International  Journal  of
Environmental Research
and Public Health
Review
Predictive Performance Models in Long-Distance
Runners: A Narrative Review
José Ramón Alvero-Cruz 1
, Elvis A. Carnero 2,3
, Manuel Avelino Giráldez García 4
,
Fernando Alacid 5
, Lorena Correas-Gómez 6
, Thomas Rosemann 7
,
Pantelis T. Nikolaidis 8,*
and Beat Knechtle 7
1
Faculty of Medicine, University of Málaga, Andalucía TECH, 29071 Málaga, Spain; alvero@uma.es
2
Translational Research Institute for Metabolism and Diabetes, Florida Hospital Sanford,
Orlando, FL 32804, USA; Elvis.AlvarezCarnero@adventhealth.com
3
Sanford Burnham Prebys Medical Discovery Institute, La Jolla, CA 92037, USA
4
Faculty of Sports Science and Physical Education, University of A Coruña, 15179 Oleiros, Spain;
manuel.avelino.giraldez.garcia@udc.es
5
Department of Education, Health Research Centre, University of Almería, 04120 Almería, Spain;
falacid@ual.es
6
Faculty of Education Sciences, University of Málaga, Andalucía TECH, 29071 Málaga, Spain; lcg@uma.es
7
Institute of Primary Care, University of Zurich, 8006 Zurich, Switzerland; thomas.rosemann@usz.ch (T.R.);
beat.knechtle@hispeed.ch (B.K.)
8
School of Health and Caring Sciences, University of West Attica, 12243 Athens, Greece
*
Correspondence: pnikolaidis@uniwa.gr; Tel.: +30-6977-8202-98
Received: 11 October 2020; Accepted: 6 November 2020; Published: 9 November 2020


Abstract: Physiological variables such as maximal oxygen uptake (VO2max), velocity at maximal
oxygen uptake (vVO2max), running economy (RE) and changes in lactate levels are considered the
main factors determining performance in long-distance races. The aim of this review was to present
the mathematical models available in the literature to estimate performance in the 5000 m, 10,000 m,
half-marathon and marathon events. Eighty-eight articles were identiﬁed, selections were made
based on the inclusion criteria and the full text of the articles were obtained. The articles were
reviewed and categorized according to demographic, anthropometric, exercise physiology and ﬁeld
test variables were also included by athletic specialty. A total of 58 studies were included, from 1983
to the present, distributed in the following categories: 12 in the 5000 m, 13 in the 10,000 m, 12 in
the half-marathon and 21 in the marathon. A total of 136 independent variables associated with
performance in long-distance races were considered, 43.4% of which pertained to variables derived
from the evaluation of aerobic metabolism, 26.5% to variables associated with training load and
20.6% to anthropometric variables, body composition and somatotype components. The most closely
associated variables in the prediction models for the half and full marathon specialties were the
variables obtained from the laboratory tests (VO2max, vVO2max), training variables (training pace,
training load) and anthropometric variables (fat mass, skinfolds). A large gap exists in predicting
time in long-distance races, based on ﬁeld tests. Physiological eﬀort assessments are almost exclusive
to shorter specialties (5000 m and 10,000 m). The predictor variables of the half-marathon are
mainly anthropometric, but with moderate coeﬃcients of determination. The variables of note in
the marathon category are fundamentally those associated with training and those derived from
physiological evaluation and anthropometric parameters.
Keywords: prediction equations; performance; long-distance runners
Int. J. Environ. Res. Public Health 2020, 17, 8289; doi:10.3390/ijerph17218289
www.mdpi.com/journal/ijerph
Int. J. Environ. Res. Public Health 2020, 17, 8289
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1. Introduction
The great popularity of long-distance running has seen an unprecedented increase in the
last 10 years.
This has generated, in coaches and athletes, a great interest in the development
of performance prediction models based on linear regression equations, with the aim of helping
many athletes in their preparation for competitions. These predictions are based on a combination
of physiological, anthropometric, nutritional and training factors (modifying frequency, volume
and intensity), most obtained in exercise physiology laboratories, through variables related to
training load [1,2].
Performance in long-distance disciplines can be deﬁned as the ﬁnal time or race time, and its
understanding is important both for designing training programs and for determining scheduled
training and race pace. However, accurate knowledge is frequently diﬃcult to obtain, especially
in long-distance races, as it would involve high training loads, which can, at times, indicate poor
race planning in inexperienced runners who normally use polarized training methods [3]. This and
other factors associated with the control of training, result in predictive models being recognized and
useful for coaches or professional runners. The physiological adaptations produced by training in
amateur runners are well understood and are generally those performed at submaximal intensities with
continuous training strategies [4]. In high-level athletes, these improvements are seen particularly with
tempo runs and short-interval training, as methods to improve performance [5]. Therefore, transferring
the results and conclusions obtained from amateur athletes to high-level athletes is not advisable [6].
Performance in endurance running is inﬂuenced by a variety of factors, both anthropometric
and training. Morphological (somatotype components) and anthropometric characteristics such as
skinfolds, body fat percentage, circumferences, lower limb length, weight, height and body mass
index appear to inﬂuence performance. Accordingly, certain characteristics have a better relationship
between energy expenditure and performance [7,8].
There are numerous studies on physiological factors in the literature on performance prediction
in long-distance runners. Classically, maximal oxygen uptake (VO2max), running economy (RE) and
anaerobic threshold (AT) stand out as the main variables that have been used to predict performance
in long-distance races [9,10], but a large gap exists in the ﬁeld of performance prediction based on
ﬁeld tests.
The aim of this narrative review was to undertake a descriptive, analytical and detailed analysis
of the determinants and predictive ability of anthropometric, physiological (laboratory test), training
and combined variables, as well as ﬁeld assessments (ﬁeld tests), to estimate performance in specialties
of long-distance races (5000 m, 10,000 m, half–marathon and marathon).
2. Materials and Methods
This document is classiﬁed as a narrative review and was carried out under a framework of
assigning key attributes based on Search, Appraisal, Synthesis and Analysis (SALSA) [11]. Accordingly,
the search was exhaustive. The synthesis is a tabular exposition of the data and the analysis may be
chronological, conceptual or thematic [11]. In general terms, this narrative review presents all the
known published works that include runners of diﬀerent levels: all of these in diﬀerent types of runner
(amateur, moderately trained, highly trained, high-level and elite) with the common denominator
that they are generally trained both in length of time and number of weekly sessions. Also included
are all studies that found associations between anthropometric and physiological parameters and
performance in the middle-distance (5000 m and 10,000 m) and long-distance (half-marathon and
marathon) events.
2.1. Search
The abstracts of original English articles registered in the Pubmed, SciELO (Scientiﬁc Electronic
Library On line), ScienceDirect and SportDiscus databases were reviewed. The terms entered in the
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search engines were as follows: “runners”, “long distance runners”, “performance”, “performance
prediction”, “anthropometric”, “physiological determinants”, “performance determinants”, “5000 m”,
“10,000 m”, “half-marathon” and “marathon”, as well as the combinations of all of them, depending on
the specialty examined.
2.2. Selection Criteria
The selection criteria were all relevant articles, as well as books and monographs. The ﬁrst
evaluation consisted of reading the abstract and the full text of the selected studies, followed by an
analysis of the results.
2.3. Exclusion Criteria
Case studies, duplicate articles and abstracts without clear and suﬃcient information
were excluded.
3. Results
The ﬂow chart (Figure 1) shows the ﬁnal selection of 58 articles, with 12 articles identiﬁed for the
5000 m modality, 13 for the 10,000 m, 12 for the half-marathon and 21 for the marathon.
Int. J. Environ. Res. Public Health 2020 16, x 
3 of 21 
 
m”, “10,000 m”, “half-marathon” and “marathon”, as well as the combinations of all of them, 
depending on the specialty examined. 
2.2. Selection Criteria 
The selection criteria were all relevant articles, as well as books and monographs. The first 
evaluation consisted of reading the abstract and the full text of the selected studies, followed by an 
analysis of the results. 
2.3. Exclusion Criteria 
Case studies, duplicate articles and abstracts without clear and sufficient information were 
excluded. 
3. Results 
The flow chart (Figure 1) shows the final selection of 58 articles, with 12 articles identified for 
the 5000 m modality, 13 for the 10,000 m, 12 for the half-marathon and 21 for the marathon. 
 
Figure 1. Diagram of study search and selection process. 
In Table 1, the variables are grouped as demographic, laboratory assessments, field test, training, 
anthropometric and others. 
Table 1. Partial and total figures for performance prediction variables in long-distance specialties. 
 
Long-Distance Specialties 
 
 
Variables 
5000 m 
10,000 m 
HM 
M 
Total 
% of Total 
Demographic 
4 
1 
1 
1 
7 
5.1 
Aerobic Metabolism 
26 
14 
3 
16 
59 
43.4 
Training 
1 
5 
2 
28 
36 
26.5 
Anthropometry 
2 
5 
16 
5 
28 
20.6 
Field test 
0 
1 
2 
0 
3 
1.47 
Others 
0 
1 
0 
3 
4 
2.94 
Figure 1. Diagram of study search and selection process.
In Table 1, the variables are grouped as demographic, laboratory assessments, ﬁeld test, training,
anthropometric and others.
Table 1. Partial and total ﬁgures for performance prediction variables in long-distance specialties.
Long-Distance Specialties
Variables
5000 m
10,000 m
HM
M
Total
% of Total
Demographic
4
1
1
1
7
5.1
Aerobic Metabolism
26
14
3
16
59
43.4
Training
1
5
2
28
36
26.5
Anthropometry
2
5
16
5
28
20.6
Field test
0
1
2
0
3
1.47
Others
0
1
0
3
4
2.94
Subtotals/Total
33
27
24
51
137
100
HM: Half-marathon, M: Marathon.
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3.1. Demographic Variables
Of the seven demographic variables, the most notable is age, which is included in all the specialties
studied. Gender is only recorded in the 5000 m specialty [12].
3.2. Aerobic Metabolism Assessment Variables
In this section, the variables were classiﬁed into two groups:
1. Maximum range (VO2max, velocity at maximal oxygen uptake [vVO2max], maximum heart
rate, maximum lactate, vVO2 with the University of Montreal Track Test, anaerobic capacity and
oxygen deﬁcit, etc.).
2. Submaximal range (VO2 at lactate threshold, lactate threshold, velocity at lactate levels of
2.5–3 and 4 mmol/L, RE, heart rate at individual anaerobic threshold (IAT), velocity at heart rate
deﬂection point, VO2 and % VO2 at AT, velocity at AT, lactate level at AT and % of peak velocity at AT).
Of particular note are vVO2max and VO2max, RE, understood as oxygen uptake at speciﬁc velocity,
VO2 at AT and velocity at the level of 4 mmol/L lactate. Thirty-one of these studies include mL/kg/min
among the variables that are associated with or are predictive factors of running performance from
middle to long distance. Additionally, 24 studies include variables such as km/h, m/min, m/s associated
with conditions obtained at VT2 (anaerobic threshold), velocity at heart rate deﬂection, IAT, ATLab (AT
in laboratory test), etc.
3.3. Training Variables
The training variables were grouped into two categories: quantitative (mean race duration,
number of training sessions per week, miles per week, km per week, training volume, miles in 8 weeks,
training in 9 weeks, years of training) and qualitative (training pace, record for 1 mile, 5 miles, 10 miles,
half-marathon time and having ﬁnished a marathon).
3.4. Field Test Variables
Only two studies measuring AT using the University of Montreal Track test [13], and covered
distance in the Cooper test [14,15]
3.5. Anthropometric Variables
These variables are classiﬁed into three categories: (i) basic measurements (height, weight,
body mass index, skinfolds and muscle circumferences), (ii) body composition fractions (fat mass,
fat-free mass and skeletal muscle mass) and (iii) somatotype components (endomorphy, mesomorphy
and ectomorphy). Other important performance-related variables are body mass index, fat mass
percentage, and skinfolds as regional indicators of adiposity associated with performance. Fifteen of
the 26 studies were conducted in the half-marathon specialty by Knechtle’s research group [8,16,17].
3.6. Other Variables
Noteworthy are also the use of a biochemical variable such as transferrin levels, as well as a model
based on data collection through a post-competition survey [14] and leg volume and heart rate changes
during the Ruﬃer test recovery period [15].
3.7. Data Management and Presentation
Tables 2–5 are individual tables for each distance (5000 m, 10,000 m) and long-distance specialty
(half-marathon and marathon) respectively and structured to display: Author, year of publication, sex,
number of participants, athletic level, dependent variable, independent variable(s) associated with
performance (correlation coeﬃcient, p-value) or if the independent variables comprise a signiﬁcant
model (equation): the coeﬃcient of determination (R2) and the standard error of the estimate (SEE),
the limits of agreement of the Bland–Altman plot (only in half-marathon) and the predictive equation.
Int. J. Environ. Res. Public Health 2020, 17, 8289
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Table 2. Multiple regression models associated with performance in 5000 m races.
Author
Year
Sex
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
Foster
1983
1
28
Well-trained
3 Miles
VO2max
−0.92
Training volume
Intensity
Tanaka
1984
1
21
Trained
5000 m
vVO2max
0.78
<0.001
0.62
nr
Ramsbottom
1987
1
55
University
VO2max
5000 m
−0.85
<0.01
0
43
5000 m
−0.80
<0.01
1987
1
55
University
5000 m
RE
0.39
<0.01
0
43
RE
0.34
<0.05
Fay
1989
0
13
Mod-Highly
5000 m (m/min)
Vlact 4 mMol/L (m/min)
0.94
0.940–0.97
nr
VO2max (ml/kg/min)
Oxygen cost of running
−0.4–(−0.63)
Velocity (m/min) = 0.346 (vLac 4 mMol/L) + 1.899 (VO2max)
Kenney
1985
1
8
Elite
5000 (time in sec)
Age + VT2 (mL/kg/min)
<0.02
0.98
nr
Time (sec) = 11555 − 5.1 (age) − 2.9 (VT2)
Weyand
1994
1–0
22–19
Competitive
5000 m
Peak O2 Def (POD)
−0.4
VO2max
High
%VO2 AT
RE at 3.6 m/s
Gender (1 = male; 2 = female)
Specialty
Time (sec) = 0.38 (POD) − 1.29 (VO2max) + 1.25 AT(%VO2)
+ 4.42 (RE) + 55.9 (Gender) − 47.4 (specialty)
(1 sprinter, 2 long-distance runner) + 1664.9
nr
nr
Takeshima
1995
1
51
Popular
5000 m (m/s)
VO2 LT (ml/kg/min)
0.87
Age
ARD
0.89
VO2 LT (ml/kg/min)
0.79
Age
VO2 LT (ml/kg/min)
0.82
Age
ARD
Velocity (m/s) = 4.436 + 0.045 (VO2 LT) − 0.033 (Age) + 0.005 (ARD)
0.89
0.27
Int. J. Environ. Res. Public Health 2020, 17, 8289
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Table 2. Cont.
Author
Year
Sex
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
Roecker
1998
1–0
339–88
Competitive
5000 m (m/s)
vPeak (km/h)
0.91
<0.001
0.940–0.97
IAT (m/s)
0.91
% Fat Mass
nr
MHR (bpm)
Max Lact (mMol/L)
Velocity (m/s) = 3.404 + 0.683 (vPeak) + 0.274 (IAT) − 0.05 (%FM)
(MHR) − 0.079 (Max Lact)
Nummela
2006
1
18
Well-trained
Velocity (m/s)
VO2max
0.55
<0.05
MART
Vel (m/s) = 0.066 (VO2max) + 0.048 (MART) − 0.549
0.728
nr
Stratton
2009
1–0
17–22
Untrained
5000 m (km/h)
VO2 max (ml/kg/min)
0.55
<0.01
V LT (km/h)
0.73
<0.01
V Max (km/h)
0.89
<0.01
Run velocity (km/h) = −1.124 + 0.514 (Vmax) + 0.267 (V LT)
0.812
2009
1–0
17–22
Trained
5000 m (km/h)
VO2 max (ml/kg/min)
0.51
<0.01
V LT (km/h)
0.76
<0.01
V Max (km/h)
0.83
<0.01
Run velocity (km/h) = −2.629 + 0.546 (Vmax) + 0.345 (V LT)
0.738
Mendes de
Souza
2014
1
10
5000 m
vVO2 max Lab
0.05
0.35
nr
1
10
5000 m
vVO2 max Montreal
0.002
0.66
nr
Dellagrana
2015
1
23
Moderately
trained
5000 (time)
vVT (km/h)
−0.64
0.001
RE at 11.2 km/h (L/min)
0.44
0.035
Fat-free mass (kg)
0.57
<0.005
5 km T (min) = 25.64 − 0.71 (vVT) − 3.38 (RE 11.2) + 0.21 (FFM)
0.71
0.67
r: correlation coeﬃcient; p: signiﬁcance level; R2: coeﬃcient of determination; SEE: standard error of estimation; vVO2max: max velocity in VO2max; RE: running economy; VLact4: velocity
at 4mMol/L; AT: anaerobic threshold; POD: peak oxygen deﬁcit; LT: lactate threshold; ARD: average running duration; IAT: individual anaerobic; threshold; MHR: maximal heart rate;
Max Lact: maximal lactate; MART: maximal anaerobic running test; vVO2maxLab: maximal velocity at exercise laboratory test: vVO2max Montreal: maximal velocity on Montreal ﬁeld
test. vVT: velocity at ventilatory threshold.
Int. J. Environ. Res. Public Health 2020, 17, 8289
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Table 3. Multiple regression models associated with performance in 10,000 m races.
Author
Year
Sex
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
Foster
1983
1
17
Well-trained
3 Miles
VO2 max
−0.94
Training volume
Intensity
Tanaka
1984
1
21
Trained
10,000 m
vVO2 max
0.96
nr
1
21
Trained
10,000 m
vAT (ml/kg/min)
0.80
<0.001
Bale
1986
1
60
Elite & Good
Time 10,000 m
Workouts (WO)per week
−0.87
0.75
2.28
Time (min) = 44.27 − 1.44 (WO)
WO + Miles (MW) per
week
−0.84
Time (min) = 46.32 − 0.91 (WO) − 0.11 (MW)
0.8
2.08
WO + MW + Running
years (RY)
−0.80
Time (min) = 46.45 −0.68 (WO) − 0.11 (MW) − 0.38 (RY)
0.83
1.92
WO + MW + RY +
Ectomorphy
−0.40
Time (min) = 47.93 − 0.68 (WO) − 0.10 (MW) – 0.38 (RY) − 0.68 (Ectomorphy)
0.86
1.78
Brandon
1987
Middle
10,000 (m/s)
VO2max (ml/kg/min)
Anaerobic Capacity (AC)
Height (cm)
10,000 (m/s) = 127.39 + 0.64 (VO2) + 0.21 (AC) + 0.4 (Height)
Fay
1989
0
13
Moderate
10,000 m (m/min)
Vlact 4 mmol/L(m/min)
0.840–0.94
High
VO2max (ml/kg/min)
Vlact 2 mmol/L(m/min)
10,000 (m/min) = 0.437 (vLA 4 mmol/L) + 2.082 (VO2max) + 8.698
10000 (m/min) = 0.728 (vLac 4 mmol/L) + 57.926
10,000 (m/min) = 0.407 (vLac 2 mmol/L) + 2.276 (VO2max) + 12.706
Morgan
1989
1
10
Well-trained
Time (min)
VO2max
−0.45
>0.05
vVO2max
−0.87
<0.01
Vel at 4 mmol/L
−0.82
<0.01
RE
0.64
<0.05
Int. J. Environ. Res. Public Health 2020, 17, 8289
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Table 3. Cont.
Author
Year
Sex
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
Petit
1997
1
15
Trained
Vel Ventilatory threshold
0.95
0.96
Vel HR def (km/h)
10,000 (km/h) = 1.03 (Vel Deﬂection HR)
Berg
1998
1
34
Mod trained
Time 10,000 m
BMI and Mesomorphy
0.61
0.38
7.3
10,000 (min) = 4.12 (BMI) − 4.5 (Mesomorphy) − 29.1
0
19
Mod trained
Time 10,000 m
Endomorphy
0.64
0.41
6.5
10,000 (min) = 37 + 3.3 (Endomorphy)
Evans
1995
0
31
Highly
trained
10,000 Pace (m/min)
VO2max
0.89
0.05
0.8
Lac Threshold
0.89
0.05
0.8
VO2 (ml/kg FFM/min)
0.81
0.05
0.66
VO2 in LT
0.84
0.05
0.71
Takeshima
1995
1
51
Trained
10,000 vel (m/s)
VO2 in LT (ml/kg/min)
0.78
0.62
nr
Age
VO2 in LT
0.81
0.67
Age
nr
Workout (min)
10,000 (m/s) = 4.371 + 0.037 (VO2 in LT) − 0.031 (Age) + 0.005 (Workout)
0.82
0.335
r: correlation coeﬃcient; p: signiﬁcance level; R2: coeﬃcient of determination; SEE: standard error of the estimate; VO2max: maximal oxygen uptake; vVO2max: velocity at VO2max;
WO: workouts; vAT: velocity at anaerobic threshold; Lact 4: velocity at 4 mmol/L; vLact 2: velocity at 2 mmol/L; RE: running economy; vHR def: velocity at heart rate deﬂection; BMI: body
mass index; FFM: fat-free mass; LT: lactate threshold; AT: anaerobic threshold; IAT: individual anaerobic threshold; HR: heart rate; Max Lact: maximal lactate; SK: skinfold.
Int. J. Environ. Res. Public Health 2020, 17, 8289
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Table 4. Multiple regression models associated with performance in half-marathon races.
Author
Year
Sex
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
L LOA
to
U LOA
Campbell
1985
1–0
88–10
Finishers
Running Speed (km/h)
Age
Height
0.18
ns
Pulse rate 1 (PR1)
−0.53
Pulse rate 2 (PR2)
−0.35
km/week (K)
0.53
<0.01
Training weeks (NW)
0.4
<0.01
BMI
−0.41
<0.01
Running Speed (km/h) = 21.3 +0.028 (K) − 0.31 (BMI) − 0.037 (PR2) + 0.012 (NW)
0.47
nr
Roecker
1998
1–0
339–88
Competitive
IAT
0.93
<0.001
Running vel at 4 mmol/L
0.91
<0.001
vVO2max
0.89
<0.001
Rüst
2011
1
84
Recreational
Race time
BMI
0.56
0.01
Skinfolds
0.360–0.53
0.005
Percent fat mass
0.49
0.01
Race time = 72.91 + 3.045 (BMI) − 3.884 (SRT)
0.44
nr
−25.1
to
25.1
Knechtle
2011
0
42
Recreational
Race time
Skinfolds
0.490–0.61
<0.001
Race time = 166.7 + 1.7 (mid axilla SK) − 6.4 (SRT)
0.71
nr
nr
nr
Muñoz
2013
1
24
Vel (km/h)
Velocity 2 at 14.6 ± 2.6 km/h
Blood Lactate at velocity 2
0.97
0.414
Vel Half-marathon (km/h) = V2 * 1.085 + (BLa2 * −0.282) − 0.131
nr
Friedrich
2014
0
83
Recreational
Race time
Weight
0.63
<0.0001
Height
0.27
0.01
BMI
0.57
<0.0001
Circumferences
0.510–0.55
<0.0001
Skinfolds
0.390–0.59
<0.0001
Skeletal Muscle mass
0.24
0.03
Fat mass
0.6
<0.0001
Friedrich
2014
1
147
Popular
Race time
Weight
0.27
0.0009
Height
−0.17
0.04
BMI
0.46
<0.0001
Arm circumference
0.37
<0.0001
Skinfolds
0.290–0.43
<0.0001
Skeletal Muscle mass
−0.07
>0.05
Fat mass
0.49
<0.0001
Int. J. Environ. Res. Public Health 2020, 17, 8289
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Table 4. Cont.
Author
Year
Sex
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
L LOA
to
U LOA
Knechtle
2014
1
147
Recreational
Race time (min)
Percent fat mass
SRT (km/h)
Race time (min) = 142.7 + 1.158 (%FM) − 5.223 (SRT)
0.42
13.3
−26
to
25.8
Knechtle
2014
0
83
Recreational
Race time (min)
Percent fat mass
SRT (km/h)
Race time (min) = 168.7 + 1.077 (%FM) − 7.556 (SRT)
0.68
9.8
−19
to
19.1
Gómez
2017
1
48
Recreational
Race time (min)
Week training (km) WT
−0.75
< 0.05
Running experience (years) RE
−0.80
< 0.05
BMI
0.64
< 0.05
Sum 6 Skinfolds (mm)
0.78
< 0.05
Race time (min) = 56.83 − 0.11 WT − 0.46 RE + 1.19 BMI + 0.16 Sum6SKF
0.82
nr
−9.2
to
12.2
2017
1
48
Recreational
Race time (min)
Peak speed (km/h)
−0.92
< 0.05
RCT (km/h)
−0.92
< 0.05
Race time (min) = 180.86 − 2.81 Peak speed − 2.77 RCT
0.90
nr
−6.7
to
6.4
2017
1
48
Recreational
Race time (min)
RCT Step rate (Hz)
−0.38
< 0.05
RCT Step length (m)
−0.87
< 0.05
Maximal step length (m)
−0.73
< 0.05
Race time (min) = 271.9 − 33.38 RCTsr − 28.38 RCTsl − 29.8 Msl
0.88
nr
−9.7
to
5.7
2017
1
48
Recreational
Race time (min)
Peak speed (km/h)
−0.92
< 0.05
RCT (km/h)
−0.92
< 0.05
Running Experience (years)
−0.75
< 0.05
Race time (min) = 169.54 − 2.51 Peak speed − 2.25 RCT − 0.37 RE
0.93
nr
−6.7
to
6.0
Alvero-Cruz
2019
1
23
Recreational
Race time (min)
Cooper test (m)
−0.92
<0.0001
Race time (min) = 201.26 − 0.03433 Cooper (m)
0.873
3.78
−7.5
to
7.4
2019
1
23
Recreational
Race time (min)
vVO2max (km/h)
−0.85
< 0.0001
Weight (kg)
0.4
0.04
Race time (min) = 156.7117 − 4.7194 vVO2max − 0.3435 Weight
0.769
5.28
9.5
to
9.7
Alvero-Cruz
2020
1
177
Recreational
Race time (min)
Cooper test (m)
−0.906
<0.0001
0
21
Recreational
Race time (min) = 205.6272 − 0.0356 Cooper (m)
0.82
5.19
−10.7
to
9.7
r: correlation coeﬃcient; p: signiﬁcance level; R2: coeﬃcient of determination; SEE: standard error of the estimate; L: Low; U: Upper, LOA: limits of agreement; nr: no reported; BMI: body
mass index; IAT: individual anaerobic threshold; vVO2max: velocity at VO2max; SRT: speed running time.
Int. J. Environ. Res. Public Health 2020, 17, 8289
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Table 5. Multiple regression models associated with performance in marathon races.
Author
Year
Sex (M/F)
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
Foster
1975
Race Time (min)
VO2max(ml/kg/min)
Time (min) = 3.45 (VO2max) + 387.3
nr
nr
Foster
1975
Race Time (min)
VO2max
Training longer in last 8 w
Pace (seconds/mile)
Time (min) = 2.75 (VO2max) − 0.022 (miles 8w) − 1 (TL8w) + 0.146 (pace) + 319.4
nr
nr
Slovic
1977
Race Time (min)
Best record in mile (min) (BR1)
Best record in 5 miles (min)
(BR5)
Best record in 10 miles
(min)(BR10)
Miles in last 8 weeks
Finisher of one marathon
Training longer in last 8 w
Time (min) = 0.45 (BR1min) − 7.9 (Finisher) − 0.08(Miles 8w) − 1.45 (TL8w(min) + 116.5
nr
nr
Slovic
1977
Race Time (min)
Best record in 5 miles (min)
(BR5)
Miles in last 8 weeks
Training longer in last 8 w
Time (min) = 6.62 (BR 5min) − 0.05(Miles 8w) − 1.45 (TL8w(min)) + 42.8
nr
nr
Slovic
1977
Race Time (min)
Best record in 10 miles
(min)(BR10)
Miles in last 8 weeks
Training longer in last 8 w
Time (min) = 2.98 (BR 10 (min) − 0.04(Miles 8w) − 1.3 (TL8w(min) + 46.6
nr
nr
Davis
1979
Race Time (min)
VO2max(ml/kg/min)
%VO2 in AT
Time (h) = 7.445 − 0.0338 (VO2max) − 0.0303 (%VO2)
0.99
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Table 5. Cont.
Author
Year
Sex (M/F)
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
Hagan
1981
1
50
Trained
Race Time (min)
VO2max
−0.63
Avg km WO in last 9 weeks
−0.64
total km
−0.67
overall WO in last 9 weeks
−0.62
Mean pace (m/min)
Time (min) = 525.9 + 7.09 km (kmWO) − 0.45 (WO speed m/min) − 0.17 (km 9 weeks)
0.71
−2.01 (VO2max, ml x kg−1 x min−1) − 1.24 (age, year)
Foster
1983
1
25
Well-trained
26.2 miles
VO2max
−0.95
Training volume
Intensity
Bale
1985
0
36
Trained
Race Time (min)
workouts/week
Time (min) = −4.42 (WO per week) + 218.5
nr
nr
1985
0
36
Trained
Race Time (min)
workouts/week
Ectomorphy
Time (min) = −3.72 (WO per week) − 7.02 (Ectomorphy) + 242.6
nr
nr
1985
0
36
Trained
Race Time (min)
workouts/week
Ectomorphy
training years (TY)
Time (min) = −3.32 (WO per week) − 6.05 (Ectomorphy) − 0.85 (TY) + 240.6
nr
nr
Hagan
1987
0
35
Combined
Race Time (min)
Mean km/day
0.77
<0.001
0.59
Training pace (m/min)
0.66
<0.001
0.44
Race Time = 449.88 − 7.61 (Mean km/day) − 0.63 (Training pace m/min)
0.82
nr
0.68
18.4
0
16
Experienced
Race Time (min)
BMI
0.7
nr
0.49
Training pace (m/min)
0.78
<0.001
0.61
Race Time = 214.24 + 393.07 (BMI) − 0.68 (training pace m/min)
0.87
nr
0.76
12.4
0
19
Novice
Race Time (min)
BMI
0.31
ns
0.1
Race Time = 369.58 − 10.1 (Mean km/day)
0..69
nr
0.48
22.2
Föhrenbach
1987
1–0
34
Race Time (min)
Mean km last 9 weeks
vLact 2,5 (m/s)
0.880–0.99
<0.001
vLact 3 (m/s)
vLact 4 (m/s)
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Table 5. Cont.
Author
Year
Sex (M/F)
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
Noakes
1990
1
20
Race Time (min)
Time in Half-M (THM)
Lact AT (mmol/L)
% peak Vel in AT (lact)
−0.88
Time (min = 1.98 (THM) + 6.23 AT (mmol/L) − 0.46 AT % vPeak mmol/L + 33.84
Time (min) = 1.94 (THM) + 5.8 AT (mmol/L) − 0.44 AT % vPeak mmol/L + 0.39 RE at 16 km/h + 16.79
Time (min) = 1.29 % vPeak mmol/L − 10.86 vLT (km/h) + 241.3
Time (min) = −4.92 vLT (km/h) − 4.46 vPeak (km/h) + 337.8
Noakes
1990
1
20
Race Time (min)
Time in Half-M
Lact AnT (mmol/L)
% peak Vel i nAT (lact)
VO2 at 16 km/h
0.760–0.9
Race Time (min)
Lact AnT (mmol/L)
% peak Vel in AT (lact)
Race Time (min)
Vel in AnT by lact in km/h
vVO2max (km/h)
Takeshima
1995
1
51
Popular
Mean Velocity (m/s)
VO2 LT (ml/kg/min)
Age
Mean Duration Workouts (min)
Mean Vel (m/s) = 0.038 (VO2 LT) − 0.031 (Age) + 0.005 (MDWO) + 3.707
0.93
0.199
Roecker
1998
1–0
339–88
Competitive
Mean Velocity (m/s)
vIAT (m/s)
0.93
<0.001
0.950–0.97
vVO2max (km/h)
0.87
<0.001
MHR
Weight
Mean Vel (m/s) = 0.546 (vIAT) + 0.293 (vVO2max) + 0.013 (km/week) − 0.0155 (MHR) − 0.0253 (Weight) + 3.4
Arrese
2006
0
8
Highly
trained
Race Time
Iliac crest SK
0.76
<0.05
Abdominal SK
0.76
<0.05
Subscapular SK
0.78
<0.05
Serum ferritin (µg/L)
−0.76
<0.05
Race Time = 7658.331 + 55.519 (Subscapular SK) − 4.834 (ferritin) + 34.895 (Sum 6 SK)
0.992
<0.001
2006
1
10
Highly
trained
Race Time
Left ventricular diameter (LVD)
−0.68
<0.05
Lactate at 10 km/h
0.91
<0.001
Lactate at 22 km/h
Race Time = 8408.623 (lact 10 km/h) − 18.255 (LVD) + 22.522 (lact 22 km/h)
0.991
<0.001
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Table 5. Cont.
Author
Year
Sex (M/F)
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
Tanda
2011
1–0
21–ene
Trained
Pace (sec/km)
K (km/week)
0.94
0.81
Pace (P) (sec/km)
0.85
Pace (sec/km) = 17.1 + 140 exp [–0.0053 K] + 0.55 (Pace)
0.81
5.77
Muñoz
2013
1
24
Vel (km/h)
Velocity 1 at 13,5 ± 0,9 km/h
(V1)
Blood Lactate at velocity 1
0.81
0.626
Vel Marathon (km/h) = V1 1.085 + (BLa2 − 0.429) − 0.170
Tanda
2013
1
126
Recreational
Pace (sec/km)
Km week
Pace training (sec/km)
Percent body fat
Pace (sec/km) = 11.03 + 98.46 exp [−0.0053 Km week] + 0.387 (Pace) + 0.1 exp [0.23 %BF]
0.81
0.64
14.3
Mooses
2013
1
20
International
IAAF scoring
Total time on treadmill
(TtT)(sec)
0.40
66.2
IAFF score = 162.30 + 0.41 (TtT)
Till
2016
1–0
40
Recreational
Race Time (min)
treadmill time (min)
Time (min) = −3.85 (treadmill time) +351.57
0.447
Salinero
2017
1
84
Amateur
Time (min)
% Body fat (%BF)
0.42
<0.001
∆ Recovery Ruﬃer test (RT)
0.37
<0.000
Half-marathon performance
(HMP)
0.81
<0.001
Time (min) = 96.1 + 2.3 (%BF) + 62.9 (RT) + 0.023 (HMP)
0.59
nr
Time (min)
% Body fat (%BF)
0.42
<0.001
∆ Recovery Ruﬃer test (RT)
0.37
<0.000
10 km performance (10 km P)
0.73
<0.001
Time (min) = 104.3 + 3.1 (%BF) + 67.3 (RT) + 0.045 (10 km P)
0.53
nr
Esteve-Lanao
2019
1–0
8–8
Recreational
Avg speed 42k (km/h)
116 days before = AnT
0.810–0.94
<0.05
Speed 42k (km/h) = SpeedAnT (km/h) 0.771 + 0.959
0.659
nr
88 days before = AnT
Speed 42k (km/h) = SpeedAnT (km/h) 0.863 − 1.463
0.714
nr
60 days before = AnT
Speed 42k (km/h) = SpeedAnT (km/h) 1.013 − 0.944
0.76
nr
32 days before = AeT
Speed 42k (km/h) = SpeedAeT (km/h) 1.012 − 1.147
0.804
nr
11 days before = AeT
Speed 42k (km/h) = SpeedAeT (km/h) 1.004 − 1.145
0.85
nr
Int. J. Environ. Res. Public Health 2020, 17, 8289
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Table 5. Cont.
Author
Year
Sex (M/F)
n
Level
Dependent Variable
Independent Variable
r
p
R2
SEE
Keogh
2020
1–0
157–103
Recreational
Time (min)
Age
BMI
Marathon experience (ME)
Predicted ﬁnish time (PFT)
Diﬀ pred vs. ﬁnish time (DPvF)
Pace St deviation
Sex
Time (min) = −5.252 + 0.162 Age + 0.319 BMI + 0.451 ME + 0.947 PFT − 0.636 (DPvF) + 2.925 Pace − 3.232 Sex
0.858
nr
r: correlation coeﬃcient; p: signiﬁcance level; R2: coeﬃcient of determination; SEE: standard error of estimation; VO2max: Maximal oxygen uptake; %VO2AT: percentage of VO2max at
anaer. threshold; Avg km WO: average km of workouts; BMI: body mass index; vLact 2.5: velocity in m/s at 2.5 mmol/L; vLact 3: velocity in m/s at 3 mmol/L; vLact 4: velocity in m/s at
4 mmol/L; AnT: anaerobic threshold; MHR: maximal heart rate; vVO2max: velocity at VO2max; LVD: left ventricular diameter.
Int. J. Environ. Res. Public Health 2020, 17, 8289
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The tables present two types of study: those without a prediction equation in which they provide
the correlations between the independent variables and the dependent variable (correlation coeﬃcient
and p-value. The studies including a prediction equation are shown in the tables with the R2 value
and the SEE. In Table 4 only, corresponding to the studies on the half-marathon, a further section is
included, pertaining to the information on bias between the predicted and the actual time, with the
limits of agreement derived from the studies by Knechtle’s [8,18,19] and other authors [14,15,20,21].
Finally, the studies with a prediction equation are presented in a highlighted text box
3.8. Variables and Models Associated with the 5000 m Event
Search: The diﬀerent keywords were combined as follows: “performance, performance prediction”,
“performance determinants”, “anthropometric and physiological determinants”, “5000 m”, “5 km”.
Appraisal: The subjects of the diﬀerent studies were generally moderately trained or highly trained
athletes of diﬀerent athletic levels (amateur, collegiate, competitive, elite), except for the study by
Stratton which includes untrained individuals [22]. Of all the studies, only a few provide coeﬃcients
for determining the independent variable [13,23–27]. The coeﬃcients of determination ranged from
0.62 to 0.98, but none of the studies reported the standard error. Additionally, the study by Stratton has
an external validation study in a subsample of subjects [22].
Synthesis: It should be noted that in all the studies, the variables most used for performance
prediction are derived from determinations of aerobic metabolism. In one study the variable is the
percentage of fat mass measured by anthropometry [28] and in another the fat-free mass [29]. Only one
study was conducted in which the velocity at VO2max in the University of Montreal Track Test, as a
ﬁeld variable, is presented as a predictor variable [13].
Analysis: Table 2 presents 12 studies from 1983 to 2015 [12,13,22–26,28–32]. The most notable
are the physiological variables such as VO2max [12,23,25,32] and vVO2max, [13,22,28,31] and RE
measurements [12,29,30,33].
Only one study examines training variables [26]. The most important anthropometric variables are
the inclusion of body composition fractions (fat mass and fat-free mass). Of the 12 studies, eight include
a prediction equation [12,22–26,28,29] (Table 2).
3.9. Variables and Models Associated with the 10,000 m Event
Search: The diﬀerent keywords were combined as follows: “performance, performance prediction,”
“anthropometric and physiological determinants,” “performance determinants,” “10,000 m,” “10 km”.
Appraisal: The subjects of the diﬀerent studies were generally trained athletes of diﬀerent
levels (amateur, competitive, elite) with the exception of the studies by Brandon [34] and Berg [35],
which included only moderately trained individuals.
Synthesis: In all the studies, the variables most used for prediction continue to be those derived
from laboratory tests.
Furthermore, these variables increase compared to the 5000 m specialty.
New variables include those from training data, such as number of training sessions, miles per
week and years of training [7]. In addition, anthropometric variables such as skinfolds [36] and
two somatotype components are beginning to be included [35] although these equations have a
low-moderate R2 (0.380–0.41).
Analysis:Table 3 presents 13 studies from 1983 to 2014 [13,23,26–28,33–46]. Physiological variables
such as VO2max [23,32–34,38] and vVO2max continue to be prominent [27,28,33]. Of the 13 studies,
seven have a prediction equation [7,23,26,28,34,37,44]. The coeﬃcients of determination (R2) of the
equations by Bale et al. (1986) are moderately high (from 0.75 to 0.86) and are based on training
variables including the number of training sessions, miles run, years of training and a somatotype
component such as ectomorphy [7,38] and the studies by Fay et al. (1989) with R2 > 0.84, based on the
velocity associated with metabolic variables such as lactate at 2 and 4 mmol/L and at VO2max (Table 3).
Int. J. Environ. Res. Public Health 2020, 17, 8289
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3.10. Variables and Models Associated with the Half-Marathon Event
Search: The diﬀerent keywords were combined as follows: “long distance runners,” “performance,
performance
prediction,”
“anthropometric
and
physiological
determinants,”
“performance
determinants,” “half-marathon”.
Appraisal: The subjects of the diﬀerent studies were generally at an amateur level and infrequently
at a competitive level (Roecker et al., 1998) [28].
Synthesis: It should be noted that the half-marathon is not an oﬃcial specialty of the Olympic
Games or the World Championships, although there are national and international competitions in this
event. Consequently, the largest number of individuals who practice this modality are amateur runners,
with diﬀerent training loads, ages and levels of experience. Multiple associations have been found
between performance and anthropometric variables, but with models of moderate predictive power
(R2 = 0.440–0.71) and with wide limits of agreement between the predicted time and the actual race
time. Finally, two studies should be mentioned due to the high coeﬃcient of determination (R2 = 0.84)
and relatively low limits of agreement obtained through the distance covered in the Cooper test as a
predictor variable [14,15]. This is a simple ﬁeld test that can be introduced into training routines and
can provide very useful information and Cooper’s test has a good accuracy and reliability in amateur
long-distance runners [20].
Analysis: Table 4 presents 11 studies from 1985 to 2020 [8,14–16,28,47–50]. Of these 11 studies,
nine were undertaken from 2011. In this section we should note the many contributions by Knechtle’s
group.
Multiple publications by these authors base their results on the relationships between
performance in half-marathon races with anthropometric variables such as skinfolds, estimated body
composition variables such as fat mass and skeletal muscle mass, and training load variables such as
average training velocity [8,48,50,51] (Table 4).
3.11. Variables and Models Associated with the Marathon Event
Search: The diﬀerent keywords were combined as follows: “long distance runners,” “performance,
performance
prediction,”
“anthropometric
and
physiological
determinants,”
“performance
determinants” and “marathon”.
Appraisal: The subjects in the diﬀerent studies are generally trained and/or highly trained and at
diﬀerent levels (amateur, competitive, elite), with the exception of the study by Hagan which includes
novice runners [41].
Synthesis: The ﬁrst studies in this ﬁeld, by Foster (1983) [32], Slovic (1977) [52], Davies and
Thompson (1979) [53], Föhrenbach et al. (1987) [39] and Noakes et al. (1990) [43], primarily relate
training variables to athletic performance.
A powerful prediction model should be mentioned
(Tanda, 2011) [54], which estimates race pace with a high coeﬃcient of determination of 0.81.
Analysis: Table 5 presents 21 studies from 1975 to 2020. Of note are the variables associated with
exercise physiology and aerobic metabolism [28,40,41,53] as well as, to a large extent, those related to
training load [26,41,52,54–56] (Table 5).
4. Discussion
The main strength of this literature review is the considerable number of publications and the
subsequent analysis of the variables that make up the prediction equations of each of the specialties.
This analytical text invites the reader and the scholar to use the assessment methods available to
evaluate athletic performance.
One of the diﬃculties we encountered in comparing the diﬀerent equations is that there is no
consensus on the deﬁnition of the type of athletes, with each author having named the type of subjects
involved. Therefore, we recommend unifying and clearly deﬁning each of the athletes and their level.
We also found great diﬀerences in the number of athletes participating in the studies, ranging from
eight subjects [24,36] to 427 including both men and women [28].
Int. J. Environ. Res. Public Health 2020, 17, 8289
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The dependent variables of the models found are diverse, as they are expressed as time in minutes,
seconds, hours; speed in m/s, m/min, km/h and, ﬁnally, the race pace in s/km. On this issue these
have been the independent variables that have deﬁned training loads, without ﬁnding work that has
inﬂuenced in a quantiﬁcation of both, strength trainings [57] and high-intensity intervals [6,58] from
which predictor variables can be extracted. The number of independent variables is two or three,
with some equations having as many as six independent variables. A piece of data missing in almost
all the studies is the variance inﬂation factor (VIF), which informs us of multicollinearity.
Some of the possible solutions to the problem of multicollinearity are the following: improvement
in the sample design by extracting the maximum information from the observed variables, elimination of
the variables suspected of causing multi-collinearity and, ﬁnally, in the case of having few observations,
increasing the sample size [59].
The identiﬁcation of physiological variables for performance prediction has at least two important
applications around sports training. The ﬁrst is the evaluation of certain deﬁning physiological
characteristics related to the sports specialty and the second is associated with training (volume and
intensity) in relation to the sports modality and especially with regard to metabolic and functional
characteristics (capacity and power, aerobic and anaerobic).
The most widely studied variables for predicting aerobic performance in running are VO2max
and vVO2max, both of which are fundamentally associated with short distances such as the 5000 m
and 10,000 m events [10,22,23,25,28,43]. This is likely because the intensities at which these races
are executed are very close to maximal intensities and thus their close correlation. VO2max is the
physiological variable that represents aerobic capacity, or in other words, the measurement of the
maximum energy produced by aerobic metabolism per unit of time. Both vVO2max and VO2max
would eﬀectively be the same as they occur essentially at the same time [28,31,43,60,61].
The variables related to the submaximum level and the variable intensities that occur in these
areas have been studied extensively in all specialties, except for the half-marathon [26,28,39,43,62].
This is related to the fact that the half-marathon has not been recognized in the international federative
sphere and, therefore there has been no interest in its study. In the half-marathon specialty, very few
studies are available: one by Campbell in 1985 [47] and another by Roecker et al. [28] Campbell ﬁnds
moderate-low correlations between some basic anthropometric parameters and running pulse rate
and weeks of training. Roecker et al. [28] observed high correlations (r > 0.89) between individual
anaerobic threshold and running velocity at an intensity of 4 mmol/L, both physiologically very similar
concepts, and vVO2max. From 2011 onwards, the following references are provided by Knechtle’s
group, which published many articles linking half-marathon times with numerous anthropometric
variables and with low-moderate correlation coeﬃcients [48] and with prediction models also with
moderate coeﬃcients of determination [19].
Many studies in the literature analyse performance prediction in aerobic specialties based on
the physiological parameters mentioned above. However, these studies, using simple or multiple
regression models, analyse the associations between physiological parameters and aerobic performance
capacity in athletes for a single distance (frequently between 1500 m and 10,000 m) [27,61,63]
Based on the studies mentioned above, it has been proposed that race distance and, therefore,
exercise intensity may inﬂuence the associations between physiological indicators and aerobic
performance. Nonetheless, no studies have addressed aerobic performance capacity in the same athletes
at diﬀerent distances with two or more physiological indicators, particularly in studies with vVO2max
and its respective time to exhaustion. As a result, it is not possible to draw the same conclusions for all
sports specialties and at diﬀerent athletic levels (amateur, highly trained, trained) [60]. The variables
related to the quantity and quality of training are almost exclusive to studies undertaken in the
marathon specialty and for diﬀerent levels of training.
A contribution of this review is the general idea that the parameters recorded at the end of the
graded exercise stress test are well understood, as are the parameters associated with aerobic and
anaerobic thresholds, in terms of both metabolism and gas exchange, since in the diﬀerent prediction
Int. J. Environ. Res. Public Health 2020, 17, 8289
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models, variables range between 85% and 99% of the stress intensities. From our point of view, it is
here, in this range of intensities where stronger associations should be sought, that would allow us to
obtain more powerful models for predicting performance.
Similarly, in the ﬁeld of ultramarathon races, which are becoming increasingly popular, variables
related to RE, associated low lactate concentrations, percentage of VO2max and the search for models
that integrate genetic aspects related to muscle damage and protein synthesis capacity should be
explored, as well as how to more accurately determine and calculate training load both in terms of
quantity and quality. In relation to genetic studies, it has been shown that polymorphisms (about 160)
in 27 genes were identiﬁed in 10,442 participants, of whom 2984 were marathon runners, leaving the
variance in the result on sports performance to be studied [64].
4.1. Practical Applications
The prediction of race time in the long-distance modalities has, above all, an initial application for
novice runners, who have little knowledge of their race paces, allowing them to adjust to constant
paces. Running paces can be modiﬁed depending on the phase of training. The knowledge of the
variables associated with performance in long-distance runners should help coaches and exercise
physiologists understand and promote the search for new variables that improve the prediction of
sports performance.
4.2. Future Research Directions
As future lines of research, we must consider aspects that are currently known as physiological
events that occur at the aerobic threshold (VT1), at the anaerobic threshold (VT2) and at maximum
intensities (VO2max). At the lactate threshold, normally below 50–60% of VO2max, we know the
lactate values, the energy expenditure for the race and the RE. These same parameters are also well
known at the anaerobic threshold, which could be estimated to be around 85% of VO2max. We have
many parameters that associate sports performance with VO2max, such as running speed, individual
anaerobic threshold, and lactate levels. In addition, we know the physiological responses when
reaching 100% of VO2max. Up to this point we can see what the exercise physiology studies have
been based on for performance. However, we believe that there is a gap in what occurs between the
aforementioned points, with regard to studying these values (percentage VO2max, RE, lactate levels,
etc.). Anaerobic capacities should also be further explored, particularly as related to the 5000 and
10,000 m events. Finally, we must not forget the quantiﬁcation of training load and of the molecular
and genetic aspects related to human performance (see Figure 2).
Int. J. Environ. Res. Public Health 2020, 17, x FOR PEER REVIEW 
18 of 21 
been based on for performance. However, we believe that there is a gap in what occurs between the 
aforementioned points, with regard to studying these values (percentage VO2max, RE, lactate levels, 
etc.). Anaerobic capacities should also be further explored, particularly as related to the 5000 and 
10,000 m events. Finally, we must not forget the quantification of training load and of the molecular 
and genetic aspects related to human performance (see Figure 2). 
 
Figure 2. Proposal for the study of long-distance runners. 
5. Conclusions 
Physiological stress assessments are almost exclusive to the short long-distance specialties (5000 
m and 10,000 m). Half-marathon predictor variables are mainly anthropometric, with moderate 
coefficients of determination and physiological and field test variables with high coefficients R2. The 
most relevant variables in the marathon modality are training variables derived from the evaluation 
of aerobic metabolism and anthropometric parameters. 
Author Contributions: Conceptualization J R A C
M A G G and E A C ; methodology J R A C
M A G G
Figure 2. Proposal for the study of long-distance runners.
Int. J. Environ. Res. Public Health 2020, 17, 8289
20 of 23
5. Conclusions
Physiological stress assessments are almost exclusive to the short long-distance specialties (5000 m
and 10,000 m). Half-marathon predictor variables are mainly anthropometric, with moderate coeﬃcients
of determination and physiological and ﬁeld test variables with high coeﬃcients R2. The most relevant
variables in the marathon modality are training variables derived from the evaluation of aerobic
metabolism and anthropometric parameters.
Author Contributions: Conceptualization, J.R.A.-C., M.A.G.G. and E.A.C.; methodology, J.R.A.-C., M.A.G.G.
and E.A.C.; investigation, J.R.A.-C., M.A.G.G. and E.A.C.; data curation, F.A. and L.C.-G.; writing—original draft,
J.R.A.-C., M.A.G.G., E.A.C., F.A. and L.C.-G.; writing—review and editing, J.R.A.-C., M.A.G.G., E.A.C., F.A., T.R.,
L.C.-G., P.T.N. and B.K.; supervision, J.R.A.-C., M.A.G.G., E.A.C., F.A., T.R., L.C.-G., P.T.N. and B.K.; funding
acquisition, J.R.A.-C. and B.K. All authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by Exercise Physiology Research Group CTS-132, Junta de Andalucía, Spain
and Institute of Primary Care, University of Zurich, Zurich, Switzerland.
Conﬂicts of Interest: The authors declare no conﬂict of interest.
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Predictive Performance Models in Long-Distance Runners: A Narrative Review.
Alvero-Cruz, José Ramón,Carnero, Elvis A,García, Manuel Avelino Giráldez,Alacid, Fernando,Correas-Gómez, Lorena,Rosemann, Thomas,Nikolaidis, Pantelis T,Knechtle, Beat