Shotmaking on the PGA TOUR: hitting it well or hitting it lucky?

A.1. How distance to the pin is computed

For each shot, other than shots taken from the tee box on par-4 and par-5 holes, the distance to the pin is the straight-line distance computed from the {X, Y} coordinate position of the ball to the {X, Y} coordinate position of the pin. Although one could obtain slightly more accurate distances by including Z coordinates, some Z coordinates are missing and a few seem inconsistent in relation to those of nearby ball positions. Moreover, including Z coordinates makes almost no difference in final computed distances.

In golf, very few par-4 and par-5 holes are intended to be played in a perfectly straight line from tee to pin. Instead, on most par-4s and par-5s, the hole’s natural routing “angles off” (“doglegs”) to the left or right from the intended drive finishing position. In such cases, the straight-line distance from tee to pin will understate the distance of the hole relative to that associated with its intended routing.

For each par-4 and par-5 hole, the median drive finishing position is computed, and it is assumed that this position is where drives are intended to be hit. The distance from the tee to the median position and distance from the same median position to the pin are added together. This becomes the estimate of hole length, tee to pin.

A.2. Recovery shots

Broadie (2012) outlines a two-step process for inferring whether a shot is likely to be a “recovery” shot, that is a shot that is “impeded by trees or other obstacles” (p. 152). Initially, a ball is identified as being eligible for the recovery classification if it lies in the rough 30 or more yards from the pin. Next, in step 1, if the absolute angle created by the finishing position of the shot taken relative to the position of the pin exceeds 15°, the shot taken is classified as a recovery shot. Alternatively, if the distance traveled by the ball once it is hit is less than 40 % of the distance to the pin, the shot is classified as a recovery shot.

In step 2, a ball not otherwise identified as a recovery shot in step 1 is identified as being in the recovery position if it lies within close proximity to a ball identified in step 1 as being in a recovery position. As explained by Broadie (2012), suppose the balls of two golfers lie in approximately the same position. “The first golfer chips back onto the fairway, and the second golfer attempts a big slice around the trees. Step 1 would identify the first golfer’s shot as a recovery shot; however, this step might not identify the second golfer’s shot as a recovery, although it started in the same position and was significantly affected by trees” (p. 153).

In this study, the methodology for identifying a recovery shot in step 2 deviates somewhat from that described by Broadie. A ball is identified as being in a recovery position if it lies within 3 feet of any ball so identified in step 1. By contrast, Broadie identifies such balls as being in the recovery position if they lie within 9 feet of recovery balls identified in step 1. However, in correspondence, Broadie indicates that he now employs a 3-foot distance in step 2 to identify balls in the recovery position and also indicates that the PGA TOUR no longer employs step 2 in identifying recovery shots. Nevertheless, step 2, as described herein, is retained for the purposes of identifying shots in a recovery position.

Finally, a detailed analysis of records in the ShotLink shot files reveals that approximately 17 % of all shots classified as recovery shots by the PGA TOUR originated from a bunker, and five originated from the fairway, shots that otherwise would not have been classified as recovery shots in this study nor in Broadie’s work.

B.1. Choosing the form of the distance function, f d i , c

In each separate year, the distance function, f d i , c , within equation (4) is estimated in connection with each shot position using natural cubic splines with the following degrees of freedom (df): tee box on par-3 holes, df = 5; tee box on par-4 and par-5 holes, bunker, and recovery position, df = 8; fairway, rough, and green, df = 10. In each case, df + 1 knots are chosen, including the two endpoints, such that the first knot after the initial endpoint includes the first 1/df fraction of data points ordered by distance, the next knot includes the second 1/df of data points, etc. Position-specific df values are selected to produce visual fits in connection of the f d i , c portion of equation (4) that are consistently smooth and of the same general shape year-by-year. Further details are provided in Section A of the supplementary document.

B.2. Minimum number of rounds and the specification of player identifiers

During the initial estimation process, no restriction was placed on the minimum number of rounds per player in a given year. However, with no restriction, some estimated fixed player and condition effects, μ _i and γ _c , were too large in absolute value to be consistent with what one would normally expect in connection with professional golf competition. This problem was eliminated by treating each player who had recorded fewer than 10 rounds in a given year as the same player when estimating equation (4) and then assigning the μ _i value so estimated to each such player individually. By treating such players in this way, the distance functions, f d i , c , and condition estimates, γ _c , should be estimated more precisely than if players with fewer than 10 rounds were eliminated altogether.

B.3. Specification of the condition identifier

With the two exceptions noted below in Section B.4, the condition of each shot taken is defined by the tournament/round combination in which the shot was taken. Initially, the author considered defining shot conditions by tournament/round/hole combinations, rather than tournament/round, to reflect that in a given round, some holes might play more difficult than others, but as described in Section B of the supplementary document, this created collinearity problems, especially for drives.

B.4. Special treatment of recovery shots and shots taken from the green

For recovery shots, when condition effects are defined by tournament/round and/or when player effects are included in the estimation of equation (4), resulting estimates of some fixed player and condition effects are too large in absolute value to be consistent with what one would expect for professional golf competition, with the same being true in connection with the other shot condition specifications listed in Section B.3 above. As a result, for recovery shots only, equation (4) is estimated without condition and player effects.

For shots taken from the green (i.e., putts), when condition effects are defined by tournament/round in the estimation of equation (4) and then transformed to corresponding Strokes Gained values, such values can be slightly negative for some putts that were holed out from a relatively short distance. This problem is essentially eliminated by defining the shot condition by tournament/round for putts with a remaining distance to the pin greater than 5 feet and by a single identifier common to all putts taken within a given year with a remaining distance less than or equal to 5 feet. The resulting distance function for putts, f d i , c , produces expected strokes to finish essentially identical to those reported in Table 5.2 of Broadie (2014), even though the estimation methodology is entirely different.