RESEARCH ARTICLE
A new approach to quantify angles and time
of changes-of-direction during soccer
matches
Tomohiro KaiID1,2, Shin HiraiID3, Yuhei Anbe1, Yohei TakaiID1*
1 National Institute of Fitness and Sports in Kanoya, Kanoya, Japan, 2 Kagoshima United FC, Kagoshima,
Japan, 3 Mizuno Corporation, Suminoe-ku, Japan
* y-takai@nifs-k.ac.jp
Abstract
Background and aims
Soccer players frequently perform change-of-directions (CODs) at various speeds during
matches. However, tracking systems have shown limitations to measure these efforts.
Therefore, the aim of the present study was to propose a new approach to measure CODs
using a local positioning system (LPS), and clarify position-related difference in profile of
CODs by using the approach.
Methods
The x- and y-coordinate data for each soccer player were measured with a local positioning
system. Speed, acceleration, jerk, and direction of speed were derived from the coordinate
data. Based on accelerations of above 2 m/s2, the onsets and ends of CODs derived from
jerk were identified (COD duration). Changes of direction of speed (θCOD) were determined
for the corresponding period. Six collegiate male soccer players performed CODs according
to 13 set angles (0–180˚; every 15˚) so that differences between θCOD and set angle could
be determined (Exp. 1). Relative frequency distributions of θCOD and number of CODs were
determined in 79 collegiate and amateur male soccer players during 9 soccer matches
(Exp. 2).
Results
In Exp. 1, θCOD was positively related to set angle (r = 0.99). Each θCOD was smaller than
the corresponding set angle, and the difference became greater with increasing COD angle.
In Exp. 2, The number of CODs in a match was 183 ± 39 across all positions. There were no
significant position-related differences in the number of CODs. The duration of a COD was
0.89 ± 0.49 s across all positions. The relative frequency distribution of θCOD revealed that
the number of CODs at 0–15˚ and 105–135˚ tended to be higher than those at other angles
during soccer matches. Further, θCOD was affected by the speed at the onset of COD during
soccer matches (Exp. 2).
PLOS ONE
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
1 / 12
a1111111111
a1111111111
a1111111111
a1111111111
a1111111111
OPEN ACCESS
Citation: Kai T, Hirai S, Anbe Y, Takai Y (2021) A
new approach to quantify angles and time of
changes-of-direction during soccer matches. PLoS
ONE 16(5): e0251292. https://doi.org/10.1371/
journal.pone.0251292
Editor: Filipe Manuel Clemente, Instituto
Politecnico de Viana do Castelo, PORTUGAL
Received: February 9, 2021
Accepted: April 26, 2021
Published: May 17, 2021
Peer Review History: PLOS recognizes the
benefits of transparency in the peer review
process; therefore, we enable the publication of
all of the content of peer review and author
responses alongside final, published articles. The
editorial history of this article is available here:
https://doi.org/10.1371/journal.pone.0251292
Copyright: © 2021 Kai et al. This is an open access
article distributed under the terms of the Creative
Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in
any medium, provided the original author and
source are credited.
Data Availability Statement: All relevant data are
within the manuscript and its Supporting
Information files.
Funding: This study was supported by a NIFS
project for TASS. The funders had no role in study
Conclusions
The current findings demonstrate that θCOD derived from direction of speed and jerk may be
a new indicator for evaluating COD during soccer matches.
Introduction
Recently, coaches and sports scientists of ball sports team use tracking technologies for design-
ing training program and players’ condition, because it has become easy to measure players’
locations in ball sports using global positioning system (GPS) and local positioning system
(LPS) [1, 2]. Many earlier studies have demonstrated the validity of position, speed and accel-
eration data obtained from such a tracking technology, compared to a 3D motion capture sys-
tem, radar/laser guns and timing gates [3–9]. Further, LPS is superior to GPS, whereas each
system has a certain validity [10]. These systems are capable of measuring players’ coordinates,
and for quantifying players’ acceleration, distance and numbers of actions in relation to speed
derived from time-motion analysis. These parameters are predictors of match outcome and
periodization on daily training [11, 12].
Besides time-motion analysis, the parameters obtained from tracking technologies are
applied to quantify CODs locomotion in sport-specific course and small-sided games [3–6, 9,
10]. In the earlier studies, various type of courses which angles of CODs are predetermined are
set [3, 5, 6, 9, 10], and small court is used [4]. Although the earlier findings demonstrate the
magnitude of speed and acceleration, the experimental design is not real soccer matches. Dur-
ing soccer matches, players perform changes-of-direction (CODs) during locomotion [13].
Notational analysis has revealed that 30% of all actions during English FA Premier League play
were CODs (e.g., forward, lateral and backward running) [14]. However, quantifying relevant
data, such as the number and type of actions, is a lengthy process [15], and notational analysis
may be arbitrary [16]. Therefore, a convenient analytic method to quantify CODs during soc-
cer matches is needed. Fitzpatrick et al. [2] demonstrated that, in the English U-18 Premier
League, the direction of players’ locomotion at a speed of 6.67 m/s or more ranged from 0˚ to
30˚ by using GPS. This suggests that during matches, youth soccer players move close to a
straight line at relatively high speeds. Further, an earlier study of soccer matches revealed that
greater distances are covered at moderate speeds of 3.89 to 5.28 m/s than at high-intensity
speeds of 5.28 to 6.39 m/s [17]. Although soccer players frequently perform CODs at various
speeds during matches, to the best of our knowledge, little information is available concerning
COD profiles during soccer matches in relation to speed by using LPS.
Force is theoretically the product of mass and acceleration. Acceleration can be useful in
describing a player’s physical load during soccer matches. Dalen et al. [1] demonstrated that
position-related differences in the number of accelerations (>2 m/s2) was found in the first
division of the Norwegian league. When a player changes direction of locomotion, he exerts a
certain force against the ground. At the same time, a certain level of acceleration is produced,
and then the direction of the player’s locomotion changes, and the speed and/or the direction
of speed changes [3]. Jerk, which is derived by differentiating acceleration by time, is used to
detect the onset of human joint movement and the magnitude of the movement [18]. There-
fore, jerk should be useful in identifying the onset and end of a COD for a given acceleration,
and the change in direction of speed should correspond to the direction of the COD.
During professional soccer matches, position-related differences in acceleration are found,
indicating that side midfielders and defenders accelerate more often than other positions [1].
PLOS ONE
Quantifying angle and time of changes-of-direction
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
2 / 12
design, data collection and analysis, decision to
publish, or preparation of the manuscript.
Competing interests: The authors have declared
that no competing interests exist.
Further, midfielders, relative to other positions, performed fewer CODs of 90 degrees or less
[14]. Considering these findings, profile of CODs would differ among positions. This study
thus proposes a new approach that uses direction of speed and jerk in quantifying CODs of
soccer players during soccer matches, and to clarify position-related difference in profile of
CODs by using the approach.
Materials and methods
Experimental design
This investigation was conducted according to the Declaration of Helsinki and approved by
the local Ethics Committee for human experimentation (#11–101). All participants were
informed of the experimental procedures and possible risks of the measurements beforehand.
Oral informed consent was obtained from each subject before each match.
This study consisted of two experiments for quantifying CODs during soccer matches in
relation to various speeds. In both experiments, players’ locations were measured with LPS. In
the first experiment 1 (Exp. 1), male soccer players performed CODs in directions determined
by 13 set angles (every 15˚, ranging from 0˚ to 180˚) while jogging at speeds of approximately
1.0 and 3.0 m/s. After the player turned at the determined location, he ran through a gate set at
a distance of 2 m from the corresponding location. The participants were asked to perform
CODs as fast and quickly as possible when they turned in a given direction. S1 Fig presents
typical trajectory data and kinematic data (to be discussed below) in each angle for one player.
In the second experiment 2 (Exp. 2), data were collected from 9 official soccer matches in
Division 1 of a regional collegiate male soccer league and the Division 5 of a regional amateur
soccer league for collegiate and amateur soccer players. Data were analyzed for the players
who played for 90 min.
Participants
In the Exp. 1, six collegiate male soccer players (age, 21.0 ± 1.5 years, height, 172.8 ± 6.1 cm,
body mass, 66.8 ± 9.2 kg; means ± SDs) participated in Exp. 1. They were field players, and
belonged in the same team competing in a national university league in Japan, and had experi-
ence of competitive soccer training for >9 years. They had participated in regular soccer-spe-
cific training for more than five days (>1.5 hours/day) per week.
Seventy-nine collegiate and amateur male soccer players (23.0 ± 4.1 years, 173.9 ± 5.1 cm,
67.5 ± 6.2 kg) involved in Exp. 2, and got in the official soccer matches in in Division 1 of a
regional collegiate male soccer league or the Division 5 of a regional amateur soccer league.
The number of players in each position was as follows; 23 players for central backs (CB,
23.4 ± 4.7 years, 177.4 ± 5.0 cm, 71.2 ± 5.7 kg), 16 players for side backs (SB, 22.6 ± 3.4 years,
171.7 ± 3.9 cm, 65.2 ± 4.7 kg), 15 players for central midfielders (CMF, 22.2 ± 2.9 years,
172.3 ± 5.0 cm, 64.8 ± 6.3 kg), 14 players for side midfielders (SMF, 23.7 ± 5.0 years,
172.3 ± 4.2 cm, 65.9 ± 4.9 kg), and 11 players for forwards (FW, 21.8 ± 3.7 years, 174.3 ± 4.5
cm, 69.8 ± 5.9 kg), respectively. Goalkeepers were excluded from data analysis.
All participants involved in Exp. 1 and 2 were free of cardiovascular, metabolic, and immu-
nologic disorders and/or orthopedic abnormalities, and were not using any medications that
affected their muscular function and size. All study participants provided informed consent,
and the study design was approved by an ethics review board (the Ethics Committee in
National Institute of Fitness and Sports in Kanoya for human experimentation (#11–101)).
PLOS ONE
Quantifying angle and time of changes-of-direction
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
3 / 12
Players’ coordinate data
X- and y-coordinate data for each player were measured with LPS (ZXY Sports Tracking,
Chyronhego, New York, USA) at a sampling frequency of 20 Hz. A belt with a sensor (approx.
20 g) under their uniform were attached for each player. In Exp.2, three examiners helped to
wear the sensor for starters before the start of soccer matches. Players were instructed to take
off the belt if they felt uncomfortable during matches. The data obtained were processed as
described below using Matlab (Mathworks ver. 2018b, New York, USA).
1 Kinematic data and filtering process.
To obtain the smoothed time-series data for jerk,
the time-series data of x- and y-coordinates were processed by a second-order Butterworth
low-pass filter employing a zero phase lag before analysis. To identify the appropriate cutoff
frequency for the low-pass filter, we repeated the filtering process at every 1 Hz from 1 Hz to 6
Hz. The time-series data for jerk with and without the filtering process are presented in S2 Fig.
As shown in S2 Fig, the use of cutoff frequencies of 3 Hz to 6 Hz resulted in noise in the
smoothed time-series data, while cutoff frequencies of <2 Hz produced less noise. Thus a 2 Hz
cutoff frequency was adopted in this study.
2 Kinematic data for each player.
To determine players’ velocity, displacement from (t-
1) to (t+1) was defined as (x(t+1)-x(t-1), y(t+1)-y(t-1)) of the smoothed coordinate data for
each player. Player speed of players (|V(t)|) in m/s was calculated by differentiating the dis-
placement by time. Player’s acceleration (|A(t)|) in m/s2 was derived by differentiating |V(t)|
by time. Finally, jerk (j(t)) in m/s3 was calculated by differentiating |A(t)| by time.
jVðtÞj ¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðxðt þ 1Þ calculated for each position. The number of CODs and analytical durations were also deter-
mined. Further, we examined the relationship between the speed at the onset of a COD and
θCOD during soccer matches.
Statistical analysis
Descriptive data are expressed as means and standard deviations (SDs). In Exp. 1, a one-way
analysis of variance (ANOVA) was used to test differences in θCOD for all combinations of set
angles. Pearson’s product-moment correlation coefficients (r) were estimated for the relation-
ships between θCOD and set angles. In Exp. 2, skewness and kurtosis were used to test whether
the relative frequency distributions of θCOD were normally distributed, according to the
method of Yokoyama [19]. A one-way ANOVA was used to test position-related differences in
number of CODs and duration of the analytical period. All statistical procedures were con-
ducted with SPSS statistical software (SPSS 25.0, IBM, New York, USA). The significance level
was set at 0.05.
Results
Differences between θCOD and the set angles (Exp. 1)
Table 1 presents descriptive data for θCOD at each set angle and the differences between set
angles and θCOD. θCOD increased with increasing set angles. Error values between the set angles
and θCOD also increased with increasing set angles. Duration of the analytical period was
1.04 ± 0.62 s. θCOD was positively related to set angles (r = 0.99), as shown in Fig 2.
Fig 1. Analysis method for θCOD. Dotted line in line plot of acceleration indicates a threshold of acceleration (2 m/s2).
https://doi.org/10.1371/journal.pone.0251292.g001
PLOS ONE
Quantifying angle and time of changes-of-direction
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
5 / 12
CODs profiles during soccer matches (Exp. 2)
Table 2 presents descriptive data on the number of CODs during the soccer matches. The
number of CODs in a match was 183 ± 39 across all positions. There were no significant posi-
tion-related differences in the number of CODs. The duration of a COD was 0.89 ± 0.49 s
across all positions.
Fig 3 shows the relative frequency distributions of θCOD during the soccer matches. The val-
ues of skewness indicate that the distributions of θCOD were symmetric for all positions, except
for SB. The skewness of SB was negative, indicating that the distribution was skewed to the left.
The kurtosis was platykurtic for positions other than FW. The distribution in FW revealed lep-
tokurtic. As seen in Fig 3, the relative frequency of CODs at 0–15˚ and 105–135˚ tended to be
higher than that of CODs at other angles. Table 3 provides descriptive data on the number of
CODs per match in each bin.
The speed at the onset of a COD was 1.36 ± 0.96 m/s, ranging from 0.01 m/s to 6.99 m/s. As
seen in Fig 4, players executed CODs in different directions at relatively lower speeds of <5 m/
s, but CODs in limited directions (-30˚-30˚) occurred at higher speeds of >5 m/s.
Discussion
This study aims to propose a new approach that uses direction of speed and jerk in quantifying
CODs of soccer players during soccer matches, and to clarify position-related difference in
profile of CODs by using the approach. As the results, change in direction of speed, θCOD,
which was derived from direction of speed and jerk, increased with increasing set angles of the
predetermined course (Exp. 1). Further, the relative frequency of θCOD during soccer matches
revealed a platykurtic distribution in positions other than FW, but, in that of FW, the distribu-
tion was leptokurtic (Exp. 2). Therefore, the θCOD proposed in this study may be an index of
Table 1. Descriptive data on θCOD and the difference between each θCOD and set angle.
Angle of CODs
θCOD
a
Dif
0˚
-3.2 ± 3.2
3.2 ± 3.2 b
15˚
12.2 ± 2.7
2.7 ± 2.7 b
30˚
23.4 ± 1.6
6.6 ± 1.6 c
45˚
35.4 ± 2.8
9.4 ± 2.9 d
60˚
45.9 ± 4.1
14.1 ± 4.1 e
75˚
57.2 ± 5.6
17.6 ± 5.4 f
90˚
68.1 ± 8.7
21.5 ± 8.5 g
105˚
77.2 ± 5.1
27.8 ± 5.1 h
120˚
89.2 ± 5.6
30.8 ± 5.6
135˚
102.5 ± 3.9
31.8 ± 4.6
150˚
112.0 ± 4.1
37.8 ± 4.0 i
165˚
131.4 ± 4.9
33.4 ± 5.2 i
180˚
155.0 ± 7.5
24.6 ± 7.7
Values are means and SDs. COD, change of direction; a, significant difference with all combinations; b, significant
difference between the corresponding angle and set angles above 60˚, c, significant difference between corresponding
angle and set angles above 75˚; d, significant difference between corresponding angle and set angles above 90˚, e,
significant difference between corresponding angle and set angles above 105˚; f, significant difference between
corresponding angle and set angles above 105˚, except for 180˚; g, significant difference between corresponding angle
and set angles above 120˚, except for 180˚; h, significant difference between corresponding angle and 150˚; i,
significant difference between corresponding angle and 180˚.
https://doi.org/10.1371/journal.pone.0251292.t001
PLOS ONE
Quantifying angle and time of changes-of-direction
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
6 / 12
angle of CODs, and profile of CODs during soccer matches obtained from θCOD may be posi-
tion-specific.
In Exp.1, each θCOD was smaller than the set angle, and the difference between each set
angle and θCOD became larger as the angle increased. This may have been due to a difference
in the set course and the trajectory of center of mass (COM) of a player’s body. For example,
in the COD at 90 deg, a player moved in an arc, rather than at a right angle, as seen in S1 Fig.
Fig 2. Relationship between θCOD and set angles. Black dotted plot indicates the mean value of each set angle. Grey dotted plots indicate individual’s data within each set
angle. Dotted line indicates approximate line.
https://doi.org/10.1371/journal.pone.0251292.g002
PLOS ONE
Quantifying angle and time of changes-of-direction
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
7 / 12
The direction of COM during change-of-direction running differed from the set angle, and
the angle for COM was smaller than the set angle [20–22]. Suzuki et al. [20] revealed that the
difference was 2˚ at 30˚, 8˚ at 60˚, and 12˚ at 90˚, and the difference increased with COD
angles. In this study, the corresponding values were 6.6˚, 14.1˚, and 21.5˚, respectively, also
becoming greater as COD angle increased.
The mean values of analytical duration were 1.04 s for Exp. 1, and 0.89 s for Exp. 2. Gran-
ero-Gil et al. [23] have defined change-of-direction locomotion as curvilinear locomotion that
lasts more than 0.8 s, and they attempted to detect CODs during soccer matches by using an
inertial sensor. The analytical durations in the present study were close to this definition, pro-
viding support for the threshold reported by Granero-Gil et al. [23]. On the other hand, the
Table 2. Descriptive data on number of CODs, analytical duration, skewness and kurtosis of frequency distribution.
Number per match (times)
Duration per COD (s)
Skewness
Kurtosis
All
183 ± 39
0.89 ± 0.49
-1.50
-31.50 b
CB
175 ± 38
0.88 ± 0.49 a
0.34
-17.91 b
SB
183 ± 43
0.90 ± 0.50
-2.20 b
-13.87 b
CMF
196 ± 38
0.90 ± 0.48
-0.11
-14.59 b
SMF
195 ± 36
0.89 ± 0.50 a
-1.00
-9.54 b
FW
173 ± 39
0.93 ± 0.50
-0.56
13.22 b
Values are means and SDs. All, all positions; CB, center backs; SB, side backs; CMF, central midfielders; SMF, side midfielders; FW, forwards
a, Significant difference in the measured variable between FW and other positions
b, Significant different from normal distribution
https://doi.org/10.1371/journal.pone.0251292.t002
Fig 3. Relative frequency distribution of θCOD per match. Each bin is set at every 15˚. A: all positions, B: center backs (CB), C: side backs (SB), D: central
midfielders (CMF), E: side midfielders (SMF), F: forwards (FW).
https://doi.org/10.1371/journal.pone.0251292.g003
PLOS ONE
Quantifying angle and time of changes-of-direction
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
8 / 12
number of CODs in the present matches was approx. 183, lower than the corresponding value
(471 times) reported by Granero-Gil et al. [23]. This discrepancy may be due to differences in
the method of analysis. In this study, θCOD was estimated based on acceleration above 2 m/s2
[1], while the earlier study used the definition above to identify changing-of-direction locomo-
tion [23]. Another reason may be due to be the technical error of acceleration measured by
Table 3. Descriptive data on number of CODs per match in each bin range.
CB
SB
CMF
SMF
FW
0–15˚
16.7 ± 5.5
21.3 ± 7
17.2 ± 5.1
21.8 ± 7.5
22.4 ± 5.9
15–30˚
13.6 ± 4.9
15.5 ± 5.5
15.5 ± 4.5
18.1 ± 5.4
15.6 ± 4.5
30–45˚
13.1 ± 4.0
12.4 ± 4.6
13.7 ± 4.0
12.8 ± 4.9
15.8 ± 4.5
45–60˚
12.2 ± 3.8
12.9 ± 4.6
15.6 ± 4.5
12.7 ± 2.9
13.4 ± 4.5
60–75˚
13.5 ± 4.5
11.8 ± 4.7
16.1 ± 4.1
12.9 ± 3.8
10.6 ± 2.8
75–90˚
14.1 ± 4.9
14.8 ± 5.0
16.9 ± 6.2
14.9 ± 4.4
15.9 ± 6
90–105˚
16.3 ± 6.4
15.9 ± 4.9
18.9 ± 4.3
18.0 ± 4.4
14.2 ± 6.2
105–120˚
18.6 ± 5.9
18.4 ± 6.4
19.9 ± 7.1
21.9 ± 6.3
17.4 ± 6.4
120–135˚
17.7 ± 6.1
20.8 ± 6.7
20.6 ± 7.3
19.1 ± 6
15.2 ± 5.1
135–150˚
16.4 ± 5.7
15.6 ± 5.4
18.2 ± 6.6
18.8 ± 6.8
13.7 ± 5.0
150–165˚
11.8 ± 4.5
14.2 ± 5.9
13.2 ± 3.6
13.1 ± 4.6
8.8 ± 4.5
165–180˚
8.0 ± 3.3
7.3 ± 3.6
7.2 ± 3.5
7.2 ± 3.5
6.6 ± 2.8
180˚
2.7 ± 1.9
2.9 ± 2.1
3.1 ± 1.9
3.5 ± 2.2
3.3 ± 2.2
Values are means and SDs. All, all positions; CB, center backs; SB, side backs; CMF, central midfielders; SMF, side midfielders; FW, forwards.
https://doi.org/10.1371/journal.pone.0251292.t003
Fig 4. Relationships between θCOD and speed at onset of changing of direction (COD). Black filled circle, the speed of more than 5 m/s; Grey filled circle, the
speed below 5 m/s. A: all positions, B: center backs (CB), C: side backs (SB), D: central midfielders (CMF), E: side midfielders (SMF), F: forwards (FW).
https://doi.org/10.1371/journal.pone.0251292.g004
PLOS ONE
Quantifying angle and time of changes-of-direction
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
9 / 12
LPS. In fact, Linke et al. [4] have demonstrated that root mean square error of acceleration in
sport-specific course ranged from 0.49 m/s2 to 1.34 m/s2.
The degree of skewness demonstrated that θCOD during soccer matches was distributed
symmetrically, except for players in the side back position. This indicates that no laterality of
angles of CODs may be found for amateur soccer players. On the other hand, the asymmetric
distribution of θCOD for SB may have been due to inter-individual differences in the distribu-
tion of θCOD among SBs. In fact, the distribution of θCOD was asymmetric distribution for only
one SB player (skewness: -2.85) but was symmetric for the remaining SB players (skewness:
-1.91 to 0.65). To this point, further investigation of a larger sample size is needed. In positions
other than FW, the kurtosis analysis revealed a platykurtic distribution of θCOD during soccer
matches, indicating that soccer players changed direction at various angles during soccer
matches. As seen in Fig 3, relative frequency of COD angles around 120 deg was more, regard-
less of left or right. Bloomfield et al. found that the number of CODs within 0˚-90˚ accounted
for more than 80% of the total number of CODs [14]. The corresponding value in this study
was approx. 50%. The discrepancy may be attributable to different analysis methods. For FW,
on the other hand, the distribution of θCOD during soccer matches was leptokurtic, indicating
that FW may perform CODs with narrower angle than other positions.
During soccer matches, θCOD ranged from 0˚ to 30˚ when speed at onset of a COD was rela-
tively high (>5 m/s) (Fig 4). Kai et al. [24] revealed that the trajectory of players above 5 m/s
was similar to liner locomotion. Fitzpatrick et al. [2] also demonstrated that direction of loco-
motion at speeds of above 6.7 m/s ranged from 0˚ to 30˚. Propulsive force decreases with
increasing running speed [25], implying that there is less space to accelerate the player’s body
at a given high speed. Taken together, this evidence suggests that soccer players perform
straight runs or CODs with a narrow direction angle (<30˚) at relatively high speeds.
There are some limitations in this study. Firstly, LPS are limited in high intensity effort such
as high speed straight running and CODs [3, 4, 6, 9]. During sport-specific course and small-
sided games, the root mean square errors of instant speed over 4.17 m/s range from 0.34 m/s to
0.39 m/s [4]. However, the values may not be enough to change relationships between instant
speed at onset of CODs and angles of CODs (Fig 4). Secondly, the approach used in this study
cannot be used to determine direction of a body. For example, if a player runs backward in the
opposite direction immediately after he moves in a straight run, the locomotion is estimated as a
COD with a 180˚ turn. Further investigation of this point is needed. Thirdly, parameters derived
from LPS may be influenced by measurement condition and experimental protocol [26],
although the validity of tracking systems is shown in earlier studies abovementioned [3–9].
Unfortunately, we have the relevant data, and further investigation is needed in this point.
In practical application, this study demonstrated that the relative distribution of θCOD was
position-specific, and θCOD was affected by speed at the onset of the COD during soccer
matches. To design regular soccer training that meet physical demands for each position,
coaches and strength conditioners for soccer players have to know what kind of locomotion is
taking place during soccer matches. Considering the current findings, the players of positions
other than FW need to perform CODs toward various direction at relatively low speed (< 5
m/s). For FW, however, it’s better to perform CODs toward narrow angle (< 30 deg) at rela-
tively high speed (> 5 m/s). Thus, the current findings may be useful information to achieve
the principle of training specificity for soccer.
Conclusion
This study proposed a new approach to quantifying angle of CODs (θCOD) during soccer
matches by using direction of speed and jerk. As the results, θCOD increases with increasing
PLOS ONE
Quantifying angle and time of changes-of-direction
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
10 / 12
the predetermined set angle, although θCOD was smaller than the predetermined set angle. Fur-
ther, the relative frequency of θCOD derived from the proposed approach revealed position-
specific, and θCOD was affected by speed at the onset of the COD during soccer matches. The
current findings suggest that the approach proposed in this study may be useful to quantify
angle of CODs during soccer matches.
Supporting information
S1 Fig. An example of typical trajectory data and kinematic data (speed, acceleration, jerk
and direction of speed) in each angle when one player performed CODs in directions
determined by 13 set angles (every 15˚, ranging from 0˚ to 180˚). A: 0˚, B: 15˚, C: 30˚, D:
45˚, E: 60˚, F: 75˚, G: 90˚, H: 105˚, I: 120˚, J: 135˚, K: 150˚, L: 165˚, M: 180˚. A bold line over-
lapped in line plot indicates an analytical period.
(ZIP)
S2 Fig. The time-series data for jerk with and without the filtering process are presented.
The use of cutoff frequencies of 3–6 Hz resulted in noise in the smoothed time-series data,
while cutoff frequencies <2 Hz produced less noise. Thus, a 2 Hz cutoff frequency was
adopted.
(TIF)
S1 Data.
(XLSX)
Author Contributions
Conceptualization: Yohei Takai.
Data curation: Tomohiro Kai, Yuhei Anbe.
Formal analysis: Tomohiro Kai.
Investigation: Yuhei Anbe.
Methodology: Shin Hirai, Yohei Takai.
Project administration: Yohei Takai.
Writing – original draft: Tomohiro Kai.
Writing – review & editing: Shin Hirai, Yohei Takai.
References
1.
Dalen T, Ingebrigtsen J, Ettema G, Hjelde GH, Wisløff U. Player Load, Acceleration, and Deceleration
During Forty-Five Competitive Matches of Elite Soccer. J Strength Cond Res. 2016; 30(2):351–359.
https://doi.org/10.1519/JSC.0000000000001063 PMID: 26057190
2.
Fitzpatrick J, Linsley A, Musham C. Running the curve: a preliminary investigation into curved sprinting
during football match-play. SPSR. 2019; 55:1–3.
3.
Frencken WG, Lemmink KA, Delleman NJ. Soccer-specific accuracy and validity of the local position
measurement (LPM) system. J Sci Med Sport. 2010; 13(6):641–645. https://doi.org/10.1016/j.jsams.
2010.04.003 PMID: 20594910
4.
Linke D, Link D, Lames M. Validation of electronic performance and tracking systems EPTS under field
conditions. PLoS One. 2018; 13(7):e0199519. https://doi.org/10.1371/journal.pone.0199519 PMID:
30036364
5.
Luteberget LS, Spencer M, Gilgien M. Validity of the Catapult ClearSky T6 Local Positioning System for
Team Sports Specific Drills, in Indoor Conditions. Front Physiol. 2018; 9:115. https://doi.org/10.3389/
fphys.2018.00115 PMID: 29670530
PLOS ONE
Quantifying angle and time of changes-of-direction
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
11 / 12
6.
Ogris G, Leser R, Horsak B, Kornfeind P, Heller M, Baca A. Accuracy of the LPM tracking system con-
sidering dynamic position changes. J Sports Sci. 2012; 30(14):1503–1511. https://doi.org/10.1080/
02640414.2012.712712 PMID: 22906154
7.
Rico-Gonza´lez M, Arcos A, Clemente FM, Rojas-Valverde D, Pino-Ortega J. Accuracy and reliability of
local positioning systems for measuring sport movement patterns in stadium-scale: A systematic
review. Appl Sci. 2020; 10(17):5994. https://doi.org/10.3390/app10175994.
8.
Sathyan T, Shuttleworth R, Hedley M, Davids K. Validity and reliability of a radio positioning system for
tracking athletes in indoor and outdoor team sports. Behav Res Methods. 2012; 44(4):1108–1114.
https://doi.org/10.3758/s13428-012-0192-2 PMID: 22477436
9.
Stevens TG, de Ruiter CJ, van Niel C, van de Rhee R, Beek PJ, Savelsbergh GJ. Measuring acceleration
and deceleration in soccer-specific movements using a local position measurement (LPM) system. Int J
Sports Physiol Perform. 2014; 9(3):446–456. https://doi.org/10.1123/ijspp.2013-0340 PMID: 24509777
10.
Hoppe MW, Baumgart C, Polglaze T, Freiwald J. Validity and reliability of GPS and LPS for measuring
distances covered and sprint mechanical properties in team sports. PLoS One. 2018; 13(2):e0192708.
https://doi.org/10.1371/journal.pone.0192708 PMID: 29420620
11.
Buchheit M, Allen A, Poon TK, Modonutti M, Gregson W, Di Salvo V. Integrating different tracking sys-
tems in football: multiple camera semi-automatic system, local position measurement and GPS technol-
ogies. J Sports Sci. 2014; 32(20):1844–1857. https://doi.org/10.1080/02640414.2014.942687 PMID:
25093242
12.
Oliva-Lozano JM, Rojas-Valverde D, Go´mez-Carmona CD, Fortes V, Pino-Ortega J. Impact of contex-
tual variables on the representative external load profile of Spanish professional soccer match-play: A
full season study. Eur J Sport Sci. 2020:1–10. https://doi.org/10.1080/17461391.2020.1751305 PMID:
32233969
13.
Bangsbo J. The physiology of intermittent activity in football. In: Reilly T, Bangsbo J, Hughes M, London
E, Spon FN, editors. Science and Football III 1997. p. 43–53.
14.
Bloomfield J, Polman R, O’Donoghue P. Physical Demands of Different Positions in FA Premier League
Soccer. J Sports Sci Med. 2007; 6(1):63–70. PMID: 24149226
15.
Stein M, Seebacher D, Marcelino R, Schreck T, Grossniklaus M, Keim DA, et al. Where to go: Computa-
tional and visual what-if analyses in soccer. J Sports Sci. 2019; 37(24):2774–2782. https://doi.org/10.
1080/02640414.2019.1652541 PMID: 31402759
16.
Franks IM, Miller G. Eyewitness testimony in sport. J Sport Behav. 1986.
17.
Barros RM, Misuta MS, Menezes RP, Figueroa PJ, Moura FA, Cunha SA, et al. Analysis of the dis-
tances covered by first division brazilian soccer players obtained with an automatic tracking method.
2007; 6(2):233–242.
18.
Flash T, Hogan N. The coordination of arm movements: an experimentally confirmed mathematical
model. J Neurosci. 1985; 5(7):1688–1703. https://doi.org/10.1523/JNEUROSCI.05-07-01688.1985
PMID: 4020415
19.
Yokoyama Y. A study on normality of the standing height in the Japanese youth. J Anthrop Soc Nippon.
1978; 86(4):313–320. https://doi.org/10.1537/ase1911.86.313.
20.
Suzuki Y, Ae M, Enomoto Y. A kinematic analysis of cutting motion with side-step and cross-step tech-
niques. Japan J Phys Educ Health and Sport Sci. 2010; 55:81–95. https://doi.org/10.5432/jjpehss.09038.
21.
Suzuki Y, Ae M, Takenaka S, Fujii N. Comparison of support leg kinetics between side-step and cross-
step cutting techniques. Sports Biomech. 2014; 13(2):144–153. https://doi.org/10.1080/14763141.
2014.910264 PMID: 25122999
22.
Vanrenterghem J, Venables E, Pataky T, Robinson MA. The effect of running speed on knee mechani-
cal loading in females during side cutting. J Biomech. 2012; 45(14):2444–2449. https://doi.org/10.1016/
j.jbiomech.2012.06.029 PMID: 22835648
23.
Granero-Gil P, Go´mez-Carmona CD, Bastida-Castillo A, Rojas-Valverde D, de la Cruz E, Pino-Ortega
J. Influence of playing position and laterality in centripetal force and changes of direction in elite soccer
players. PLoS One. 2020; 15(4):e0232123. https://doi.org/10.1371/journal.pone.0232123 PMID:
32324801
24.
Kai T, Horio K, Aoki T, Takai Y. High-intensity running is one of the determinats for achieving score-
box possession during soccer matches. Football Sci. 2018; 15:61–69.
25.
Cavagna GA, Komarek L, Mazzoleni S. The mechanics of sprint running. J Physiol. 1971; 217(3):709–
721. https://doi.org/10.1113/jphysiol.1971.sp009595 PMID: 5098087
26.
Rico-Gonza´lez M, Los Arcos A, Rojas-Valverde D, Clemente FM, Pino-Ortega J. A Survey to Assess
the Quality of the Data Obtained by Radio-Frequency Technologies and Microelectromechanical Sys-
tems to Measure External Workload and Collective Behavior Variables in Team Sports. Sensors. 2020;
20(8). https://doi.org/10.3390/s20082271 PMID: 32316325
PLOS ONE
Quantifying angle and time of changes-of-direction
PLOS ONE | https://doi.org/10.1371/journal.pone.0251292
May 17, 2021
12 / 12

A new approach to quantify angles and time of changes-of-direction during soccer matches.
Kai, Tomohiro,Hirai, Shin,Anbe, Yuhei,Takai, Yohei