RESEARCH ARTICLE
The Correlation between Running Economy
and Maximal Oxygen Uptake: Cross-Sectional
and Longitudinal Relationships in Highly
Trained Distance Runners
Andrew J. Shaw1,2*, Stephen A. Ingham1, Greg Atkinson3, Jonathan P. Folland2
1 English Institute of Sport, Loughborough University, Loughborough, United Kingdom, 2 School of Sport,
Exercise and Health Sciences, Loughborough University, Loughborough, United Kingdom, 3 Health and
Social Care Institute, Teesside University, Middlesbrough, United Kingdom
* a.shaw@lboro.ac.uk
Abstract
A positive relationship between running economy and maximal oxygen uptake (V̇O2max)
has been postulated in trained athletes, but previous evidence is equivocal and could have
been confounded by statistical artefacts. Whether this relationship is preserved in response
to running training (changes in running economy and V̇O2max) has yet to be explored. This
study examined the relationships of (i) running economy and V̇O2max between runners,
and (ii) the changes in running economy and V̇O2max that occur within runners in response
to habitual training. 168 trained distance runners (males, n = 98, V̇O2max 73.0 ± 6.3
mLkg-1min-1; females, n = 70, V̇O2max 65.2 ± 5.9 mL kg-1min-1) performed a discontinuous
submaximal running test to determine running economy (kcalkm-1). A continuous incre-
mental treadmill running test to volitional exhaustion was used to determine V̇O2max 54 par-
ticipants (males, n = 27; females, n = 27) also completed at least one follow up assessment.
Partial correlation analysis revealed small positive relationships between running economy
and V̇O2max (males r = 0.26, females r = 0.25; P<0.006), in addition to moderate positive re-
lationships between the changes in running economy and V̇O2max in response to habitual
training (r = 0.35; P<0.001). In conclusion, the current investigation demonstrates that
only a small to moderate relationship exists between running economy and V̇O2max in highly
trained distance runners. With >85% of the variance in these parameters unexplained
by this relationship, these findings reaffirm that running economy and V̇O2max are primarily
determined independently.
Introduction
Running economy (RE) and maximal oxygen uptake (V̇O2max) are two of the primary determi-
nants of endurance running performance [1–4]. The combination of RE and V̇O2max, defined as
the velocity at V̇O2max (vV̇O2max), has been found to account for ~94% of the inter-individual
PLOS ONE | DOI:10.1371/journal.pone.0123101
April 7, 2015
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OPEN ACCESS
Citation: Shaw AJ, Ingham SA, Atkinson G, Folland
JP (2015) The Correlation between Running
Economy and Maximal Oxygen Uptake: Cross-
Sectional and Longitudinal Relationships in Highly
Trained Distance Runners. PLoS ONE 10(4):
e0123101. doi:10.1371/journal.pone.0123101
Academic Editor: Oyvind Sandbakk, Norwegian
University of Science and Technology, NORWAY
Received: October 31, 2014
Accepted: February 27, 2015
Published: April 7, 2015
Copyright: This is an open access article, free of all
copyright, and may be freely reproduced, distributed,
transmitted, modified, built upon, or otherwise used
by anyone for any lawful purpose. The work is made
available under the Creative Commons CC0 public
domain dedication.
Data Availability Statement: All relevant data are
within the paper.
Funding: These authors have no support or funding
to report.
Competing Interests: The authors have declared
that no competing interests exist.
variance in running performance over 16.1 km [5]. Consequently, exceptional values of both RE
and V̇O2max are considered requirements for success in elite endurance competitions, and en-
durance runners strive to improve both parameters through training in order to maximise
performance. As the margin of success is extremely small in elite distance running, subtle en-
hancements in either parameter could result in substantial performance gains. Therefore,
understanding the relationship of RE and V̇O2max both between and within individuals is neces-
sary to understand and optimise performance.
Within cohorts of trained [6,7] and elite [8] distance runners, it has been suggested that a
superior RE, quantified as the submaximal oxygen uptake, is associated with a lower V̇O2max.
These findings have been used to postulate that superior economy compensates for a lower
V̇O2max in some individual to achieve a similar performance level [3,8,9]. However, these inves-
tigations have often been restricted to small sample sizes (<25 participants [3,6,8]), and the va-
lidity of their statistical techniques has been questioned due to the expression both variables
relative to body mass (i.e. mLkg-1min-1); creating a common divisor that is known to produce
spurious correlations [10]. Partial correlation analysis would provide an appropriate method to
account for the influence of body mass on both variables whilst avoiding statistical artefacts,
however this method has yet to be used to examine the relationship between RE and V̇O2max.
Furthermore, studies have solely employed oxygen cost (OC) as a measure of RE, rather than
the more valid and comprehensive measurement of energy cost (EC; [11]). Thus, whether a
genuine association exists between RE and V̇O2max remains unclear from the limited cross-
sectional observations to date.
Moreover, the concurrent alterations in RE and V̇O2max that occur within athletes over time
with training might further reveal if there is an inherent association between these variables,
whilst also informing the optimisation of both variables and thus performance. Previous inves-
tigations in well trained athletes have noted enhancements in cycling efficiency following
short-term, intensive endurance training, but with no change in V̇O2max evident [9,12,13]. In
contrast, a recent investigation reported an association between individual changes in cycling
efficiency and V̇O2max in response to endurance training and across a competitive season; de-
spite no change in mean group V̇O2max [14]. These preliminary findings highlight the signifi-
cance of this relationship for elite endurance athletes, as enhancements in either RE or V̇O2max
might only be achievable at the expense of the other variable. However, this previous investiga-
tion was limited to measurements of gross efficiency, with no data presented on movement
economy. Moreover, analysis of this longitudinal relationship was restricted to observations
within small cohorts of athletes, and with responses to run training yet to be explored.
The primary aim of the current investigation was to explore the cross-sectional relationship
between V̇O2max and RE, quantified as EC (OC data are also presented for comparative pur-
poses), within a large cohort of highly trained distance runners. The secondary aim was to ex-
amine the longitudinal relationship between the changes in V̇O2max and RE occurring within
athletes in response to endurance training.
Materials and Methods
Overview
The cross-sectional investigation involved retrospective analysis of data from 168 healthy en-
durance trained athletes with competitive distances ranging from 800m to the marathon
(males, n = 98; females, n = 70; Table 1), who undertook testing and monitoring as part of their
sport science support from the English Institute of Sport. The following tests were performed
after written informed consent was obtained as a part of sports science support provision,
with procedures approved by the Internal Review Board of English Institute of Sport. Of the
Correlation between Running Economy and V̇O2max
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participants assessed, 97 (males, n = 57; females, n = 40) were classed as middle distance run-
ners, defined by a primary competitive distance3000m [15], with 71 classed as long distance
runners (males, n = 41; females, n = 30). During the season following their final visit, athlete’s
best performance times in their primary competitive distance were 89.1±6.1% and 91.2±4.4%
of the current British record for males and females, respectively. Data were collected from two
laboratories, with all tests conducted as part of athlete support services between November
2004 and April 2013. Participants provided informed consent prior to physiological assess-
ments, in addition to an athlete agreement providing permission for the use of their data in
anonymous retrospective analysis. During each visit to the laboratory, participants completed
first submaximal and then maximal running assessments (detailed below). Participants wore
appropriate clothing (shorts and a vest or t-shirt) and racing shoes, and laboratory conditions
were similar throughout all running assessments (temperature 20.6±1.9°C, relative humidity
45.9±9.8%). As differences in RE and V̇O2max have been noted between sexes [16–18], males
and females were analysed separately for cross sectional analyses.
The longitudinal aspect of the study was based on 54 participants (males, n = 27; females,
n = 27) from amongst the larger cohort of 168 runners, that had completed at least one follow
up assessment, with a median trial separation of 203 days (range: 37–2567 days) in order to as-
sess within-athlete changes in both RE and V̇O2max over time. The number of repeat assessments
in the longitudinal analysis varied between participants, with a median of 3 visits per athlete
(range: 2–10 visits), summating to 182 assessments in total. No evidence is currently available re-
garding sex differences in the concurrent alterations in RE and V̇O2max in response to habitual
endurance training, thus data for males and females were combined for longitudinal analysis.
Protocol
Submaximal running assessments.
Following a warm-up (~10 min at 10–12 kmh-1),
participants completed a discontinuous submaximal incremental test consisting of six to nine
stages of 3 minutes continuous running, with increments of 1 kmh-1 on a motorised treadmill
of known belt speeds (HP cosmos Saturn, Traunstein, Germany) interspersed by 30 s rest peri-
ods for blood sampling. As the speeds assessed were typically between 10.5 kmh-1 and 18
kmh-1, treadmill gradient was maintained at 1% throughout submaximal assessments in order
to reflect the energetic cost of outdoor running [19]. This protocol has been shown to reliable
measures of running economy when quantified as both EC and OC (typical error ~3%; [20]).
Moreover, the controlled laboratory environment enabled assessments of EC whilst avoiding
the confounding influence of air resistance that is evident during outdoor running as speed
Table 1. Physiological and anthropometrical characteristics of athletes within the cross sectional and longitudinal investigations.
Cross sectional
Longitudinal sub-group
Females
Males
Females
Males
(n = 70)
(n = 98)
(n = 27)
(n = 27)
Age (yrs)
23±4
23±6
23±5
21±3
Body mass (kg)
55.2±4.7
67.1±7.1
55.4±4.3
66.6±6.0
Stature (cm)
169±5
179±7
168±4
179±6
V̇O2max (mLkg-1min-1)
65.2±5.9
73.0±6.3
64.5±4.9
73.6±5.9
vLTP (kmh-1)
15.5±1.2
17.2±1.3
15.7±1.2
17.6±1.1
Running economy (kcalkg-1km-1)
1.15±0.09
1.14±0.09
1.13±0.06
1.13±0.07
V̇O2max, maximal oxygen uptake; vLTP, velocity at lactate turnpoint.
doi:10.1371/journal.pone.0123101.t001
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increases [21]. Recent performance times of participants were used to determine an appropri-
ate starting speed to provide ~4 speeds prior to lactate turnpoint (LTP). Increments were
continued until blood lactate concentration had risen exponentially, typically defined as an in-
crease in blood lactate of ~2 mmolL-1 from the previous stage. HR (s610i, Polar, Finland) and
pulmonary gas exchange (detailed below) were monitored throughout the test.
Maximal running assessments.
V̇O2max was determined by a continuous incremental
treadmill running ramp test to volitional exhaustion. After a warm-up, participants initially
ran at a speed 2 kmh-1 below the final speed of the submaximal test and at a 1% gradient. Each
minute, the incline was increased by 1% until volitional exhaustion. The test duration was typi-
cally 6–8 minutes.
Measurements
Anthropometry.
Prior to exercise on laboratory visits, body mass was measured using dig-
ital scales (Seca 700, Seca, Hamburg, Germany) to the nearest 0.1 kg. Stature was recorded to
the nearest 1 cm using a stadiometer (Harpenden Stadiometer, Holtain Limited, UK).
Pulmonary gas exchange.
Breath-by-breath gas exchange data was quantified via an auto-
mated open circuit metabolic cart (Oxycon Pro, Carefusion, San Diego, USA). Participants
breathed through a low dead-space mask, with air sampled at 60 mLmin-1. Prior to each test,
two point calibrations of both gas sensors were completed, using a known gas mixture (16%
O2, 5% CO2) and ambient air. Ventilatory volume was calibrated using a 3 L (±0.4%) syringe.
This system has previously been shown to be a valid apparatus for the determination of oxygen
consumption (V̇O2) and carbon dioxide production (V̇CO2) at both low and maximal exercise
intensities [22]. As previous data from our laboratory has demonstrated a steady state V̇O2,
and V̇CO2 is achieved within the first 2 minutes of each stage for highly trained endurance run-
ners [20], mean values from breathe-by-breathe measures over the final 60 seconds of each
stage were used to quantify V̇O2, carbon dioxide production V̇CO2, and RER.
Blood lactate.
A 20μL capillary blood sample was taken from the earlobe for analysis of
blood lactate ([La]b) (Biosen C-line, EKF diagnostics, Germany). The LTP was identified via
the modified Dmax method [23]. LTP was quantified as the point on the third order polynomi-
al curve fitted to the speed-lactate relationship that generated the greatest perpendicular dis-
tance to the straight line formed between the stage proceeding an increase in [La]b greater than
0.4 mmol.L-1 (lactate threshold) and the final stage. The four stages prior to LTP were identi-
fied for each participant, with an average of these four stages used to quantify OC and EC.
Calculation of running economy.
V̇O2 and V̇CO2 during the final minute of each sub-
maximal stage were used to calculate EC. Updated nonprotein respiratory quotient equations
[24] were used to estimate substrate utilisation (gmin-1) during the monitored period. The
energy derived from each substrate was then calculated by multiplying fat and carbohydrate
usage by 9.75 kcal and 4.07 kcal, respectively, reflecting the mean energy content of the
metabolised substrates during moderate to high intensity exercise [25]. EC was quantified as
the sum of these values, expressed in kcalkm-1. V̇O2 during the final minute of each submaxi-
mal stage was used to determine oxygen cost (OC) in mLkm-1 to enable comparisons to
previous investigations.
Statistical analyses. Data are presented as mean±SD for all dependant variables. Data
analysis was conducted using SPSS for windows (v21; IBM Corporation, Armonk, NY). When
an individual visited the laboratory for repeated assessments, an average of the assessments
was calculated and used for the cross sectional analysis. Pearsons product-moment coefficients
were calculated to assess the relationship between body mass and EC, OC and V̇O2max. As body
mass was strongly related to both RE measures (EC, OC) and V̇O2max, partial correlations
Correlation between Running Economy and V̇O2max
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controlling for body mass, and associated 95% confidence intervals (CI), were used to assess
the relationship between absolute V̇O2max and both EC and OC. This method removes the in-
fluence of body mass on both RE and V̇O2max whilst avoiding spurious correlations created by
correlating two variables with a common divisor [26]. For graphical display of these relation-
ships, values of EC and V̇O2max adjusted for body mass for each individual were calculated
based on individual residuals. This involved summating the individual’s residual, in compari-
son to the cohort relationship with body mass (e.g. EC vs body mass), with the group mean for
that variable [27]. For the longitudinal analysis, in order to assess any relationships between
the changes over time in absolute V̇O2max and the changes in both EC and OC over repeat visits,
partial correlation coefficients were calculated using ANCOVA [28]; providing a comprehen-
sive model that accounts variations in both body mass and the number of visits per athlete.
Cohen's d effect size descriptors (trivial 0.0–0.1, small 0.1–0.3, moderate 0.3–0.5, large 0.5–0.7,
very large 0.7–0.9, nearly perfect 0.9–1, perfect 1) were used to infer correlation magnitude
[29]. Significance was accepted at P0.05.
Results
Participant Characteristics
Participant characteristics are shown in Table 1. The well trained status of the participants was
emphasised by the high V̇O2max and vLTP values for both males and females.
Cross-sectional analysis
Partial correlation analysis controlling for body mass, revealed small positive relationships be-
tween EC and V̇O2max (males r = 0.26, CI 0.07–0.44, P = 0.009; females r = 0.25, CI 0.02–0.46,
P = 0.036; Fig 1), and a moderate positive relationship between OC and V̇O2max (males r = 0.33,
CI 0.14–0.50, P = 0.001; females r = 0.33, CI 0.10–0.52, P = 0.006).
Longitudinal analysis
Partial correlation analysis from ANCOVA revealed moderate positive relationships between
the changes in EC and V̇O2max over time (r = 0.35; CI 0.19–0.49, P < 0.001; Fig 2), and changes
in OC and V̇O2max over time (r = 0.44; CI 0.29–0.57, P < 0.001).
Discussion
The present investigation explored the cross-sectional and longitudinal relationships between
RE and V̇O2max in a large cohort of highly trained distance runners. The major contribution
of this study to the field is that only a small to moderate association exists between RE and
V̇O2max (R2 ~ 12%) when body mass is appropriately accounted for. With >85% of the vari-
ance in these parameters unexplained by this relationship, these findings reaffirm that RE and
V̇O2max are primarily determined independently.
Cross-sectional analysis revealed a small positive between-participant relationships between
V̇O2max and the metabolic cost of running, when quantified as both EC (r ~ 0.25) and OC
(r ~ 0.33). These results support the findings of Pate et al. [7], who reported a similar relation-
ship (r = 0.29) between submaximal V̇O2 and V̇O2max in a similarly large cohort of habitual
distance runners. Conversely, a stronger, moderate positive relationship has been reported be-
tween submaximal V̇O2 and V̇O2max in smaller cohorts of elite distance runners (r = 0.59; [8])
and physically active individuals (r = 0.48; [30]). However, all aforementioned investigations
are confounded by statistical artefacts that arise when correlating two variables with common
divisors [10,26], and thus should be regarded with caution. Within the current study, spurious
Correlation between Running Economy and V̇O2max
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correlations between RE and V̇O2max were avoided by removing the influence of body mass
with partial correlations, which enabled the true relationship between these variables to be ex-
amined. As a lower metabolic cost is reflective of a more economical runner, our findings con-
firm the existence of a small inverse association between RE and V̇O2max in endurance runners.
The longitudinal analysis of the relationship between the changes in RE and the changes in
V̇O2max within participants in response to training has not previously been documented. Sup-
porting the findings from our cross sectional analysis, a moderate positive relationship
(r = 0.35) was observed between the changes in EC and V̇O2max over repeated assessments.
Fig 1. Scatter plot of energy cost (Kcalkm-1) adjusted for body mass (BM) vs V̇O2max (Lmin-1)
adjusted for BM for both females (A; n = 70; r = 0.25; P = 0.036) and males (B; n = 98; r = 0.26; P = 0.009)
within the cross-sectional analysis.
doi:10.1371/journal.pone.0123101.g001
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Moreover, these findings support recent observations from competitive road cyclists that
highlighted a similar moderate relationship (r = 0.44) between changes in gross efficiency and
V̇O2max across a training season [14].
It has been postulated that variations in lipid oxidation rates between individuals might, in
part, explain the relationship between OC and V̇O2max that some previous studies have docu-
mented; with a higher V̇O2max facilitating greater lipid oxidation and consequently a greater
OC during sub-maximal exercise [7]. Whilst OC may be sensitive to lipid oxidation, the calcula-
tion of EC includes the RER and thus is insensitive to differences in substrate metabolism. The
influence of substrate metabolism could conceivably explain the marginally stronger relation-
ship observed between OC and V̇O2max, than EC and V̇O2max, in both the cross sectional
(r ~ 0.33 vs r ~ 0.25) and longitudinal observations (r = 0.44 vs r = 0.35). More importantly, a
positive relationship was documented between EC and V̇O2max that is clearly independent of
variations in lipid metabolism.
The mechanisms that underpin the small relationship between EC and V̇O2max remain un-
clear. It has been argued that for athletes of a similar, high performance level, there would be
an inevitable relationship between EC and V̇O2max in order to produce a similar velocity at
V̇O2max [31]. However, we have found no evidence for this possibility, despite all the partici-
pants in this study being highly trained and high performing runners, perhaps in part because
of the variable performance ability of the athletes. It is also possible that less economical run-
ners recruit a larger muscle mass (braking, oscillation etc.) and it is conceivable that this could
contribute to a higher V̇O2max. However there is considerable evidence that V̇O2max during
whole body exercise such as running is largely dependent on oxygen delivery rather than utili-
sation [32], which might question this explanation. Thus, further investigation would be re-
quired to identify the factors driving the interdependence of EC and V̇O2max.
Though reaching statistical significance, the association between RE and V̇O2max was
small. The current study found only ~ 7% (between-participant cross sectional data) and 12%
Fig 2. Scatter plot of the changes over time in energy cost (Kcalkm-1) adjusted for body mass (BM) vs
the changes over time in V̇O2max (Lmin-1) adjusted for BM (r = 0.35; P < 0.001) within the longitudinal
analysis.
doi:10.1371/journal.pone.0123101.g002
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(within-participant longitudinal data) of the variance in RE was explained by V̇O2max. This
small association likely reflects the distinct nature of these variables and their physiological
determinants. V̇O2max is known to be determined by factors such as cardiac output [33], total
haemoglobin mass [34], and mitochondrial capacity [1]. Conversely, RE is thought to be
closely associated to multiple biomechanical and anthropometrical factors, including effective
storage and re-utilisation of elastic energy [35,36], vertical oscillation [37] and ground contact
time [38]. As there are few common determinants of both RE and V̇O2max, adaptations
that lead to enhancements in one of these variables are unlikely to directly influence in the
opposing variable.
In conclusion, the current investigation demonstrates that only a small to moderate rela-
tionship exists between running economy and V̇O2max in highly trained distance runners.
With >85% of the variance in these parameters unexplained by this relationship, these findings
reaffirm that running economy and V̇O2max are primarily determined independently.
Acknowledgments
The authors would like to thank Dr Barry Fudge, Dr Jamie Pringle, Dr Charles Pedlar and Kate
Spilsbury for their time and efforts collecting data on behalf of the English Institute of Sport
that enabled this retrospective analysis, in addition to David Green for his time and assistance
during data collation.
Author Contributions
Conceived and designed the experiments: AJS JPF SAI. Performed the experiments: AJS JPF
SAI. Analyzed the data: AJS JPF SAI GA. Contributed reagents/materials/analysis tools: AJS
JPF SAI GA. Wrote the paper: AJS JPF SAI GA.
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The correlation between running economy and maximal oxygen uptake: cross-sectional and longitudinal relationships in highly trained distance runners.
Shaw, Andrew J,Ingham, Stephen A,Atkinson, Greg,Folland, Jonathan P