ArticlePDF Available

Abstract

This study compared the kinematics of upper body and cue stick among players of various skill levels when performing back spin and top spin shots. Twenty-eight male cue sports players were assigned to the novice (n = 10), intermediate (n = 9), or skilled groups (n = 9). The back spin and top spin tests were administrated while kinematic data were recorded using a 3D motion capture system. The results revealed greater upper limb joint ranges of motions (all p < 0.05), maximum angular velocities (all p < 0.05), and cue tip speed in the back spin than top spin shots (p < 0.001). None of joint kinematic or shot performance variables investigated was significantly different among the three skill levels (all p > 0.05). For the head movement, the novice group exhibited greater anteroposterior displacement than the skilled group (p = 0.020). In conclusion, except for the head movement, the upper body and cue stick kinematics did not significantly differ among players with varied skill levels. Greater joint ranges of motions and angular velocities were required to generate a faster cue tip speed for the back spin shots when compared with the top spin shots.
Influence of expertise level on techniques of applying top and back spins in cue sports
Jing Wen Pan1, John Komar1, Chen Yang2, Pui Wah Kong1,3
1Physical Education and Sports Science Academic Group, National Institute of Education, Nanyang
Technological University, Singapore
2Department of Kinesiology and Physical Education, McGill University, Montreal, Canada
3Office of Graduate Studies and Professional Learning, National Institute of Education, Nanyang
Technological University, Singapore
Jing Wen Pan, MS
Physical Education and Sports Science Academic Group, National Institute of Education, Nanyang
Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
ORCID: https://orcid.org/0000-0002-6692-368X
Email: nie173748@e.ntu.edu.sg
John Komar, Ph.D.
Physical Education and Sports Science Academic Group, National Institute of Education, Nanyang
Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
ORCID: https://orcid.org/0000-0002-2063-4065
Twitter: @J_Komar
Email: john.komar@nie.edu.sg
Chen Yang, Ph.D.
Department of Kinesiology and Physical Education, McGill University, Montreal, Quebec H2W 1S4,
Canada
ORCID: https://orcid.org/0000-0002-9945-7435
Email: chen.yang4@mail.mcgill.ca
Pui Wah Kong, Ph.D. (*Corresponding author)
Physical Education and Sports Science Academic Group, National Institute of Education, Nanyang
Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
ORCID: https://orcid.org/0000-0001-9531-9214
Twitter: @venikong
Email: puiwah.kong@nie.edu.sg
Abstract
This study compared the kinematics of upper body and cue stick among players of various skill levels
when performing back spin and top spin shots. Twenty-eight male cue sports players were assigned to
the novice (n = 10), intermediate (n = 9), or skilled groups (n = 9). The back spin and top spin tests were
administrated while kinematic data were recorded using a 3D motion capture system. The results
revealed greater upper limb joint ranges of motions (all p < 0.05), maximum angular velocities (all p <
0.05), and cue tip speed in the back spin than top spin shots (p < 0.001). None of joint kinematic or shot
performance variables investigated was significantly different among the three skill levels (all p > 0.05).
For the head movement, the novice group exhibited greater anteroposterior displacement than the
skilled group (p = 0.020). In conclusion, except for the head movement, the upper body and cue stick
kinematics did not significantly differ among players with varied skill levels. Greater joint ranges of
motions and angular velocities were required to generate a faster cue tip speed for the back spin shots
when compared with the top spin shots.
Keywords: billiards, pool, kinematic, range of motion, angular velocity
Introduction
Cue sports are a variety of popular games played with a cue stick, for example, billiards (e.g., 8-
ball, 9-ball, and 10-ball), and snooker. Previous studies have applied 2D video analyses to evaluate the
shot performance by measuring the ball movements on the snooker/billiards table (Chung et al., 2014;
Haar et al., 2020, 2021; Pan, Komar, & Kong, 2021; Pan, Komar, Sng, et al., 2021). While the physics
behind cue sports has been well studied (Jankunas & Zare, 2014; White, 2017), biomechanical research
on the human movements are rather sparse (Haar et al., 2020; Kong et al., 2021; Kornfeind et al., 2015).
Kornfeind and co-workers (2015) described the 3D kinematics of the cue stick in 20 highly ranked
European players when performing 18 predefined, such as draw shot (back spin), follow shot (top spin),
stop shot, and break shot. They found that compared with the break shot, other shots came with
relatively lower cue stick accelerations at impact. In snooker, a case study on one elite player (Kong et
al., 2021) revealed similar upper limb kinematics, ground reaction forces, and centre of pressure patterns
across five different types of shots during the cueing movement. Another study on billiards profiled the
joint kinematics of the learning progress in beginners who had little or no playing experience (Haar et
al., 2020). The authors found that right-handed players’ right shoulder mainly contributed to the cueing
movement while other joints involved less. These earlier studies provided descriptive data of various
types of shots which can serve as useful references for players and coaches. However, the lack of
biomechanical comparison between players of various skill levels makes it difficult to identify the
characteristics associated with skilled performances. Thus, it is of interest to compare the techniques
employed by skilled and less-skilled players when executing cue sports shots.
In the study on billiards by Haar and co-workers (2020), great angular velocities were reported for
shoulder abduction/adduction and internal/external rotation. However, anecdotal coaching guidelines
emphasised that skilled players should keep the body fixed during the cueing movement (Leider, 2010;
Pejcic & Meyer, 1993). Hence, the authors attributed the unexpected obvious shoulder movements to
the participants being beginners (Haar et al., 2020). On the other hand, postural variation was observed
in skilled performance when executing precision tasks (Arutyunyan et al., 1968, 1969; Müller & Sternad,
2009; Serrien et al., 2018). In these precision tasks, functional variability was reflected by higher
postural variation (i.e., higher range of motion for joints or more joints involved) that allowed for
continuous compensation between joints in order to maintain pointing/aim stability (Arutyunyan et al.,
1968, 1969). In other words, higher variability is meant to increase robustness of the performance. For
instance, in air pistol shooting, which requires high level of precision, postural variations have been
shown to help maintain stance stability (Arutyunyan et al., 1968, 1969). In addition, it is not necessary
for elite archers to minimise their body movements during aiming to stabilise the orientation of the
arrow (Serrien et al., 2018). It is currently unclear whether fixed or varied body stabilisation strategies
are desirable for precision tasks in cue sports.
Applying spins on the cue ball is a common strategy to park the cue ball at an appropriate position
for the next shot. Back spin shots, which require the player to hit the cue ball below its equator, can
produce reverse spins and draw back the cue ball after collision with the object ball. When striking the
cue ball above the equator as seen in top spin shots, the cue ball continues running forward after hitting
the object ball. Skilled players can precisely control the amount of the spin applied to regulate the end
position of the cue ball. Across different types of shots in cue sports, there is essentially one primary
cueing movement which usually consists a few practice swings and a final stroke (Kong et al., 2021).
To conduct different spin shots, players might adopt different techniques to deliver the cue stick in order
to manipulate the speed and height of the cue tip at impact. Hence, studying the upper body kinematics
in different spin shots can shed light on understanding cue sports techniques and provide valuable
information for coaches, scientists, and players. This study aimed to examine the influence of expertise
level on the upper body and cue stick kinematics during back spin and top spin shots. It was
hypothesised that 1) the kinematics of the upper body and cue stick would differ among cue sports
players of different skill levels, and 2) the kinematics would differ between the top spin and back spin
shots.
Materials and Methods
Participants
This present study was approved by the Nanyang Technological University Institutional Review
Board (Protocol Number: IRB-2019-05-013). All methods of this study were performed in accordance
with the Declaration of Helsinki. Participants provided written consent to participate in the study. A
priori power analysis shows that at least 27 participants (9 in each group) are required (α = 0.05, effect
size f = 0.333, power = 0.80). The effect size f was calculated from a partial Eta-squared of 0.1 (medium
effect size for two-way Analysis of Variance). Twenty-eight male participants (25 were right-handed, 3
were left-handed) of various skill levels were recruited, ranging from recreational players to national
team athletes. All of them had at least one year playing experience and were active cue sports players
during the time of this experiment. The exclusion criteria were that participants 1) were injured within
3 months of the study, 2) had surgery history to the shoulder, elbow, wrist, or hand, or 3) were
experiencing any pain or discomfort when playing cue sports (Pan, Komar, & Kong, 2021).
Participants were required to warm up on the 9-ball pool tables for approximately 10 minutes using
a new set of pool balls (diameter: 57.2 mm, Cyclop ZEUS Tournament TV set, Xinzhan Co., LTD,
Shanghai, China). After that, a 15-ball test was conducted to examine their overall skill levels (Pan,
Komar, & Kong, 2021). Participants were instructed to pot as many as they can consecutively in one
single visit with the 15 object balls lined up in the middle line of the pool table. In each trial, the actual
number of balls potted was used to indicate the performance. Hence, the total number in the best 2 out
of 3 trials (maximum number was 2 × 15 = 30) was used, and the participants were assigned to novice
(N, n = 10), intermediate (I, n = 9), or skilled (S, n = 9) groups (Table 1).
Table 1. Participants’ characteristics of the three groups.
Novice
(N, n = 10)
Intermediate
(I, n = 9)
Skilled
(S, n = 9)
p
η2p
post-hoc
Age [years]
25.8 (2.5)
23.4 (3.6)
29.1 (10.8)
0.193
0.117
Height [cm]
172.5 (5.0)
174.6 (6.8)
171.2 (6.3)
0.503
0.053
Body mass [kg]
68.8 (10.2)
74.0 (14.4)
69.0 (13.2)
0.609
0.039
Experience [years]
3.8 (4.0)
4.9 (3.0)
11.4 (8.6)
0.089
0.280
Balls potted
5.4 (2.3)
12.1 (1.9)
21.6 (4.5)
< 0.001*
0..838
N<I
N<S
Balls potted refers to the number of balls potted in the 15-ball test (sum of best 2 out of 3 trials).
Significant difference (p < 0.05) is shown in bold text and indicated by an asterisk.
Experimental procedures
Two types of 9-ball shots, including the back spin and top spin tests, were adopted from a previous
study (Pan, Komar, & Kong, 2021) and conducted in the present study. Familiarisation and practices
were allowed prior to the tests. Participants performed 10 successful trials, with the object ball potted
into the middle pocket, in each type of shot. If the participants failed to pot the object ball, they were
required to repeat the trials until achieved 10 successful trials. In the back spin test, an object ball (red
in this schematic representation, Figure 1) was placed at specific spot which can be determined by the
‘diamonds’ at the pool table cushions. Back spin was applied on the cue ball, which was originally set
at the centre of the head string, when potting the object ball. Due to the reverse spin, the cue ball should
return to the target represented by a piece of paper (7.5 cm × 5.3 cm); an error distance was measured
as the absolute distance between the actual end position of the cue ball and the target centre if the
participant failed to do so. In the top spin test, the cue ball was expected to follow the object ball to roll
forward upon impact and park at the target in front (Figure 1); an error distance was obtained where
necessary.
Figure 1. Schematic representations of the back spin and top spin tests. In both tests, a cue ball (white)
and an object ball (red) were used. Participants were required to pot the object ball and apply
appropriate spin onto the cue ball such that the cue ball can travel and stop at the target, which was
represented by a piece of paper (grey).
Data acquisition
In order to measure shot performance, a digital camera (30 Hz, model EX-100, Casio Computer
CO., LTD, Tokyo, Japan) was used to record the ball positions on the pool table for each shot. To
facilitate the kinematic data acquisition, 24 passive retro-reflective markers (14 mm) were placed on
the upper body of the participant, alongside 3 markers on the cue stick (Figure 2). The 24 markers
included 4 markers on the head (FHD, BHD, RHD, LHD), 4 on the trunk (STRN, XIPH, C7, T8), 4 on
the pelvis (RASI, LASI, RPSI, LPSI), 10 on the bilateral acromion process (RSHO, LSHO), medial
epicondyle (RELM, LELM), most caudal-medial point on ulnar styloid (RWRU, LWRU), most caudal-
lateral point on radial styloid (RWRR, LWRR), and 3rd metacarpal head (R3MC, L3MC), and 1 on the
lateral epicondyle (RELL/LELL) and 1 on the 5th metacarpal head (R5MC/L5MC) for the cue-wielding
arm only. Three markers were placed at the cue tip, cue stick middle, and butt, respectively. An 8-camera
motion capture system (Vicon MX, Oxford Metrics Ltd., Oxford, UK) was used to record the ball and
participant’s upper body kinematic data (joint angles, angular velocities) at 250 Hz. The origin of the
coordinate system was set at the centre of the bottom cushion. The mediolateral direction was defined
as parallel to the bottom cushion, and anteroposterior direction was perpendicular to the bottom cushion.
Figure 2 Example of one participant executing shots with retro-reflective markers fixed on the upper
body and cue stick.
Data analyses
To analyse the shot performance, an error distance was measured with the software Kinovea
(version 0.8.27, Kinovea, Bordeaux, France) (Pan, Komar, & Kong, 2021). A smaller error distance
indicates better shot performance, and vice versa. A custom upper extremity model was built comprising
the pelvis (CODA model; RASI, LASI, RPSI, LPSI), trunk (STRN, XIPH, C7, T8), head (FHD, BHD,
RHD, LHD), and bilateral upper arms (RSHO, RELM, RELL; LSO, LELM, LELL), forearms (RELM,
RELL, RWRR, RWRU; LELM, LELL, LWRR, LWRU), and hands (RWRR, RWRU, R3MC, R5MC;
LWRR, LWRU, L3MC, L5MC) following the methods provided by Gates et al. (2016) using Visual3D
(v6.01.36, C-Motion, Germantown, MD, USA). Raw kinematic data were low-pass filtered using a
fourth-order Butterworth filter at the cut-off frequency of 10 Hz, which was determined by the results
of the residual analysis (Kong et al., 2021; Winter, 2009). Kinematics of the shoulder, elbow, and wrist
of the cue-wielding arm, as well as the cue stick were obtained. Joint angles were defined and calculated
following the recommendation of International Society of Biomechanics (ISB) (Gates et al., 2016; Wu
et al., 2005). In each shot, the negative elevation of shoulder, elbow flexion/extension, and wrist
abduction/adduction were obtained (Gates et al., 2016). One direction was selected for each joint since
the movement in these directions directly associate with the cue stick delivery. Positive shoulder angles
and angular velocities represent shoulder elevation; negative values represent shoulder negative
elevation. Positive elbow angles and angular velocities represent elbow flexion; negative values
represent elbow extension. Positive wrist angles and angular velocities represent wrist abduction;
negative values represent wrist adduction. Cue stick angle was computed as the angle between the cue
stick and the pool table (horizontal plane) at impact (Kornfeind et al., 2015).
There is primarily only one cueing movement in cue sports, which contains a few practice swings
and one final stroke. For the final stroke, based on the position of the cue tip in the anteroposterior
component (Figure 3), five key moments can be identified: a) start of back swing, b) end of back swing,
c) start of forward swing, d) impact, and (e) end of follow through (Kong et al., 2021). Cue stick angle,
cue tip height, and cue tip speed at ball-cue tip impact (key moment d) were identified. The ranges of
motions (ROM) of upper limb joint angles were obtained from the start of forward swing to the end of
follow-through (from key moment c to e, shaded area in Figure 3), as this phase directly contributes to
cue tip speed and position. The maximum angular velocities, which were the maximum values of the
angular velocities, were also extracted from this phase. To investigate the head movement, the
displacement of a marker placed above participants’ right ear was obtained from the same phase. It was
defined as the difference between the maximum and minimum marker coordinates in the mediolateral,
anteroposterior, and vertical components. Similarly, the displacement of the marker fixed on the 8th
thoracic vertebra (T8) was identified to assess the trunk movement.
Figure 3 Five key moments [a (start of back swing), b (end of back swing), c (start of forward swing),
d (impact), and e (end of follow through)] determined by the anteroposterior displacement of the cue
tip in the final stroke. A greater cue tip displacement value indicates cue tip being in a more forward
position, and vice versa.
Statistical analyses
Data are expressed as mean (standard deviation). The data were imported into JASP (version 0.14.1;
JASP Team, 2020) statistical software for analyses. To compare the shot performance (error distance)
among the three groups, a one-way analysis of variance (ANOVA) was conducted. A mixed-model
ANOVA (2 Tests × 3 Levels) was performed to compare the kinematic data of the three groups between
the back spin and top spin tests. The within-participant factor was Test (back spin shot versus top spin
shot), while the between-participant factor was Level (novice, intermediate, skilled). When deviations
from sphericity occurred, p values were corrected using Greenhouse-Geisser epsilon correction of the
mean epsilon was lower than 0.75. When the mean epsilon was above 0.75, Huynh-Feldt correction
was applied. Bonferroni adjusted post-hoc comparisons were performed where necessary. The effect
size for partial Eta-squared (ηp2) was interpreted as small (0.01 ηp2 < 0.06), medium (0.06 ηp2 <
0.14), or large (ηp2 ≥ 0.14) (Lakens, 2013). All statistical tests were set at the 0.05 level.
Results
According to the results of one-way ANOVA, no significant between-group differences were found
in either the back spin (p = 0.086) or top spin shots (p = 0.388). In the back spin shot, the novice,
intermediate, and skilled groups showed the error distances of 44.1 (24.3), 31.1 (16.3), and 26.1 (5.2)
cm, respectively; the error distances were 12.8 (5.5), 9.9 (2.6), and 11.7 (4.7) cm, respectively in the
top spin shot. Concerning the kinematic variables, the results of two-way ANOVA showed that there
was a significant main effect of Test (all p < 0.001, Table 2) for cue stick angle, cue tip height, and cue
tip speed. The back spin test was characterised by greater cue stick angle, higher cue tip speed and lower
cue tip height when compared with the top spin test. However, there was no significant main effect of
Level (all p > 0.05), reflecting similar kinematics across players of all skill levels. In addition, no
significant interaction effect was found between the Test and Level (all p > 0.05).
Table 2. Comparisons of cue stick and upper limb joint kinematics among the three groups in the back
spin and top spin tests.
Level
Test
Interaction
Back spin
Top spin
p
η2p
p
η2p
p
η2p
Cue stick
Cue stick angle [o]
N
6.1 (2.1)
4.0 (0.4)
0.260
0.155
<0.001*
0.891
0.444
0.083
I
5.1 (0.8)
3.9 (0.4)
S
5.5 (0.7)
4.0 (0.4)
Cue tip height [cm]
N
2.1 (0.4)
4.0 (0.4)
0.221
0.172
<0.001*
0.995
0.529
0.076
I
1.9 (0.3)
3.9 (0.4)
S
1.8 (0.3)
4.0 (0.4)
Cue tip speed [m/s]
N
3.3 (1.5)
1.0 (0.1)
0.492
0.066
<0.001*
0.953
0.532
0.053
I
3.0 (0.3)
1.0 (0.1)
S
2.8 (0.1)
1.0 (0.1)
Range of motion [o]
Shoulder
N
8.8 (5.0)
4.8 (6.0)
0.959
<0.001
0.015*
0.543
0.054
0.305
I
8.1 (5.0)
5.8 (4.0)
S
11.6 (8.1)
2.4 (1.8)
Elbow
N
57.4 (21.7)
26.1 (26.8)
0.330
0.130
<0.001*
0.886
0.139
0.219
I
60.0 (10.5)
30.3 (23.7)
S
57.0 (10.4)
9.9 (16.5)
Wrist
N
13.4 (5.9)
4.5 (4.7)
0.209
0.178
<0.001*
0.847
0.448
0.096
I
11.6 (3.4)
7.2 (6.5)
S
10.3 (5.4)
2.3 (2.9)
Maximum angular velocity [o/s]
Shoulder
N
46.3 (39.6)
22.4 (12.0)
0.112
0.274
0.008*
0.610
0.042*#
0.397
I
52.5 (40.2)
26.3 (18.3)
S
102.1 (75.1)
18.2 (11.4)
Elbow
N
363.6 (96.7)
81.9 (71.5)
0.131
0.224
<0.001*
0.948
0.677
0.048
I
396.9 (96.1)
119.6 (112.5)
S
354.2 (122.4)
27.7 (38.3)
Wrist
N
134.8 (36.6)
35.4 (26.9)
0.078
0.273
<0.001*
0.907
0.332
0.129
I
116.8 (29.7)
54.5 (53.7)
S
105.2 (41.2)
15.5 (18.8)
N denotes the novice group. I denotes the intermediate group. S denotes the skilled group. Shoulder
denotes shoulder negative elevation. Elbow denotes elbow flexion/extension. Wrist denotes wrist
abduction/adduction. Significant difference (p < 0.05) is shown in bold text and indicated by an asterisk.
# denotes significant differences between skilled players performing the back spin tests than other 5
conditions according to the Bonferroni adjusted post hoc comparisons (all p < 0.05).
For most joint ROM and maximum angular velocities in the cue-welding arm, there was no
significant main effect of Level (all p > 0.05, Table 2) while a significant main effect of Test (all p <
0.005) was identified with all values greater in the back spin test than the top spin test. Only for the
maximum angular velocity in shoulder negative elevation, there was a significant interaction effect of
Level × Test (p = 0.042, η2p = 0.397). Post hoc comparison revealed that skilled players performed the
back spin test with higher shoulder angular velocity than the other 5 conditions (all p < 0.05).
For anteroposterior head displacement (Figure 4 a to c), there was a significant main effect of Level
(p = 0.020, η2p = 0.466) with the novice group exhibiting greater displacement than the skilled group
(mean difference = 0.4 cm, 95% confidence interval [0.1, 0.6] cm). In both mediolateral and vertical
head displacements, there was a significant main effect of Test (p = 0.031 and 0.016, respectively) with
greater displacement in the back spin test than the top spin test. Regarding the trunk movement, the
back spin test was characterised by greater displacements than the top spin test in all three directions
(all p < 0.05, Figure 4 d to f). There was no significant difference among the three groups in any trunk
movement variables (all p > 0.05).
Figure 4. Comparisons of head and trunk displacements among the three groups in the mediolateral,
anteroposterior, and vertical components when executing the back spin and top spin tests. The error
bar represents group standard deviation. Comparisons were assessed using two-way ANOVA and
Bonferroni post-hoc test. The significant post-hoc difference between the novice and skill groups is
indicated by an asterisk in the head movement in the anteroposterior component.
Discussion and implications
This study compared the kinematics of upper body, cue stick, and shot performance among players
of various skill levels when performing the back spin and top spin tests. The cue-wielding arm, trunk,
and cue stick kinematics were not significantly different among the novice, intermediate, and skilled
groups. Greater joint ROM, maximum angular velocities, cue tip speed, and cue stick angle were
observed in the back spin shots compared with the top spin shots for all three groups. During the cueing
movement, the novice group showed greater magnitudes of head movements in the anteroposterior
direction than the skilled group. No significant differences in shot performance were observed among
the novice, intermediate, and skilled groups in either the back spin or top spin shots.
The first hypothesis that the kinematics of the upper body and cue stick would differ among the
three groups with various skill levels is not supported by the results of the current study. It is somewhat
surprising that there were no significant joint ROM differences among the novice, intermediate, and
skilled players. Since the shoulder is supposed to be kept fixed during the cueing movement according
to high level coaching and training content (Leider, 2010; Pejcic & Meyer, 1993), one should not expect
great shoulder ROM or angular velocities, in particular for skilled players. In the present study, the
maximum angular velocity in shoulder negative elevation ranged from 18.2 to 102.1o/s when performing
the top spin test (Table 2). The maximum shoulder angular velocities were much lower than those
reported by Haar and co-workers (approximately 86 to 229o/s in all three directions) although their test
did not require great cue tip speed or strong spins (Haar et al., 2020). This discrepancy in results could
be due to the difference in participants’ skill levels. Indeed, in the current study, all participants had at
least one year playing experience while those in the study by Haar and co-workers had no or very little
experience in playing billiards (Haar et al., 2020). The playing experience of the participants in the
present study may also explain the lack of between-group differences. Significant kinematic differences
were only identified in the shoulder maximum angular velocities according to the post hoc analysis
(Table 2), which showed that the skilled group had the greatest maximum angular velocities when
performing the back spin tests compared with other conditions, although their shoulder ROM was
relatively small and similar. This could be because of the greater cue tip speed required in the back spin
test than in the top spin test, and can be explained by the leading joint hypothesis (Dounskaia, 2005),
which states that the leading joint (shoulder in the cueing movement) generates powerful interaction
torques at the subordinate joints (elbow and wrist). However, less skilled may be unable to utilise the
shoulder to generate powerful interaction torques at the elbow and wrist. Generally, cue stick and cue-
wielding arm kinematics did not show significant difference among the three groups. It is possible that
with one year of practice, players would have grasped the basic techniques of performing back spin and
top spin shots and therefore no substantial differences in the kinematic patterns were found. In addition,
while the kinematics of the independent joints were not different among the players, inter-joint
coordination may vary across skill levels. Future studies could further investigate the joint coordination
strategies of players with different skill levels rather than joint kinematics in isolation.
Pertaining to how cue sports players stabilise their body when executing the cueing movements,
this study examined the head and trunk displacements (Figure 4). Greater head movement in the
anteroposterior direction was found in the novice group compared with the skilled group (Figure 4 b).
This is in line with the coaching guidelines stipulating that skilled players were able to fix the body
while only allowed the elbow and wrist movements to deliver the cue stick (Leider, 2010; Pejcic &
Meyer, 1993). This result is contrasting with the concept of ‘postural variations’ postulating that high
level athletes can adopt varied body postures to maintain stance stability (Arutyunyan et al., 1968, 1969).
In other precision sports, postural variations were considered promising (Arutyunyan et al., 1969;
Serrien et al., 2018) and ubiquitous due to the inherent dynamics of the human body (Kantz & Schreiber,
2004). The flexibility offered by varied body postures provides advantages when the participant is
dealing with a precision task (Latash et al., 2002). Observations from the present study showed that
skilled cue sports players did not move their body much during the cueing movement as reflected by
the small magnitude in head and trunk displacements. Interestingly, postural variations represented by
greater head displacement was identified in novice cue sports players instead of more skilled players
had smaller magnitudes of head movements. According to common coaching guidelines, greater upper
body displacement of novices may impair stance stability and shooting performance and the cue tip
could not strike on the correct position on the cue ball (e.g., lower part in back spin shots and upper part
in top spin shots). Hence, fixed body was employed by skilled players in cue sports. In the
abovementioned studies on air pistol shooting (Arutyunyan et al., 1969) and archery shooting (Serrien
et al., 2018), fine finger moves in small magnitudes were primarily involved and varied body postures
could compensate the stance stability. However, during the cueing movement which requires large
magnitude of elbow and wrist movements, the other body parts should keep still for better stance
stability. Furthermore, air pistol shooting and archery athletes stand only on their feet, while in cue sport,
the bridge hand was placed on the pool table for the purpose of supporting the cue stick. The players’
body weight being partially distributed on the pool table may contribute to providing stance stability.
Owing to the differences in movement nature and stance posture between cue sports and other precision
sports, this present study does not support the concept of ‘postural variations’. Cue sports players are
recommended to minimise non-relevant head movements when delivering the cue stick.
The second hypothesis is verified as significant differences in the cue-wielding arm and cue stick
kinematics were observed between the back spin and top spin tests. When performing the back spin
shots, the cue tip was lower than that in the top spin shots (mean difference = -2.0 cm, 95% confidence
interval [1.9, 2.1] cm). By striking the cue ball on a precise position, the correct type of spin (i.e., back
spin if hitting below the equator, and top spin if hitting above the equator) can be produced. By
observing the cue ball trajectory upon impacting the object ball, it can be confirmed that the participants
generally applied the spin in the correct direction for both back spin (cue ball travelled back) and top
spin (cue ball continued to move forward). This is further supported by the lower cue tip height in the
back spin shots compared with the top spin shots. Learning from coaches and elite players, players
should not elevate the cue stick butt when delivering the cue stick, in order to try to keep the cue stick
parallel to the playing surface of the pool table. While the cue stick angle in the back spin test was
significantly greater than in the top spin test, it was approximately within the range of 4o to 6o for all
participants. This observation confirmed that the cue stick butt was not much elevated regardless of the
type of spin applied to the cue ball. According to the feedbacks provided by the participants during the
experiment sessions, the back spin test was more difficult than the top spin test. Participants’ subjective
perceived challenge corresponded well with the higher cue tip speed required in the back spin test than
the top spin test. While the cue tip speed in the current study (around 1 m/s for the top spin test and 3
m/s for the back spin test) were both lower than those reported in the earlier snooker study (roughly 2.5
m/s for top spin test and 4 m/s for the back spin test) (Kong et al., 2021), it should be acknowledged
that the snooker table are bigger (356.9 cm × 177.8 cm) than the 9-ball table and the shot distances were
longer than the settings in this study, and hence, greater cue tip speeds and stronger spins were needed
in snooker than the results of this present study. The greater joint ROM and maximum angular velocities
in the back spin test were likely to contribute to the higher cue tip speed at impact than the top spin test.
The higher cue tip speed for the back spin shots could be a requirement for sufficient back spins to draw
the cue ball backward upon impacting the object ball. Collectively, coaches and players should note the
different techniques in the cue-wielding arm to effectively deliver the cue stick when executing back
spin and top spin shots.
There were a few limitations to the current study. Firstly, this study only investigated the forward
swing and follow-through phases of the cueing movement because these phases directly contributed to
the cue stick delivery. Future studies may consider including other phases, such as the aiming phase and
practice swings, which may relate to stance stability and aiming accuracy. Secondly, all participants had
at least one-year playing experience in the present study, and this may have contributed to the lack of
between-group differences. Complete beginners were not included in this study because they may not
be able to perform the required back spin and top spin shots. It will be of interest to explore the learning
progress of beginners over time to see when the kinematics of the cueing movement start to stabilise.
Thirdly, the participant allocation using the 15-ball test may be over-simplistic. While the 15-ball test
was effective in examining players’ overall skill levels and associated with specific skills (Pan, Komar,
& Kong, 2021), no significant differences in top spin or back spin shot performance (error distance)
were observed in this study across the novice, intermediate, and skilled players grouped according to
their 15-ball test results. The grouping method could also contribute to the lack of between-group
differences in upper body kinematics. Hence, it is worth considering utilising other approaches, such as
cluster analysis, to rank or group participants. Lastly, this study only investigated the kinematic
variables of joints in isolation. In the future, studies are warranted to assess the inter-joint coordination
when delivering the cue stick. Other aspects, such as muscle activation and joint kinetics could also be
studied to better understand the cueing movement.
Conclusion
In the back spin and top spin shots, no significant differences in shot performance were found among
the novice, intermediate, and skilled groups. When performing cue sports shots, the kinematics of cue-
wielding arm, trunk, and cue stick were not significantly different among players of different skill levels.
Compared with the top spin shots, greater joint range of motion and angular velocities were required in
the back spin shots to effectively deliver the cue stick at a higher speed at impact. Greater magnitude of
head movements in the anteroposterior direction was observed in the novice players compared with the
skilled players, suggesting that novice players exhibit non-relevant head movements which may impair
stance stability. Future studies could consider investigating other aspects of the cueing movement such
as inter-joint coordination and muscle activation.
Acknowledgements
The authors would like to thank Mr Michael Chan for his assistance in data collection. We gratefully
acknowledge Ms Dawn Guo and Ms Mui Kheng Tay for their help with the experiment pool table
arrangement. Appreciation is expressed to Ms Lily Liew and Mr Sharik Sayed from Cuesports
Singapore Academy.
Disclosure statement
No potential conflict of interest was reported by the authors.
Funding
This project was supported by Office of Education Research Start-up Grant (SUG 12/18 KPW) from
National Institute of Education, Nanyang Technological University, Singapore. The first author (JWP)
of this article was supported by the China Scholarship Council (CSC).
References
Arutyunyan, G. A., Gurfinkel, V. S., & Mirskii, M. L. (1968). Investigation of aiming at a target.
Biophysics, 13(3), 642645.
Arutyunyan, G. A., Gurfinkel, V. S., & Mirskii, M. L. (1969). Organization of movements on
execution by man of an exact postural task. Biophysics, 14(6), 11621167.
Chung, D. H. S., Griffiths, I. W., Legg, P. A., Parry, M. L., Morris, A., Chen, M., Griffiths, W., &
Thomas, A. (2014). Systematic snooker skills test to analyze player performance. International
Journal of Sports Science & Coaching, 9(5), 10831105. https://doi.org/10.1260/1747-
9541.9.5.1083
Dounskaia, N. (2005). The internal model and the leading joint hypothesis: implications for control of
multi-joint movements. Experimental Brain Research, 166(1), 116.
https://doi.org/10.1007/s00221-005-2339-1
Gates, D. H., Walters, L. S., Cowley, J., Wilken, J. M., & Resnik, L. (2016). Range of motion
requirements for upper-limb activities of daily living. The American Journal of Occupational
Therapy, 70(1), 7001350010p1-7001350010p10. https://doi.org/10.5014/ajot.2016.015487
Haar, S., Sundar, G., & Faisal, A. A. (2021). Embodied virtual reality for the study of real-world
motor learning. PLOS ONE, 16(1), e0245717. https://doi.org/10.1371/journal.pone.0245717
Haar, S., van Assel, C. M., & Faisal, A. A. (2020). Motor learning in real-world pool billiards.
Scientific Reports, 10(1), 20046. https://doi.org/10.1038/s41598-020-76805-9
Jankunas, J., & Zare, R. N. (2014). Why some pool shots are more difficult than others. Resonance,
19(2), 116122. https://doi.org/10.1007/s12045-014-0015-0
Kantz, H., & Schreiber, T. (2004). Nonlinear time series analysis (2nd ed.). Cambridge University
Press. https://books.google.com.sg/books?id=RfQjAG2pKMUC
Kong, P. W., Pan, J. W., Chu, D. P. K., Cheung, P. M., & Lau, P. W. C. (2021). Acquiring expertise
in precision sport what can we learn from an elite snooker player? Physical Activity and
Health, 5(1), 98106. https://doi.org/10.5334/paah.111
Kornfeind, P., Baca, A., Boindl, T., Kettlgruber, A., & Gollnhuber, G. (2015). Movement variability
of professional pool billiards players on selected tasks. Procedia Engineering, 112, 540545.
https://doi.org/10.1016/j.proeng.2015.07.240
Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: a practical
primer for t-tests and ANOVAs. Frontiers in Psychology, 4(NOV), 112.
https://doi.org/10.3389/fpsyg.2013.00863
Latash, M. L., Scholz, J. P., & Schöner, G. (2002). Motor Control Strategies Revealed in the Structure
of Motor Variability. Exercise and Sport Sciences Reviews, 30(1).
https://journals.lww.com/acsm-
essr/Fulltext/2002/01000/Motor_Control_Strategies_Revealed_in_the_Structure.6.aspx
Leider, N. (2010). Pool and billiards for dummies. Wiley Publishing.
https://books.google.com.sg/books?id=C-
mt6DVhbHkC&dq=Leider,+N.+Pool+%26+Billiards+for+Dummies+(Wiley,&source=gbs_navl
inks_s
Müller, H., & Sternad, D. (2009). Motor learning: changes in the structure of variability in a
redundant task. In Advances in Experimental Medicine and Biology (Vol. 629, Issue 585, pp.
439456). https://doi.org/10.1007/978-0-387-77064-2_23
Pan, J. W., Komar, J., & Kong, P. W. (2021). Development of new 9-ball test protocols for assessing
expertise in cue sports. BMC Sports Science, Medicine and Rehabilitation, 13(1), 9.
https://doi.org/10.1186/s13102-021-00237-9
Pan, J. W., Komar, J., Sng, S. B. K., & Kong, P. W. (2021). Can a good break shot determine the
game outcome in 9-ball? Frontiers in Psychology, 12.
https://doi.org/10.3389/fpsyg.2021.691043
Pejcic, B., & Meyer, R. (1993). Pocket billiards: fundamentals of technique & play. Sterling
Publishing Co., Inc.
Serrien, B., Witterzeel, E., & Baeyens, J.-P. (2018). The uncontrolled manifold concept reveals that
the structure of postural control in recurve archery shooting is related to accuracy. Journal of
Functional Morphology and Kinesiology, 3(3), 48. https://doi.org/10.3390/jfmk3030048
White, C. (2017). A comparative study of two types of ball-on-ball collision. Physics Education,
52(4), 045013. https://doi.org/10.1088/1361-6552/aa6d2a
Winter, D. A. (2009). Biomechanics and motor control of human movement (4th ed.). John Wiley &
Sons, Inc. https://doi.org/10.1002/9780470549148
Wu, G., van der Helm, F. C. T., (DirkJan) Veeger, H. E. J., Makhsous, M., Van Roy, P., Anglin, C.,
Nagels, J., Karduna, A. R., McQuade, K., Wang, X., Werner, F. W., & Buchholz, B. (2005). ISB
recommendation on definitions of joint coordinate systems of various joints for the reporting of
human joint motionPart II: shoulder, elbow, wrist and hand. Journal of Biomechanics, 38(5),
981992. https://doi.org/10.1016/j.jbiomech.2004.05.042
Article
Full-text available
Background Simulation models have been applied to analyze daily living activities and some sports movements. However, it is unknown whether the current upper extremity musculoskeletal models can be utilized for investigating cue sports movements to generate corresponding kinematic and muscle activation profiles. This study aimed to test the feasibility of applying simulation models to investigate cue sports players’ cueing movements with OpenSim. Preliminary muscle forces would be calculated once the model is validated. Methods A previously customized and validated unimanual upper extremity musculoskeletal model with six degrees of freedom at the scapula, shoulder, elbow, and wrist, as well as muscles was used in this study. Two types of cueing movements were simulated: (1) the back spin shot, and (2) 9-ball break shot. Firstly, kinematic data of the upper extremity joints were collected with a 3D motion capture system. Using the experimental marker trajectories of the back spin shot on 10 male cue sports players, the simulation on the cueing movements was executed. The model was then validated by comparing the model-generated joint angles against the experimental results using statistical parametric mapping (SPM1D) to examine the entire angle-time waveform as well as t -tests to compare the discrete variables ( e.g. , joint range of motion). Secondly, simulation of the break shot was run with the experimental marker trajectories and electromyographic (EMG) data of two male cue sports players as the model inputs. A model-estimated muscle activation calculation was performed accordingly for the upper extremity muscles. Results The OpenSim-generated joint angles for the back spin shot corresponded well with the experimental results for the elbow, while the model outputs of the shoulder deviated from the experimental data. The discrepancy in shoulder joint angles could be due to the insufficient kinematic inputs for the shoulder joint. In the break shot simulation, the preliminary findings suggested that great shoulder muscle forces could primarily contribute to the forward swing in a break shot. This suggests that strengthening the shoulder muscles may be a viable strategy to improve the break shot performance. Conclusion It is feasible to cater simulation modeling in OpenSim for biomechanical investigations of the upper extremity movements in cue sports. Model outputs can help better understand the contributions of individual muscle forces when performing cueing movements.
Article
Full-text available
This study aimed to quantify the break shot characteristics and identify their significance in predicting the game outcomes in 9-ball tournaments. The break shots of 275 frames (241 men’s, 34 women’s) of professional tournaments were analyzed from two aspects: (1) cue ball position, represented by the distance between the cue ball and the table center, and (2) ball distribution, indicated by the standard deviation of Voronoi cell areas determined from all remaining balls on the table. Spearman correlation and binary logistic regression were utilized to identify associations and to predict the frame outcomes, respectively. Results showed that the more balls falling into the pockets during the break, the more clustered the remaining balls (rs = 0.232, p < 0.001). The closer the cue ball ending toward the table center, the more balls potted in the visit immediately after the break (rs = −0.144, p = 0.027). Neither cue ball position nor ball distribution could predict table clearance or winning of a frame. In conclusion, pocketing more balls during the break is associated with more clustered balls remaining on the table. Parking the cue ball near the table center after the break can facilitate potting more balls immediately after.
Article
Full-text available
Snooker can be an attractive life-long physical activity, given its popularity across all age groups in Asia and Europe. However, scientific research on the cueing movement is limited. This case study presented the biomechanical profiles of the cueing movement in an elite male snooker player (age 37 years old, height 173 cm, body mass 70 kg). Kinematics of the upper limb and cue stick were examined in five selected snooker tasks (warm-up, stun, top spin, back spin, and stop shots) using the Vicon motion capture system. Ground reaction forces and centre of pressure characteristics were recorded using two Kistler force platforms. Results showed that the cueing movement was contributed primarily by elbow flexion/extension and much less wrist flexion/extension. The high degree of cue stick position overlap between the practice swing and final stroke indicated high level of cueing precision. Weight transfer between feet revealed a slight lean towards the left foot throughout the final stroke, confirming that the elite player was able to maintain high stance stability when executing the cueing movement. Results presented in the present study can serve as a reference for practitioners and scientists to detect error, enhance training, and improve performance in snooker. For practical applications, snooker players are advised to stabilise their shoulder during the cueing movement and deliver the cue stick primarily via elbow movements.
Article
Full-text available
Motor-learning literature focuses on simple laboratory-tasks due to their controlled manner and the ease to apply manipulations to induce learning and adaptation. Recently, we introduced a billiards paradigm and demonstrated the feasibility of real-world-neuroscience using wearables for naturalistic full-body motion-tracking and mobile-brain-imaging. Here we developed an embodied virtual-reality (VR) environment to our real-world billiards paradigm, which allows to control the visual feedback for this complex real-world task, while maintaining sense of embodiment. The setup was validated by comparing real-world ball trajectories with the trajectories of the virtual balls, calculated by the physics engine. We then ran our short-term motor learning protocol in the embodied VR. Subjects played billiard shots when they held the physical cue and hit a physical ball on the table while seeing it all in VR. We found comparable short-term motor learning trends in the embodied VR to those we previously reported in the physical real-world task. Embodied VR can be used for learning real-world tasks in a highly controlled environment which enables applying visual manipulations, common in laboratory-tasks and rehabilitation, to a real-world full-body task. Embodied VR enables to manipulate feedback and apply perturbations to isolate and assess interactions between specific motor-learning components, thus enabling addressing the current questions of motor-learning in real-world tasks. Such a setup can potentially be used for rehabilitation, where VR is gaining popularity but the transfer to the real-world is currently limited, presumably, due to the lack of embodiment.
Article
Full-text available
Background This study aimed to develop new test protocols for evaluating 9-ball expertise levels in cue sports players. Methods Thirty-one male 9-ball players at different playing levels were recruited (recreational group, n = 8; university team, n = 15; national team, n = 8). A 15-ball test was administered to indicate overall performance by counting the number of balls potted. Five skill tests (power control, cue alignment, angle, back spin, and top spin) were conducted to evaluate specific techniques by calculating error distances from pre-set targets using 2D video analysis. Results Intra-class correlation analyses revealed excellent intra-rater and inter-rater reliability in four out of five skill tests (ICC > 0.95). Significant between-group differences were found in 15-ball test performance ( p < 0.001) and absolute error distances in the angle ( p < 0.001), back spin ( p = 0.006), and top spin tests ( p = 0.045), with the recreational group performing worst while the national team performing best. Greater inter-trial variability was observed in recreational players than the more skilled players ( p < 0.005). Conclusions In conclusion, the 9-ball test protocols were reliable and could successfully discriminate between different playing levels. Coaches and researchers may employ these protocols to identify errors, monitor training, and rank players.
Article
Full-text available
The neurobehavioral mechanisms of human motor-control and learning evolved in free behaving, real-life settings, yet this is studied mostly in reductionistic lab-based experiments. Here we take a step towards a more real-world motor neuroscience using wearables for naturalistic full-body motion-tracking and the sports of pool billiards to frame a real-world skill learning experiment. First, we asked if well-known features of motor learning in lab-based experiments generalize to a real-world task. We found similarities in many features such as multiple learning rates, and the relationship between task-related variability and motor learning. Our data-driven approach reveals the structure and complexity of movement, variability, and motor learning, enabling an in-depth understanding of the structure of motor learning in three ways: First, while expecting most of the movement learning is done by the cue-wielding arm, we find that motor learning affects the whole body, changing motor-control from head to toe. Second, during learning, all subjects decreased their movement variability and their variability in the outcome. Subjects who were initially more variable were also more variable after learning. Lastly, when screening the link across subjects between initial variability in individual joints and learning, we found that only the initial variability in the right forearm supination shows a significant correlation to the subjects’ learning rates. This is in-line with the relationship between learning and variability: while learning leads to an overall reduction in movement variability, only initial variability in specific task-relevant dimensions can facilitate faster learning.
Article
Full-text available
In this study, we examine the structure of postural variability in six elite-level recurve archers using the uncontrolled manifold concept. Previous research showed equivocal results for the relationship between postural control and shooting accuracy, but these studies were mainly limited to a descriptive approach to postural variability/stability and did not take the simultaneous movements of the upper limb joints into account. In this study, we show that the goal-equivalent variability which stabilizes the orientation of the arrow in space is significantly larger than that of the non-goal-equivalent variability in arrows of high accuracy (score 9 or 10). Conversely, arrows of lower accuracy (score 6, 7, or 8) failed to reach significant thresholds throughout the majority of the aiming phase. This analysis reveals that it is not necessary (or even possible) for elite archers to minimize the movements of all degrees of freedom during aiming, but rather that the structure of variability of the redundant kinematic chain is exploited so that the relevant performance variable (orientation of the arrow) is stabilized.
Article
Full-text available
This paper describes three methods of measuring the coefficient of restitution (CoR) for two different types of ball-on-ball collision. The first collision type (for which two different CoR measurement procedures are described) is a static, hanging steel ball forming part of a Newton’s cradle arrangement, which is then hit by its adjacent identical ball, swinging down from an angle. The second scenario (for which one CoR measurement procedure is described) is a snooker ball interaction in which the cue ball rolls in, and collides with, a static coloured ball (both balls being of a resin composition). The investigation requires only readily available and inexpensive equipment, together with an open-source video analysis programme, called ‘Tracker’². Perhaps surprisingly, the experiment yields widely differing CoR values for the two types of interaction. This variance cannot be solely accounted for by the difference in physical properties of the respective balls’ compositions. The paper then describes, in theoretical terms, the details of the dynamic interactions in each example, and hence validates the surprising discrepancy in the two results obtained empirically.
Article
Full-text available
Objective: We quantified the range of motion (ROM) required for eight upper-extremity activities of daily living (ADLs) in healthy participants. Method: Fifteen right-handed participants completed several bimanual and unilateral basic ADLs while joint kinematics were monitored using a motion capture system. Peak motions of the pelvis, trunk, shoulder, elbow, and wrist were quantified for each task. Results: To complete all activities tested, participants needed a minimum ROM of -65°/0°/105° for humeral plane angle (horizontal abduction-adduction), 0°-108° for humeral elevation, -55°/0°/79° for humeral rotation, 0°-121° for elbow flexion, -53°/0°/13° for forearm rotation, -40°/0°/38° for wrist flexion-extension, and -28°/0°/38° for wrist ulnar-radial deviation. Peak trunk ROM was 23° lean, 32° axial rotation, and 59° flexion-extension. Conclusion: Full upper-limb kinematics were calculated for several ADLs. This methodology can be used in future studies as a basis for developing normative databases of upper-extremity motions and evaluating pathology in populations.
Article
Full-text available
Parameter values characterizing the motion of the cue during impact in pool billiards have been determined for selected shots. 20 elite players performed 18 predefined tasks comprising follow, draw, stop shots and breaks. 3D-kinematics were obtained using a motion analysis system comprising 8 cameras operating at 250 Hz and a high speed camera capturing with 5000 Hz. Longitudinal accelerations of the cue stick were recorded with 5 kHz using an accelerometer, mounted on the butt cap of the cue. Coefficients of variation for the parameter values obtained range from 3.9% (height of impact point of maximum follow shot) to 58.3% (elevation angle of 10-ball break). The average cue stick motion is basically non-accelerated (-0.060 +/- 0.508 ms-2) at ball impact for all of the tasks except for the breaks (3.918 +/- 0.164 ms-2). Despite the high number of DOF in the input configuration the tested pool billiard players achieved very similar outcomes.
Article
The physics behind the game of billiards is rather well understood as is our grasp of classical mechanics. We present here a mathematical explanation of why slice shots are more difficult than direct shots. Despite a large number of treatises dedicated to the study of physics of billiards, it appears that the simple explanation has escaped our attention until now. We show that high impact-parameter shots impart a larger angular spread to the object ball, compared to head-on shots. The effect can be understood in terms of a non-linear relationship between the impact parameter and the scattering angle, and the fact that a real-world pool player does not have a perfect cue ball control; in other words, the impact parameter distribution is not a delta function, but has a finite spread. To keep the mathematics simple and not to obscure the underlying physical principles our treatment ignores the ball’s spin, friction, and other well-known effects in the game of pool.