T U M
W P
e ISOPAR Method
Michael Stöckl, Peter Lamb & Martin Lames
Faculty of Sports and Health Sciences Connollystrasse 32 80809 Munich Germany [email protected] [email protected]
June 27, 2011 Abstract e ISOPAR method is a method for characterizing the difficulty of golf holes and allows the per- formance of shots to be analyzed. e 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. ese ISOPAR values can, a) be visualized on an ISOPAR map and, b) lead to a new performance indicator called Shot ality, which is the difference between the ISOPAR values of the starting position and finishing position, respectively. e Shot ality 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 & Bartle, 2002) and are referred to as performance indica- tors. Classical performance analysis techniques in golf have focused on classes of golf shots (James, 2007), such as driving distance, approach shot accuracy and puing average (James & Rees, 2008). Measures like greens in regulation, average pus 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 pu is the result of the approach shot to the green. So a good puing average describes not only puing ability but also all previous shots on the hole – it is a composite measure.
erefore, if independent measures for different types of golf shots existed then strengths and weak- nesses 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, play- ing conditions, etc.) and the stroke sequence is more suitable than simply an analysis of frequencies of discrete events.
2 Baground
Cochran and Stobbs (1968) introduced the idea of an independent measure of performance, which they represented by the difference between the distance to the hole before and aer the shot. e number of shots required to hole out from certain distances, for pros, was used to create a model which could be
1 used to determine the value of an individual shot. 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 put forth by Cochran and Stobbs (Broadie, 2011; Fearing, Acimovic, & Graves, 2011; Minton, 2011)¹. Fearing et al.
(2011) applied various regression models to achieve the probability of making a pu and a prediction of the distance remaining aer a missed pu. From this the authors have demonstrated a more valid method for describing the performance of individual shots, called strokes gained, from which they assess performance relative to the field. Broadie (2011) takes a similar approach using distance to the hole but expands the analysis off the green and includes a classification of the ball location. Average performance of PGA TOUR players are used as the benchmark from which comparisons of performance can be made.
Strokes gained can then be used to explain the contributions of each shot to the total score. Both models provide very sophisticated models of puing 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 perfor- mance (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 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 un- derstood. 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. is means that although a well played shot tends to set up an advantage on the ensuing shot compared to a poorly
¹see PGA TOUR Academic Data Program page, available at: http://www.pgatour.com/stats/academicdata/ for de- tailed explanations of these projects.
2 played one, a well played shot will not likely predict the performance of the ensuing shot. is question has not been properly addressed in the literature, mainly because of the lack of a genuine performance indicator for individual shots.
3 e ISOPAR method
3.1 e concept
Here we present two analogies to help explain the following methods. In meteorology, lines of equal barometric pressure are ploed on geographical maps. ese maps are called isobar maps and the lines are isobar lines. e term isobar (iso - meaning equal and bar - meaning pressure) is used appropriately as the isobar map shows lines of equal pressure. Small diameter, closed lines represent minima and maxima by which, areas of low-pressure and high-pressure can be identified. Densely packed isobar lines indicate a steep gradient of air pressure. Meteorologists can therefore make weather predictions using isobar maps. Our second analogy is to contour maps used in geography to show elevation. Similar to isobar lines, lines of equal elevation are ploed on geographical maps. Here, densely packed lines represent steep ascents and descents. In both analogies, lines that are relatively close together represent steep changes in pressure or elevation, respectively. Likewise, lines that are relatively widely spaced represent areas of lile change in pressure or elevation.
For golf, we have developed the ISOPAR method for calculating a gradient of difficulty for a golf hole.
e output can then be ploed on a map of the golf hole to visualize the difficulty of certain areas. We call these maps ISOPAR maps and a detailed explanation of how they are calculated is provided below.
3.2 Development and testing
e three-dimensional spatial coordinates (x,y,z) of the green gives the first of three sets of triplets,
(xg,yg,zg), where g represents the number of measuring points. When available, this set of triplets can be used for ploing the physical contour of the green.
For each ball position, (x,y), the corresponding number of strokes, z, required for the player to hole out are used in the calculation. is gives our second of three sets of triplets (xp,yp,zp). For example, if a player took four shots on a hole, that player contributed four data points to our dataset: the x,y
3 coordinates from the location of the first shot with a corresponding z value of 4 and the x,y coordinates from the second shot and a corresponding z value of 3 and so on.
3.2.1 Computing ISOPAR values and maps
Before explaining the details of the algorithm for computing the ISOPAR values and maps, a rough overview of the steps involved in calculating an ISOPAR map for a green is given (see Stöckl, Lamb, &
Lames, 2011):
1. Assign a grid to the green (Figure 1).
2. Calculate the ISOPAR value of every grid point subject to all measuring points with a modified
application of the exponential smoothing algorithm.
3. Compute a surface out of the ISOPAR values of the grid points using a smoothing spline interpo-
lation (Fahrmeir, Kneib, & Lang, 2009) to finely remove rough edges.
4. Calculate the ISOPAR map which consists of ISOPAR lines.
e following explains the steps for computing ISOPAR values and maps in detail. All computations were performed in MATLAB (e Mathworks, Inc.).
Assign grid to green: A grid with a specified mesh size is assigned to the green (Figure 1). e ISOPAR values are computed at the grid nodes. For positions which lie between grid nodes the ISOPAR values must be estimated. erefore, a grid with an extremely small mesh size represents the data very well, while a very large mesh size does not. However, there is a trade-off between representational power and computational intensity. A mesh size which optimizes this trade-off should be used.
Exponential smoothing algorithm: From Step 1, coordinates (xi j,yi j) were assigned to the grid nodes.
e corresponding zi j values which represent the ISOPAR values were then calculated; this gives the
final set of triplets, (xi j,yi j,zi j),i = 1,...,m, j = 1,...,n. e algorithm used here is a well known smoothing algorithm; however, our application of the algorithm differs slightly from most applications. Typical applications of the exponential smoothing algorithm are in time-series analyses and based on pairs (xk,yk),k = 1,...,t, from which the value yt+1
4 Figure 1: e mesh grid shown on the green. Inner green line represents the edge of the green and the outer green line represents the edge of the fringe. (xi j,yi j) represents coordinates for a grid point and blue dots represent ball positions.
at time xt+1 is computed. e modified application of this algorithm for calculating ISOPAR values is based on the measuring points (xp,yp,zp), p = 1,...,q (q = number of sample points). e ISOPAR values zi j are computed based on these triplets. To use the exponential smoothing algorithm, which is based on pairs, we transformed the triplets into two-dimensional pairs, respectively. e transformation for every grid node was achieved by ordering the measuring points in ascending order (the nearest point first) with respect to the Euclidean distance
√ 2 2 di jp = (xi j − xp) + (yi j − yp) (1)
to the measured ball positions. is allowed the triplets from above to be wrien as pairs (di jp,zp). With the pairs sorted as described, we could use the exponential smoothing algorithm to calculate the ISOPAR values. In these pairings, (di jr,zr) represents the ball position with the shortest distance to the respective grid node and (di j1,z1) represents the ball position with the largest distance to the grid
5 (a) 6th hole (b) 18th hole
Figure 2: e ISOPAR maps for (a) the 6th hole at Bay Hill in the fourth round of the 2009 tournament and (b) the 18th hole in the fourth round of the 2008 tournament. e green line represents the edge of the green, the flag position is shown as a black dot. iso2.0 is shown in magenta. node. e exponential smoothing is calculated by
r−2 k r−1 zi j = α ∑(1 − α) zr−k + (1 − α) z1, (2) k=0 where 0 ≤ α ≤ 1 is the smoothing parameter (Hamilton, 1994).
e ISOPAR lines are calculated from the ISOPAR values (Figure 2). e ISOPAR lines, similar to the isobar lines used in our meteorological analogy, are the lines of intersection between planes which are parallel to the x,y plane in certain intervals and the surface which is calculated with the triplets
(xi j,yi j,zi j). e result is a contour map which empirically characterizes how many strokes “the field” took from each position on the green. Each line on the contour map is one of these lines of intersection, thus we argue that the ISOPAR lines give a visual representation of the difficulty of any shot on the green.
Smoothing spline interpolation: Because of the space between the grid nodes, the grid surface must be smoothed. Figure 3 shows the difference between the raw surface and the smoothed surface using a
6 (a) (b)
Figure 3: Example of a portion of the grid surface (a) without smoothing and (b) with smoothing spline interpolation. cubic smoothing spline interpolation (Fahrmeir et al., 2009).
n m ∫∫ 2 2 2 min β ∑ ∑(zi j − f (vi j)) + (1 − β)λ (D f (x,y)) dxdy (3) f i=1 j=1 where ∂ 2 ∂ 2 ∂ 2 D2 = + 2 + , ∂ 2x ∂x∂y ∂ 2y ( ) xi j vi j denotes the vector with entries , λ = 1 in our case and β is the smoothing parameter. When yi j β = 1, f is a natural spline interpolant – the cubic spline interpolant; when β = 0, f is a least square fit surface and as β → 1, the data remain relatively similar to the input.
Calculating the ISOPAR map: e ISOPAR lines were calculated in MATLAB. e ISOPAR lines are lines of intersection between the smoothed surface (calculated in the previous subsection) and planes which are parallel to the x,y-plane in certain intervals. For implementing the ISOPAR method we used intervals of 0.2, however, this value is not critical. e value for the interval should depend on the objectives of and resources available to the user.
3.2.2 e performance indicator: Shot ality
Shot ality (SQ) is a post-hoc assessment of a shot taken. To determine Shot ality the difference in
ISOPAR value at the starting position (IPVbe f ore) and the ISOPAR value at the finishing position (IPVa fter)
7 of the shot is calculated.
SQ = IPVbe f ore − IPVa fter (4)
Shot ality, as its name implies, represents the quality of a shot played. A shot of average performance, with respect to the data set (in this case the ShotLink™database), receives, by definition, a Shot ality score of 1 (proof shown below). A shot with a Shot ality higher than 1 is considered a well played shot and likewise, a shot with a Shot ality score of less than 1 is a poorly played shot.
A unique property of Shot ality allows consecutive shots, which are performed in sequence
(1,...,np) ending with the ball being holed, by a given player p to be weighted so that the sum of their
Shot ality scores (SQ j) equals the ISOPAR value of the beginning position (IPV1) of the sequence:
np np−1 (4) − − ∑ SQ j = ∑ (IPVj IPVj+1) + IPVnp 0 j=1 j=1 − − − − = IPV1 IPV2 + IPV2 IPV3 + ... + IPVnp−1 IPVnp + IPVnp 0
= IPV1. (5)
− We have included 0 in the the final term IPVnp 0 to make clear that it represents the Shot ality of the final shot played on the hole (zero shots are required once the ball is holed).
Consider a hypothetical sequence of two pus on a green which starts from a position with an
ISOPAR value of 2.1. If the first pu missed, leaving a pu with an ISOPAR value of 1.1, the Shot ality scores must be 1.0 for the first pu and 1.1 for the second, which adds up to the beginning ISOPAR value of the sequence. If the first pu had been much worse, the holed second pu would necessarily have a higher value, the first lower, and then still add up to 2.1. If the second pu were missed, we now have a three shot sequence and these three Shot ality scores then add up to 2.1. is concept applies to a sequence of shots of any length including the sequence of all shots played on a hole, as long as the final shot in the sequence results in the ball being holed. To follow this example, no maer the player’s score on the hole, the values of the Shot ality scores will add up to the ISOPAR value of the starting point of the sequence: the ISOPAR value at the tee (IPVTee). is leads us to another interesting property of Shot ality. In the ShotLink™database all tee shots recorded on the same hole (and the same round) are assigned the same x,y coordinates – a single point. For this reason, we use the average score (Save)
8 for the hole as the ISOPAR value at the tee
p ∑ S j j=1 IPV = S = , (6) Tee ave p
where S j are the hole scores for all p different players on the hole. erefore, the sequence of all Shot ality scores for each player must add up to the average score for the hole. For example, another hypothetical golfer might score a birdie on a par 4 which has an average score of 3.92 which might involve a series of shots as follows: a good drive (SQ = 1.20), an slightly beer than average approach from that position (SQ = 1.05) and a very good pu (SQ = 1.67).
As mentioned above, the average Shot ality of all shots played on a hole (SQave) must be 1 and can now be shown by
p n j 1 · SQave = p ∑ ∑ SQi j=1 i=1 ∑ S j j=1 p (5) 1 · = p ∑ IPVTee j=1 ∑ S j j=1 1 · · = p p IPVTee ∑ S j j=1 p ∑ S j (6) 1 j=1 = · p · p p ∑ S j j=1 = 1, (7)
where p is the number of different players on the hole and n j is the number of shots played on the hole by each player.
9 4 Applying the ISOPAR method to ShotLink™data
While the methods of Fearing et al. (2011), Broadie (2011) and Minton (2011) can be used to make very good generalizations about the expected outcome of a shot based on its distance, the ISOPAR method is useful for answering a slightly different question. Given the factors which directly contribute to the performance of the field, how were certain shots performed with respect to the performance of the field?
4.1 Reading ISOPAR maps
4.1.1 Putting
To read the ISOPAR maps we use the naming convention isoN to represent the ISOPAR line with value
N, shown in Figure 2. e iso2.0 line is of importance, beyond iso2.0, 3-pus exist. Figure 4 shows the distribution of 1-, 2- and 3-pus on the 18th green at Bay Hill in 2008. e iso2.0 line is a result of the 3-pus shown in the figure.
Lorensen and Yamrom (1992), and later Penner (2002), modeled the difficulty of puing with different amounts of break and elevation change and from different distances. e authors showed that, not surprisingly, much more precision was required by the player as puing distance, break and elevation change increased. e ISOPAR maps visualize these factors as well as many other subtle factors which affect puing performance.
Since puing distance obviously increases outward from the hole, linearly and equally in all di- rections, the iso-lines should be circular on a flat green. However, since slopes are not symmetrically distributed across the green, the shape of the iso-lines can be useful in identifying easy or more difficult areas from which to pu. Useful characteristics of iso-lines are their a) circularity, b) density and c) their distance from the hole. If the map consists of circularly paerned iso-lines one can conclude that shot difficulty does not depend on the direction from which the stroke is taken. As the iso-lines become more elliptical certain areas of the green must be considered more favorable to pu from. e spread, or density, of iso-lines can be used to identify the severity of the gradient of difficulty on the green. A steep gradient is expected to coincide with undulated areas of the green but has not been empirically shown with ShotLink™data yet. e distance of the iso-lines from the hole can of course also be used to indicate difficulty of a pu. Reference values could be used as a comparison to provide context to the value of the iso-lines (e.g. Broadie, 2008; Cochran & Stobbs, 1968; Fearing et al., 2011; Tierney & Coop,
10 Figure 4: e distribution of iso-lines, 1-, 2- and 3-pus on the 18th green in the 4th round of the Arnold Palmer Invitational in 2008.
1998).
4.1.2 Off-green shots
Although originally developed for puing, ISOPAR maps can also be used to visualize the difficulty of the rest of the hole, i.e. landing areas and areas surrounding the green. Similar to ISOPAR maps of the green, if the iso-lines were circular and evenly spaced then we would conclude that the rough, bunkers, etc. have no impact on the difficulty of the shot – they do not influence performance. However, we do not expect this to be the case. What ISOPAR maps are useful for, with respect to off-green shots, is identifying how advantageous a good drive is (e.g. a long drive or a drive that provides a good angle for the approach) and how hazardous hazards are (e.g. rough, bunkers, etc.). For example, if the ISOPAR
11 contour changed dramatically at the boundary of a hazard, such as a bunker, it would be obvious that this should be a hazard to avoid. On the other hand, one might find that a certain hazard poses no disadvantage so a more aggressive strategy can be adopted.
4.2 Performance analysis: Bay Hill in 2008 and 2009
To demonstrate the ISOPAR method we have used the ShotLink™data from the Arnold Palmer Invita- tional presented by MasterCard in 2008 and 2009. In both years the tournament was won by Tiger Woods sinking dramatic pus on the final hole. ese tournaments give us an opportunity to demonstrate per- formance analysis of the field using the ISOPAR method, as well as an analysis of the performance of
Woods in both years.
In this section Shot ality is used as a performance indicator. Additionally, a new concept derived from Shot ality is introduced. Similar to strokes gained, already in use by the PGA TOUR, we assess the advantage gained relative to the average by a well played shot (or vice versa). Terminologically, we prefer Shots Saved instead of shots gained because a long pu made, saves instead of gains the player shots. erefore, Shots Saved represents the difference between the Shot ality of any shot and Shot
ality of the average shot, which represents the field and has been shown to be exactly 1
Shots Saved = SQ − 1. (8)
4.2.1 Individual putts
e ISOPAR method, because it is based on shot locations, can give Shot ality scores to individual shots. Table 1 shows the top-ten pus for the Arnold Palmer Invitational in 2008 and 2009, respectively.
Notably, the pus with the highest Shot ality scores are not necessarily the longest pus. For example, in 2009 Daniel Chopra made a 31.2 foot pu on the 15th hole in the first round which had the highest
Shot ality score of all pus in that year’s tournament, despite pus of more than double the length being holed by other players.
Tiger Woods’ winning pus in each year are shown in Table 1 in bold face (see also Figure 5 in
Appendix A). In 2008, the winning pu was the best pu by Woods of the week and the 42nd best pu out of over 11,000 pus in the entire tournament. In 2009, Woods’ winning pu was not his best of the
12 Table 1: Top-ten pus measured by Shot ality for the Arnold Palmer Invitational in 2008 and 2009.
2008 SQ Hole Round Distance () 1. Davis Love III 1.99 7 1 43.6 2. Bill Haas 1.99 2 1 61.1 3. D.A. Points 1.98 15 2 33.0 4. Charley Hoffman 1.98 3 1 36.8 5. Shaun Micheel 1.97 1 2 36.3 6. Mark Wilson 1.97 15 1 29.8 7. Tom Pernice Jr. 1.95 11 4 22.4 8. Brian Davis 1.95 6 2 23.0 9. Billy Mayfair 1.92 12 1 27.1 10. Kenneth Ferrie 1.91 2 1 41.0 42. Tiger Woods 1.83 18 4 24.2 n = 11,107
2009 SQ Hole Round Distance () 1. Daniel Chopra 2.12 15 1 31.2 2. J. J. Henry 2.11 8 1 55.7 3. D. J. Trahan 2.11 1 2 33.7 4. Zach Johnson 2.09 7 3 35.9 5. Ben Curtis 2.03 9 2 45.0 6. Fred Couples 2.01 11 2 37.9 7. Brian Gay 2.00 11 3 29.8 8. Aaron Baddeley 2.00 10 3 25.3 9. Heath Slocum 1.99 9 3 73.3 10. Jerry Kelly 1.95 18 4 38.1 40. Tiger Woods 1.84 13 1 16.4 203. Tiger Woods 1.69 18 4 15.9 n = 11,116
week, his best was on the 13th hole in the first round and was the 40th best pu of the week. His winning pu was the 203rd best pu of the week, again, out of just over 11,000 pus. is reveals exactly how well Tiger Woods performed on his final pu of the tournament, with the tournament on the line, two years in a row. One can, of course, argue that the winning pu was just one of 270 shots played in the tournament, and they all contributed equally to the outcome. However, we must acknowledge, first that the preceding shots in the tournament were played sufficiently well so that Woods had a chance to make a winning pu on the last hole; and second, the final pu is not like the rest because the consequences are known. In this sense we must appreciate the performance of Woods on these specific shots.
13 4.2.2 Shots Saved on and off the green
Table 2 shows the top puing performers of the tournament and their off-green performance. On-green performance is calculated as above, however, calculating Shot ality scores off the green is still under development. erefore, the off-green Shots Saved can be calculated based on the average score of the
field (hole, round or tournament) and the on-green score, which is already calculated. For example, in
2008, Tiger Woods’ score of 270 was 13.73 strokes beer than the average score of 283.73. Of the 13.73 stroke margin between his score and the field we calculated that he gained 1.13 on the green and, as a result, the remaining 12.60 strokes must have been from off the green.
In Table 2, the Shots Saved performance indicator is introduced and shows a large discrepancy be- tween Shots Saved on the green and Shots Saved off the green. At first glance it appears as though puing, because of the few Shots Saved, is much less important than shots played off the green: this may in fact be the case but the topic requires some discussion first.
Shot ality and consequently, Shots Saved, are independent measures of performance because the same metric is used for all shots. is means that any shot played can be directly compared to any other shot played. With that in mind, a speculative explanation for the discrepancy between on-green and off-green performance involves two factors: 1) ere is a greater range of possible Shot ality scores for off-green shots compared to on-green shots. 2) a PGA TOUR player will typically take more off-green shots than on-green shots, so the number of elements in the off-green sum is greater than the elements in the on-green sum. Combined, these two factors may explain the discrepancy between Shots Saved on and off the green.
Anecdotally, one might notice in Table 2 that Brad Faxon is at the top of the Shots Saved on the green list in 2009 (he was not in the field in the 2008 tournament). Each year on the PGA TOUR, no maer how it is measured (number of pus, pus per GIR, or just how smooth the stroke looks to an expert eye), Brad Faxon is always among the best puers. In the 2009 tournament Faxon was the best puer and ranked fourth worst off the green. Clearly, Faxon was only able to make the cut in this particular tournament because of superior puing. As mentioned, Faxon is usually one of the best puers on the
PGA TOUR according to conventional statistics. ese conventional statistics (i.e. pus per GIR) as we have already mentioned are a composite of previous shots played on the hole. If independent measures of performance, such as the ISOPAR method, had been available we may have noticed that Faxon was
14 Table 2: Top-ten puers in the Arnold Palmer Invitational in 2008 and 2009.
2008 Shots Saved Shots Saved on the green off the green 1. Ken Duke 1.48 8.24 2. Tiger Woods 1.13 12.60 3. Hunter Mahan 0.79 8.94 4. Mark Wilson 0.47 -0.74 5. Carl Peersson 0.06 7.67 6. Woody Austin -0.46 6.19 7. Ian Poulter -0.47 1.20 8. Nick Watney -0.66 5.39 9. Frank Lickliter II -0.92 6.65 10. Joe Ogilvie -1.08 4.81 n = 71
2009 Shots Saved Shots Saved on the green off the green 1. Brad Faxon 1.32 -1.46 2. Lee Janzen 1.19 5.67 3. Lucas Glover 1.06 6.80 4. Daniel Chopra 0.58 8.28 5. Padraig Harrington 0.54 7.32 6. Zach Johnson 0.48 10.38 7. Tiger Woods -0.03 13.89 8. Ben Crane -0.06 7.92 9. Paul Goydos -0.34 3.20 10. Cliff Kresge -0.40 4.26 n = 73
an even beer puer than previously thought.
In Table 3, the leaders’ on- and off-green performance is shown. In both years, Woods performed, as the winner should, well on and off the green. He ranked 2nd in puing in 2008 and 7th in 2009. Off the green he ranked 9th in 2008 and in 2009, 5th. Combined, these performances on and off the green were good enough for him to win. As exemplified by Vijay Singh, Niclas Fasth, Alex Cejka and Tom Pernice Jr. in 2008 and by Jason
Gore in 2009, it is possible to finish high in the tournament standings with relatively poor puing, if off-green performance is exceptional. e converse situation, in which poor off-green performance is balanced by excellent puing seems less profitable (for further context, see Table 4 in Appendix B which
15 Table 3: Top-ten finishers in the Arnold Palmer Invitational in 2008 and 2009.
2008 Puing Shots Saved Off-green Shots Saved rank on the green rank off the green 1. Tiger Woods 2 1.13 9 12.60 2. Bart Bryant 11 -1.10 5 13.83 T3. Cliff Kresge 43 -4.70 2 15.42 T3. Vijay Singh 54 -6.26 1 16.98 T3. Sean O’Hair 16 -1.66 10 12.39 T6. Ken Duke 1 1.48 30 8.24 T6. Hunter Mahan 3 0.79 26 8.94 T8. Niclas Fasth 57 -6.82 3 14.55 T8. Alex Cejka 51 -5.33 7 13.06 T8. Carl Peersson 5 0.06 34 7.67 T8. Tom Pernice Jr. 55 -6.59 4 14.32 T8. Tom Lehman 30 -3.59 16 11.32 T8. Bubba Watson 34 -3.68 15 11.41 n = 71
2009 Puing Shots Saved Off-green Shots Saved rank on the green rank off the green 1. Tiger Woods 7 -0.03 5 13.89 2. Sean O’Hair 32 -2.58 1 15.44 3. Zach Johnson 6 0.48 21 10.38 T4. Pat Perez 15 -0.91 20 10.77 T4. John Senden 22 -1.76 11 11.62 T4. Sco Verplank 25 -2.04 10 11.90 T4. Nick Watney 27 -2.20 9 12.06 T8. Daniel Chopra 4 0.58 30 8.28 T8. Jason Gore 55 -6.24 2 15.10 T8. Kenny Perry 28 -2.35 15 11.21 n = 73
shows the boom ten players each year).
Using Shots Saved, we were able to rank all the players in the field according to their on-green and off-green performance. e correlation (Spearman’s rank) between tournament rank and puing rank was ρ = .28 in 2008 and ρ = .44 in 2009. e correlation between tournament rank and off-green rank in 2008 was ρ = .79 and ρ = .70 in 2009. ese correlations are compelling evidence that off- green performance contributes to overall performance more than on-green performance. We should not discount the importance of puing, since it also is strongly correlated with overall performance.
We mentioned in the Shots Saved on and off the green section that there is a discrepancy between the
16 sum of Shots Saved on the green and the sum of Shots Saved off the green; and here show that off- green performance contributed more to overall performance than on-green performance. It should be noted that the discrepancy between on- and off-green Shots Saved is not what implies the importance of off-green performance, rather the rankings in off-green performance. ose who were among the best off-green performance stood a beer chance of doing well in the tournament. Indeed, good off- green performance must be accompanied by on-green performance if one is to beat the best players in the world. ese findings simply suggest that off-green performance is likely more important than previously thought.
5 Final remarks
e results presented here are specific to the Arnold Palmer Invitational in 2008 and 2009, further analyses need to be conducted to determine whether these results are unique or typical to PGA tournaments. e
ISOPAR calculation for the entire hole is still being developed and, as of this writing, is nearly complete
(see Figure 6 in Appendix C). Upon completion of this project we expect to be able to generate statistics based on Shot ality for the PGA TOUR. We welcome any feedback from readers to help us improve and find new uses for the ISOPAR method.
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18 19 Appendices
A ShotLink™, Google Earth and ISOPAR maps
(a) 2008
Figure 5: ISOPAR map for the 18th hole at Bay Hill during the Arnold Palmer Invitational presented by MasterCard in 2008. Orange lines are shown at intervals of 0.2 ISOPAR value, ball positions are shown as yellow dots and the winning pu by Tiger Woods was taken from the red ‘X’, the hole is shown as a black dot.
20 (b) 2009
Figure 5: ISOPAR map for the 18th hole at Bay Hill during the Arnold Palmer Invitational presented by MasterCard in 2009. Orange lines are shown at intervals of 0.2 ISOPAR value, ball positions are shown as yellow dots and the winning pu by Tiger Woods was taken from the red ‘X’, the hole is shown as a black dot.
21 B Shots Saved for the lowest finishers
Table 4: Shots Saved on and off the green for the lowest ten finishers of the 2008 and 2009 Arnold Palmer Invitational.
2008 Shots Saved Shots Saved on the green off the green T62. George McNeill -4.67 2.40 T62. Davis Love III -3.66 1.39 T64. Paul Goydos -4.47 1.20 T64. Steve Elkington -3.00 -0.27 T64. Andrew Magee -2.97 -0.30 T64. Fred Couples -1.77 -1.50 T68. Robert Gamez -7.88 2.61 T68. Marc Turnesa -7.44 2.17 70. Steve Lowery -4.27 -4.00 71. Heath Slocum -9.39 -0.88 n = 71
2009 Shots Saved Shots Saved on the green off the green T64. Boo Weekley -11.36 8.22 T64. Luis Oosthuizen -1.10 -2.04 T66. Skip Kendall -6.20 2.06 T66. Richard Johnson -4.48 0.74 T66. Kevin Streelman -3.52 -0.62 T66. Aaron Baddeley -2.99 1.15 T70. Oliver Wilson -8.63 2.49 T70. Brian Davis -5.08 -1.06 72. Woody Austin -4.81 -2.33 73. Bart Bryant -4.49 -5.65 n = 73
22 C ISOPAR map of an entire hole
Figure 6: e ISOPAR method is still under development to include ISOPAR maps off the green. Here an early ISOPAR map of the 10th hole at Bay Hill in the fourth round of the 2009 Arnold Palmer Invitational is shown.
23