running speed. Anthropometric variables showed no consistent association with performance. Significant correlations were observed for speedLT, V˙O2max per kilogram, V˙O2max, and speedV˙O2max per kilogram with performance speed for all subgroups.



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ANCOVA results.

Not surprisingly, the ANCOVA identified significant differences in running speeds attributable to the main effects sex and distance (800 vs 1500 m; both P < 0.0001), but with no sex-by-distance interaction. The analysis also identified V˙O2max and ECON as covariate predictors (both P < 0.0001), but body mass (m) and speedLT failed to make a significant contribution to the prediction of running speeds (both P > 0.05). The proportional allometric models can be expressed as

with R 2 = 95.9% (k 1 = 0.348, SEE = ± 0.029, and k 3 = −0.246 SEE = ± 0.038) and the error ratio (the standard deviation of residuals about the fitted log-linear regression model, equation 1), s = 0.0174 or 1.76%, having taken antilogs. Note that the above models for running speeds can be rearranged and expressed as a V˙O2max-to-ECON ratio within a curvilinear power function as follows:

The running speeds and the fitted curvilinear power-function models for the male and female 800-m and 1500-m athletes can be seen in Figure 1.



The results from the cross-validation assessment found that the predicted performance speed (using the model from the original 62 athletes) explained 93.6% of the variance in the actual performance speeds of the 14 independent athletes (standard deviation about the fitted regression line, s = 0.14 m·s−1). The predicted and actual mean performance speeds were 6.52 and 6.47 (m·s−1) respectively, resulting in a mean difference of 0.05 ± 0.15 (m·s−1) (P >0.05). On the basis of these differences, the 95% limits of agreement were 0.05 ± 0.29 (m·s−1), with a coefficient of variation of 2.25%. The actual and predicted running speeds from the cross-validation assessment can be seen in Figure 2.



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This study demonstrates strong associations between aerobic capability and MDR performance in a homogenous group of national and international standard male and female running athletes. We identified the curvilinear power-function ratio model (V˙O2max·ECON−0.71)0.35 as the most important determinant of 800-m and 1500-m running performance, explaining 95.9% of the variance in running speed. Not only does the model confirm and validate the ratio of V˙O2max divided by ECON0.71 as the best determinant of elite MDR performance, but the model was also able to confirm the anticipated and/or highly plausible curvilinear association between running speed and aerobic energy supply; that is, with an equal increment of V˙O2max, the model suggests that the corresponding increase in speed would be proportionally less. This curvilinear association, identified by the power-function exponent of 0.35, is shown in Figure 1.

The above-curvilinear power function exponent, 0.35, is not dissimilar to known curvilinear associations between cycling speed and energy expenditure (20,25). On level ground, the power demand of cycling is thought to be proportional to the cube of the cyclists' speed (13,23). Consequently, the speed of a cyclist should also be proportional to the cube root (0.33) of the power expended. It is reassuring to note that the curvilinear association and associated power-function exponent, between running speed and energy expenditure, is almost identical to that anticipated in cycling.

The literature contains numerous definitions and calculations (2) for the ratio between V˙O2max and ECON, typically provided as a running intensity (in this case, speed) associated with V˙O2max. Studies show a strong (r = 0.87-0.93) association with long-distance running (> 10 km) or longer MDR (3-5 km) performance (9,16,19). Significant relationships have also been observed between a similar measure of "maximal aerobic velocity" and 1500-m running performance (r = 0.62-0.72) in trained athletes, but the association with 800 m is not consistently evident (5,17,24). Subgroup correlations between speedV˙O2max and performance speed are consistently shown for subgroups in the current study, highlighting speedV˙O2max as one of the strongest predictors of performance speed (using linear regression). Consideration of the fuller picture with pooled groups, using a proportional curvilinear power function, confirms the importance of the interplay between V˙O2max and ECON, as shown by the small proportion of unexplained variation in performance speed.

Previous studies have noted the importance of V˙O2max and 800-m and 1500-m male and female performance. During 800-m and 1500-m running, it is estimated that runners will attain approximately 88% and 94% of V˙O2max, respectively (28). Moreover, ECON has not been strongly linked with 800-m and 1500-m events (11,14), and, currently, individual linear correlations do not support a consistent association. Here, V˙O2max may only present one dimension of the aerobic capability response, For example, the time constant of "switch-on" and the time spent at a high proportion of V˙O2max may also be important factors that explain the potential for aerobic energy turnover.

It is possible that only when ECON is factored with V˙O2max does ECON become a significant covariate, as for speedV˙O2max (22). The current work develops the interplay of ECON with V˙O2max as an integrated measure by redeveloping the ratio by which each is expressed against the other, therefore superseding speedV˙O2max and eliminating it from consideration as a covariate. Because speedV˙O2max is based on a 1:1 ratio standard, one might assume that if, for example, an athlete were to possess a moderate V˙O2max but an exceptional ECON, the ratio between the two variables would suggest that he or she could compete to a similar standard with an athlete with an exceptional V˙O2max but only a moderate ECON. Because effective MDR is an exercise in economic execution of high-speed running, such a relationship would make mechanistic sense (4,6). ECON is a global parameter that is difficult to attribute to just a few factors, but it is highly influenced by, for example, neuromuscular coordination, type, and condition of the muscle-fiber pool recruited (9,30). However, the current model indicates that V˙O2max makes a greater contribution than ECON to the determination of MDR performance. Thus, given a theoretical example of a female 800-m runner with a V˙O2max of 3.5 L·min−1 and an ECON of 13 L·km−1 (resulting in an estimated performance speed of 6.25 m·s−1, or an 800-m time of 2:08.3), a 10% improvement in either variable would result in a 0.21 and 0.15 m·s−1 (or 800-m times of 2:03.9 and 2:05.1) improvement in estimated performance speed, respectively. Thus, it would seem that applicable priority should be afforded toward V˙O2max development or concomitant fast running speed, which would necessitate a high V˙O2, for performance gains.

A notable outcome of the above parsimonious power-function model was the absence of body mass (m) and speedLT, which failed to make any additional contribution to the prediction of the athletes' running speeds. Whether lactate per se does indeed influence the tolerance of work is not clear; this has been discussed elsewhere (7). Despite speedLT being identified as a strong correlate of performance for several groups, this could be an artifact of the athlete's capability to operate aerobically, and thus the limitation or control of their lactate (and associated acidity) accumulation would also be inherent in their V˙O2max and ECON ability. Alternatively, lactic acidosis could be of little metabolic importance to the determination of events as short as 100-260 s (10). Indeed, it is not clear whether accumulation of lactate in the muscle and blood is of detriment to the muscle's ability to sustain action, or whether blood lactate is a surrogate marker of muscle fatigue, by which it acts to provide sensory information to the brain regarding relative exercise intensity. The strength of linear association might be linked to the development of submaximal indices through the use of mixed-intensity training stimuli (including above and below the speedLT) performed by middle-distance athletes (26).

When we cross-validated the power-function ratio model (V˙O2max·ECON−0.71)0.35 derived from the original 62 athletes, using the actual running speeds of the 14 independent athletes, the model explained 93.6% of the variance in their actual speeds, with the unexplained error about the fitted regression line being s = 0.14 m·s−1. Indeed, on the basis of the 95% limits of agreement, there was no significant bias between the actual and predicted running speeds, there was a mean difference of 0.05, and the within-participant range of errors of ± 0.29 (m·s−1) would be accepted as remarkably accurate/precise (a coefficient of variation of 2.23%) by coaches, athletes, and academics alike.

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The current study provides further insight into our understanding of the measure of speedV˙O2max as a predictor variable of MDR, and of how a curvilinear ratio modification is able to enhance the explanation of differences in performance that the simple ratio standard of V˙O2max divided by ECON does not. Thus, consideration of a curvilinear V˙O2max:ECON ratio approach seems to improve the understanding of the determinants of MDR performance.

The results of the present study do not constitute endorsement by ACSM.

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