Differences in kinematics and driver performance in elite female and male golfers

ABSTRACT

The aim of this study was to compare swing kinematic differences between women and men and investigate which variables predict clubhead speed (CHS) and carry distance (CD) whilst accounting for individual variation. Methods: Swing kinematics and driver performance data were collected on 20 (10 women) elite golfers (HCP 0.7 ± 1.4). We used Bayesian T-test for between sex comparison of swing kinematics and Bayesian Analysis of covariance (ANCOVA) to produce general linear models for CHS and carry distance for elite female and male golfers separately. Results: There was strong evidence that the driver performance variables CHS and CD were decreased in women compared to men, and two kinematic variables; time to arm peak speed downswing and angular wrist peak speed were slower in women. The ANCOVAs identified very strong to overwhelming evidence that participant as a fixed factor was a determinant of CHS for both women and men but was not a determinant of CD. Conclusion: when looking to enhance driver performance among high-level golfers, coaches should be aware that variables that determine CHS and CD differ among women and men and if the aim is to improve CHS coaches should not forget the importance of individual swing characteristics.

KEYWORDS:

• Bayesian inference
• clubhead speed
• carry distance
• golf performance
• sex differences

Introduction

The importance of hitting long distances in golf, in particular driving, has had a lot of attention in both a research and coaching context and research highlights the importance of studying driving distance to golf performance (Hellström, Nilsson, & Isberg, 2014). Swing biomechanical variables are different between individuals (Brown et al., 2011; Horan & Kavanagh, 2012) and there may be no common swing technique for optimal swing performance. The relationship between swing biomechanics and driver performance among elite male golfer has been well investigated. Neal, Lumsden, Holland, and Mason (2007) reported that a successful clubface to ball impact is not influenced by segmental speed and timings of segmental peak speed but more likely by other factors that affect small changes in the orientation of the clubface at impact. What might be considered optimal swing characteristics for male golfers might not be generalised to female golfers and there is a paucity of studies investigating the relationship between swing biomechanics and driver performance among high-level female golfers. Identifying kinematic factors that influence the ability to hit further, in particular, clubhead speed (CHS) and driving distance, is an important area for developing golf performance.

The final position (displacement) of the golf ball after each shot is what determines the success of the shot and the likelihood of an advantageous subsequent shot. Carry distance (CD) is the striking distance from impact to landing, excluding role. CD is of interest for driver performance particularly in light of recent research showing players with a longer striking distance have lower scores (Hellström et al., 2014). CD, and as such driver performance, is dependent on the optimisation of several variables of which CHS is probably the most important determinant. The consequence of poor clubface and ball alignment is increased ball rotation which gives a change in vertical and/or horizontal ball trajectory and ultimately a reduction in shot outcome consistency and reduced CD (Betzler, Monk, Wallace, & Otto, 2012). Launch angle, along with ball angular velocity and other external conditions, determines how long the ball will be airborne and initial ball speed dictates the distance the ball covers during the time it is airborne. Most biomechanics swing performance studies to date have studied the relationship between swing biomechanics and CHS (Brown et al., 2011; Horan, Evans, & Kavanagh, 2011) or ball speed (Brown et al., 2011; Chu, Sell, & Lephart, 2010; Kwon, Han, Como, Lee, & Singhal, 2013) with only a few including CD (Fletcher & Hartwell, 2004; Neal et al., 2007; Verikas, Vaiciukynas, Gelzinis, Parker, & Olsson, 2016) and even less combing CHS and CD. Both CHS and CD should be concurrently investigated to determine an effective golf swing by CHS and CD and to better understand what characterises an effective golf swing.

Previous studies investigating sex differences in swing kinematics have shown several differences between female and male golfers where a common finding is that women have larger range of motion of thorax and pelvis rotation at the top of the backswing (Horan et al., 2011; Zheng, Barrentine, Fleisig, & Andrews, 2008). Zheng et al. (2008) studied differences in swing kinematics amongst PGA and LPGA players, and found LPGA players had a lower maximum velocity of the wrists, left wrist extension velocity, and clubhead velocity than PGA players. Explanations for many of the sex-differences in swing kinematics are related to anatomical differences. For example, lower segmental velocity is accredited to women having less muscle mass, reducing absolute force production and reducing the velocity of movement (Horan, Evans, Morris, & Kavanagh, 2010). Height and arm length also have a strong relationship with CHS, this is due to the increased distance (radius) between the golfer’s centre of rotation and the ball which generates greater linear velocity at any given angular velocity (Wells, Elmi, & Thomas, 2009). So even though women generally are shorter and have lesser upper body lean muscle mass than men this is not the only reason for differences in swing kinematics, and thus, it can be challenging for a coach or other support staff to apply these varying findings in a proactive coaching manner.

Analysing performance variables at the between-participant level whilst accounting for within-participant level offers an opportunity to better understand performance outcome (Langdown, Bridge, & Li, 2012; Stenling, Ivarsson, & Lindwall, 2016), however, research presenting deterministic models of driver performance among elite female golfers are lacking. One study (Brown et al., 2011) applied a deterministic approach to driver performance in a group of low handicap female golfers and showed that increased pelvis-thorax separation at the top of the backswing and increasing pelvis-thorax translation was associated with greater CHS. Furthermore, the study introduced a fixed factor in an analysis of covariance (ANCOVA) to account for within-participant variation and showed that female golfers had their unique stratagies of how to optimise CHS. These results can guide a coach to focus on both pelvis-thorax separation and translation at the top of the backswing whilst taking into account the players’ individual attributes when looking to improve CHS. Only a few studies have investigated swing kinematic variables whilst simultaneously exploring CHS and either ball speed or CD (Verikas et al., 2016; Wang, Yang, Ho, & Shiang, 2015). It is of interest to concurrently study both CHS and CD, to determine which factors influence either CHS and/or CD, to better understand what characterises an effective golf swing and to see if this differs between female and male golfers.

Study aim

There is a need for studies on elite golfers investigating both CHS and CD, comparing female and male swing kinematics characteristics. Information from such studies would add to the current body of knowledge regarding the biomechanics of the golf swing for elite-level golf players. Thus, the aim of this study was to (1) compare kinematic differences between female and male elite golfers, and (2) investigate which swing kinematics variables best describe CHS and CD for women and men independently. We hypothesise that there are differences in swing kinematics between women and men and the variance in CHS and variance in CD will be associated with the same swing kinematic variables.

Methods

Participants

Twenty elite golfers were included in the study, 10 women and 10 men, age 21.6 ± 2.0 years. All were right-handed, had a maximum handicap of −2.0 registered with the Swedish golf association (average +0.7 ± 1.4 strokes), and were playing competitive golf at an international level. This study was approved by the regional Swedish ethics committee (Lund, Dnr 2016/12) and all the participants gave written consent to participate in the study.

Data collection

Swing kinematic data were collected using a five sensor electromagnetic motion capture system at 240Hz (Polhemus Inc. Colchester, VT, USA) together with Advanced Motion Measurement software (AMM 3D, Phoenix, Arizona, USA), equipment previously used in golf research (Cheetham et al., 2008). The manufacturer (Polhemus Inc. Colchester, VT, USA) report the statics accuracy as 0.01 cm and 0.15 °, the dynamic accuracy has been reported as 0.71mm RMS (Nafis, Jensen, Beauregard, & Anderson, 2006), and the mean difference for hand angular speed in the golf swing between the electromagnetic system and an optoelectronic system (ProReflex MCU1000 System, Qualysis AB, Gothenburg, Sweden) has been reported as 25°/s (Tinmark, Hellstrom, Halvorsen, & Thorstensson, 2010). The system consists of one transmitter which contains three orthogonal coils generating three different electromagnetic fields and four sensors (Polhemus Inc. Colchester, VT, USA) which also contain three orthogonal coils recording the magnetic flux in each field. The four sensors were attached to the body segments using Velcro stretch straps. The orientation of the orthogonal global coordinate system was such that the positive x-axis pointed parallel to the shot direction, the positive Z-axis vertically upwards, and the positive y-axis forward from the right-handed golfer. Placement of the sensors and anatomical alignment are described in Table 1.

Table 1. Placement of magnetic sensors and landmarks used to construct the segments in the anatomical alignment

Local reference frame	Sensor placement	Landmarks used for anatomical alignment	Defined joint coordinate system
Club	Below Grip	Top of grip. Anterior and posterior middle handle/grip. Anterior and posterior Hozel. Club head, bottom groove at heel. Club head, bottom grove at toe. Club head, top groove at toe.	Mid-point between anterior mid-handle and posterior mid-handle (origin). Line between Mid-point, anterior mid-handle and posterior mid-handle and hozel (y vector). Line perpendicular to the plane formed by the Y-axis (Z vector). Common line perpendicular to the Z and X axis, pointing forward (X-vector).
Left hand		Point directly inferior of the styloid process of the ulna Point directly inferior of the styloid process of the radius 2^nd metacarpal 5^th metacarpal	Mid-point between point directly inferior of the styloid process of the ulna and point directly inferior of the styloid process of the radius (origin). Line between point directly inferior of the styloid process of the ulna and point directly inferior of the styloid process of the radius process (Y vector). Line perpendicular to the plane formed by the Y-axis (Z vector). Common line perpendicular to the Z and X axis, pointing forward (X-vector).
Left arm	Posterior upper arm	Left acromion process. Lateral epicondyle Medial epicondyle.	Acromion process (origin). Line connecting acromioclavicular to mid-point between lateral epicondyle and medial epicondyle pointing to the glenohumeral (Y vector). Line perpendicular to the plane formed by the Y-axis (Z vector). Common line perpendicular to the Z and X axis, pointing forward (X-vector).
Thorax	On T5	Left Acromioclavicular process. Right Acromioclavicular process. Right side mid-axillary line thorax, high. Right side mid-axillary line thorax, low	Mid-point between left and right acromioclavicular joint (origin). Line between left and right acromioclavicular process (Y vector). Line perpendicular to the plane formed by the Y-axis (Z vector). Common line perpendicular to the Z and X axis, pointing forward (X-vector).
Pelvis	Sacrum	Superior point left greater trochanter. Superior point right greater trochanter. point several inches above the trochanter point and aligned to be parallel with a visualised line from the left PSIS to the pubic symphysis	Mid-point of the left and right greater trochanter (origin). Line between left and right greater trochanter (Z vector). Line between the origin and point midway between left PSOS and pubic symphysis, parallel to the estimated pelvis tilt (Y vector). Common line perpendicular to the Z and X axis, pointing forward (X-vector).

Club and ball characteristics at pre-impact, impact, and post-impact were recorded with a radar launch monitor system (Trackman3e, v3.2, Trackman, Denmark). Doppler radar devices and stereoscopic devices have been shown to have a mean offset of 0.12 m/s and an R² value of 99.8% between measurements for CHS (Betzler et al., 2012). We selected radar technology for measuring linear CHS, firstly, as it is the velocity of the centre of mass of the driver rather than the angular velocity of the club that is a determining factor of ball speed. Secondly, shaft stiffness and the bending of the shaft during the swing have an impact on CHS calculations (Joyce, Burnett, Cochrane, & Reyes, 2016). We allowed players to use their drivers with different shaft stiffness which increased ecological validity, which was also a factor when selecting radar technology, over camera-based systems, in the current study. Radar systems are often placed behind the ball and therefore track CD. Camera systems, on the other hand, have good reliability for measuring face orientation at impact but report CD less accurately (CD is calculated from initial ball trajectory).

All golf tests were performed on a driving range where the launch monitor was set up 2.5 m behind the ball. Each participant used premium Callaway range balls and their golf club. All participants performed a golf-specific warm-up of their choice for a maximum of 10 min. Participants were then instructed to hit 5 balls with their driver and use the swing that was as ‘normal‘ as possible, for example when playing from a tee on a standard par-4 hole. Between each shot, participants were instructed to walk out of the tee (strike) area and wait for 30 seconds before commencing their pre-shot routine for the subsequent trial. A trial was excluded if the participant reported improper contact was made with the ball or the ball landed over 17.5 metres away from the centre line and a new trial was performed.

Data reduction

The swing events were determined from sensors on the club where the address sample was determined by searching backwards through the shaft angular speed curve, from 0.1 sec before the top, to the first sample that is less than 10 d/s. The top of the backswing (TOB) was determined as the point of the lowest angular velocity of the club shaft between backswing and impact. Shaft velocity is the angle between shafts at points 1 + n and n, divided by the sample time. The impact was determined as the sample before the clubhead reaches the position on the x-axis equivalent to where it was at address. This sample was cross-validated by reviewing the velocity curve graph and checking that the impact point is the sample before clubhead velocity drops rapidly. The electromagnetic transmitter is the global reference frame; the (0,0,0) reference point. Each sensor creates a local reference frame for the segment to which it is attached and tracks the segment’s full six-degrees-of-freedom of motion, with respect to the transmitter, for the entire swing. This method creates local coordinate systems based on anatomically relevant positions with the axes aligned to each body segment (Table 2). Pelvic rotation is calculated using the joint coordinate system method (Grood & Suntay, 1983) using the global coordinate system as the proximal segment and the pelvis segment as the distal segment, the same method is used for thorax segment. The lead arm segment was calculated using the humerus joint coordinate system (Wu et al., 2002) relative to the thorax (Table 2). The club segment was based on the rigid shaft model, and though real golf shafts have bending properties, the rigid shaft models estimated CHS has been reported to have a strong relationship (R² = 0.99) with actual CHS (Cheetham, 2014). Means and standard deviation of all variables investigated in this study are reported in Table 2.

Table 2. Definition of kinematic variables

Variable	Description
Golf position
Address	The address sample was determined by searching backwards through the shaft angular speed curve, from 0.1 sec before top, to the first sample that is less than 10 d/s.
TOB	Determinted as the point of lowest angular velocity of the club shaft between backswing and impact.
Impact	The sample prior to when the clubhead reaches the position on the X-axis equivalent to where it was at address.
Displacement
Thorax lift	Vertical displacement of the origin of the thorax segment
Thorax sway	Horizontal, medial-lateral, displacement of the origin of the thorax segment
Thorax thrust	Horizontal, anterior-posterior, displacement of the origin of the thorax segment
Pelvis Lift (cm)	Vertical displacement of the origin of the pelvis segment
Pelvis sway	Horizontal, medial-lateral, displacement of the origin of the pelvis segment
Pelvis thrust	Horizontal, anterior-posterior, displacement of the origin of the pelvis segment
Translational
Wrist set (°)	The angle of the left forearm with respect to a Z-vector
Wrist stretch (°)	The change in amplitude between wrist angle TOB and smallest wrist angle reached during the downswing
Shoulder adduction (°)	The angle of the humerus with respect to thorax and is measured around the local X-axis of the shoulder
Minimum shoulder adduction (°)	The smallest value of shoulder adduction during the downswing
Shoulder stretch (°)	The change in amplitude of between shoulder adduction TOB and smallest shoulder adduction reached during the downswing
Thorax rotation (°)	Rotation of the thorax around its local Y-axis
Thorax lateral bend (°)	Rotation of the thorax around its local X-axis
Thorax flexion (°)	Rotation of the thorax around its local Z-axis
Spine rotation (°)	Pelvis rotation subtracted from thorax rotation
Spine lateral flexion (°)	Pelvis lateral bend subtracted from thorax lateral bend
Spine flexion (°)	Pelvis flexion subtracted from thorax flexion
Spine rotation TOB (°)	The maximum value of spine rotation during the downswing
X-factor (°)	The amplitude of spine rotation at TOB
X-factor stretch (°)	The change in amplitude of between X-factor and the greatest spine rotation reached during the downswing
Pelvis rotation (°)	Rotation of the pelvis around its local Y-axis
Pelvis lateral bend (°)	Rotation of the pelvis around its local X- axis
Pelvis flexion (°)	Rotation of the pelvis around its local Z-axis
Temporal
Wrist speed (ω)	The resultant angular velocity, from all three rotation vectors
Arm peak speed (ω)	The resultant angular velocity, from all three rotation vectors
Thorax peak speed(ω)	The resultant angular velocity, from all three rotation vectors
Pelvis peak speed(ω)	The resultant angular velocity, from all three rotation vectors

Statistical analysis

All results are reported as the mean ± standard deviation (SD). A Bayesian independent T-test was used to test for between-sex differences in kinematics. A Bayesian analysis of covariance (ANCOVA) (computer software JASP, Version 0.8.0.0) was used to investigate which covariates were likely to explain the variance in CHS and CD for women and men separately (5 trials, women n = 10, men n = 10). The prior distribution odds were set at 1 due to a lack of prior studies to guide a decision in setting the odds differently, the r scale for fixed effects was set at 0.5. The Bayes factor (BF) is the likelihood of the findings compared to the alternative hypothesis. We applied the following thresholds to describe the size of the BF; 1–3 anecdotal, 3–10 moderate evidence, 10–30 strong, 30–100 very strong, 100–1000 extreme, >1000 overwhelming evidence (Nuzzo, 2017). Due to the possibility for a high number of variables that could be included in the final models, we will focus the discussion on variables with at least strong evidence for inclusion. All results included in the models will be reported in the Results section, but we will mainly discuss results with strong evidence.

Results

The independent Bayesian T-test was used to test for between-sex differences in swing kinematics and driver performance between women and men (Table 3). Differences in driver performance between women and men were for CHS 41.5 ± 2.2 m/s and 50.8 ± 1.7 m/s (BF = 2.036e +6) and for CD 185.8 ± 20.6 m and 233.6 ± 16.3 m (BF = 822.4), respectively indicating extremely strong evidence that women had slower CHS and less CD when compared to men. Also, strong evidence was found for kinematic variables where women had a later time to arm peak speed DS (BF = 31.5), and slower wrist peak speed (BF = 20.4) compared to men. Moderate evidence was found where women had slower arm peak speed (BF = 7.6), slower arm acceleration DS (BF 5.2) and longer downswing time (BF = 5.2) than men.

Table 3. Bayesian T-tests for kinematic differences between women and men

	Group	Mean	SD	BF₁₀	error %
Driver Performance
Carry distance (m)	Women	185.8	20.6	822.44**	1.870e -6
	Men	233.6	16.3
CHS (m/s)	Women	41.5	2.2	2.036e +6**	2.461e -9
	Men	50.8	1.7
Displacement
Thorax sway TOB (cm)	Women	−1.5	2.9	0.49	1.062e -4
	Men	−0.4	3.5
Thorax thrust TOB (cm)	Women	5.9	2.7	0.45	7.419e -5
	Men	5.2	2.7
Thorax lift TOB (cm)	Women	−3.7	3.4	0.47	5.838e -6
	Men	−4.7	2.5
Thorax sway BI (cm)	Women	0.9	5.8	0.7	0.01
	Men	−2.4	5.9
Thorax thrust BI (cm)	Women	0.2	3.1	0.54	0.01
	Men	−1.2	3.4
Thorax Lift BI (cm)	Women	1.9	3.9	0.47	6.327e -6
	Men	3.2	4.7
Pelvis sway TOB (cm)	Women	−0.7	4.2	0.42	5.021e -5
	Men	−0.05	2.3
Pelvis thrust TOB (cm)	Women	4.0	2.3	0.53	0.01
	Men	3.1	2.6
Pelvis lift TOB (cm)	Women	−3.3	1.1	0.40	5.751e -6
	Men	−3.2	1.6
Pelvis sway BI (cm)	Women	7.5	3.2	1.64	4.074e -4
	Men	10.3	2.6
Pelvis thrust BI (cm)	Women	5.4	3.0	0.40	4.850e -6
	Men	5.5	3.0
Pelvis lift BI (cm)	Women	3.0	2.8	0.40	3.238e -6
	Men	2.8	3.6
Translational
Wrist set TOB (°)	Women	92.8	10.4	0.50	2.825e -4
	Men	88.9	11.5
Wrist stretch (°)	Women	7.0	6.9	0.44	8.229e -5
	Men	8.7	6.8
Shoulder adduction TOB (°)	Women	41.2	6.3	0.40	6.754e -6
	Men	41.1	5.8
Shoulder stretch (°)	Women	3.6	3.3	0.40	6.181e -6
	Men	3.7	3.3
Thorax rotation TOB (°)	Women	−100.4	8.0	1.04	0.01
	Men	−92.4	12.6
Thorax rotation BI (°)	Women	28.3	7.9	0.94	0.01
	Men	21.0	12.2
Spine lateral bend TOB (°)	Women	−35.5	8.9	0.90	0.01
	Men	−40.9	6.5
Spine lateral bend BI (°)	Women	25.7	6.5	0.42	5.344e -5
	Men	27.0	7.3
Spine flexion TOB (°)	Women	0.1	15.6	1.17	0.01
	Men	10.7	10.3
Spine flexion BI (°)	Women	−8.3	23.8	0.81	2.550e -4
	Men	−20.1	10.2
Spine rotation TOB (°)	Women	57.8	13.4	0.77	3.025e -4
	Men	51.4	5.8
X-factor stretch (°)	Women	3.8	4.7	0.41	1.745e -5
	Men	3.2	4.0
Pelvis rotation TOB (°)	Women	−42.4	8.7	0.57	0.01
	Men	−38.3	9.5
Pelvis rotation BI (°)	Women	51.3	11.9	1.01	0.01
	Men	41.9	13.5
Temporal
Backswing time (s)	Women	0.89	0.13	0.41	1.371e -5
	Men	0.88	0.17
Downswing time (s)	Women	0.28	0.03	5.21*	7.712e -4
	Men	0.24	0.02
Follow through time (s)	Women	0.73	0.12	0.45	7.333e -5
	Men	0.77	0.12
Time to arm peak speed (s)	Women	0.08	0.01	31.49**	2.927e -4
	Men	0.07	0.01
Time to thorax peak speed (s)	Women	0.08	0.02	0.43	6.643e -5
	Men	0.07	0.02
Time to pelvis peak speed (s)	Women	0.11	0.02	0.61	0.01
	Men	0.09	0.02
Arm peak speed (ω)	Women	969.9	104.9	7.76*	2.740e -5
	Men	1115.3	102.8
Thorax peak speed (ω)	Women	697.0	74.1	0.40	5.816e -6
	Men	699.8	78.0
Pelvis peak speed (ω)	Women	474.2	59.2	0.40	6.231e -6
	Men	476.3	82.4
Wrist peak speed (ω)	Women	1016.8	150.9	20.37**	6.108e -4
	Men	1301.4	190.7
Arm acceleration DS (α)	Women	5101.4	1178.0	5.20*	7.721e -4
	Men	6565.9	1094.9
Thorax acceleration DS (α)	Women	3611.9	928.4	1.00	0.01
	Men	4219.6	702.1
Pelvis acceleration DS (α)	Women	2841.5	566.3	1.38	0.01
	Men	3320.3	542.2

CHS = clubhead speed, CD = carry distance, TOB = top of backswing, DS = downswing, BI = ball impact.

Clubhead speed for women and men

To investigate which covariates could explain the variance in driver performance, Bayesian ANCOVAs were performed for women and men separately. For women, using only CHS as the outcome variable a model was produced showing extremely strong evidence (BF = 2.437e +16) over the null model (Table 4). This model identified two covariates (wrist peak speed, BF = 1.7, and thorax peak speed, BF = 2.1) with anecdotal evidence for inclusion as determinants of the variance in CHS between female golfers. Furthermore, there was extremely strong evidence for the inclusion of participants (BF = 473015.5) as a fixed factor in the model, indicating a strong reliance on individual techniques for creating CHS among the female group.

Table 4. Bayesian ANCOVA model explaining variance for clubhead speed for women and men

Models	P(M)	P(incl)	BF 10	BF Inclusion	% error
Model for women
Null model	0.125		1
Participant + wrist peak speed + thorax rotation peak speed	0.125		2.437e +16		1.984
Effects
Participant		0.50		473015.5
Thorax rotation peak speed		0.50		2.118
Wrist peak speed		0.50		1.677
Model for men
Null model	0.031		1
Participant + thorax lift BI +spine flexion BI + thorax thrust TOB + shoulder adduction TOB	0.031		15700.44
Effects
Participant		0.50		54.809
Thorax lift BI		0.50		2.79
Spine flexion BI		0.50		2.306
Thorax thrust TOB		0.50		19.551
Shoulder adduction TOB		0.50		0.84

TOB = top of backswing, DS = downswing, BI = ball impact.

The Bayesian ANCOVA for men only with CHS as the outcome variable produced a model with extremely strong evidence (BF = 15700.44) over the null model (Table 4). This model identified one covariate with strong evidence (thorax thrust TOB, BF = 19.5) and three covariates; thorax lift at ball impact, spine flexion ball impact, shoulder adduction TOB (BFs = 0.8–2.8) with anecdotal evidence for inclusion as determinants of the variance in CHS. Similar to the women’s CHS ANCOVA, for male golfers the model showed extremely strong evidence for inclusion of participants (BF = 54.8) as a fixed factor in the model, indicating a strong reliance on individual technique for creating CHS among the male golfers in line with that of the female golfers.

Carry distance for women and men

For the outcome variable CD in female golfers, a Bayesian ANCOVA produced a model with extremely strong evidence (BF = 3.497e+7) over the null model (Table 5). Three covariates with extremely strong evidence were identified; arm peak speed (BF = 562), wrist set TOB (BF = 29.6), Trunk lateral bend ball impact (BF = 3691), and two with anecdotal evidence; thorax rotation TOB (BF = 1.4) and pelvis lift TOB (BF = 2.4) were included in the model determining variance in carry between female golfers.

Table 5. Bayesian ANCOVA model explaining variance for carry for women and men

Models	P(M)	P(incl)	BF 10	BF Inclusion	% error
Model for women
Null model	0.031		1
Arm peak speed + Wrist set TOB + Thorax rotation TOB + Pelvis lift TOB + Trunk lateral bend BI	0.031		3.497e +7
Effects
Arm peak speed		0.500		561.811
Wrist set TOB		0.500		29.695
Thorax rotation TOB		0.500		1.387
Pelvis lift TOB		0.500		2.378
Trunk lateral bend BI		0.500		3691.915
Model for men
Null model	0.031		1
X-factor stretch + Wrist peak speed + pelvis acceleration + pelvis peak speed	0.031		5.555e +8		8.205e -5
Effects
X-factor stretch		0.50		7.45
Wrist peak speed		0.50		14.60
Pelvis acceleration		0.50		12.63
Pelvis peak speed		0.50		75.26

TOB = top of backswing, DS = downswing, BI = ball impact.

With CD as the outcome variable for male golfers extremely strong evidence (BF = 5.555e +8) over the null model was found (Table 5). This model identified three covariates with strong evidence; wrist peak speed (BF = 14.6), pelvis acceleration DS (BF = 12.6), and pelvis peak speed (BF = 75). Additionally, X-factor stretch (BF = 7.5) had moderate evidence for inclusion as determinants of the variance in carry between men. Interestingly, in contrast to the model for CHS, there was no evidence for the inclusion of the participant as a fixed factor in the model for neither women nor men, indicating less reliance on individual swing techniques for creating carry among elite golfers.

Discussion and implications

In the present study, our between sexes comparison of female and male swing kinematic variables showed strong evidence that women take more time to reach peak arm speed DS and have lower peak wrist speeds than men. We used Bayesian ANCOVA models, which account for the impact of intra-participant swing variation, to produce general linear models for CHS and CD for elite female and male golfers separately. The novel findings in the present study were that both women and men rely more on individual swing techniques to generate CHS whereas CD relied much less on individual swing techniques. The variables which determine CHS are not the same among the female and male golfers.

Between sex differences in driver performance

As expected, our study showed strong evidence for between-sex differences in the driver performance variables where women have slower CHS and shorter CD. In the current study CHS was 41.4 m/s for elite women and 50.8 m/s for elite men which is very similar to CHS measurements on an elite golf population by Horan & Kavanagh (2012) (women = 40.4 m/s, men = 49.1 m/s) whereas the average CHS reported by Zheng et al. (2008) is lower (women = 32.0 m/s, men = 34 m/s). Mean CHS for male golfers in our study is also very similar to the CHS (50.9 m/s) during the 2017 men’s PGA TOUR (Professional Golf Association [PGA], 2018a) which indicate that our male golfers match the CHS of world-class golfers. On the other hand, CD for men (233.6 m) in the present study is 20 m less than the average CD (255.1 m) for men on the 2017 PGA TOUR (Professional Golf Association [PGA], 2018b). It appears that the male golfers in our sample have enough CHS but do not transfer the energy as efficiently from driver to the golf ball during impact as the PGA golfers. Comparisons of our women’s CHS and CD with those on the LPGA TOUR are more difficult as the LPGA TOUR does not officially report either of these variables. However, the 2017 LPGA TOUR report CD with roll, which is 45 m longer (230.4 m) than the CD (without roll) of 185.8 m by the female golfers in our study (Ladies Professional Golf Association [LPGA], 2018).

Between sex differences in swing kinematics

In the present study, we found that between sex differences in golf swing kinematic variables were associated with more distal located but no proximal located segments. Elite female golfers took more time to reach peak speed in the lead arm, had lower wrist peak speed, less lead arm peak speed, less lead arm acceleration, and longer downswing time when compared to elite male golfers. Our findings are in line with Zheng et al. (2008) who observed that female golfers have slower angular velocities in more distal located segments, elbow and wrist, compared to male golfers. Zheng et al. (2008) further noted that women have a greater incidence of injury at the elbow and wrist compared to men and speculated that the wrists are a weaker link in the kinetic chain among female golfers. The lower velocities achieved by women compared to men may be attributed to the ability to transfer momentum from proximal to distal segments, a notion supported by Horan et al. (2010) who observed lower thorax angular velocity and acceleration among female when compared to male golfers. Studies have shown the most active muscles during the downswing are the pectoralis muscles along with flexor bursts in the forearms (McHardy & Pollard, 2005) and that lower segmental velocities may be attributed to lesser body mass and upper body muscle mass among women. Similarly, Horan et al. (2010) found that female golfers had a longer downswing duration but no significant difference in pelvis or thorax rotation at TOB, which is similar to the findings in our study that show that the downswing takes more time for women than men. Interestingly, even though women reach arm peak speed somewhat later than men, both sexes reach arm peek speed at the same relative time (29%) of the downswing duration.

Intra-participant variation on CHS and CD for women and men separately

The golf swing is often characterised as a complex movement with a high amount of movement variability during the backswing and downswing but reducing towards near-zero variability at ball contact (Horan & Kavanagh, 2012). Our results for CHS from the ANCOVA revealed strong to overwhelming evidence for the inclusion of the participants as a fixed factor and an important CHS variable for both female and male golfers. Our results support previous research by Brown et al. (2011) who presented the inclusion of participant as a fixed factor when investigating the relationship between swing characteristics and driver performance among high-level female golfers (average handicap 1.75). Interestingly, the evidence (size of Bayes factor) for the inclusion of participants as a fixed factor was a lot greater for the female group compared to the male group, which suggests that the female golfers in our study were more reliant on individual strategies to generate CHS than the males. Other studies investigating movement variability amongst golfers have reported similar findings that elite female golfers have a greater variance in pelvis and thorax kinematics at the mid-point of the downswing (Horan et al., 2010), and a more varied muscle activation profiles during the backswing and downswing (Verikas et al., 2016) compared to male golfers. The greater variability in swing kinematics may not be detrimental to performance, for example, higher-skilled golfers have greater motor abundance and better motor synergy (coordination) than lower-skilled golfers (Morrison, McGrath, & Wallace, 2016) and developing control over the abundant degrees of freedom in the body may be important for achieving higher skill levels in golf. The knowledge that elite golfers rely heavily on individual strategies to generate CHS should be taken into account when coaching high-level golfers.

In contrast to the large reliance on individual movement strategies to reach CHS for both sexes, the ANCOVA models that explained variation in CD did not include the participant covariate in the final model, indicating that for elite golfers individual swing technique is rather trivial when generating CD. This makes sense because impact characteristics represent the last changeable factor in the golf swing and determine ball trajectory, and previous research has reported that highly skilled golfers prefer a similar and straighter ball trajectory than intermediate level golfers (Morrison, McGrath, & Wallace, 2017). Skilled golfers must organise the abundant degrees of freedom in the body (Morrison et al., 2016) to control clubhead kinematics for similar kinematics at impact. This is supported by research investigating compensatory variability that describes how some aspects of sports performance that requires stability may only be successful when other factors are allowed to vary (Horan et al., 2011). Our results show that clubhead-to-ball impact and subsequent ball trajectory require stability whilst the way CHS is generated can vary.

Model for CHS in women and men separately

The ANCOVA results for the female group showed overwhelming evidence for participants as a fixed factor as discussed above, but the other variables included in the model for CHS were of anecdotal evidence only and included thorax rotation peek speed and wrist peak speed. Wrist movements during the downswing are frequently examined in both scientific (Brown et al., 2011; Joyce, Burnett, et al., 2016; Sprigings & Neal, 2000) and coaching literature and there is a small body of evidence that indicates wrist, and more importantly, wrist strength is a conceivable weak link in the kinetic chain among golfers with lesser striking distance. Furthermore, Horan et al. (2010) suggested that absolute force production being generated could explain thorax speed. Interestingly, for female golfers, the only kinematic variables which appear to be important in explaining the variance in CHS are associated with the ability to generate greater speed and presumably strength, and the ability to generate greater power is likely an important aspect for increased driving performance among female golfers. Therefore, one interpretation of our results could be that female golfers and coaches looking to increase segmental speed could consider using strength training to increase muscle mass along with swing technique training.

Aside from the reliance on individual strategies for CHS, ANCOVA results for the male group exposed four variables associated with greater CHS, with a majority being related to the torso. Only thorax thrust TOB had strong evidence for being positively associated with greater CHS. Our findings confirm previous research that thorax motion is associated with higher CHS (Chu et al., 2010; Morrison et al., 2017), and may be associated with a more vertical swing plane, height and arm length of a player (Morrison et al., 2017). Taller golfers may have more hip flexion and more thorax lateral bend during their golf swing which in combination with thorax rotation, such as at TOB, may bring about greater thorax thrust. Alternatively, greater CHS among taller players may be due to an increased ability to swing the arms further during the backswing and allow for an increase in the work on the club and therefore greater CHS (Hellström, 2009). Unfortunately, we did not collect anthropometric data, and cannot verify this speculation in the present study. A strong linear correlation (r = 0.71–0.77) between height, arm length, and CHS has been reported in a previous study (Wells et al., 2009) and it has been speculated (Hellström, 2009) that a quadratic equation between arm and shaft length and CHS might be stronger than a linear correlation. Our findings show a relationship between thorax thrust TOB, spine flexion ball impact, and CHS that suggests that player height is a factor that determines CHS. Research investigating and combining the impact height, arm length, and shaft length have on both swing kinematics and CHS is currently lacking and more investigations are required.

Model for CD in women and men separately

The ANCOVA results for the female group showed extremely strong evidence that arm peak speed, wrist set TOB, and trunk lateral bend ball impact are associated with greater CD. There is a moderate amount of research supporting our findings that greater trunk lateral bend is associated with longer CD. For example, Joyce, Chivers, et al., (2016) found that reduced trunk lateral bending at impact was associated with a higher ball launch angle and reduced CD, and lower launch angles were associated with greater CD among high-level male golfers (handicap = 5.0), however, research investigating CD in high-level female golfers is scarce. Lateral bending may allow for the body to rotate effectively whilst attaining a posture that aligns the body and clubhead to a position required for greater driver performance. There is a paucity of research investigating the relationship between arm kinematics and CD, however, indirect evidence that shoulder and arm muscle activity is important during CD is given in an electromyography and swing kinematics study including a mix of both female and male high-level golfers (Verikas et al., 2016). It was found that shoulder and lower arm muscles (extensor digitorum communis, flexor carpi radialis, and upper and mid trapezius), activity during both the backswing and the early forward swing were associated with 7-iron CD (Verikas et al., 2016).

For the male group, ANCOVA results showed strong evidence that wrist peak speed, pelvis acceleration, and pelvis peak speed positively associated with greater CD. We speculate that pelvis acceleration and pelvis peak speed are factors that have an important role in X—factor stretch (moderate evidence for CD). This is supported by previous studies that found a strong relationship (r = 0.50) between torso-pelvis separation speed and ball speed (Myers et al., 2008), and greater pelvis horizontal rotation in the early downswing among highly-skilled golfers (handicap ≤ −5.0) compared to lower-skilled golfers (handicap −20 to −36) (Okuda, Gribble, & Armstrong, 2010). Creating more X-factor stretch during the downswing, partly by rotating the pelvis earlier and faster during the transition at TOB and early downswing, likely create tension in the trunk and hip muscles and uses the stretch-shortening cycle for more efficient power generation (Okuda et al., 2010). Some studies have suggested that too much pelvic rotation (around its local Y-axis) is detrimental to the modern golf swing (Gluck, Bendo, & Spivak, 2008; Joyce, Chivers, et al., 2016), other studies have indicated that early acceleration of the pelvis is important for an optimal proximal to distal sequence (Cheetham et al., 2008). It is unclear why the pelvis kinematic variables are included in the model explaining the variance in CD but not in the model for CHS, Early acceleration could be one reason since these variables all reach peak speed early in the downswing and may then permit for more time to align the club head with the ball for longer CD. As such we can assume that pelvis speed and acceleration are in some way associated with a more effective impact and transference of energy between clubhead and ball.

Limitations

In total we collected data from 100 swings which is less than the >1000 swings required for null hypothesis significance testing (NHST), the small sample size in NHST reduces the power of subsequent statistical analyses which increases the risk of a type 2 error. We chose to apply Bayesian inference testing in the current study for two reasons; firstly, Bayesian inference yields the conceptually more attractive probability that the null hypothesis is true given the data (Pataky & LaFortune, 2015), and as such conclusions made by Bayesian inference are less affected by sample size. Secondly, a Bayesian approach within exercise and sports science has been demonstrated to be a simple and effective way of analysing small effects that are easy to interpret compared to NHST (Mengersen, Drovandi, Robert, Pyne, & Gore, 2016). Also, a limitation of the electromagnetic system used is the modest recording frequency of 240 Hz when our results show peak arm speeds greater than 1100 °/s which implies that the lead arm would have rotated about 4 degrees between two measurement frames. Higher sampling frequencies such as 500 or 1000 Hz should be used to gain a deeper insight into the golf swing. This system was chosen because it has been speculated (Langdown et al., 2012) and shown (Carson, Collins, & Richards, 2016) that swing kinematics differs within participants when hitting into a net compared to hitting out onto a driving range. The different computational methods used to calculate segments can cause inconsistency in values between different devices/methods (Kwon et al., 2013). The current study applied the joint coordinate system method using the global coordinate system as the proximal segment and the thorax or pelvis segment as the distal segment and subtracted the pelvis value form the thorax value similarly to Cheetham (2014). This is different from other methods where hip and shoulder angles are projected onto the transverse plane or by computing the relative orientation of the upper torso to the pelvis using a Cardan rotation sequence (Kwon et al., 2013).

Conclusions

In conclusion, women have significantly longer downswing times and reduced lead arm velocity and wrist velocity than men. The ANCOVAs revealed that for elite golfers, both women and men rely heavily on individual strategies to generate CHS, but not for CD which seems to require more universal movement strategies, albeit different for elite female and male golfers. Furthermore, the variables which determine CHS are not the same among the female and male golfers. Greater CHS among women is explained by greater segmental peak speed whilst greater CHS among men is mainly determined by variables associated with the thorax. When aiming to improve driver performance a coach should first decide whether CD or CHS needs to be improved. Coaches should be aware of different variables that determine CHS and CD among women and men, and if the aim is to improve CHS then coaches should remember the importance of individual swing characteristics. Finally, one major conclusion not shown in statistical terms is that there are many similarities in swing kinematics between female and male golfers’ swings, but when we analyse the swing kinematics for elite golfers subtle differences appear if the player is female or male and in generating CHS and CD. The many similarities and subtle differences are important for coaches to keep in mind and our results highlight the importance of context, in our case, sex and outcome variables.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Knowledge Foundation (KK-stiftelsen) of Sweden under Grant 2012/0319.