The 8th Australasian Conference on Mathematics and Computers in
Sport, 3-5 July 2006, Queensland, Australia
THE APPLICATION OF AN EXPLORATORY FACTOR ANALYSIS TO INVESTIGATE
THE INTER-RELATIONSHIPS AMONGST JOINT MOVEMENT DURING PERFORMANCE
OF A FOOTBALL SKILL
1Department of Exercise Science & Sport Management, Southern Cross
University, Lismore, NSW, Australia
2School of Education, Southern Cross University, Lismore, NSW, Australia
3Graduate Research College, Southern Cross University, Lismore, NSW, Australia.
Journal of Sports Science and Medicine (2006) 5, 517 - 524
Google Scholar for Citing Article
|Many studies have investigated the kinematics of sports skills
with the majority describing the kinematics of the technique or investigating
significant kinematic variables that affect performance. Many sports
skills are complex three-dimensional movements involving many joints.
However, few studies have investigated the relationships between kinematic
variables during performance of such skills. The aim of this study
was to investigate the inter- relationships among three-dimensional
kinematic variables during performance of a lofted instep soccer kick.
A motion analysis system was used to collect kinematic data for 13
skilled amateur soccer players attempting a standardised lofted instep
kick. Three-dimensional angular displacement patterns were reported
for the thoracolumbar spine and right hip joints. Two-dimensional
angular displacement data was reported for the right knee and ankle
joints. An exploratory rather than confirmatory factor analysis was
applied, as there is currently no established theory regarding the
kinematics of a lofted instep kick. Factors were extracted using the
Maximum Likelihood Solution and orthogonally rotated using Varimax
with Kaiser normalisation. The inter-relationship among biomechanical
variables within the seven extracted factors was analysed with each
factor revealing previously unknown inter-relationships among variables
for different aspects of the kick. The use of exploratory factor analysis
has shown the complex three-dimensional kinematic inter-relationships
for a lofted instep kick. An understanding of these relationships
could prove useful to coaches when instructing, and in the development
of coaching programmes related to the lofted instep kick.
WORDS: Soccer, kicking, three-dimensional kinematics.
The most widely studied skill in football is kicking (Lees and
with the majority of studies reporting on the two-dimensional (2D)
and three-dimensional (3D) kinematics of the low or maximum velocity
instep kick (Barfield et al., 2002;
Isokawa and Lees, 1988;
Lees and Nolan, 2002;
Lees et al., 2005;
Levanon and Dapena, 1998;
Shan and Westerhoff, 2005).
There are many types of kick used in a game of football, including
the lofted instep kick, the aim of which is to propel the ball high
and over long distances. Few studies have analysed the 3D kinematics
of a lofted instep kick (Browder et al., 1991;
Prassas et al., 1990).
An understanding of the biomechanics of kicking can assist the coaching
process (Lees, 2003).
Coaching experience, combined with knowledge of a mechanical model
of the desired performance, is regarded as necessary for a coach
to correct performance (Elliott, 2001;
More studies on the lofted instep kick are needed to provide detailed
information on the kinematics of the skill and ensure that existing
coaching literature is correct (Prassas et al., 1990).
Anderson and Sidaway, 1994
analysed the co-ordination of the low instep kick using timing variables
and angle-angle plots. Few studies have used a factor analysis (or
similar technique) to examine relationships between kinematic variables
in kicking (Hodges et al., 2005).
The purpose of this study was to identify and interpret the inter-relationships
amongst 3D kinematic variables for a lofted instep kick. As there
is currently no established theory regarding the kinematics of a
lofted instep kick, an exploratory rather than confirmatory factor
analysis was applied to summarise the kinematic data.
male and female skilled amateur soccer players (23.9 ± 6.1 yrs;
74.7 ± 12.0 kg; 1.73 ± 0.10 cm, previous experience 13.9 ± 6.0 yrs),
volunteered for the study. During data collection subjects were
required to perform 20 trials of a right-foot lofted instep kick.
They were required to take a two-step angled approach of 45 - 60o
towards a stationary soccer ball and kick the ball over a 2m high
net aiming for a target (which represented a kick of approximately
35m). The emphasis of the task was on height and distance not accuracy.
Successful kicks were categorised according to distance, 15- 27.6m,
27.7- 34.9m and 35m+. Twelve retro reflective markers were used
to define the thorax, pelvis, thigh, knee and foot, two markers
were placed on the ball. Subjects were videoed using a four camera
(50 Hz) motion analysis system. Up to three trials from each distance
category were selected for further processing and analysis.
Video data of each kick from final toe-off of right foot preceding
foot-ball impact to end of active follow-through, was digitised
and processed using Peak Motus version 7.0. Spatial data was optimally
filtered, the level chosen by the Jackson Knee Point Method and
all angles calculated relative to a neutral standing posture. Post
impact resultant ball velocity and pre impact resultant foot velocity
were calculated manually from scaled co-ordinate data. 3D angular
displacement patterns were reported for the thoracolumbar spine
(relative motion between thorax and pelvis) and right hip joints.
2D angular displacement data was reported for the right knee and
ankle joints. Range of motion (ROM) during follow-through for each
joint was also calculated.
The kinematic variables for the thoracolumbar spine, right hip,
knee and ankle joints chosen for inclusion in the exploratory factor
analysis were: peak angular displacements between toe-off and foot-ball
impact; angular displacements at toe-off, heel-strike and impact;
and, ROM during follow-through. Additionally angular displacement
data was time normalised between toe-off and foot-ball impact and
timing of peak values were then reported as a percentage of total
kick time. Timing of peaks were included in the analysis as were
horizontal, vertical and resultant post-impact ball velocities and
resultant pre-impact foot velocity. Due to an insufficient number
of 35m+ kicks in relation to the number of biomechanical variables,
kicks of all distances were included in the exploratory factor analysis.
The factor analysis was carried out using SPSS version 11.0. Factors
were extracted using the Maximum Likelihood Solution and orthogonally
rotated using Varimax with Kaiser normalisation. Cattell's scree
test (Stevens, 1996,
Kim and Mueller, 1978)
was used to determine the number of factors to be extracted. Examination
of the scree plot indicated that no more than seven factors should
be extracted. Factors were extracted from the rotated factor matrix
by selecting variables with a factor loading of > | 0.4 | for
inclusion within that factor (Hair et al., 1998;
As a result a few variables were common to more than one factor.
Timing of peak hip extension, abduction and external rotation, thoracolumbar
spine extension, knee flexion, ankle plantar-flexion and ankle ROM
during follow-through and foot velocity were poorly represented
in the factor solution. As a result they were omitted from the interpretation
of each factor.
1 shows that the first seven factors obtained from the following
factor analysis accounted for 67.6% of the variance. Factor one
appears dominant, accounting for the largest amount variance (19.87%),
subsequent factors account for decreasing amounts.
one (Table 2) was largely influenced
by hip rotation and abduction variables. A decrease in hip joint
internal rotation at impact and point of maximum internal rotation
(heel-strike to impact) was associated with an increase in external
hip joint rotation at toe-off, heel-strike and also peak motion
(toe-off to heel-strike). Hip abduction angles at point of maximum
(between heel-strike and impact) and impact increased along with
the hip joint external rotation variables and hip extension at toe-off.
The combination of increased hip abduction, external rotation and
extension at toe-off indicated that the more hip extension at toe-off
and external rotation in the earlier part of the kick (toe-off to
heel-strike), the more hip abduction between point of maximum and
impact. Decreased impact angles for hip internal rotation, and increased
hip abduction and thoracolumbar spine rotation (thorax to right,
pelvis to left) angular displacements, are seen to relate to increased
knee flexion, at impact. Thus, hip motion prior to and at impact
is associated with knee flexion at impact. This association may
be result of compensatory movement by the knee to ensure appropriate
foot placement at impact.
Factor two (Table 3) indicates
that increased knee flexion of the kicking limb at heel-strike is
associated with an increase in peak knee flexion (heel-strike to
impact) slightly later in the kick. Hip joint abduction at toe-off
and heel-strike increases in line with the knee flexion variables
suggesting that increased hip abduction in the earlier stages of
the kick is related to increased knee flexion later.
Increases in hip joint abduction early on in the kick (at toe-off
and heel-strike) also relate to increases in hip abduction/adduction
ROM in follow-through. Increases in these hip abduction and knee
flexion variables are associated with a decrease in plantar flexion
of the ankle throughout the entire kick. A decrease in plantar flexion
of the ankle at toe-off is associated with decreased plantar flexion
values at heel-strike and impact as well as smaller maximum/minimum
Factor three (Table 4) indicates
that an increase in thoracolumbar spine adduction (thorax up on
right, pelvis down on right) at toe-off is associated with increased
thoracolumbar spine adduction throughout the whole kick, and vice
versa. In opposition to increases in thoracolumbar spine adduction,
hip external rotation at heel-strike and hip abduction at impact
decrease. The decreased external hip rotation at heel-strike may
be associated with movements of the thorax and pelvic segments that
increase thoracolumbar spine adduction in earlier parts of the kick.
Also, as the side-to-side tilt of the pelvis influences the magnitude
of both thoracolumbar spine and hip abduction/adduction a relationship
between the movements of these joints is perhaps logical. The specific
variables included in factor three suggest that only hip abduction/adduction
variable related to spine adduction was hip abduction at impact.
Thoracolumbar spine extension angles dominate factor four (Table
5), where a decrease/increase in spine extension at toe-off
is associated with a change at point of maximum extension (toe-off
to heel-strike) and at heel-strike.
The inter-relationships with the remaining variables suggest, that
a decrease in thoracolumbar spine extension at toe-off, point of
maximum, and at heel-strike is associated with an increase in hip
extension at point of maximum (between toe-off and heel-strike)
and at heel-strike.
Increases in ball velocities were associated with decreased peak
hip extension, hip extension at heel-strike and peak hip external
rotation for factor five (Table
6). As peak hip extension and external rotation occur between
toe-off and heel-strike, these associations suggest a decreased
external rotation in the
earlier part of the kick immediately followed by a shorter backswing
of the kicking leg as a result of decreased peak hip extension are
related to increases in ball velocities. A decrease in external
hip rotation suggests a reduced rotation away from the intended
flight of the ball in the early stages of the kick is related to
increases in ball velocities and reductions in hip extension but
external hip rotation variable only accounted for 17.7% of variance
on this factor.
relating to orientation of the thoracolumbar spine during the initial
part of the kick dominate factor six (Table
7). The inter-relationships indicate that increased thoracolumbar
spine transverse rotation (thorax to left, pelvis to right) at toe-off
is associated with increases at peak (toe-off to heel-strike) and
heel-strike. Increases in spine rotation in the first part of the
kick are also seen to relate to increased hip abduction/adduction
ROM in follow-through. Time of minimum thoracolumbar spine adduction
(thorax up on R, pelvis down on R) occurs just after toe-off and
decreases in association with increases in spine rotation variables.
The greater the spine rotation at toe-off the closer to toe-off
minimum spine adduction occurs.
For factor seven (Table 8),
the inter-relationships indicates that the greater the knee flexion
at toe-off the greater the knee flexion at impact (or vice versa),
suggesting that a player who requires more or less knee flexion
at impact may also be instructed to increase or decrease knee flexion
(as appropriate) at toe-off. However, a decrease in knee flexion
at toe-off indicates the players are taking a longer final stride
prior to kicking leading to a relative increase in kick time allowing
more time to swing the kicking leg backwards and to extend the knee
at impact. An increase in knee flexion angles was associated with
a delay in the time of maximum thoracolumbar spine adduction (thoracolumbar
spine remained adducted the entire kick). The further the pelvic
segment was orientated down to the right (thorax up on right, pelvis
down on right) decreased the distance between the pelvis and the
ground, and more knee flexion may have been required to clear the
foot prior to impact.
Smaller hip joint flexion and thoracolumbar spine flexion and transverse
rotation values at impact corresponded to a kick with increased
knee flexion at impact, indicating that the body will be in a more
upright and more forward position. The time of minimum thoracolumbar
spine adduction was inversely related to time of maximum thoracolumbar
spine adduction and knee flexion.
is a complex three-dimensional movement and exploratory factor analysis
has proved an effective technique for describing and summarising
the inter-relationships between the spine and hip, knee and ankle
joints of the kicking limb for a lofted instep kick. Interpretation
of the seven factors has provided a practical insight into the complexities
of the inter-relationships apparent in lofted instep kicking.
Combined with knowledge of ideal characteristics of lofted instep
kick performance, the identification of specific associations between
similar or different joints in varying planes of motion is of potential
benefit to a coach when attempting to improve a player's technique.
Interpretation of the factors has allowed the identification of
similar variables that increase (or decrease) in association with
each other for every measurement throughout the entire kick. If
a coach requires a performer to increase or decrease the magnitude
of a specific movement at some later point in the kick, knowing
these associations indicates whether increases or decreases in the
same type of movement earlier in the kick is likely to contribute
to the desired response. Knowledge of these associations will remove
the need for the coach to make assumptions regarding the inter-relationships
amongst movement patterns and stop erroneous feedback being provided
in an attempt to correct the motion.
Likewise, knowledge of positive and negative associations among
variables for different joints and / or planes of motion, for similar
and opposing phases of the kick, also identified in the preceding
analysis, are potentially useful to a coach. These inter-relationships
indicate which other movements are likely to be affected if one
particular aspect of the kicking action is altered. Having identified
a critical aspect of kicking movement to alter, knowledge of other
associated movement characteristics provides a coach and performer
with the choice of more than one variable to focus on altering.
As suggested in the interpretations of some factors, associations
between different joints could be due to the influence of a common
segment to both, such as the pelvic segment common to thoracolumbar
spine and hip joints and thigh common to hip and knee joints, regardless
of whether the motion was in the same plane. Further investigation
is required to determine the mechanisms of these inter- relationships.
Although factor analysis is a non-dependent statistical process,
the interpretation of factor five indicated that decreases in peak
hip extension just after toe-off and at heel-strike (suggesting
a shorter backswing of the kicking leg) are associated with increased
ball velocities. Lees and Nolan, 2002
reported increased hip (thigh-trunk) ROM for instep kicks under
speed compared to accuracy conditions and Lees et al., 2005
found increases in hip (thigh-trunk) ROM to correlate positively
with ball velocity in low maximum velocity instep kicking. The contradictions
between the literature and the interpretation of factor five could
be due to the differing aims of a lofted instep kick compared to
a maximal velocity instep kick. In addition, the hip extension variables
discussed did not load very high on factor five, peak hip extension
and extension at heel-strike accounting for 23.8% and 20.3% of the
variance respectively, suggesting they are of limited importance
to the interpretation overall. Further investigation of these inter-relationships
is warranted for different types of kick and with differing aims,
such as maximal distance, speed or accuracy, to understand the associations
between hip extension and ball velocity in lofted instep kicking.
Similarly further analysis is recommended to explore the positive
inter-relationship between knee flexion at toe-off and impact partially
describing factor seven. An increase in knee flexion at toe-off
indicates the players are taking a shorter final stride prior to
kicking therefore, it is possible that a relatively shorter kick
time will result in with less time to extend the knee in preparation
for impact resulting in an increased knee flexion at impact. Isokawa
and Lees, 1988
suggested there might be two types of kicking patterns for a one-step
instep kick. The first involving a large backswing and longer kicking
time, the second a small backswing with the lower limb moved forward
sharply by knee extension and shorter kicking time. The inter-relationships
amongst variables in factor seven suggests two types of kicking
action, although further investigation is needed on of expert technique
to determine this definitively.
In combination with the existing coaching literature and developments
in defining an 'ideal' kinematic model of a lofted instep kick,
the inter-relationships among variables identified using factor
analysis may be used to aid the development of coaching programmes
and coaching points. Such knowledge proving particularly useful
if the kinematic variables of interest are difficult to observe
or control by the performer, the developed coaching points could
then be based on other variables that inter-relate with those deemed
critical to performance.
of an exploratory factor analysis to 3D biomechanical data has revealed
previously unknown inter- relationships among variables for different
aspects of a lofted instep kick. Interpretation of the factors has
shown in detail, the complex inter-relationships that exist. An
understanding of these relationships could prove useful to coaches
when instructing, and maybe useful in the development of coaching
programmes related to the lofted instep kick.
Motion analysis of lofted instep kick.
among biomechanical variables within 7 factors analysed.
factor revealed previously unknown inter-relationships among variables
for different aspects of the kick.
these relationships could prove useful to coaches in the development
of the lofted instep kick.
Employment: PhD candidate.
Degree: BSc (hons).
Research interests: Biomechanics of football.
Employment: Head of Department of Exercise Science and Sports
Research interests: Biomechanics of sport.
Employment: Senior Lecturer in Sport, Health & PE.
Degree: BPE, MEdStud, PhD, GradDipPE.
Research interests: Skill learning/performance analysis.
Employment: University Statistician.
Research interests: Research methodology.