A comparison of kicking accuracy for elite rugby players and a robotic kicker

Transcription

1 International Journal of Performance Analysis in Sport 2015, 15, A comparison of kicking accuracy for elite rugby players and a robotic kicker Claire L. Flemmer and Rory C. Flemmer School of Engineering and Advanced Technology, Massey University, Turitea Campus, Palmerston North, 4410, New Zealand Abstract This work reports the average place kicking accuracy as a function of field position for players in the last two Rugby World Cup competitions and compares this accuracy with that of a robotic kicker. Human kicker angular standard deviation varies from 2.1 to 7.0 degrees over kicking distances from 35.3 to 52.8m. The robot kicks an average distance of 44.2 ± 2.4m with an angular standard deviation of 2.2 degrees. The results show that human kickers become less accurate as they have to strike the ball harder in order to reach greater distances. At a distance of 44m, the robotic kicker is considerably more accurate than human kickers. Unlike human kickers, the robotic kicker has a consistent kick style and is therefore a useful tool for research into the mechanics, kinematics and dynamics of placekicking a rugby ball. Key words: rugby, kicking, robotic, place-kick, accuracy 1. Introduction There is some ambiguity in the terminology of foot-sports balls. In this paper the round foot ball will be referred to as a soccer ball and the oval ball as a rugby ball. Only rugby ball kicking accuracy is considered here. The performance of the goal kicker has a profound effect on the outcome of most rugby games (Young et al., 2010; Hart et al., 2014; Sinclair et al., 2014) but there is relatively little scientific research into kicking. One of the problems with such research is that it is impossible for a human to kick a rugby ball exactly the same way twice. There are variations in a number of factors such as the point of contact (on the ball and on the boot), the angle of impact, the position of the ball, the relative position of the kicker s body and the speed/angular momentum of the impacting foot. With this in mind, a humanoid kicking robot, with a kicking leg designed to mimic the human kicking movement, was tested to determine whether it could be used as a tool for research into kicking. The average place kicking data from the last two Rugby World 112

2 Cup competitions was used to compute the statistical accuracy of the kickers as a function of field position. This was then compared with the kicking accuracy of the kicking robot. A review of the background to this research includes the way in which kicking accuracy is measured, the availability of kicking accuracy statistics and methods for testing kicks. The way in which the kicking accuracy of humans is measured has advanced from using carbon paper marks on a board for soccer kicking (Finnoff et al., 2002) to recording soccer ball hit position on an electronic target (Hennig and Sterzing, 2010) and, finally, to video/camera systems and markers for American Football League (AFL) punt kicks (Dichiera et al., 2006). In this work, the accuracy of the kickers in the 2011 and 2007 Rugby World Cup competitions is defined as the percentage of each kicker s successful shots at goal. There are few published statistics on kicking accuracy; Spamer et al. (2009) reported an average place-kick distance and accuracy for elite under 16 New Zealand rugby players of 37.59m ± 4.37m and Holmes et al. (2006) measured the average place-kick distance of elite rugby union players at 53.7 ± 5.7m with an average ball speed of 26.4 ± 3.0ms -1. Ball (2008) cited Australian Rules football players kicking a 50m drop punt kick with a rugby ball speed of 25.0ms -1. Scurr and Hall (2009) reported kicking accuracy for amateur soccer players. The kicking statistics of individual professional rugby players are not published, but there are companies, such as Verusco (in New Zealand) and Opta (in London) who collect and sell such data (under confidentiality agreements with their customers), together with software that allows the element of difficulty of a kick as a function of distance and angle to be deduced. A comparison of kicking accuracy for Aaron Cruden and Dan Carter, drawn from one such database, is reported in the online website, The Roar (2011). Only the kicking success rate (percentage successful kicks out of attempted kicks) of individual kickers is reported publicly, for example, by Gilbert (2013). Nel (2013) discusses the way in which goal kicking success can be used to derive a ranking for goal kickers. English rugby ball manufacturer, Gilbert, uses human kickers to test new styles of rugby ball. Impacting machines and robots are also used to test balls under more repeatable impact conditions. A mechanical kicking machine for soccer and rugby balls reported by Holmes et al. (2007), with an A-frame and a servo motor to accelerate the kicking leg can achieve a maximum ball speed of 50ms -1. They do not specify which of the two types of balls achieved this speed nor do they give the kick distance and accuracy/repeatability. Adidas are sponsoring research using this machine (Fraser et al., 2012). The oil manufacturer, Castrol, developed the world s fastest kicker robot, in the Ichi-GO project, capable of kicking soccer balls at over 200 kph (55.5ms -1 ) consisting of an engine driving a flywheel attached to a steel kicking leg (Ackerman, 2009; Held, 2010). A robotic soccer-ball kicking leg called Roboleg was developed to test soccer balls and footwear using spring-loaded actuators (Schempf et al., 1995). However Roboleg was abandoned as a test robot because of problems with the control system (Ronkainen et al., 2010). Ganapati (2010) reports the kicking ability of a 340-lb titanium robot called Ziggy competing (unsuccessfully) against placekicker Joe Nedney of the San Francisco 49ers football team. 113

3 This brief review of the literature indicates that published statistics on professional kicking accuracy are very sparse and that research into kicking is limited because a human kicker cannot kick the same way twice. This has led to the development of a few mechanical kicking devices. This work makes three contributions to the field of sports science. Firstly, it provides statistical data on the place kicking accuracy as a function of field position for elite rugby players. Secondly it describes the performance of a robotic kicker that has a consistent kicking mechanism and, as such, is a valuable tool for scientific research into the theory of kicking. Finally, the kicking accuracy of the robot is reported and compared with the accuracy of human kickers. 2. Methods The average place kicking accuracy (successful kicks as a percentage of total attempts) as a function of field position for kickers from the past two Rugby World Cups (2011 and 2007) is shown in Table 1 (pers. comm. Ian Savage, Gilbert Rugby). The data represents approximately 1,000 attempts to kick for goal. Table 1 Average place kicking accuracy for the 2007 and 2011 Rugby World Cup competitions. Position # Distance Strip Success (%) 1 Short Left 83 2 Short Mid 96 3 Short Right 80 4 Mid Left 51 5 Mid Mid 73 6 Mid Right 48 7 Long Left 33 8 Long Mid 45 9 Long Right 29 The 9 positions on the rugby field are shown in Figure

4 kick angle, θ Figure 1 Left half of the rugby field showing the field positions with distances shown in metres on the bottom and left borders of the field. The kicks were analysed in terms of angular performance, rather than ball position as it passed the cross-bar. A perfect kick (in still conditions) would be directed to a vertical line passing through the centre of the cross-bar. Real kicks would have some variation from the perfect angle. At any kicking position, it was assumed that the actual angle of each kick would follow a normal distribution about an angle centred on the midpoint of the goal posts, i.e.: P(x) = 1 e x2 2πσ 2 2σ 2 (1) where P(x) is the probability that a specific kick will have an angular deviation, x, from the perfect, measured in degrees, and σ is the standard deviation. The area, A, under the graph of P(x) between +x and x, for any x, is the fraction of successful kicks between these two limits, i.e. the success expressed as a fraction. Thus: A = x x P(x)dx (2) To restate, if a kicker aims at posts which subtend an angle of 2 x degrees from where he places the ball, then, due to variation in execution, if he did a large number of kicks, his normal distribution of angular variation would extend out very wide. But only those kicks whose angles lay between ± x from the aiming point would be successful. Thus if we know this subtended angle (the value of x) and we know the probability of success 115

5 i.e. the fraction which succeeded, we can compute the standard deviation, σ, for the particular conditions, as a measure of the kicker s accuracy. Equation (2) was integrated numerically for σ = 1 to produce a normalized look up table (LUT) of A versus x. For a particular kick position where the probability of success, A, is known (Table 1), this allows computation of the value of x, expressed as a fraction of σ. For example, the average kicker at position number 1 in Figure 1, sees a half angle to the posts of 2.85 degrees at a distance of 35.3m. He has a probability of success of A=0.83. Thus x =2.85 degrees and, from our lookup table, we can establish that an interval extending from σ to σ will contain a probability of Therefore, this kicker has a normal distribution such that 1.35 σ corresponds to 2.85 degrees and his standard deviation, σ, is 2.85/1.35 or 2.1 degrees. Thus, the average kicker at position one has a standard variation, σ of 2.1 for a kick distance of 35.3m. Similar calculations were performed for all the positions reported and the values are reported in the Results section. A humanoid kicking robot was built as a research tool in order to provide a consistent kicking mechanism to investigate the mechanics, kinematics and dynamics of place kicking a rugby ball. The robot is shown in Figure 2 with former All Black rugby player, Andrew Mehrtens. Its design is registered in New Zealand (design number ) and the mechanical design is described in detail in Flemmer and Flemmer (2014). The robot stands on its left leg and swings its right leg to kick. The kicking leg is articulated at the knee so that the motion of the foot parallels closely that of a human foot during kicking. Air rams and sophisticated pneumatic circuitry control the leg during kicking. The pneumatic system operates at 800KPa (8 bar) and this provides forces of about 4,000N and 2,655N to the upper and lower leg respectively. Preliminary calculations indicated that this would give a foot speed of about 28ms -1. This is well up in the range of professional kickers (Holmes et al., 2006; Ball, 2008). The robot has an automated aiming system; a CCD camera located in the nose of the robot and artificial vision software recognises the goal posts and controls a lead-screw mounted transversely at the rear of the chassis, moving the rear of the chassis up to 100mm on either side of the centre point so that the robot leg is aimed directly between the posts. The robot is controlled from a laptop. Enclosed in a black steel box behind the robot, is a large lead-acid battery and an air compressor. Wheels on the box can be lowered down so that the robot can be moved using the front pull bar. 116

6 (a) Robot with Andrew Mhertens (b) Side view Figure 2 The humanoid kicking robot. A Gilbert 2011 World Cup rugby ball was inflated to the regulation pressure (69kPa) and placed vertically on the kicking tee with the kick-point in the middle of the flat panel of the ball (i.e. in the mid-point between 2 adjacent seams). The robot kicked the ball towards a target, 30 times in mildly gusty wind conditions. A marker was used to record the ball position on the field and the distances from the tee to the impact point were measured. For each kick, the x- and y-distances (Figure 3) were recorded. From these, the mean distance kicked (average y-value) and the standard deviation were computed. 117

7 Success (%) target ball position y tee x Figure 3 Measurement of the ball position for the robotic kicker. 3. Results Figure 4 shows the average kicking success (%) as a function of distance for the Rugby World Cup kickers kicking in the left field, mid field and right field Left Mid Right Distance (m) Figure 4 Kicking success as a function of distance for left-, mid- and right-field positions. 118

8 Standard deviation (degrees) There is a linear correlation between the success and the distance kicked which has the functional form: Success(%) = 2.42Distance(m) (3) with coefficient of determination, R 2 = (i.e. a correlation coefficient of r = ). The computed kick distance, angle θ, x-value and standard deviation, σ, for human kickers are listed in Table 2 Table 2 Computed average standard deviation for kickers at nine field positions. Position # Distance(m) θ( ) x-value σ( ) These results are shown on Figure Left Mid Right Distance (m) Figure 5 Standard deviation as a function of kick distance and field position. 119

9 Table 3 shows the measured x- and y- values for the kicking robot. Table 3 Kicking robot results. Kick # x(m) y(m) Kick # x(m) y(m) On average the robot kicks a y-distance of 44.2 ± 2.4m with a sideways (x-direction) standard deviation of ± 1.7m (2.2 degrees).this implies a success rate of 87% at 44.2m. Weather station data showed gusty side wind conditions but the kicks were done as each gust died down. The lowest side wind speed over the 30 kicks was about 1.1ms -1. For an average ball flight time of 3s this side wind would, at a very crude estimate, blow the ball 3.3m off target if the wind were exactly perpendicular to the direction of the ball. 4. Discussion Figure 4 shows that for the average kicker in the last two Rugby World Cup competitions, accuracy (expressed as percentage successful place kicks out of attempted kicks) has an inverse linear variation with distance from the posts. The greater the distance from the posts, the less accurate the kick. The functional form of this variation is given in equation (3) with a correlation coefficient of For the same distance from the posts, kicking from the left side of the field is slightly more accurate than kicking from the right side of the field. This is expected because most kickers are rightfooted and prefer kicking with their right foot from the left side of the field. Kicking from the mid-field positions is slightly less accurate than kicking from the sides at similar distance from the posts. Perhaps players perceive a greater degree of difficulty in kicking from the sides (perceiving a smaller distance between the posts) and so, try harder and kick more accurately. Figure 5 shows that the standard deviation for kicks from the left side of the field is slightly lower than for the right side of the field (for the same distance between the kicker and the goal posts). Standard deviation increases with distance from the goal 120

10 posts and this is expected; the less accurate the kick, the more spread in the normal distribution about the goal posts and the greater the standard deviations. Therefore the further the distance from the goal posts, the less accurate the kicking. The standard deviation of kicks from the mid-field is much higher (i.e. less accurate) than that from the sides for similar distances from the goal posts. This is somewhat surprising. Further, although there are only 3 data points for mid-field kicking, the standard deviation appears to asymptote to a value of about 3.8 degrees at zero distance from the goal posts. This may be an artefact of the assumption of the normal distribution (equation (1)) where, for a kick distance of zero, the kick angle is infinite. The data represents approximately 1,000 attempts to kick for goal from all positions on the field. However, it is harder to kick from the left and right sides compared with the mid-field, particularly at positions that are either very close or very far from the goal posts (positions 1, 3, 7 and 9 on Figure 1). Only the very top kickers would attempt kicks for goal from these positions, with most kickers electing to kick for touch instead of for goal. In slightly windy conditions, the robotic kicker kicked an average distance (y-value) of 44.2 ± 2.4m with a standard deviation in the x-value of 1.7m or 2.2 degrees. It is likely that the ball s variation in the x-direction is mainly caused by wind since the robotic mechanism operates consistently. Human kickers over a similar distance (field positions 4, 6 and 8) had standard deviations from 4.2 to 5.7 degrees (Table 2). The robotic kicker is significantly more accurate than the average place kicker in the last two Rugby World Cup competitions. Since the robotic kicker kicks very reproducibly, its standard deviation would be essentially constant over shorter kick distances. The wind conditions for the professional kickers are not known and would affect accuracy but in general sports stadiums are more sheltered than an open field. The reproducibility and accuracy of the robotic kicker makes it a useful tool for further research into the theory of kicking. The kick distance of the robot is at the high end of the distances kicked by professional rugby and soccer players (Holmes et al., 2006; Ball, 2008). Mechanical kicking machines described by Schempf et al. (1995), Ackerman (2009) and Held (2010) can get faster ball speeds (up to 50ms -1 ) in tests done on both rugby and soccer balls, but do not specify the kick distance and accuracy/repeatability. Both types of balls have similar official weight; the rugby ball must be g according to the International Rugby Board rules and the soccer ball must be g according to the English Football Association rules. A soccer ball, being round, would suffer less drag and therefore travel faster and longer than a rugby ball. 5. Conclusions Using data from the last two Rugby World Cup competitions, the average place kicking accuracy as a function of field position is presented. Kicking accuracy decreases linearly with increasing distance from the goal posts. Kicking from the left side of the field is more accurate than kicking from the right (for similar distance from the goal 121

11 posts). Kicking from the mid-field is less accurate than kicking from either left- or rightfield. This may be because a kicker on the side sees a much small distance between the goal posts than a kicker in mid-field and therefore aims more carefully. The robotic kicker, kicking in slightly windy conditions, is more accurate than the average World Cup kickers, kicking in varying wind conditions. In future work an anemometer will be fitted into the robot head to measure the wind speed and adjust the aiming mechanism to compensate for wind speed. The robot achieves a reasonable kick distance, both in terms of what professional kickers can achieve and what other mechanical kicking devices can achieve. It kicks very accurately and reproducibly and is consequently a useful tool for research into the theory of kicking. 6. Practical application The practical findings and relevance to sports performance are two-fold. Firstly this research presents the average place kicking accuracy as a function of field position in the past two Rugby World Cup competitions (2011 and 2007). This is very rare data (as shown in the literature review) because individual kicking accuracy is a closely guarded secret which is not published. Although the matches are publically available, and it is possible for an individual to collect the kicking data, the reality is that companies collect and sell kicking data from matches under confidentiality agreements with their customers. Secondly, this research reports the performance of a humanoid robotic kicker, capable of kicking a distance of 44.2m and kicking more accurately than the professional players. The robotic kicker always kicks the same way and therefore provides a valuable tool for scientific research into kicking. 7. Acknowledgements The authors acknowledge gratefully the following contributions to this research effort. Gilbert Rugby s chief research and development engineer, Ian Savage, provided data on the average place kicking accuracy as a function of field position for kickers from the past two Rugby World Cup competitions. The pneumatics company, SMC, donated the pneumatic components used in the robotic kicker. The contribution was administered by Kevin Buckley of the Palmerston North branch of SMC. The kicking robot was built as a marketing tool to promote the School of Engineering and Advanced Technology (SEAT) at Massey University in New Zealand. SEAT provided partial funding for the project. 122

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