International  Journal  of
Environmental Research
and Public Health
Brief Report
Race Analysis of the World’s Best Female and Male
Marathon Runners
Véronique Billat 1,2,*,†
, Damien Vitiello 1,†, Florent Palacin 1, Matthieu Correa 1 and
Jean Renaud Pycke 1,3
1
Université de Paris, EA3625-Institut des Sciences du Sport Santé de Paris (I3SP), 75015 Paris, France;
damien.vitiello@parisdescartes.fr (D.V.); palacinﬂorent@gmail.com (F.P.);
matthieucorrea37@gmail.com (M.C.); jeanrenaud.pycke@univ-evry.fr (J.R.P.)
2
Véronique Billat, Université de Paris, EA 3625-Institut des Sciences du Sport Santé de Paris (I3SP), 1 rue
Lacretelle, 75015 Paris, France
3
Université d’Evry Val d’Essonne, UMR8071—CNRS-Laboratoire de Mathématiques et Modélisation
d’Evry (LaMME), 91037 Evry, France
*
Correspondence: veroniquelouisebillat@gmail.com; Tel.: +33-(0)786117308
†
Equally contributing authors.
Received: 23 December 2019; Accepted: 9 February 2020; Published: 13 February 2020


Abstract: Background: Beyond the diﬀerence in marathon performance when comparing female
and male runners, we tested the hypothesis that running strategy does not diﬀerent according to
sex. The goal of the present study is to compare the running strategy between the best female and
male marathon performances achieved in the last two years. Methods: Two aspects of the races were
analyzed: (i) average speed relative to runner critical speed (CS) with its coeﬃcient of variation and (ii)
asymmetry and global tendency of race speed (i.e., the race’s Kendall τ). Results: The females’ best
marathons were run at 97.6% ± 3% of CS for the new record (Brigid Kosgei, 2019) and at 96.1% ± 4.4%
for the previous record (Paula Radcliﬀe, 2003). The best male performances (Eliud Kipchoge, 2018
and 2019) were achieved at a lower fraction of CS (94.7% ± 1.7% and 94.1% ± 2.3% in 2018 and 2019,
respectively). Eliud Kipchoge (EK) achieved a signiﬁcant negative split race considering the positive
Kendall’s τ of pacing (i.e., time over 1 km) (τ = 0.30; p = 0.007). Furthermore, EK ran more of the
average distance below average speed (54% and 55% in 2018 and 2019, respectively), while female
runners ran only at 46% below their average speed. Conclusions: The best female and male marathon
performances were run diﬀerently considering speed time course (i.e., tendency and asymmetry), and
fractional use of CS. In addition, this study shows a robust running strategy (or signature) used by
EK in two diﬀerent marathons. Improvement in marathon performance might depend on negative
split and asymmetry for female runners, and on higher fractional utilization of CS for male runners.
Keywords: running strategy; critical speed; endurance; performance; health
1. Introduction
For 20 years, marathon racing has gained popularity given that it is one of the rare sporting
events in which elite and non-elite runners compete at the same time, despite some athletes completing
the race in twice the time of others. Although males are nearly able to ﬁnish the race in under two
hours (Eliud Kipchoge (EK): 2 h 01 min 39 s in Berlin, 2018, and 2 h 02 min 37 s in London, 2019), the
milestone for female runners of 2 h 15 min was broken by Brigid Kosgei (BK) (2 h 14 min 04 s) in 2019
during the Chicago marathon, 16 years after the previous world record of Paula Radcliﬀe (PR) at the
London marathon in 2003.
Beyond speculation on the future of performance or on the comparison of relative performance
in males and females [1,2], the goal of this study is to test the hypothesis that running strategy does
Int. J. Environ. Res. Public Health 2020, 17, 1177; doi:10.3390/ijerph17041177
www.mdpi.com/journal/ijerph
Int. J. Environ. Res. Public Health 2020, 17, 1177
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not diﬀer according to sex. We consider that both female and male marathoners might beneﬁt from a
training program based on their perception to improve their performance. Indeed, this may allow
them to have a more positive asymmetry, a lower coeﬃcient of variation of speed, and to run at a
higher percentage of their critical speed (CS) during the entire race. Therefore, this study analyzed two
aspects of the races: (i) the average runner’s speed relative to their CS [3–5], with the coeﬃcient of
variation and (ii) the tendency of the pace and its asymmetry [6].
2. Materials and Methods
To achieve this study, pacing (i.e., time per distance) run by EK (35 years old, Berlin 2018 and
London 2019), BK (25 years old, Chicago 2019) and PR (29 years old, London 2003) were examined.
Data were retrieved from the World Athletics website on 14th October 2019. A computation of the
average speed per distance was achieved by dividing distance per time unit.
2.1. Critical Speeds (CS)
The average speed relative to runner CS, with the coeﬃcient of variation, was calculated. CS was
calculated from the runner’s personal best performances in the 3000 m and half marathon (run in less
than 1h for EK, and 1 h 04 min 28 s and 1 h 05 min 40 s for BK and PR, respectively).
The CS was calculated using the following equation [7]:
Dlim = α + β tlim
(1)
Dlim = distance; α = constant reserve; β = critical speed; tlim = record time.
2.2. Global Tendency of Pace and Its Asymmetry
Here, the trend in speed time series (i.e., Kendall’s τ non-parametric rank correlation coeﬃcient) [8]
and the pacing design (i.e., asymmetry characteristics of the race) [6] were compared. Here is the
equation of Kendall’s τ:
τ = 2 / n(n − 1)
X
i<j
K(vi, vj)
(2)
vi = ith value of a speed; vj = jth value of a speed; i < j = i indicates a period of time prior to j; sum
being performed over the n(n − 1)/2 distinct unordered couples of indices {i, j}, so that τ takes values in
between −1 and 1.
We sought to establish running strategy or signature in real race format for the same runner (EK),
and for male and female oﬃcial best marathon performances.
3. Results
3.1. Average Marathon Speed Relative to Marathoners’ Critical Speed and Coeﬃcient of Speed Variation
The male and female marathon races were run at diﬀerent percentages of the CS (Table 1).
Int. J. Environ. Res. Public Health 2020, 17, 1177
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Table 1. Average marathon speed relative to male and female marathoners’ critical speed and coeﬃcient
of speed variation.
Speed
Critical
Speed
(km)
Speed (% Critical Speed)
Skewness
(% km
below
Mean
Speed)
Pace / Trend
Athlete
Place /
Year
Time
Mean
SD
Variation
Coeﬃcient
Mean
SD
Variation
Coeﬃcient
Kendall’s t
p-Value
E.
Kipchoge
London
/2019
2 h 02 min
37 s
20.67
0.51
2.48%
21.6
94.1
2.3
2.44%
55
−0.0289
0.8000
E.
Kipchoge
Berlin
/2018
2 h 01 min
39 s
20.78
0.35
1.68%
21.6
94.7
1.7
1.80%
54
0.3000
0.0069
P.
Radcliﬀe
London
/2003
2 h 15 min
25 s
18.89
0.30
1.59%
19.6
96.0
4.4
4.58%
32
0.0050
0.7227
B. Kosgei
Chicago
/2019
2 h 14 min
04 s
18.82
0.65
3.45%
19.29
97.6
3.4
3.45%
46
0.0955
0.4891
Data are presented in means ± SD and percentages.
Indeed, the best female marathon performances were run at 97.6% ± 3% of CS for the new record
(BK, 2019) and 96.1% ± 4.4% for the previous record (PR, 2003), while the best male performance (i.e.,
EK, Berlin 2018) was run at a lower fraction of CS (94.7% ± 1.7%).
3.2. Speed Trend and Asymmetry Characteristics
EK (male athlete) achieved a large negative split race considering pace with a positive Kendall’s
τ (0.30; p = 0.007) and ran more of the average distance below average speed (Figure 1) (54%). By
contrast, there were no trends in previous and current marathon world records of BK and PR (female
athletes) (Figure 2). Their races were not optimal in regard to speed asymmetry as BK (66%) and PR
ran 46% of the distance above their average speed.
Int. J. Environ. Res. Public Health 2020, 17, x FOR PEER REVIEW 
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Table 1. Average marathon speed relative to male and female marathoners’ critical speed and 
coefficient of speed variation. 
  
  
  
Speed 
Critic
al 
Spee
d 
(km) 
Speed (% Critical 
Speed) 
Skewne
ss                                      
(% km 
below 
mean 
speed) 
Pace / Trend 
Athlete 
Place / Year 
Time 
Mean 
SD 
Variatio
n 
Coefficie
nt 
  
Mea
n 
SD 
Variatio
n 
Coeffici
ent 
  
Kendall'
s t 
p-
value 
E. 
Kipchoge 
London / 
2019 
2h02
min37
s 
20.67 
0.5
1 
2.48% 
21.6 
94.1 
2.3 
2.44% 
55 
-0.0289 
0.8000 
E. 
Kipchoge 
Berlin / 
2018 
2h01
min39
s 
20.78 
0.3
5 
1.68% 
21.6 
94.7 
1.7 
1.80% 
54 
0.3000 
0.0069 
P. 
Radcliffe 
London / 
2003 
2h15
min25
s 
18.89 
0.3
0 
1.59% 
19.6 
96.0 
4.4 
4.58% 
32 
0.0050 
0.7227 
B. Kosgei 
Chicago / 
2019 
2h14
min04
s 
18.82 
0.6
5 
3.45% 
19.29 
97.6 
3.4 
3.45% 
46 
0.0955 
0.4891 
Data are presented in means ± SD and percentages. 
3.2. Speed Trend and Asymmetry Characteristics 
EK (male athlete) achieved a large negative split race considering pace with a positive Kendall’s 
τ (0.30; p = 0.007) and ran more of the average distance below average speed (Figure 1) (54%). By 
contrast, there were no trends in previous and current marathon world records of BK and PR (female 
athletes) (Figure 2). Their races were not optimal in regard to speed asymmetry as BK (66%) and PR 
ran 46% of the distance above their average speed. 
Figure 1. Speed trend and asymmetry characteristics in the world’s fastest male marathoner. The 
curve (dotted line) represents the time course of Eliud Kipchoge’s running speed during the London 
marathon in 2019. The curve (dashed line) represents the time course of his running speed during the 
Berlin marathon in 2018. These curves represent the percentage of the mean speed achieved in each 
distance unit during the entire marathon. 
Figure 1. Speed trend and asymmetry characteristics in the world’s fastest male marathoner. The curve
(dotted line) represents the time course of Eliud Kipchoge’s running speed during the London marathon
in 2019. The curve (dashed line) represents the time course of his running speed during the Berlin
marathon in 2018. These curves represent the percentage of the mean speed achieved in each distance
unit during the entire marathon.
Int. J. Environ. Res. Public Health 2020, 17, 1177
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Int. J. Environ. Res. Public Health 2020, 17, x FOR PEER REVIEW 
4 of 6 
 
 
Figure 2. Speed trend and asymmetry characteristics in the world’s fastest female marathoners. The 
curve (solid line) represents the time course of running speed during the previous world record 
marathon reached by Paula Radcliffe during the London marathon in 2003. The curve (dotted line) 
represents the time course of running speed during the new world record reached by Brigid Kosgei 
during the Chicago marathon in 2019. These curves represent the percentage of the mean speed 
achieved in each distance unit during the entire marathon. 
4. Discussion 
To the best of our knowledge, this is the first study to compare the running strategy between the 
best male and female marathoners, based on a previous statistical analysis jointly using the trend and 
asymmetry of the race [6]. In this study, it was demonstrated that EK, PR, and BK (i) did not use the 
same running strategy and (ii) did not use the same fraction of their respective CS. Finally, EK 
achieved his two best performances using the same running signature on two different marathon 
routes (2 h 01 min 39 s in Berlin 2018, and 2 h 02 min 37 s in London 2019). 
This study demonstrated that females ran at a constant pace considering their Kendall’s τ was 
between −0.05 and 0.05 [6]. It was also highlighted that world records are broken using a running 
strategy based on running speeds below median speed, unlike popular marathoners who run more 
distance at speeds above the median [9]. This may be due to the fact that lower level runners (>2 h 20 
min) run at too high a target that they cannot maintain beyond the 26th km, where the average speed 
(i.e., final performance) is reduced and is therefore lower than the median speed. These results may 
ask questions of the perception of physiological load, the plan of action to produce speed variations 
(or not), and the strategy of the U-race, which is conducive to performance but which requires a high 
reserve of power. This latter point may imply training protocols based on running acceleration and 
deceleration [10]. Therefore, high intensity interval training using both positive and negative 
acceleration to attain VO2max at a wide range of speeds may allow an increase of endurance capacity 
and anaerobic power, which are required to achieve top performances in the marathon [11–13]. 
The present work also examined the newly established marathon world records (in 2019, for 
both EK and BK) using an assessment of the race speed asymmetry [6]. We also examined pacing 
variability and confirmed that this was run at and below 3% in marathons [14]. The speed coefficient 
of variation of EK was within 1.7%, indicating a relative pacing strategy. In addition, the asymmetry 
of the speed time series of the runners was also analyzed. Our results suggest the possibility of 
Figure 2. Speed trend and asymmetry characteristics in the world’s fastest female marathoners.
The curve (solid line) represents the time course of running speed during the previous world record
marathon reached by Paula Radcliﬀe during the London marathon in 2003. The curve (dotted line)
represents the time course of running speed during the new world record reached by Brigid Kosgei
during the Chicago marathon in 2019. These curves represent the percentage of the mean speed
achieved in each distance unit during the entire marathon.
4. Discussion
To the best of our knowledge, this is the ﬁrst study to compare the running strategy between the
best male and female marathoners, based on a previous statistical analysis jointly using the trend and
asymmetry of the race [6]. In this study, it was demonstrated that EK, PR, and BK (i) did not use the
same running strategy and (ii) did not use the same fraction of their respective CS. Finally, EK achieved
his two best performances using the same running signature on two diﬀerent marathon routes (2 h
01 min 39 s in Berlin 2018, and 2 h 02 min 37 s in London 2019).
This study demonstrated that females ran at a constant pace considering their Kendall’s τ was
between −0.05 and 0.05 [6]. It was also highlighted that world records are broken using a running
strategy based on running speeds below median speed, unlike popular marathoners who run more
distance at speeds above the median [9]. This may be due to the fact that lower level runners (>2 h
20 min) run at too high a target that they cannot maintain beyond the 26th km, where the average speed
(i.e., ﬁnal performance) is reduced and is therefore lower than the median speed. These results may
ask questions of the perception of physiological load, the plan of action to produce speed variations
(or not), and the strategy of the U-race, which is conducive to performance but which requires a
high reserve of power. This latter point may imply training protocols based on running acceleration
and deceleration [10]. Therefore, high intensity interval training using both positive and negative
acceleration to attain VO2max at a wide range of speeds may allow an increase of endurance capacity
and anaerobic power, which are required to achieve top performances in the marathon [11–13].
The present work also examined the newly established marathon world records (in 2019, for both
EK and BK) using an assessment of the race speed asymmetry [6]. We also examined pacing variability
and conﬁrmed that this was run at and below 3% in marathons [14]. The speed coeﬃcient of variation
of EK was within 1.7%, indicating a relative pacing strategy. In addition, the asymmetry of the speed
time series of the runners was also analyzed. Our results suggest the possibility of establishing a world
Int. J. Environ. Res. Public Health 2020, 17, 1177
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record (i.e., Berlin 2018) by running below the average pace, thanks to a very fast start and ﬁnish, in
the classical format of the marathon.
Finally, the marathon should not be a constant speed race [15] and new strategies of running must
be addressed to allow better performance in the future. As VO2max is not suﬃcient to distinguish
high level marathon runners (2 h 11 min–2 h 16 min) from elite marathon runners (less than 2 h
11 min) [16], this parameter may be used in parallel with average running speed and CS to propose a
new pacing strategy adapted to the level of marathoners. Indeed, this study highlighted that average
speed represents 94% of CS. The value is close to personal best one-hour record, meaning that the
runner might be able to double his time limit just by decreasing his speed by 5%. Finally, another way
of optimizing the running strategy might be the development of runners’ anaerobic capacity and their
ability to use a higher fraction of their CS during the marathon.
5. Practical Applications
-
A new training program based on athletes’ perception could be introduced to better adapt their
speed while running a marathon.
-
New training methods in marathon running could optimize the running strategy to allow the
marathoner to have a positive asymmetry and a lower coeﬃcient of variation of speed during
the race.
-
The CS is a crucial parameter that might be improved by new training methods since a high
fraction of the CS is achieved in both female and male marathon world records.
-
A performance target for coaches and athletes should be the maintenance of constant pace just
below average pace and at 95% of the CS.
6. Conclusions
Due to the already high fraction of CS achieved in marathons by females and also for the world’s
best performance by EK, this parameter and the average speed achieved in each km might be two
parameters to consider in elaborating a new running strategy to improve performance in marathon
and short events, as already reported [16]. In addition, optimizing the running strategy with positive
asymmetry and lower coeﬃcient of variation of speed might allow marathoners to run more slowly at
almost a constant pace, just below the average pace, and at 95% of CS in accordance with their higher
speed reserve. However, future research on other marathoners is necessary to conﬁrm diﬀerence in
running strategy between females and males and to verify consistency of running signature for a
single marathon.
Author Contributions: Conceptualization, D.V., V.B.; Methodology, D.V., J.R.P., V.B.; Software, M.C., F.P.;
Validation, D.V., V.B.; Formal Analysis, M.C., J.R.P.; Investigation, M.C., F.P.; Resources, V.B.; Data Curation, F.P.;
Writing—Original Draft Preparation, D.V., M.C., V.B.; Writing—Review & Editing, D.V.; Visualization, M.C., J.R.P.;
Supervision, D.V., V.B.; Project Administration, D.V., V.B. All authors have read and agreed to the published
version of the manuscript.
Funding: This research received no external funding.
Acknowledgments: The research team would like to thank our Australian, Eddy C., for his proofreading of
the manuscript.
Conﬂicts of Interest: The authors declare no conﬂict of interest.
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Race Analysis of the World's Best Female and Male Marathon Runners.
Billat, Véronique,Vitiello, Damien,Palacin, Florent,Correa, Matthieu,Pycke, Jean Renaud