A Fuzzy-based Software Tool Used to Predict 110m Hurdles Results
During the Annual Training Cycle
Krzysztof Przednowek
1
, Krzysztof Wiktorowicz
2
, Tomasz Krzeszowski
2
and Janusz Iskra
3
1
Faculty of Physical Education, University of Rzeszow, Rzeszow, Poland
2
Faculty of Electrical and Computer Engineering, Rzeszow University of Technology, Rzeszow, Poland
3
Faculty of Physical Education and Physiotherapy, Opole University of Technology, Opole, Poland
Keywords:
110m Hurdles, Predictive Models, Fuzzy Systems, R Programming Language.
Abstract:
This paper describes a fuzzy-based software tool for predicting results in the 110m hurdles. The predictive
models were built on using 40 annual training cycles completed by 18 athletes. These models include: ordi-
nary least squares regression, ridge regression, LASSO regression, elastic net regression and nonlinear fuzzy
correction of least squares regression. In order to compare them, and choose the best model, leave-one-out
cross-validation was used. This showed that the fuzzy corrector proposed in this paper has the lowest predic-
tion error. The developed software can support a coach in planning an athlete’s annual training cycle. It allows
the athlete’s results to be predicted, and in this way, for the best training loads to be selected. The tool is a
web-based interactive application that can be run from a computer or a mobile device. The whole system was
implemented using the R programming language with additional packages.
1 INTRODUCTION
Nowadays a variety of computer tools and methods
play an important role in sport training. Both com-
petitors and coaches are looking for new solutions
that can support the training process. One aspect of
such support can be the use of regression models to
predict results. Prediction can be used to calculate
performance results (Edelmann-Nusser et al., 2002;
Maszczyk et al., 2011; Przednowek et al., 2014) or to
identify sporting talent (Papi
´
c et al., 2009; Roczniok
et al., 2013). For example, in the paper (Edelmann-
Nusser et al., 2002), the authors use artificial neu-
ral networks to predict swimmers’ competitive per-
formance. The neural models were cross-validated
and the results show that the modeling was very pre-
cise. The paper (Przednowek et al., 2014) describes
the use of linear and nonlinear multivariable models
as tools to predict 400m hurdles results. Another pa-
per (Haghighat et al., 2013) presents a review of data-
mining techniques that are used for prediction in var-
ious sporting disciplines.
Despite the existence of methods for prediction in
sport, there is lack of tools that could be used by a
coach during the training process, particularly in the
110m hurdles. Available software such as Kinovea,
Physics Toolkit and SkillSpector can be used for the
biomechanical analysis of human motion based on
video sequences (Omorczyk et al., 2014; Sañudo
et al., 2014; Gavojdea, 2015). For example, Sañudo et
al. (Sañudo et al., 2014) use Kinovea software to de-
termine the mean propulsive velocity and the maximal
velocity during a bench press. In the paper (Gavojdea,
2015), Kinovea and Physics Toolkit are used to ana-
lyze the double salto backward tucked. Another ap-
plication, named Lince (Gabin et al., 2012) is used in
the design of observational systems, video recording,
the calculation of data quality and the presentation of
results. In another paper (Randers et al., 2010), the
authors compare different multi-camera systems used
for football match analysis. Papic et al. (Papi
´
c et al.,
2009) developed a fuzzy expert system for scouting
and evaluating young sports talent. A similar system
is presented in (Louzada et al., 2016), where the au-
thors carried out talent identification in soccer using
a web-oriented expert system. In the 110m hurdles,
the coach can use the tool to estimate the parameters
of hurdle clearance (Krzeszowski et al., 2016). These
parameters are estimated using the particle swarm op-
timization algorithm and they are based on analysis of
the images recorded with a 100 Hz camera.
From the literature review, it can be seen that there
is a need to develop tools supporting sports training.
The main contribution of this paper is, therefore to
176
Przednowek, K., Wiktorowicz, K., Krzeszowski, T. and Iskra, J.
A Fuzzy-based Software Tool Used to Predict 110m Hurdles Results During the Annual Training Cycle.
DOI: 10.5220/0006043701760181
In Proceedings of the 4th International Congress on Sport Sciences Research and Technology Support (icSPORTS 2016), pages 176-181
ISBN: 978-989-758-205-9
Copyright
c
 2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

Table 1: Description of variables used to construct the models.
Variable Description x x
min
x
max
y Predicted 110m hurdles result [s] 14.02 13.26 15.13
x
1
Age [years] 21.9 18.0 28.0
x
2
Body height [cm] 187.3 181.0 195.0
x
3
Body mass [kg] 77.8 71.0 83.0
x
4
Body mass index 22.1 20.3 23.5
x
5
Current 110m hurdles result [s] 14.33 13.34 15.40
x
6
Maximal and technical speed [m] 12513 5800 17970
x
7
Technical and speed exercises [m] 5925 2470 10200
x
8
Speed and specific hurdle endurance [m] 11961 3150 20400
x
9
Pace runs [m] 64087 25780 100300
x
10
Aerobic endurance [m] 328631 80600 550000
x
11
Strength endurance [m] 20638 1850 46595
x
12
Strength of lower limbs [kg] 291119 96400 658600
x
13
Trunk strength [amount] 38442 5240 145000
x
14
Upper body strength [kg] 3352 1630 4850
x
15
Explosive strength of lower limbs [amount] 1244 0 2214
x
16
Explosive strength of upper limbs [amount] 656 213 1850
x
17
Technical exercises – walking pace [min] 456 130 1110
x
18
Technical exercises – running pace [min] 574 195 1450
x
19
Runs over hurdles [amount] 778 362 1317
x
20
Hurdle runs in varied rhythm [amount] 1077 320 1850
develop a fuzzy-based software tool for results pre-
diction in the 110m hurdles. This tool is created as a
web application that can be run from a computer or a
mobile device. It allows training loads to be planned
across the annual training cycle so the athlete achieves
their expected results.
2 MATERIAL
The training data contain 40 records. These records
were collected from 18 highly trained athletes (mean
result in the 110m hurdles: 14.02 s) aged between 18
and 28. The athletes were members of the Polish Na-
tional Team. Each record contains an athlete’s param-
eters and that athlete’s training program across the an-
nual training cycle. The models for result prediction
were build using 21 variables (Tab. 1). The input vari-
ables x
1
− x
5
represent the athlete’s parameters, the in-
put variables x
6
− x
20
represent the training loads and
the output variable y represents the predicted 110m
hurdles result. The training loads were classified on
the basis of work (Iskra and Ryguła, 2001), but it
should be noted that this classification can be formu-
lated in different ways. In this paper, the values of
these loads are the sum of all the loads of the same
type realized during the annual training cycle. The
110m hurdles results were registered before and after
the cycle.
3 PREDICTIVE MODELS
3.1 Problem Formulation
We considered the regression problem with p inputs
(predictors) X
j
and one output (response)
ˆ
Y . The goal
was to build the predictive model
ˆ
Y = f (X
1
, . . . , X
p
)
based on a data set containing n observations in the
form of pairs (x
i
, y
i
), where i = 1, . . . , n, p = dim(x).
In this paper, we use:
• linear models in the form of ordinary least
squares (OLS), ridge regression, least absolute
shrinkage and selection operator (LASSO) and
elastic net regression,
• nonlinear model in the form of fuzzy rule base sys-
tem (FRBS).
The detailed description of the linear models can be
found in (Wiktorowicz et al., 2015). The fuzzy model
is described in the next section.
Due to the small amount of data (n = 40), the
models are compared using the leave-one-out cross-
validation method (Arlot and Celisse, 2010). The idea
of this method is based on the separation of subsets of
learning data from the data set. Each subset is formed
by removing only one record from the data set, which
becomes the testing pair. The predictive quality of a
model is expressed by the root of the mean square er-
ror of cross-validation (RMSE
CV
) calculated as
A Fuzzy-based Software Tool Used to Predict 110m Hurdles Results During the Annual Training Cycle
177

RMSE
CV
=
s
1
n
n
∑
i=1
(y
i
− ˆy
−i
)
2
(1)
where ˆy
−i
is the output of a model constructed on the
data set after removing the pair (x
i
, y
i
). Moreover, we
use the fitness measure expressed by the root mean
square error of training (RMSE
T
) defined as
RMSE
T
=
s
1
n
n
∑
i=1
(y
i
− ˆy
i
)
2
(2)
where ˆy
i
is the output of a model constructed on the
full data set.
3.2 Fuzzy Regression Model
The fuzzy model proposed in this paper is constructed
in the following steps.
1. Cross-validation of the OLS model
ˆ
Y = f
OLS
(X
1
, . . . , X
p
) (3)
for the data (x
i
, y
i
). The error in the ith step of
cross-validation has the form
d
i
= y
i
− ˆy
−i
(4)
where ˆy
−i
= f
OLS
(x
−i
).
2. Constructing the fuzzy (nonlinear) model
ˆ
D = f
FUZZY
(X
1
, . . . , X
p
) (5)
for the data (x
i
, d
i
). This model predicts the er-
rors obtained in Step 1, that is it determines
ˆ
d
i
=
f
FUZZY
(x
i
). The best fuzzy model can be chosen
on the basis of cross-validation conducted, for ex-
ample, with varying numbers of fuzzy sets.
3. Cross-validation of the OLS model with the cor-
rected error in the form
d
new
i
= y
i
− ( ˆy
−i
+
ˆ
d
i
) (6)
where ˆy
−i
and
ˆ
d
i
are determined by (3) and (5),
respectively.
3.3 Comparison of Models
The regression models were calculated in R (R Core
Team, 2016). The lm.ridge function from the
"MASS" package (Venables and Ripley, 2002) was
used to calculate the OLS and the ridge regressions.
The LASSO regression and the elastic net regres-
sion were obtained with the enet function included
in the "elastic net" package (Zou and Hastie, 2016).
The fuzzy regression model was calculated using
frbs.learn from the "frbs" package (Riza et al.,
2 3 4 5 6 7 8 9 10 11 12 13
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
number of fuzzy sets
cross-validation error for
ˆ
d
Figure 1: Cross-validation error for
ˆ
d as a function of the
number of fuzzy sets. The smallest error is obtained for
eight sets.
2015). The learning method was the Wang-Mendel
algorithm (Wang and Mendel, 1992).
The parameters of the applied models are shown
in Table 2. In the fuzzy model, five Gaussian mem-
bership functions are used, the t-norm is "minimum",
the defuzzification is the "weighted average method",
and the implication is "minimum". The number of
fuzzy sets was determined by calculating the cross-
validation errors. These errors are shown in Fig. 1 as
a function of the number of fuzzy sets (changing from
2 to 13). From Fig. 1 it is seen that the best model
is obtained for eight sets. The errors RMSE
CV
and
RMSE
T
for the models under consideration are pre-
sented in Table 3. It shows that the proposed fuzzy re-
gression model has the lowest RMSE
CV
and the high-
Table 2: Parameters of models.
Regression Parameters
OLS —
RIDGE lambda = 16.1
LASSO lambda = 0, s = 0.04
ENET lambda = 0.16, s = 0.56
FUZZY method.type = "WM"
num.labels = 8
type.mf = "GAUSSIAN"
type.tnorm = "MIN"
type.defuz = "WAM"
type.implication.func = "MIN"
Table 3: Summary of errors.
Regression RMSE
CV
[s] RMSE
T
[s]
OLS 0.3807 0.1302
RIDGE 0.2276 0.1641
LASSO 0.2397 0.1495
ENET 0.1996 0.1562
FUZZY 0.0851 0.2852
icSPORTS 2016 - 4th International Congress on Sport Sciences Research and Technology Support
178

Figure 2: Screenshot of the application for result prediction in 110m hurdles.
est RMSE
T
. It means that it can predict the result
better than the linear models, but it has the worst fit to
the data.
4 GRAPHICAL USER
INTERFACE
The graphical user interface was implemented in R
language using the libraries shiny, shinythemes and
shinydashboard. This interface is a web-oriented
application and therefore it requires only a web
browser and an Internet connection to be used. The
current version of the developed system is available
on https://hurdles.shinyapps.io/prediction.
The application consists of two tabs labeled "Result
prediction" and "About".
The "Result prediction" tab is used for entering
data and for result prediction (Fig. 2). The input vari-
ables are grouped into five boxes: "Athlete’s param-
eters", "Training loads – endurance", "Training loads
– technique and rhythm", Training loads – strength",
and "Training loads – speed". The value of each input
can be modified using appropriately scaled sliders.
For example, the box "Training loads – endurance"
presented in Fig. 3 has five sliders for changing the
endurance training loads. Each slider has its range
determined on the basis of the minimum and maxi-
mum values in the database (Tab. 1). For instance, the
slider "Pace runs" ranges from 25000m to 101000 m
with each step equal to one meter.
In the last box, labeled "Predictive model"
(Fig. 4), the user can choose one of the developed re-
A Fuzzy-based Software Tool Used to Predict 110m Hurdles Results During the Annual Training Cycle
179

Figure 3: Screenshot of the box for entering endurance
training loads.
Figure 4: Screenshot of the box for result prediction.
gression models. Two textOutput fields display the
current and predicted results. Prediction of the result
is performed automatically after changing the value
in any box in this tab. In this way, the user can mod-
ify training loads and observe the changes that occur
in the expected result. The training program should
correspond to the inputs specified in Tab. 1.
The "About" tab contains information about the
application and the authors.
5 CONCLUSIONS
In this paper a fuzzy-based software tool for result
prediction in the 110m hurdles was presented. The
prediction is based on the following models: OLS re-
gression, ridge regression, LASSO regression, elastic
net regression and OLS regression with fuzzy correc-
tion. The best prediction was obtained by the pro-
posed fuzzy model, but it has the lowest fitness to the
data. The parameters of the models can be also vali-
dated in future using an independent group of athletes
with different training conditions.
The whole application, composed of the predictive
models and the graphical user interface, was created
in R programming language. The simple interface al-
lows an athlete’s parameters and training loads to be
changed. In this way, the coach can predict the ex-
pected result and select individual components of the
training for a given athlete.
Further work will focus on the development of the
proposed application, which involves implementing
individual user accounts, the preparation of an ath-
lete databases and creating reports. In addition, a new
computational module will be developed for generat-
ing training loads.
ACKNOWLEDGEMENTS
This work has been supported by the Polish Min-
istry of Science and Higher Education within the re-
search project "Development of Academic Sport" in
the years 2016-2018, project no. N RSA4 00554.
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