Skill and Randomness on the PGA Tour Roland Minton Roanoke College minton@roanoke.edu

Skill or Randomness? “One necessary (but not sufficient) sign of a good statistic is that whatever it measures is somewhat repeatable; if it’s not repeatable, then it’s probably random, and if it’s random, then we don’t really care about it.” Rob Vollman et al Stat Shot On baseball fielding statistic UZR varying: “It is an unreliable predictor of future performance.” Baumer/Zimbalist The Sabermetric Revolution Not repeatable implies bad stat or not a skill. Corollaries: Winning close games is luck. Clutch players do not exist. . Question: How do golf statistics stack up?

Strokes Gained The new standard in golf statistics is Strokes Gained. Quickly, … 420-yard par 4. Average score by PGA Tour golfers: 4.12 Tee shot: in fairway, 150 yards from hole. Average score: 3.96 Approach shot: on green 15 feet away. Average score: 3.72 Putting: 2 putts 4.00 Strokes Gained par 4 tee shot: - 0.16 Strokes Gained fairway 125-150: - 0.24 Strokes Gained putting: + 0.28 ShotLink measures all shots on the PGA Tour to the inch.

Strokes Gained Categories Putting Fringe Greenside Bunker Fairway 0-50, 51-100, 101-150, 151-200, 201-250 Intermediate Rough 0-50, 51-200, 201-250 Primary Rough 0-50, 51-200 Miscellaneous 0-50, 51-200 Layup Recovery Penalty Tee shots par 3, par 4, par 5 See www.roanoke.edu/mcsp/Minton/ShotLink.html

Strokes Gained Categories Putting Fringe Greenside Bunker Fairway 0-50, 51-100, 101-150, 151-200, 201-250 Intermediate Rough 0-50, 51-200, 201-250 Primary Rough 0-50, 51-200 Miscellaneous 0-50, 51-200 Layup Recovery Penalty Tee shots par 3, par 4, par 5 See www.roanoke.edu/mcsp/Minton/ShotLink.html

Autocorrelation Tee 4 Putt Fairway Tee 3 Years 2005-2015, top 250 in ShotLink data set ~ 2000 instances of consecutive player-years Correlation of year n stats to year n+1 stats Tee 4 Putt Fairway Tee 3

Autocorrelation 1-6’ 7-12’ 13-22’ 23-32’ >48’ 33-48’ Years 2005-2015, top 250 in ShotLink data set ~ 2000 instances of consecutive player-years Correlation of year n stats to year n+1 stats 1-6’ 7-12’ 13-22’ >48’ 33-48’ 23-32’

More Correlations Years 2005-2015, top 250 in ShotLink data set Correlation of stats in same year Strokes Gained putting 8’ to Strokes Gained putting other distances Strokes Gained putting 3’ to Strokes Gained putting other distances Strokes Gained fairway 150 yards to Strokes Gained fairway other distances Strokes Gained fairway 180 yards to Strokes Gained fairway other distances Strokes Gained par 5 tee shots 550 yards Strokes Gained par 5 tee shots other distances Strokes Gained par 3 tee shots 180 yards Strokes Gained par 3 tee shots other distances Strokes Gained par 4 tee shots 450 yards Strokes Gained par 4 tee shots other distances

No Skill in Golf?

No Skill in Golf? Strokes Gained does measure performance on a given shot. My “average” for comparison is based only on distance, lie. The standard of the average PGA Tour pro is exacting. Performance in golf has a large noise component. Bill James Underestimating the Fog. Selection bias? Players who have a bad year one year are not likely to be in the data set the next. Some players have consistent strengths and weaknesses. Most on the PGA Tour do not. Short putting and driving are the shot types that are the most consistent from year to year.

Any Questions? minton@roanoke.edu www.roanoke.edu/mcsp/minton/ShotLink.html www.roanoke.edu/mcsp/minton/SportsMath.html