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Regression Rules Everything

This post will be number/graph heavy, but it explains perhaps the most important concept in predicting golf performance – everyone regresses to the mean, no matter their performance. The below are two charts that show this effect in action. The first uses large buckets and compares all players performance in seasons with N > 50 rounds with their performance (regardless of N) in the subsequent season. The following shows similar data, broken down more at a more granular level, which also includes which percentage of seasons meet the criteria. Read the buckets as seasons within 0.05 standard deviations.



In the first graph, all golfers better than +0.30 (approximately Tour average) in year 1 declined in year 2. Those worse (think Challenge Tour average) did not improve or decline, on average. Only those who performed very poorly in year 1 actually improved. For those better than PGA Tour average, the decline was fairly uniform (~0.05 to ~0.10 standard deviations). Remember, these are the aggregation of huge samples; many players improved at all skill levels, but on average regression/decline ruled everything.

In the second graph, the most important lesson is how rare the truly elite seasons are. Only roughly 1/4 of seasons came in below -.15 (which is roughly the talent level of the average PGA Tour card holder). The cut-off for the top 5% of seasons (2010-2012) came in at -0.45. Also, the regression of almost all players is evident; no bucket better than +0.35 improved in the subsequent season.

This data is fairly strong evidence that we should expect decline from most performances, on average. In fact, based on the rarity of rounds and the demonstrated regression, we should be skeptical about predicting any elite performance to be repeated the following season.

The Aging Curve for PGA Tour Golfers (Part III) – Using Bayesian Prior

Several weeks ago I posted a two studies on aging among PGA Tour golfers, the most recent of which compared sequential seasons, regressing both seasons to PGA Tour average based on the number of rounds a golfer had played in the seasons. DSMok1 suggested modifying the amount and degree of regression by including a better prior, which makes more sense than regressing every golfer to the same mean. Instead of simply adding 25.5 rounds of average play to each golfer’s season, I found a Bayesian prior based on play in the prior season and measured the change in performance from that prior in the following season.

Sample and Design:

I included every player with >20 PGA Tour rounds in a season for 2010, 2011, and 2012. This limited my sample to 703 seasons. I then gathered data for YR N-1, YR N, and YR N+1 (ie, 2009, 2010, and 2011 for golfers with >20 rounds in 2010) on all major Tours (PGA, European,, and Challenge).

Using the equation ((prior mean/prior variance)+(observed mean/observed variance))/((1/prior variance)+(1/observed variance)) I found my prior expectation on performance, inputting data from YR N-1 for prior mean and variance and from YR N for observed mean and variance. That equation adjusts the observed performance based on what we’ve observed in the prior season to generate a true-talent level (True YR N) for YR N+1. I used the same equation to find the true-talent level for YR N+1. I inputted the prior generated from YR N-1 and YR N as the prior mean and the data for YR N+1 as the observed mean. This produced True YR N+1. I then compared both True YR N and True YR N+1to find the change in true-talent for each age group.

I weighted the results using the harmonic mean rounds played in YR N and YR N+1. For example, there were 18 golfers for age 26, so I took the sum of each harmonic mean of rounds and divided each golfer’s change in true talent by their share of the total rounds. This produced my total change in true-talent due to age for each age-group.

If a golfer had no performance in YR N-1 I used +0.08 (slightly below PGA Tour average) as their YR N-1 prior. In most cases, these players qualified via Qualifying School and +0.08 is the observed true-talent for Q-School golfers for 2009-2013. Only 8 golfers had 0 rounds in YR N-1 however.


20    -0.05    2
21    -0.06    3
22    -0.01    6
23    -0.05    8
24    -0.07    9
25    -0.11    11
26    -0.13    18
27    -0.13    23
28    -0.14    29
29    -0.12    36
30    -0.13    34
31    -0.11    39
32    -0.12    36
33    -0.11    34
34    -0.13    34
35    -0.12    36
36    -0.11    37
37    -0.10    42
38    -0.08    26
39    -0.05    30
40    -0.01    21
41    0.03    35
42    0.07    28
43    0.12    19
44    0.13    17
45    0.15    13
46    0.21    17
47    0.25    19
48    0.31    13
49    0.36    12
50    0.35    9
51    0.45    4
52    0.47    2

bayesian aging


The curve generated is very similar to that of the prior study regressing to a mean of +0.00. The peak is slightly lower and the decline is deeper in the late 40s, but otherwise this study supports my prior conclusion of aging with a peak in the mid 30s and subsequent decline.

What Stats Don’t Suggest

Posts like this really agitate me as a golf fan interested in analytics. I’m not sure what annoys me more: the complete disregard for stats as more than trivia or the complete lack of insight it provides. Whichever, this post is a perfect example of everything that’s wrong with how people talk about golf stats. Nothing in that in post has even a whiff of predictive value; there’s no attempt to actually figure out what the stats suggest about players who should be more successful at Summerlin. Instead, we get pseudo-insight like “par 4 scoring demands our attention” and “all five winners ranked inside the top 20 in Strokes Gained Putting”. Well, of course par 4 scoring is important – over half the holes on every course on Tour are par 4s. Guys who can’t score on par 4s can’t be successful on Tour. And of course strokes gained putting is important. Gaining strokes on the field is a certain prerequisite for winning or contending in a tournament.

That’s enough picking on Rob Bolton, who might have a handle on fantasy golf, but is monumentally out of his league when forced to discuss stats. What this post is for is to discuss how successful a golfer has to be at putting to contend at or win a golf tournament. There’s nothing predictive here; everything I’m going to talk about is descriptive.  I downloaded the per tournament results for every 2013 PGA Tour player, including their finishing position and their average Strokes Gained Putting/round during the tournament. Using that data I found how successfully golfers who finished highly putted. Results below in bullet-form.

  • Tournament winners exceeded their season average for Strokes Gained Putting/round by 1.3 strokes/round – 5.2 strokes/tournament.
  • Those finished T10 or better exceeded their season average for SGP by 0.9 strokes/round – 3.6 strokes/tournament.
  • Tournament winners averaged 1.44 strokes gained/round; while those T10 or better averaged 0.92 strokes gained/round.
  • Tournament winners averaged finishing 13th in Strokes Gained Putting for the week while those T10 or better averaged finished 27th for the week.

Clearly, putting very well is necessary to contend for or win a tournament. Nothing in that is novel in the least. Nothing about that is predictive in the least. It just indicates that guys who win do so because they’re playing and putting better than they normally do. Claiming that SGP is important this week ignores completely that it’s important every single week. Moreover, it’s not more important in birdie-fests like this week. SGP counts strokes gained on the field. Golfers this week are going to hole a lot more putts than normal on Tour both because they’ll have disproportionately closer putts and putts of a certain length will be disproportionately easier than normal. However, that just means the threshold for gaining putts on the field is higher.

Best Rounds of 2013 (and the best round ever?)

The 2013 PGA Tour season concluded today at the Tour Championship. I hope to write some more comprehensive season retrospectives in the next few months, but with events remaining on both the and European Tours, a complete recap will come at the end of the calendar year. However, a short post on the best PGA Tour rounds of the season is appropriate. These are the top-five rounds relative to the field and adjusted for the strength of the field (so a 67 at Merion is roughly equal to a 61 at TPC Scottsdale).

5. Boo Weekley, 4th round at the Tampa Bay Championship
The Copperhead Course at Innisbrook is considered fairly difficult and averaged a 71.6 during the final round. Weekley started the round six back of the trio of Justin Leonard, Kevin Streelman, and George Coetzee and in 35th place, but jumped all the way to solo 2nd with a 63, 8.6 strokes better than the field. Weekley followed up this performance with his first victory since 2008 at the Colonial.

4. Keegan Bradley, 1st round at the Byron Nelson Championship
Keegan’s opening round 60 was the second on the PGA Tour in 2013, following Phil’s 60 at the Waste Management Open on a very easy TPC Scottsdale course. The field played TPC Four Seasons in 69.8 that day. Keegan entered the final round in the lead, but Sang-Moon Bae beat him by a stroke to claim his first PGA Tour title.

3. Tiger Woods, 2nd round at the WGC-Bridgestone
Tiger has always dominated at Firestone, but this year’s seven stroke victory was something special. His 2nd round 61 followed a first round 66 and opened up a comfortable seven stroke lead that he would take into the clubhouse Sunday. The field played Firestone in 71.2 during this round.

2. Matt Kuchar, 3rd round at the BMW Championship
This round got lost in the hoopla around the #1 round on this list, but Kuchar shot a 61 when Conway Farms played to a 70.3. Unfortunately for Kuchar, he started the round 16 strokes back of the leader and followed his 61 with a 73 to finish T24. His week was a pretty good example of why momentum likely doesn’t exert influence over golf performance.

1. Jim Furyk, 2nd round at the BMW Championship
It’s funny that Conway Farms was lit-up for the two best rounds of the year as it actually played much more difficult than either East Lake or TPC Boston, which saw a 64 and 62 as the lowest rounds. The field shot 71.1, meaning Furyk’s round registered around 13 strokes better than what an average PGA Tour player would’ve shot that day. Like Kuchar, Furyk didn’t play particularly well in the other three rounds and settled for solo third.

I haven’t checked my entire database, but I’m pretty confident it is the best round on the three major tours since at least 2008. The other two 59s (Appleby in 2010 at the Greenbrier and Goydos in 2010 at the John Deere) came on very easy courses, as did David Duval’s 59 at the 1999 Bob Hope Classic and Chip Beck’s 59 at the Las Vegas Invitational. Bill Barnwell investigated where it ranks all-time at Grantland and determined it was 9th best all-time. He didn’t adjust for the talent of the field however (the BMW field was around 0.3 standard deviations better than PGA average) which would boost Furyk’s round above all but the top four on Barnwell’s list and make it the best round since 1996.

What’s Changed – Zach Johnson

This week the Tour travels to Illinois for the John Deere Classic, a birdie-fest notable for the poor field it attracts in advance of next week’s Open Championship in Scotland. After winning last season, Zach Johnson has been installed as the second favorite by bookmakers and fantasy columnists, behind 2009-2011 champion Steve Stricker and ahead of Louis Oosthuizen and Keegan Bradley. This on its own is not particularly notable; past champions who also happen to be good players are considered favorites at most events, especially when the John Deere field contains only four of my top 25 players by both Z-Score and OWGR. What is particularly strange here is that Zach Johnson has been thoroughly mediocre so far this season. After a four year streak from 2009-2012 that marked him as a consistent top 25 player in the world by Z-Score (between -0.62 and -0.35 all four seasons), he’s fallen off precipitously to -0.13 over 51 rounds. Now, golfers play more poorly than normal over half seasons due to plenty of factors ranging from random variation to injury to genuine deterioration of skill. I’m not as concerned about whether Zach Johnson will continue to play well below his career average as I am interested in just why he’s playing so poorly this year and which parts of his game are responsible for the regression.

First, I will examine what made Johnson such a prolific player in past seasons, specifically focusing on 2012. This analysis will be using the Strokes Gained method, breaking down shots into Putting, Driving, Approach shots, and Scrambling shots. For this, I’ve created Strokes Gained – Driving, Strokes Gained – Approach Shots, and Adjusted Scrambling using publically available PGA Tour stats, and will use the PGA Tour’s own Strokes Gained – Putting stat. I have already explained how my Adjusted Scrambling stat is calculated; the other two will be introduced in coming weeks. For now, it’s important to know 1. the stats are measured in strokes above and below the field and 2. I try to isolate how well a golfer is performing in one area by adjusting for distance of shot, starting position, and what happens in subsequent shots.

Zach Johnson’s 2012 was a great season. He ranked 20th in the world according to my Z-Score Method, won two tournaments, earned four other top tens, and missed only a single cut. His success was driven by great putting and approach shots – he ranked 5th and 7th in those metrics, saving a total of 1.4 strokes relative to the field. His tee shots were a weakness, but cost him less than 0.1 strokes. He made up an equal number of strokes by scrambling well above-average, which combined with his great putting kept him out of bogey trouble when he missed the green. In short, he was as efficient as all but the most elite (Tiger, Rory, Adam Scott) golfers, performing well in three areas, while minimizing his losses in the weakest part of his game.

This season everything has gone off the rails. Starting with his approach shots, Johnson has fallen from 5th to barely above-average, and that’s the only part of his game that has even been above-average. He’s never rated highly in Greens in Regulation because, as a very short driver, he faces longer approach shots. Because of that it’s hard to get a sense of a decline in this area just by looking at the normally cited stats (he’s actually improved his GIR rank from 2012). In 2012, his approach shots yielded 2.72 expected birdies (sum of the probability that a birdie putt will be holed based on its distance). This figure ranked 45th on Tour, despite Zach Johnson hitting his approach shots from much further distances than most of the elite players. This year, he’s ranked only 112th.

More damaging has been his putting. Johnson was 7th on Tour in Strokes Gained – Putting in 2012, gaining 0.6 strokes on the field per round just from putting. For whatever reason, Johnson has really struggled on the greens this year and has essentially been average, losing 0.04 strokes versus the field this year. That itself is stunning. He had scored seasons of 0.38, 0.58, 0.57, and 0.60 strokes gained/round since 2009, and suddenly looks no different than the average Tour golfer at putting. I can speculate about all sorts of reasons for this decline – less practice, less preparation, age related yips, etc. – but obviously this is a huge problem. Johnson cannot return to his old form without regaining his putting stroke. Plenty of guys (Vijay, Adam Scott, Lee Westwood) are or have been great players despite not being good putters, but they’re fantastic tee-to-green players. Johnson needs to compensate for his inability to drive the ball far.

Johnson’s has struggled scrambling this year, but not to the point where it’s costing him more than a few hundredths of a stroke/round, and his driving hasn’t noticeably changed. But it’s apparent that all the decline we’re seeing from Zach this year is due to his inability to generate good looks for birdie and to putt at an elite level. I’d certainly bet on him regaining his form – he’s still only 37 and has extensive history of high level play – but I think it’s crazy to consider him a better player at this point than Keegan Bradley or Louis Oosthuizen.

Greenbrier Classic – Final Round

If we ever needed a lesson that golf is inherently random and statistics can only do so much to predict what will happen, Sunday’s final round at the Greenbrier certainly provided it. Johnson Wagner entered the final round leading Jimmy Walker by two strokes, with Jonas Blixt sitting three back. By the time Wagner was teeing off on #10 to start the back nine, Walker had not managed to close the gap at all, while Blixt had birdied #9 and #10 to get within a single stroke. From there, Blixt used several fantastic approach shots to set-up birdies, while Wagner made three crucial bogeys to fall out of the lead – handing Blixt his second PGA victory in less than a year. My analysis of the back nine will attempt to quantify strokes gained and lost on the field by each shot Wagner and Blixt made on the back nine, similar to my look at the Travelers.

What was remarkable random about the back-nine was what shots Blixt hit to set-up birdies. Blixt is fairly categorized a player very reliant on his putting for success (he was 2nd in 2012 and 47th this season). He does not hit his approach shots well, sitting nearly at the bottom in GIR, even when we account for his below average performance on tee shots. However on Sunday, Blixt’s two best shots were his approaches on #12 and #16 that set-up birdies – both worth around 3/4ths of a stroke. On the flipside, his normally sterling putting failed him on #11, #13, and #17 setting up two bogeys and depriving him of what would’ve been a decisive birdie.

On the par 5 #12, Blixt sat 108 yards from the hole after his lay-up. From there the average player hits to around 20 feet. Instead, Blixt hit a beauty to five feet, setting up a birdie that tied him with Wagner at -13. Later at the par 4 #16, Blixt was 173 yards in the fairway, a location from which the average pro hits to around 30 feet. Blixt hit an iron to nine feet, producing a make-able birdie putt that he drained to draw ahead of Wagner at -13. His approach here was his 2nd best of the day, behind the approach on #12, and his subsequent putt was his 3rd best shot.

However, along with those great approaches came three awfully poor putts which resulted in a par and two bogeys. On the long par 4 #11, Blixt missed the green, but chipped to 6 feet. PGA players make 2/3rds of those putts; Blixt not only missed but ran it three feet past, leaving a miss-able putt for bogey that he made. He hit another equally poor putt on the long par 4 #13. After laying-up, Blixt hit to 7 feet, but blew his par putt four feet past the hole. He would make the four footer for bogey. Again on the par 5 #17, Blixt was standing over a 7 footer that would’ve put him three clear of Wagner. Seven footers are 55% putts normally, so Blixt’s miss cost him over half of stroke, but at least he didn’t blow it several feet past the hole.

In total, Blixt’s back nine shots were worth: -0.44 strokes (tee shots), +1.85 strokes (approach shots), +0.48 strokes (short game), and -0.35 strokes (putts).


Johnson Wagner’s back nine was, succinctly, a disaster. He began it with a two stroke lead over Blixt that was quickly shortened to one stroke after Blixt’s birdie ahead of him on #10. At this point, no one else was any better than -11, while Wagner sat at -14. From there, Wagner bogeyed three of the next five holes and watched Blixt draw two strokes ahead of him for the win. For a guy who has been a steadily good putter (29th, 39th, and 41st in Strokes Gained in 2011-13), the flat stick failed him on Sunday. Two of his three worst shots were missed par putts inside 10 feet (on #11 and #13).

It was #15 that really sunk him though. He started #15 even with Blixt at -12. As we saw earlier, Blixt would go onto birdie #16, but Wagner would not have been in terrible position if he had parred #15 and moved on, as 16-18 aren’t difficult holes. His tee shot on the par 3 #15 was poor, ending up in the rough 14 yards from the pin. From there, PGA players bogey about half the time. Wagner blew his next shot 33 feet past the pin, leaving him a nearly guaranteed bogey. Within 15 minutes between Wagner’s bogey on #15 and Blixt’s birdie on #16, the  tournament was all but over.

For the back-nine, Wagner finished -0.23 strokes (tee shots), -0.17 strokes (approach shots), -0.71 strokes (short game), and -1.29 strokes (putts), a thoroughly miserable performance for a guy who is a PGA Tour player because of his ability to putt.


greenbrier component stats


What’s Changed? – Billy Horschel

One of the most significant stories on the PGA Tour this year has been the emergence of Billy Horschel as one of the best golfers week in and week out.. After racking up only three top-tens in his first two largely mediocre seasons on Tour, Horschel’s earned a top-ten in seven of seventeen starts this year, missing only a single cut along the way, and earning his first Tour victory in New Orleans. His arrival to the general golf public came at the US Open where he was in the final group Saturday and finished T4.

The incredible thing about Horschel’s emergence has been how poor he played in his first two years on Tour. He entered the Tour in 2010 through Qualifying School after a brilliant collegiate career at Florida, but made only four starts due to an injury. He re-earned his card in Qualifying School again, but had a poor year (+0.14 by my Z-Score Method & only 140th on the Money List). His conditional status in 2012 only allowed him to finish 147th on the Money List (-0.12 by Z-Score for PGA and rounds), but he managed to again qualify for the Tour in Q-School. So through two full seasons, he had shown himself to be roughly PGA average. In 2013, though, he’s played to -0.50 – the 18th best performance in the world.

While it’s not completely unheard of for a player to improve as much as Horschel did, it is very rare. Horschel’s improvement from 2012 to 2013 was -0.39 standard deviations. That is the 19th largest improvement from one year to the next in the last five seasons, from a sample of over 800 pairs of seasons (I restricted my examination to golfers with 50+ rounds in each season). Many of the improvements ahead of him are from golfers with established high levels of performance regaining form, such as Jim Furyk in 2012, Adam Scott in 2010, Sergio Garcia in 2011, and Angel Cabrera  this season. Whether due to nagging injury, personal trouble, lack of focus/preparation, etc. those guys fell from performing at a high level, but were able to regain their form the next season. Other golfers went from being extremely bad (below Tour average), to just mediocre. Much rarer  are the genuine breakthroughs where a golfer goes from being quite average to very good. Among those ahead of Horschel, only Webb Simpson in 2011 improved from average or better to playing elite level golf.

So how is Billy getting it done? What has he improved on since last season that has allowed him to earn the top 10s and maiden victory? To examine this I’m going to use what I’ll refer to as Component Stats. These are stats measuring how well a player scrambles, drives the ball, hits approach shots, and putts. To measure performance, I’ve created three of my own stats plus I’ll be using the publicly available Strokes Gained – Putting. For the other three, I’ve already introduced Adjusted Scrambling and I’ll be introducing my Approach and Driving stats in the next few weeks. For now, just remember that the stats are measured in strokes above and below the field and try to isolate how well a golfer is performing in one area by adjusting for distance of shot, starting position, and what happens in subsequent shots.

By this method, in 2012, Horschel was only substantially better than PGA Tour average at driving – where he gained nearly half a stroke on the field. He was average at scrambling, slightly below average at putting, and slightly above average at hitting approach shots. In short, he was much like dozens of other Tour golfers who survive because they’re very good at one skill and good enough at everything else. What separates the elite from those golfers is the elite only have one weak spot in their game. Of the best 25 golfers by Z-Score in 2012, only Robert Garrigus ranked below average in more than one of the four statistical components. Only three of the top 50 (Ben Curtis and Lee Westwood also) ranked below average in more than one category. As long as Horschel could only rely on his driving, he was not going to be able to distinguish himself.

I have no particular insight into what Horschel changed in his preparation in 2013; people have credited maturity gained from working with a sports pyschologist. What I do know is that Horschel has delivered far better performances putting and hitting approach shots this season. His Strokes Gained Putting has improved from -0.09 to +0.50 strokes this season – one of the largest improvements year-to-year – and improved by almost a half a stroke on approach shots; a total improvement of a full stroke. Horschel’s driving has remained well above average, and though his scrambling has regressed by 0.20 strokes (he’s only successfully scrambling 59% of the time despite putting lights out overall and hitting from closer lies), that hasn’t hurt him much.










All in all, Horschel’s improvement has been worth 2/3rds of a stroke. A to-be-posted regression analysis shows that golfers a stroke better than PGA Tour average earn ~$65,000/tournament more than average golfers or about $1.5 million over a typical season, just to provide a financial benchmark to evaluate his improvement.

The question now is whether Horschel can maintain his performance going forward. My research has shown it’s correct to regress samples of around half a season by adding 25 rounds worth of average performance. That would expect Horschel to perform at around -0.36, equal to something like the 35th best player in the world. My weighted and regressed two year Z-Score method predicts something similar. However, if Horschel has made genuine changes to his preparation and mental approach to the game, we may not be seeing a golfer playing above his head, but rather one pushing his ceiling higher.

Travelers Championship – Final Round

Though Ken Duke and Chris Stroud entered the final round of the Travelers having zero combined PGA Tour victories and trailing co-leaders Bubba Watson, Charley Hoffman, and Graham DeLaet, by Sunday evening, Duke had won his first title, on the second hole of a playoff with Stroud, while Stroud took home his largest ever check. The final round featured two critical moments; the first when solo leader Bubba Watson dropped his drive on the par 3 16th in the water, making triple bogey and torpedoing his chance to win and the second when, having overshot the 18th green and facing a make-or-break situation, Stroud drained his chip to force a playoff with Duke.

To evaluate how Duke and Stroud made it to the playoff Sunday, I copied down each shot taken on the back nine Sunday using the PGA Tour’s ShotLink data. I then employed the Strokes Gained method popularized by Mark Broadie to evaluate the quality of each tee shot, approach, chip, pitch, and putt. This method uses distance from the hole and location of the ball to generate the average number of shots a PGA Tour golfer will take to complete the hole at the end of each shot. If that average is more than one shot less than at the end of the previous shot, the golfer “gained” strokes on the field, while if the average is less than one shot lower than at the end of the previous shot, the golfer “lost” strokes on the field. The strokes gained method does not factor in anything but location of the ball, so severity of the rough or bunkers, speed of the greens, intensity of the wind, etc. are not explicitly accounted for, however, TPC River Highlands played essentially to par this week (70.2 Field Average compared to a Par of 70).

Ken Duke entered the final round at -8, two back of the three leaders and one behind Stroud. He played the front nine in -1 and entered the back nine with a chance to win, as none of those who entered the day ahead of him had placed any more distance between them. Duke made four birdies on the back nine, two set-up by fantastic approach shots and two on long putts.

On the long 462 yard par 4 10th, Duke hammered his drive 316 yards, an above-average drive, and followed with a beautiful approach to 5 feet. That approach took Duke from 2.90 expected strokes to only 1.25 expected strokes, a gain of 0.65 strokes, his 4th most important shot of the back nine. However, that was his only notable above-average “long” shot on the back nine. Most of his remaining tee shots and approaches were quite poor.

Instead, he relied on his short game and putting to survive. On the par 4 12th, Duke hit a poor tee shot and then a poor approach into the rough around 13 yards from the hole. From there, most players take 2.42 strokes to finish. Duke chipped to less than a foot, a shot worth 0.42 strokes gained. Then on the short par 4 15th after he ended up in the rough from around 40 yards off the tee. Duke hit a perfect pitch shot to six feet, setting up a great birdie opportunity which he converted. The average player sitting in the rough from 40 yards takes 2.75 strokes to finish up; Duke’s pitch to six feet was worth 0.35 strokes. On 18, after hitting an extremely nervy tee shot and getting his second to just shy of the green, Duke chipped across the surface to less than two feet, almost guaranteeing a par on the hole. That shot was worth 0.36 strokes gained.

His putting was also very strong though. His birdie putt on 15 from six feet was worth 0.40 strokes, but that was only his third most important putt of the day. Coming off a birdie at 10, Duke hit a quality approach to seventeen feet, removing the threat of bogey, but birdie was doubtful as only around 20% of putts are holed from that distance. However, Duke rolled it in for a gain of 0.80 strokes. His most important putt was on 13 though. Three straight below average shots had left Duke on the green, but at 46 feet birdie was looking extremely unlikely. PGA golfers hole less than 3% of their 40+ foot putts, while three putting almost 15% of the time. On the shorter par 5, Duke was looking at a legitimate possibility of bogeying. Instead, he meandered his 46 foot putt in for birdie, a putt worth an enormous 1.07 strokes gained, his best of the round.


In contrast to Duke, who had eight shots that gained more than a 1/3rd of a stroke – seven of which were putts or short shots (pitches, chips, etc.) – Stroud had only two shots that gained more than 1/3rd of a stroke and two shots that lost him over 0.5 strokes against the field.

Stroud entered the back nine -1 for the day and -10 for the tournament and reeled off three straight pars without any excitement on 10 through 12. On 13, he hit a wonderful short approach from 22 yards that left him with a seven foot putt for birdie. While such a putt isn’t a guarantee, the average player makes it around 60% of the time. Stroud’s miss was worth -0.55 strokes gained. Stroud rebounded on the short par 4 15th by holing a ten footer for birdie, 0.60 strokes gained.

As Duke finished up his round at -12, Stroud teed off on 18 needing a birdie to force a playoff. After an ideal drive left him with only 2.78 expected strokes, Stroud flew his 93 yard approach shot well over the green, a miserable shot that cost him -0.54 strokes and all but eliminated him from contention. From 17 yards, the average PGA player takes 2.32 strokes to finish up. When Stroud rolled in his chip, he gained a whopping 1.32 strokes on the field and forced Duke into a playoff for the Championship.


The two took different paths to the playoff; Duke rode a series of high quality chips, pitches, and putts to birdies and par saves, while Stroud relied on steady play and that one huge moment on 18.