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Test of the Classic Model for Predicting Endurance Running Performance


Medicine & Science in Sports & Exercise: May 2010 - Volume 42 - Issue 5 - p 991-997
doi: 10.1249/MSS.0b013e3181c0669d

Purpose: To compare the classic physiological variables linked to endurance performance (V˙O2max, %V˙O2max at lactate threshold (LT), and running economy (RE)) with peak treadmill velocity (PTV) as predictors of performance in a 16-km time trial.

Methods: Seventeen healthy, well-trained distance runners (10 males and 7 females) underwent laboratory testing to determine maximal oxygen uptake (V˙O2max), RE, percentage of maximal oxygen uptake at the LT (%V˙O2max at LT), running velocity at LT, and PTV. Velocity at V˙O2max (vV˙O2max) was calculated from RE and V˙O2max. Three stepwise regression models were used to determine the best predictors (classic vs treadmill performance protocols) for the 16-km running time trial.

Results: Simple Pearson correlations of the variables with 16-km performance showed vV˙O2max to have the highest correlation (r = −0.972) and %V˙O2max at the LT the lowest (r = 0.136). The correlation coefficients for LT, V˙O2max, and PTV were very similar in magnitude (r = −0.903 to r = −0.892). When V˙O2max, %V˙O2max at LT, RE, and PTV were entered into SPSS stepwise analysis, V˙O2max explained 81.3% of the total variance, and RE accounted for an additional 10.7%. vV˙O2max was shown to be the best predictor of the 16-km performance, accounting for 94.4% of the total variance. The measured velocity at V˙O2max (PTV) was highly correlated with the estimated velocity at vV˙O2max (r = 0.8867).

Conclusions: Among well-trained subjects heterogeneous in V˙O2max and running performance, vV˙O2max is the best predictor of running performance because it integrates both maximal aerobic power and the economy of running. The PTV is linked to the same physiological variables that determine vV˙O2max.

1Exercise Physiology Department, Lynchburg College, Lynchburg, VA; and 2Department of Exercise, Sport, and Leisure Studies, The University of Tennessee, Knoxville, TN

Submitted for publication June 2009.

Accepted for publication September 2009.

Address for correspondence: James E. McLaughlin, Ph.D., Exercise Physiology Department, Lynchburg College, 1501 Lakeside Dr, Lynchburg, VA 24501; E-mail:

Elite distance runners maintain high speeds over long distances. The question "What allows them to run this fast?" has intrigued scientists over the years and has generated a considerable body of evidence describing the physiological factors related to distance running performance (3,4,8,10-13,15,19,24,30,31,33). The four physiological factors that have been linked to distance running performance include maximal oxygen uptake (V˙O2max), running economy (RE), fractional utilization of V˙O2max (%V˙O2max), and blood lactate accumulation (LT) during submaximal exercise (37).

Maximal oxygen uptake is one of the most common measurements made in exercise physiology because it sets the upper limit for ATP production via oxidative phosphorylation and, because of its dependence on maximal cardiac output, is frequently used as an indicator of cardiorespiratory fitness (5). V˙O2max varies dramatically in the population at large, from 20 mL·kg−1·min−1 for cardiac patients to more than 80 mL·kg−1·min−1 for elite endurance cyclists, runners, and cross-country skiers (31-33). In the 1920s, Hill (18), Hill and Lupton (19), and Hill et al. (20) established the link between running speed and oxygen consumption and the concept of an upper limit in oxygen consumption (V˙O2max). "In running the oxygen requirement increases continuously as the speed increases, attaining enormous values at the highest speeds; the actual oxygen intake, however, reaches a maximum beyond which no effort can drive it" (18). Hill et al. (20) also suggested that the maximal oxygen intake was limited by central rather than peripheral factors: "The oxygen intake fails to exceed this value, not because more oxygen is not required, but because the limiting capacity of the circulatory-respiratory system has been attained." However, it was not until almost 50 yr later that researchers began to study the link between V˙O2max and running performance in a systematic manner. In 1973, Costill et al. (10) reported a strong negative correlation (r = −0.91) between V˙O2max and the time to complete a 10-mile race in a group of runners who varied greatly in V˙O2max. These findings were consistent with Hill's views on the importance of V˙O2max in distance running performances, but as one might expect, as the differences in V˙O2max between runners become smaller and smaller, other factors must contribute to the differences in running performance.

Most distance races are not run at 100% of V˙O2max. If two runners have similar V˙O2max values, the one who can run at a higher percentage of his/her V˙O2max will outperform the other in a race (10). Therefore, the oxygen used in a race is a function of V˙O2max and the percentage of V˙O2max (%V˙O2max) that can be sustained for the duration of the run (9). The %V˙O2max that can be maintained in long-distance races has been shown to be closely linked to the lactate threshold (LT) (10,15), and this is a common test used to identify the %V˙O2max.

RE (how much oxygen is being used at a standard running speed) also impacts the speed that can be maintained in an endurance race. Other factors being equal, the more economical runner will have a higher speed at the same V˙O2, allowing that runner to reach the finish line first.

These three variables (V˙O2max, %V˙O2max [LT], and RE) have been used in the classic model of predicting distance running performance (5,22). Joyner (22) has used this simple physiological model to estimate human performance in the marathon.

This model, illustrated in Figure 1, shows that the performance V˙O2 (V˙O2 at LT) (11) is a product of the %V˙O2max at LT and the V˙O2max. It also shows that the velocity at V˙O2max is a product of the V˙O2max and the RE.



Noakes (28,29) and Noakes et al. (30) have questioned this approach to predicting distance running performance from these laboratory tests. They suggested that peak treadmill running velocity (PTV) is at least as good a predictor of running performance as the LT (30) and that muscle factors related to maximal power production, not the cardiovascular system, limit maximal running performance (28). Consistent with that, they proposed that the peak running speed that an athlete can achieve during a maximal treadmill test is the best predictor of performance in a marathon (28-30).

Clearly, there are some strong differences in opinion regarding the factors affecting distance running performance. First, the suggestion that muscle factors are related to maximal power generation being linked to endurance performance is at odds with a model in which oxidative energy production is central. Second, although the measurement of PTV may be a good predictor of distance running performance (21,30,34,35,37), it is a running test being used to predict a running performance, not a physiological model predicting performance. However, it is possible that PTV is directly related to oxidative processes, and this may help explain why the PTV predicts distance running performances.

Therefore, the purpose of this investigation was to compare the classic laboratory tests (V˙O2max, %V˙O2max at LT, and RE) with the PTV test to see which is the best predictor of performance in a simulated 16-km time trial in a group of subjects who differ greatly in V˙O2max.

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Seventeen healthy, well-trained male (n = 10) and female (n = 7) distance runners volunteered to participate in this study. Descriptive characteristics of the subjects are presented in Table 1. To reduce the risks to subjects, only those volunteers who met the American College of Sports Medicine's criteria for an "apparently healthy" adult were allowed to participate (1). In addition, all subjects were required to be running at least 20 miles·wk−1 for at least the last 6 months, have no contraindications to exercise, not taking any prescription drugs, not suffering from any metabolic disorder that could affect metabolic measurements (e.g., thyroid problem, diabetes, etc.), and be currently participating in interval workouts.



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Experimental Protocols

Each subject reported to the Applied Physiology Laboratory on five separate occasions, for 1-2 h per visit, with several days between tests. On the first visit, each subject reported in a rested condition at least 3 h postprandial after refraining from alcohol consumption and strenuous exercise for 24 h. Each subject filled out a medical history questionnaire and read and signed an informed consent form approved by the University of Tennessee's Institutional Review Board. Height was measured to the nearest 0.1 cm with a stadiometer, and weight was measured to the nearest 10 g on an electronic scale (Tanita Corp., Tokyo, Japan) associated with the Bod Pod® instrumentation. The scale was calibrated using a two-point calibration technique at 0 and 20 kg. Percentage of body fat was measured using whole-body plethysmography (Bod Pod®; Life Measurement Instruments, Concord, CA). Finally, each subject was taken through a familiarization process relative to the equipment and instrumentation to be used. This included an opportunity to run on the treadmill at a variety of speeds and be fitted with a nose clip and mouthpiece to be used as part of the data collection process.

On each of the four subsequent visits, subjects reported to the laboratory at least 3 h postprandial, with no formal exercise being performed 24 h before the visit. Each subject completed a maximal aerobic power test, an LT test, an RE test, and a peak treadmill velocity test in randomized order. Each subject also completed a 16-km time trial at the Tom Black track on the University of Tennessee campus.

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Maximal aerobic power test (V˙O2max).

The V˙O2max test was performed on a motorized treadmill (Quinton Q65; Quinton Instrument, Co., Bothell, WA) at a speed commensurate with the subject's current 10-km race pace. The subjects were allowed to warm up and were then fitted with a Vacumed mouthpiece connected to a Hans-Rudolph 2700 series large two-way valve (Kansas City, MO) and nose clip to allow oxygen uptake to be measured continuously with a ParvoMedics TrueMax 2400 metabolic cart (Consentius Technologies, Sandy, UT). The metabolic cart was calibrated before each test according to the specifications of the manufacturer; this system has been shown to be accurate for measuring oxygen uptake (6). The speed of the treadmill remained constant throughout the test, whereas the elevation was increased by 1%·min−1 until the subjects reached volitional exhaustion. The subjects were given verbal encouragement throughout the test. HR was measured continuously with a Polar heart monitor (Polar Electro, Inc., Kempele, Finland) interfaced with the metabolic cart. RPE using the 20-point Borg scale was recorded during the final 15 s of each stage. A fingertip blood sample (100 μL) for lactate determination was obtained immediately after exercise and was analyzed with an automated lactate analyzer (YSI-2300 STAT Plus), which was calibrated before each use according to the specifications of the manufacturer (Yellow Springs Instruments, Inc., Yellow Springs, OH). The highest V˙O2 value obtained by the subjects in this study at the end of the incremental exercise test was considered V˙O2max.

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LT test.

LT was determined using a discontinuous, horizontal treadmill (Q55XT; Quinton, Seattle, WA) running protocol. The initial treadmill velocity was set at 150 m·min−1 with an increase of 10 m·min−1 during each subsequent 3-min stage. Treadmill speed was verified during each stage with a SHIMPO DT 107 handheld digital tachometer (Nidec-Shimpo America Corp., Itasca, IL). The tachometer was calibrated to an accuracy of ±0.1 rpm by the manufacturer according to standards set by the National Institute of Standards and Technology. The treadmill was stopped for 30 s at the end of each stage for blood sampling. Blood samples (100 μL) were taken at rest and at the end of each stage using the finger stick method and were placed in a collection tube with a lysing agent to prevent clotting and to stop cell metabolism. They were analyzed immediately after the conclusion of the test with an YSI-2300 STAT Plus automated lactate analyzer (Yellow Springs Instruments, Inc). HR was measured continuously with a Polar heart monitor, and both HR and RPE were recorded during the last 15 s of each stage. The test continued until the subjects reached an RPE of approximately 17 on the 20-point Borg scale (representing very hard work, but not all-out effort) or asked to stop.

An examination of the blood lactate-velocity relationship determined LT. The highest velocity attained that was not associated with an elevation in lactate concentration above baseline (resting) levels, as determined by two observers, was designated as the velocity associated with LT. A lactate elevation of at least 0.2 mM (the measurement error for the YSI-2300 STAT Plus) was required for LT determination. Velocities associated with fixed blood lactate concentrations of 2.0 and 3.0 mM were determined from the curvilinear rise in blood lactate observed from the velocity-blood lactate relationship (17,40,41).

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RE test.

Each subject completed an RE test to determine the oxygen cost of running at four different speeds. The subjects were allowed to warm up for 5-10 min before the start of the test. The test was performed on a treadmill starting with a speed 30 m·min−1 below the subject's current 10-km race pace and was increased by 15 m·min−1 for each of the four stages. Treadmill speed was verified as previously described. Each subject ran on the treadmill for 5 min at each stage, and oxygen uptake was measured continuously with the metabolic cart. The metabolic cart was calibrated before each test according to the specifications of the manufacturer. The last 2 min of each 5-min stage was used to determine the V˙O2 for that stage. HR was measured continuously using a Polar heart monitor.

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PTV test.

The PTV test was performed on a treadmill starting with a speed 50 m·min−1 below the subject's current 10-km race pace. The subjects were allowed to warm up for 5-10 min before the start of the test. The elevation remained at 0% for the duration of the test, while the treadmill speed was increased by 1 km·h−1 each minute. Treadmill speed was verified during each stage as described previously. Subjects were encouraged to run for as long as possible, but the test ended immediately on the subject's request or on any sign that the subject was unable to continue safely. PTV was defined as the last velocity that was maintained for a full 60 s (30). HR was measured throughout with a Polar heart monitor.

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16-km time trial.

In an attempt to simulate a race as closely as possible, the subjects were asked to report to the University of Tennessee's Tom Black track and to perform their typical prerace routine. The time trial consisted of 40 laps around the 400-m track and was started at 8 a.m. with all runners starting together. Invitations were also extended to runners not participating in the study to have a wider variety of speeds represented in an attempt to minimize large gaps between runners. Each subject had an "official scorer" who recorded the time to complete each lap (splits) on a data sheet, provided feedback to the runner, and kept track of the number of laps completed. An "aid station" was set up on the track with water, sports drinks, and carbohydrate replacement (GU®, Power Gel®, and energy bars), so the runners had ready access to whatever they were accustomed to in races of this distance.

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Statistical Analysis

Statistical analyses were conducted using the statistical software package SPSS version 17.0 (SPSS, Inc., Cary, NC). Tests for normality were carried out and indicated that the 16-km run time and all predictor variables were normally distributed. Linear regression analysis was used to determine which of the variables measured from the laboratory tests was the best predictor of the time to complete the 16-km run. Data were also analyzed with the stepwise model selection procedure. Stepwise model selection performs a forward inclusion and a backward elimination to determine the most important contributors to the dependent variable. The default inclusion and exclusion criteria, namely the probability of F to enter ≤0.050 and the probability of F to remove ≥0.100, were used in these analyses.

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Table 2 presents the results from the maximal aerobic power tests. The mean V˙O2max values confirm that the subjects were well conditioned and that the range from 41.4 to 68.1 mL·kg−1·min−1 verifies that they were heterogeneous. The HRmax, RERmax, RPEmax, and LApeak values are consistent with values for having achieved V˙O2max.



Table 3 contains the data from the LT tests and lists the velocities achieved at the blood lactate inflection point (LT) and the velocities at fixed blood lactate values of 2 and 3 mM. The %V˙O2max at the LT was estimated by taking the velocity at LT linking the corresponding V˙O2 for that velocity from the RE curve (V˙O2 at LT) and dividing the V˙O2 at LT by the V˙O2max.



Table 4 contains the data for the performance-related variables. RE was compared at 82% V˙O2max because that was the mean percentage of V˙O2max sustained for the 16-km time trial.



The simple Pearson product-moment correlations of the variables with 16-km running performance are listed in Table 5. As shown, the velocity at V˙O2max had the highest correlation to performance, whereas the percentage of V˙O2max at the LT had the lowest. The blood lactate inflection point (LT), V˙O2max, and PTV were also highly correlated (r = −0.903 to r = −0.892) with the 16-km running time.



Linear regression analysis using the 16-km run time as the dependent variable and the variables in the classic model (V˙O2max, %V˙O2max at LT, and RE) as the independent variables produced a model summary with an R 2 = 0.954. Thus, 95.4% of the variation in the 16-km run time was explained by these variables. Adding the PTV variable increased the R 2 to 0.978. When all of these variables (V˙O2max, %V˙O2max at LT, RE, and PTV) were entered into the SPSS stepwise analysis, V˙O2max alone explained 90.2% of the total variance. The second entering variable was RE, which accounted for an additional 7.1% of the total variance. The total variance accounted for in this two-variable model was 97.3%. Additional variables did not increase the predictive power of the model.

As shown in Table 5, these variables (velocity at LT, V˙O2max, and PTV) each independently explained approximately 80% of the variance in the 16-km run time. The velocity at V˙O2max (vV˙O2max), which incorporates V˙O2max and RE, explained 94.4% of the variance in the 16-km performance.

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This study shows that V˙O2max, RE, and PTV are all highly related to the 16-km running performance. Linear regression analysis found that the variables from the classic model (V˙O2max, %V˙O2max at LT, and RE) plus the PTV test explained 97.8% of the variation in the 16-km run time. From these variables (V˙O2max, %V˙O2max at LT, RE, and PTV), SPSS stepwise analysis identified V˙O2max as the best single predictor of performance, explaining 90.2% of the total variance in the 16-km run time. RE accounted for an additional 7.1%.

The relationship between V˙O2max and performance in this study is very similar to the findings of others who found a high inverse correlation between V˙O2max and performance times among runners who were heterogeneous in terms of V˙O2max (7,10,14,15,25,26,30). The correlation coefficient in this study is almost identical to that found by Costill et al. (10) (r = −0.91 vs r = −0.902), who also measured 10-mile run time. In addition, Farrell et al. (15) found a similar correlation coefficient, r = 0.89, between 15-km (9.3-mile) pace and V˙O2max in experienced male runners heterogeneous for V˙O2max and performance. Noakes et al. (30) reported a slightly lower correlation, r = −0.81, between V˙O2max and running performance in a slightly longer run of 21.1 km (∼12 miles) in a group of male marathon and ultramarathon specialists heterogeneous for V˙O2max. In line with that, Davies and Thompson (14) reported that the relationship between 5-km race time and V˙O2max was r = −0.85 in male ultramarathon runners somewhat heterogeneous in V˙O2max and that it grew weaker as the distance increased. In contrast, Stratton et al. (37) reported much lower correlations between V˙O2max and 5000-m run performance before (r = 0.55) and after (r = 0.51) 6 wk of endurance training in previously untrained subjects. In general, the relationship between V˙O2max and running performance was similar to other studies using well-trained runners, confirming its importance as a physiological variable linked to distance running performance.

The high correlation coefficient between RE and 16-km run time (r = 0.812) in the current study is similar to that found by Noakes et al. (30) (r = 0.76-0.90) but in contrast with other studies that used subjects heterogeneous for V˙O2max and performance (10,26). Costill et al. (10) found no relationship between RE and performance and concluded that the differences in V˙O2 at selected submaximal running speeds are "random and insignificant." Morgan et al. (26) also reported no significant relationship between RE and 10-km run time (r = 0.30, P > 0.05) in well-trained runners.

The identification of the LT as a good predictor of performance in this study was not surprising and is in agreement with several other investigations (16,30,36,39) that have been conducted since the landmark study of Farrell et al. in 1979 (15) linked the onset of plasma lactate accumulation to the race pace in long-distance races. Although V˙O2max sets the upper limit for aerobic performance, it cannot be sustained for more than 10-15 min. The LT incorporates the V˙O2max, the RE, and the fraction of V˙O2max that can be sustained in events lasting beyond 10-15 min to determine the running velocity in a competition (23). In their study, Farrell et al. (15) reported a strong relationship (r ≥ 0.91) between the treadmill velocity corresponding to onset of plasma lactate accumulation (defined as the velocity just before the exponential increase in plasma lactate) and performance at all distances (races of 3.2, 9.7, 15, and 19.3 km). Numerous other investigators (16,30,36,39) have reported that the accumulation of lactate was highly correlated with distance running performance.

The significant inverse correlation between PTV and 16-km run time found in this investigation (r = −0.892) is in agreement with others who have measured this variable, indicating that this treadmill-based performance measure is a good predictor of endurance performance (21,30,34,35). Noakes et al. (30) showed the closest agreement in their study of marathon and ultramarathon runners heterogeneous for V˙O2max and performance over a variety of distances. When they included all of the runners, they found correlations of −0.94, −0.93, and −0.91 for distances of 10, 21.1, and 42.2 km, respectively. In contrast, Scrimgeour et al. (35) reported a much lower correlation for PTV (r = 0.72) in marathon and ultramarathon runners homogeneous for V˙O2max but heterogeneous for performance over distances from 10 to 90 km.

The ability of highly trained distance runners to sustain a high percentage of their maximal aerobic power has been reported by several investigators (9,10,14,15,35). Costill et al. (10) reported that highly trained distance runners maintained 80%-91% of V˙O2max during a 10-mile race. In the study by Farrell et al. (15), intensities ranged from 79% to 98% of V˙O2max during 10,000-m races and from 68% to 88% of V˙O2max during marathons. Davies and Thompson's (14) subjects averaged 94% of their V˙O2max for a 5-km race and 82% of their V˙O2max over a standard 42-km marathon. Finally, and consistent with the other studies, Scrimgeour et al. (35) reported that their subjects sustained 85.8% of their V˙O2max in 10-km races and 80.7% of their V˙O2max for the 21.1-km distance. The values found in the current study (mean = 82.2% V˙O2max, range = 75.6%-87.5% V˙O2max) are very similar to those reported previously. However, it is not surprising that the correlation between the percentage of V˙O2max sustained for the 16-km time trial (82.2%) and 16-km run time was only r = −0.291 because the range of values for the %V˙O2max sustained for the 16-km time trial was so small (75.6%-87.5%).

If the percentage of V˙O2max that can be sustained in a run does not vary greatly in a group of runners, then the remaining two variables in the physiological prediction model (RE and V˙O2max) would have to explain most of the variation in performance. Such was the case for vV˙O2max, which incorporates both of these variables into its calculation. When the calculated velocity at V˙O2max (vV˙O2max) was examined against 16-km run performance, the R 2 was 0.954.

The finding that vV˙O2max was the best predictor of performance in this study is similar to the findings of Morgan et al. (25,26) and Murray et al. (27). Performance variations among well-trained runners are reflected by individual differences in vV˙O2max, which is a composite variable accounting for both V˙O2max and RE. Attaining a high vV˙O2max can be accomplished by having either a high V˙O2max or a very economical running style. Pollock (31) reported a 16% difference in V˙O2max values for Frank Shorter and Steve Prefontaine (71.3 and 84.4 mL·kg−1·min−1, respectively), yet their best time for 3 miles was virtually identical (<0.2-s difference) (29) because Shorter had exceptional RE. Shorter's submaximal V˙O2 at 12 mph was only 57 mL·kg−1·min−1 compared with 65 mL·kg−1·min−1 for the mean value of elite American mid- to long-distance runners (31).

Given the relationship between vV˙O2max and distance running performance in this investigation, it should be no surprise that PTV is highly correlated with distance running performance. In essence, PTV is the measured velocity at V˙O2max (with a horizontal running protocol) because it is defined as the highest treadmill running velocity attained during the V˙O2max test, where Daniels' (12) is the estimated velocity at V˙O2max because it is the result of extrapolating the steady-state oxygen consumption values out to V˙O2max. With this relationship (measured vs calculated vV˙O2max), one would expect these two variables to be highly correlated with each other, and indeed, in this study, the correlation coefficient was r = 0.8867 (Fig. 2). In their article proposing the PTV as a predictor of endurance performance, Noakes et al. (30) stated:



The physiological determinants of peak treadmill running velocity are not known. If the absolute rate of oxygen consumption was the most important determinant of peak treadmill running velocity, then the V˙O2max would be an equivalent predictor of running performance. That it is not indicates that the absolute rate of oxygen consumption cannot be the principal determinant of the peak treadmill running velocity.

These data argue otherwise. The velocity achieved at the end of an all-out treadmill test seems to reflect both the V˙O2max and the RE. Because the PTV represents a velocity that is only maintained for 1 min as opposed to the 5-min submaximal measurements of RE used to calculate the vV˙O2max, it is also likely that there is a small anaerobic contribution to the PTV. Data from the current study support this view because the average PTV was 16 m·min−1 faster than the calculated vV˙O2max (293.2 vs 276.9 m·min−1, respectively). This suggests that the PTV is directly related to the vV˙O2max, a reflection of the oxidative demands of distance running. We would like to acknowledge the limitations that our small sample size may have on this research.

In summary, the classic model of endurance running performance closely predicts 16-km time trial performance. The classic model incorporates three physiological variables (V˙O2max, %V˙O2max at LT, and RE) to explain interindividual variation in distance running ability. In the present study, there was little variability in the %V˙O2max at LT, which left the other two variables (V˙O2max and RE, which can be combined to calculate vV˙O2max) to explain most of the variation in performance. PTV, which is the highest speed attained at the end of a graded exercise test with a horizontal running protocol, was also highly correlated with endurance running performance. In our view, this is because performance in both of these tests (PTV and 16-km time trial run) is linked, to a large extent, to the same physiological variables.

No funding was obtained for this investigation from the National Institutes of Health, the Wellcome Trust, the Howard Hughes Medical Institute, or any other sources.

The results of the present study do not constitute endorsement by the American College of Sports Medicine.

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