ISOPAR: A Performance Analysis Project on the ShotLink™ Database Michael Stöckl Department of Sport Science, University of Vienna, Vienna, Austria [email protected] Peter Lamb School of Physical Education, Sport and Exercise Sciences, University of Otago, Dunedin, New Zealand [email protected] January 12, 2017 Original version: June 27, 2011 Abstract ISOPAR is a method for modelling playing characteristics of golf holes and allows the performance of shots to be analyzed. The method is based on the ball locations provided by ShotLink™ and the subsequent number of shots required to hole out from each respective location. ISOPAR values are calculated which represent the number of shots the field would require to hole out. These ISOPAR values can, a) be visualized on an ISOPAR map and, b) lead to a new performance indicator called Shot Quality, which is the difference between the ISOPAR values of the starting position and finishing position, respectively. The Shot Quality score can also be used to determine how many shots were saved per shot, or per type of shot, with respect to the performance of the field. 1 Introduction In performance analysis, characteristics of a process which describe how an outcome was achieved are used to assess the performance itself (Hughes & Bartlett, 2002) and are referred to as performance indicators. Classical performance analysis techniques in golf have focused on classes of golf shots (James, 2007), such as driving distance, approach shot accuracy and putting average (James & Rees, 2008). Measures like greens in regulation, average putts per green and driving distance are intended to describe players’ abilities to perform certain types of shots, yet these abilities are not actually assessed. For example, the beginning position of a putt is the result of the approach shot to the green. So a good putting average describes not only putting ability but also all previous shots on the hole – it is a composite measure. Therefore, if independent measures for different types of golf shots existed then strengths and weaknesses of a player’s game could be assessed (Ketzscher & Ringrose, 2002). Currently, golf performance analysis lacks performance indicators which reflect the influence one shot has on the next. For example, on each hole there is a chain of events which starts on the tee and ends once the ball is holed. Each shot represents an event and the final position of shot n determines the starting position for shot n +1. A model preserving the playing characteristics of the environment (for example, physical contours, playing conditions, etc.) and the stroke sequence is more suitable than simply an analysis of frequencies of discrete events. 2 Background Cochran and Stobbs (1968) had the idea to manually collect shot data (ball locations) and to analyze performance based on these data. They wanted to measure the performance of professional golfers in different aspects of the game and figure out which aspects of the game the leading golfers are better at than the rest of the field. In the context of this study Cochran and Stobbs developed a model for calculating 1 probabilities and the average number of remaining shots for holing out from certain (ranges of) distances. At the time of their study the lack of modern technology prevented them from collecting more data and enhancing their approach. Landsberger (1994) built on the work of Cochran and Stobbs by refining the approach. Landsberger’s Golf Stroke Value System (GSVS) provided a starting point for more recent work on establishing independent measures of performance. Recent projects have emerged which have looked to further advance the shot value idea (Broadie, 2012; Fearing, Acimovic, & Graves, 2011; Minton, 2011)1. Broadie (2008, 2012) developed statistical models to calculate probabilities of holing out and derived benchmarks as average number of remaining shots from the probabilities. One model provides benchmarks for holing out on the green based on the distance to the hole and another model computes benchmarks for holing out off the green, which additionally includes a classification of the ball location. Using these benchmarks Broadie has demonstrated a more valid method for describing the performance of individual shots, called Strokes Gained. Strokes gained can be used to explain the contribution of each shot to the total score. Based on the shot value idea of Broadie (2008), Fearing et al. (2011) came up with a similar approach which is limited to the green. They applied various regression models to achieve the probability of making a putt and a prediction of the distance remaining after a missed putt. In addition to the distance to the hole used by Broadie, Fearing et al. (2011) consider the strength of the field and the difficulty of the green. From this they illustrate the use of these benchmarks to assess performance to individual shots using the same shot value idea as Broadie (2012). The PGA TOUR uses this approach as a measure for individual shots, which is called Strokes Gained - Putting. Both approaches provide very sophisticated models of putting performance with respect to the distance from the hole. In the absence of independent measures of individual shot performance, several studies (Clark III, 2004; James, 2007; James & Rees, 2008; Scheid, 1990) have looked at the temporal variance of consecutive golf scores – both hole scores and round scores. Analyses of round scores showed very low correlations between scores of consecutive rounds when considered with respect to external influences on performance (i.e. weather conditions and course setup). Analyses of hole scores also showed low correlations between successive holes, again considering external influences like hole par and difficulty. Aside from the obvious fact that good players tend to shoot good scores and poor players tend to shoot poor scores, these 1see PGA TOUR Academic Data Program page, available at: http://www.pgatour.com/stats/academicdata/ for detailed explanations of these projects. 2 results suggest that performance in golf is not subject to “streakiness”. In other words, the nature of the performance of individual shots which make up hole and round scores seems not to be well understood. In summary, consecutive round scores do not depend on one another, and consecutive hole scores do not depend on one another. However, individual shots played on the same hole present a different scenario; these shots make up a continuous chain of events so that the finishing position of shot n represents the starting position for shot n + 1. Although shots on the same hole are related, one would expect the same lack of “streakiness” that has been demonstrated in the literature. This means that although a well played shot tends to set up an advantage on the ensuing shot compared to a poorly played one, a well played shot will not likely predict the performance of the ensuing shot. 3 The ISOPAR method 3.1 Framework The previous described approaches of Broadie (2012) and Fearing et al. (2011), on which first measures for individual shots are based, are statistical and developed to predict performance and to compare performance to benchmarks of expected performance. Our approach is different from that and is specifically aimed at characterizing the performance of individual shots based on their location and the relevant factors affecting the shot, rather than just the distance to the hole. The framework of the ISOPAR project comes from a systems perspective and has been empirically applied to many levels of analysis of human movement and performance (e.g. Davids, Glazier, Araujo, & Bartlett, 2003; Kelso, 1995; Mayer-Kress, Liu, & Newell, 2006). The central concept is that neurobiological systems behave as complex systems and theories from physical sciences, e.g. dynamical systems theory, are appropriate for understanding and modeling human performance. Accordingly, golf performance is an emergent property of self-organizing dynamics and the confluence of constraints influencing the golfer (Newell, 1986). We have subsequently applied this perspective to golf performance on the PGA TOUR measured by ShotLink™. The underlying assumption is that each shot a player faces, represents a new set of constraints and the player must adapt to the constraints associated with the shot, which can be divided up into three main categories: environment, organism, task (Newell, 1986). The constraints do not necessarily prescribe one particular response (e.g. shot type), instead they guide the response selection of the golfer by excluding certain responses (Kugler, 3 Kelso, & Turvey, 1980). Stöckl and Lames (2011) have demonstrated the ISOPAR method for visualizing constraints in putting. A player’s putting performance is determined by a combination of environmental constraints (e.g. slope of the green, distance to the hole, green speed, weather conditions), organism constraints (e.g. psychological influences on the player, player’s green reading ability, player’s putting ability) and task constraints (striking the golf ball with a club so that it rolls into the hole). The idea of visualizing the confluence of constraints off the green, by which the performance of players is determined, can be extended to entire holes to illustrate difficulty on a hole represented by the number of remaining shots – since each shot is part of a player’s shot sequence. Off the green, a player’s performance is also guided by the interaction of environmental, organism, and task constraints, however, their details may differ. For example, environmental constraints are the hole design (straight hole compared to a doglegged fairway), ball lie (e.g. fairway, rough, sand), line to the green (e.g. are there trees or other objects blocking the line to the green?), or weather conditions (e.g. wind, rain); organismic constraints can be psychological influences affecting the player, player’s perception of the best tactics, picking the ‘right’ club, or the player’s ability to execute the shot; task constraints are similar to those for putting, in that the player hits the ball with a club with the intention of the ball finishing close to, or in, the hole.