Estimating Running Performance Combining Non-invasive Physiological Measurements and Training Patterns in Free-Living

Abstract

In this work, we use data acquired longitudinally, in free-living, to provide accurate estimates of running performance. In particular, we used the HRV4Training app and integrated APIs (e.g. Strava and TrainingPeaks) to acquire different sets of parameters, either via user input, morning measurements of resting physiology, or running workouts to estimate running 10 km running time. Our unique dataset comprises data on 2113 individuals, from world class triathletes to individuals just getting started with running, and it spans over 2 years. Analyzed predictors of running performance include anthropometrics, resting heart rate (HR) and heart rate variability (HRV), training physiology (heart rate during exercise), training volume, training patterns (training intensity distribution over multiple workouts, or training polarization) and previous performance. We build multiple linear regression models and highlight the relative impact of different predictors as well as trade-offs between the amount of data required for features extraction and the models accuracy in estimating running performance (10 km time). Cross-validated root mean square error (RMSE) for 10 km running time estimation was 2.6 minutes (4% mean average error, MAE, 0.87 R^2), an improvement of 58% with respect to estimation models using anthropometrics data only as predictors. Finally, we provide insights on the relationship between training and performance, including further evidence of the importance of training volume and a polarized training approach to improve performance.

Full text

Estimating Running Performance Combining Non-invasive Physiological
Measurements and Training Patterns in Free-Living
Marco Altini and Oliver Amft1
Abstract— In this work, we use data acquired longitudinally,
in free-living, to provide accurate estimates of running per-
formance. In particular, we used the HRV4Training app and
integrated APIs (e.g. Strava and TrainingPeaks) to acquire
different sets of parameters, either via user input, morning
measurements of resting physiology, or running workouts to
estimate running 10 km running time. Our unique dataset
comprises data on 2113 individuals, from world class triathletes
to individuals just getting started with running, and it spans
over 2years. Analyzed predictors of running performance
include anthropometrics, resting heart rate (HR) and heart
rate variability (HRV), training physiology (heart rate during
exercise), training volume, training patterns (training intensity
distribution over multiple workouts, or training polarization)
and previous performance. We build multiple linear regression
models and highlight the relative impact of different predictors
as well as trade-offs between the amount of data required
for features extraction and the models accuracy in estimating
running performance (10 km time). Cross-validated root mean
square error (RMSE) for 10 km running time estimation was
2.6minutes (4% mean average error, MAE, 0.87 R2), an
improvement of 58% with respect to estimation models using
anthropometrics data only as predictors. Finally, we provide
insights on the relationship between training and performance,
including further evidence of the importance of training volume
and a polarized training approach to improve performance.
I. INTRODUCTION AND RELATED WORK
Medium and long distance running is becoming popular,
with millions of people worldwide participating in running
events from 5 km to the marathon distances. While human
performance in running has been analyzed in elite athletes as
well as recreational ones for decades, the scientific commu-
nity is still investigating different aspects behind the limits of
human performance, as recently shown by the Nike break-
ing2 project [1]. Being able to accurately estimate running
performance can be helpful at several levels. First, we could
provide individuals with better race pacing strategies, which
are often guessed based on limited data. Secondly, we could
also tailor training plans to individual abilities, therefore
reducing injury risk.
Different anthropometric, physiological, and training char-
acteristics influence human performance in running. Low
body fat has been associated with better times [2], similarly
to low resting heart rate (HR) and higher heart rate variability
(HRV) [3]. Other physiological parameters measured in the
lab, for example lactate threshold and V O2max, have also
been linked to better running times. In our recent work we
have shown how V O2max estimated from running work-
outs highly correlates with running performance in events
1M. Altini and O. Amft are with Friedrich-Alexander Universitat
Erlangen-Nurnberg (DE) email: altini.marco@gmail.com
between the 10 km and the marathon [4]. Training related
variables, such as training volume (distance per week), as
well as average training speed have been associated to
improved running performance too. Recently, interest has
shifted to training patterns analyzed over weeks or months.
For example, most elite athletes train in a so-called polarized
regime, in which most workouts are carried out at low
intensities, and a few at very high intensity, as opposed
to moderate intensity training, more typical of recreational
runners [5], [6]. Even in recreational runners, a shift to a
polarized training regime resulted in performance improve-
ments [7].
Most literature published on estimating running perfor-
mance however is constrained by small sample size and a
rather homogeneous sample (for example only men, or a
narrow age range or performance range). Variables included
in the model are acquired under laboratory conditions or
supervised settings that are not practical (V O2max, lactate
threshold, biomechanics [2]) Finally, parameters are analyzed
in isolation (for example the impact of polarized training
on performance [5]) and running time estimates accuracy is
suboptimal or has not been cross-validated.
In the past few years, we have witnessed fast technological
developments and integrations between different platforms
and services (e.g. public APIs), resulting in increased avail-
ability of multivariate data streams acquired from mobile
applications and wearable sensors (e.g. GPS, accelerometer,
physiological data). Such developments are providing scien-
tists with data at a scale that is typically not manageable in
regular laboratory studies, and therefore with the opportunity
of providing additional insights on the relation between
physiology, training and performance. While several mobile
applications and wearable sensors have been released on the
market, providing users with metrics reflecting behavior (e.g.
steps taken, distance ran, etc.) limited work has been carried
out to provide insights on the individual’s performance
ability outside of laboratory settings.
In this work we propose the first longitudinal, large scale
analysis of running performance with respect to a wide set
of variables either self-acquired or acquired automatically
and non-invasively in free-living, without laboratory tests
or supervision. Analyzed variables include anthropometrics,
resting physiology, training physiology, training volume,
training patterns and previous performance.
In particular, we used the HRV4Training app [8], [9]
to collect data from 2113 individuals of different fitness
levels, over a time period of 2years, and developed multiple
linear regression models to highlight the relative impact of

different predictors on running performance estimation. We
show that running performance (10 km time) can be esti-
mated accurately from data acquired in free-living, without
supervision or specific laboratory tests. Besides providing
practical estimation models that could be employed by recre-
ational runners to tailor training programs, we also provide
additional insights on the relationship between training and
performance, including confirmative evidence of the impor-
tance of polarized training.
II. DATA ACQUISITION
A. Measurement Protocol
Users downloaded the HRV4Training app from the Ap-
ple Store or Google Play Store and agreed to provide
collected measurements and annotations for research pur-
poses via a consent form embedded in the application.
The HRV4Training app allows a user to measure resting
physiological data (HR and HRV) using the phone camera or
external sensors, and was recently validated with respect to
electrocardiography (ECG) [10]. The application instructed
users to perform the measurement right after waking up while
still lying, to limit the effect of other stressors. In addition,
users could link the HRV4Training app to other services,
such as Strava or TrainingPeaks, so that not only morning
measurements, but also workouts performed during the day,
and associated GPS and heart rate data, would be collected
automatically in the app.
B. Dataset
Data was collected using the HRV4Training app during
2016 and 2017. A total of 2113 users (1891 male, 222
female) met the inclusion criteria: training with a heart rate
monitor, linking the app via third party APIs to collect
workouts data, including at least one 10 km, and taking at
least a month of morning physiological measurements. A
user’s best 10 km time was automatically identified as the
fastest 10 km workout over the 2years, and used as reference
for this analysis. For each identified best 10 km time, the
previous 3months of data were used to extract features re-
lated to a user training volume and patterns. Totally, 464809
morning physiological measurements and 296739 running
workouts were acquired during the 2years longitudinal
study, for an average of 220 morning measurements and 140
workouts with heart rate data per person. Anthropometric
characteristics and reference 10 km times of the users are
listed in Table I.
TABLE I
USE RS ANT HROPO METR IC DATA AND R EF ER EN CE 10 KM TIME
mean sd min max
age (years) 39.80 8.70 18.00 69.08
bmi (kg/m2) 23.24 2.51 16.65 36.59
weight (kg) 73.34 10.53 42.00 122.00
height (cm) 177.41 7.69 149.00 205.00
10km time (minutes) 49.8 7.2 34.2 75.0
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Non−Polarized
Polarized
Feb Mar Apr May Jun Jan Apr Jul
120
130
140
150
160
170
140
150
160
170
Date
Running heart rate (bpm)
Moderate intensity
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FALSE
TRUE
a) Training polarization features: heart rate data
Non−Polarized
Polarized
FALSE TRUE FALSE TRUE
0
30
60
90
0
10
20
30
Moderate intensity
Count
Moderate intensity
FALSE
TRUE
b) Resulting distribution of workouts at different intensities
Fig. 1. a) Heart rate data for an individual training under a non-polarized
approach (left) and an individual training under a polarized approach (right).
Moderate intensity was defined as HR within 5% of a user’s average.
b) Resulting training intensities distributions highlighting how a more
polarized approach involves less time spent at moderate intensities. Here
we set an arbitrary threshold of 30% of workouts carried out at moderate
intensity, to assign a user to the polarized or non-polarized category, only
for visualization purposes.
III. DATA ANALYSIS
A. Features
We computed features representative of different aspects
that may contribute to running performance. Then, we cre-
ated the following sets to analyze their impact on estimation
accuracy:
•Ant: anthropometrics data. A user’s body mass index
(BMI), age and gender.
•Rest: resting physiological data (HR and HRV). HR
was computed as the mean HR during the daily morn-
ing measurement, while as HRV feature we used the
square root of the mean squared RR intervals difference
(rMSSD), a marker of parasympathetic activity [3], [9].
•Vol: training volume and speed. Average workout dis-
tance and speed.
•TrPhy: physiological data during training. We computed
the speed to HR ratio, a feature that relies on the fact
that a more fit (faster) runner would maintain a lower
HR while running at a certain speed, with respect to
less fit (slower) runners. This parameter is the main
predictor behind V O2max estimation models relying on
sub-maximal tests or workouts data [4], [11].
•Pol: training polarization. Training polarization refers
to training at different intensities, typically avoiding
moderate intensity training. We derived features from
workouts summaries to analyze the impact of training
polarization on estimated performance. Features were:
percentage of workouts performed at speeds 5% above
or below a user’s average workout speed and the per-
centage of workouts where HR was within 5% of a

user’s average HR rate, a feature used to represent lack
of polarization (see Fig. 1).
•Performance: past running performance. Finally, the
last feature set included all previous features plus the
best 10 km time found in the 3months preceding the
fastest time, as previous running performance is highly
predictive of future running performance.
We chose to compute training polarization features as devi-
ations from a user’s average. By avoiding range, maximum
and minimum values we maintain the algorithm’s robustness
to measurement inaccuracies and outliers which often occur
in free-living. All features were computed over the 3months
preceding a user best 10 km time, depending on available
data. An example of features collected is shown in Fig. 2.
B. Running performance estimation
Running performance (10 km running time) was estimated
using multiple linear regression (MLR) models and the
different sets of predictors listed in Sec. III-A. MLR was used
so that coefficients could be easily analyzed and interpreted,
in order to provide further evidence on the importance of
different parameters in the context of running performance.
C. Statistics and performance measures
MLR models were validated using 10-fold cross-
validation. At each iteration, 10% of the data was randomly
selected for validation, while from the remaining 90%, all
users with at least 20 workouts were used as training set.
By selecting only users with a minimum amount of data, we
ensured training patterns could be meaningfully estimated.
However, we validated our models on all users, even the ones
including little data, so that the relation between available
data and accuracy could be investigated. We report Root
Mean Square Error (RMSE) in minutes, Mean Percentage
Error (MPE), in percentage, Pearson’s correlation and ex-
plained variance (R2) for all cross-validated MLR models.
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20
25
30
35
1_q 2_q 3_q 4_q
Quantiles of 10 km performance
BMI (kg/m^2)
a) BMI (Ant)
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1_q 2_q 3_q 4_q
Quantiles of 10 km performance
Arbitrary unit
c) Heart rate to speed ratio (TrPhys)
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25
1_q 2_q 3_q 4_q
Quantiles of 10 km performance
kilometers per workout
b) Training load (Vol)
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0.00
0.25
0.50
0.75
1.00
1_q 2_q 3_q 4_q
Quantiles of 10 km performance
%
d) 'Non−polarized' trainings (Pol)
Fig. 2. Examples of features used to estimate 10 km running performance.
Data were split into quartiles for clarity.
3
4
5
6
7
5 10 15 20 25 30
Trainings included
RMSE (minutes)
a) 10 km time estimate, RMSE
4
6
8
10
5 10 15 20 25 30
Trainings included
MPE (%)
b) 10 km time estimate, MPE
Fig. 3. RMSE and MPE when different amounts of workouts are included
in the analysis. 15 workouts seem sufficient to extract meaningful features
and minimize estimation error.
IV. RESULTS AND DISCUSSION
A. Workouts number
Results of running time estimation for different amounts
of included workouts are shown in Fig. 3. From this analysis,
15 workouts seem sufficient to extract meaningful features
and minimize estimation error.
B. Feature sets
Feature sets introduced in Sec. III-A were used as pre-
dictors in MLR models. Results were best for feature set
Performance, with a RMSE of 2.68 minutes. Estimation was
least accurate when using only anthropometrics data (set
Ant, RMSE = 6.27 minutes) and improved progressively
when adding resting physiological data (HR and HRV, set
Rest, RMSE = 6.07 minutes), training volume and speed
(average kilometers per workout and average speed per
workout set Vol, RMSE = 4.04 minutes), physiological data
during training (speed to heart rate ratio, set TrPhys, RMSE =
3.96 minutes) and training patterns (percentage of workouts
at low and high intensities, set Pol, RMSE = 3.64 minutes).
All results are reported in Table II while Fig. 4 shows Bland-
Altman plots and R2for four MLR models.
TABLE II
RMSE, MPE AND PER AS ON ’S CO RR EL ATIO N FO R TH E D IFF ER EN T
MO DE LS D EV EL OP ED I N TH IS S TU DY.
Feature set RMSE (minutes) MPE (%) r
Ant 6.27 9.91 0.53
Rest 6.07 9.56 0.57
Vol 4.04 6.25 0.84
TrPhys 3.96 6.08 0.85
Pol 3.64 5.52 0.87
Performance 2.68 4.10 0.93

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R2=0.33
0.6
0.8
1.0
1.2
0.6 0.8 1.0 1.2
Predicted − Rest
Reference
10 km time estimation, Rest feature set
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R2=0.71
0.6
0.8
1.0
1.2
0.6 0.8 1.0 1.2
Predicted − Vol
Reference
10 km time estimation, Vol feature set
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R2=0.76
0.6
0.8
1.0
1.2
0.6 0.8 1.0 1.2
Predicted − Pol
Reference
10 km time estimation, Pol feature set
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R2=0.87
0.6
0.8
1.0
1.2
0.6 0.8 1.0 1.2
Predicted − Performance
Reference
10 km time estimation, Performance feature set
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0.4
0.7 0.8 0.9 1.0 1.1
Mean, (Reference + Fitted)/2
Residuals
Bland−Altman − Rest feature set
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0.0
0.4
0.6 0.8 1.0
Mean, (Reference + Fitted)/2
Residuals
Bland−Altman − Vol feature set
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−0.4
0.0
0.4
0.6 0.8 1.0 1.2
Mean, (Reference + Fitted)/2
Residuals
Bland−Altman − Pol feature set
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−0.4
0.0
0.4
0.7 0.9 1.1
Mean, (Reference + Fitted)/2
Residuals
Bland−Altman − Performance feature set
Fig. 4. Bland-Altman plots for four models: Ant,Vol,Pol and Performance.
C. Coefficients
MLR models coefficients could not be reported for all
models due to space restrictions. We report here the sign
of the model’s coefficients as they provide insights on the
relation between predictors and estimated performance. In
particular, it is of interest to determine the impact of features
representative of training patterns as derived from workouts.
In our analysis, age, BMI, resting HR, speed to HR ratio and
time spent at moderate HR intensity entered the model with a
positive sign, meaning that a lower value for these predictors
is associated with a faster 10 km. On the other hand,
HRV (rMSSD), average distance and speed, percentage of
workouts performed 5% faster or 5% slower than the average
training entered the model with a negative coefficient. Thus,
according to our dataset and analysis, a more polarized train-
ing regime, with a higher percentage of workouts preformed
either faster or slower than the average workout, as well as
a lower percentage of workouts performed at moderate HR
intensity, is associated with improved performance.
V. CONCLUSIONS
In this work, we used data acquired longitudinally, in free-
living, to provide accurate estimates of running performance
on a dataset of 2113 runners of all levels. We investigated the
relation between anthropometrics data, resting physiology,
training patterns and performance, showing that running
performance can be estimated accurately. The estimation
models developed in this work do not require laboratory
tests, and could be practically employed by the growing
community of recreational runners to estimate performance
and tailor training plans. Results for different feature sets
are consistent with previous results from smaller studies
[3], [7], [5], [4], showing a positive correlation between
higher estimates of V O2max, higher HRV, lower HR, higher
training volume, higher training speed, a more polarized
training regime and running performance.
Our analysis focused on readily available parameters that
can be easily acquired and processed in free-living. However,
more variables could be integrated as metrics linked to
biomechanics and running power are also becoming available
in the consumers market. Additionally, results could be
backed up by an additional laboratory validation. Future
work will aim at both including more parameters as well
as looking at performance changes over time to determine
the estimation model’s ability to track such changes.
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