Golf Analytics

How Golfers Win

Tag Archives: jimmy walker

Sony Open Recap

Jimmy Walker’s your winner, beating the field by nine strokes (!) with a dominant Sunday performance. His performance relative to the field was the best since Martin Kaymer stomped everyone at Pinehurst last June and his winning margin was the largest on Tour in six years. Adam Sarson has a great recap here.

Walker’s Fourth Win:

Walker’s win was comprehensive – he led the tournament in putting and was 2nd in long game (tee shots+approach shots) play (to K.J. Choi no less). In fact, if he had just putted at an average level this tournament, he would’ve tied English, Woodland, and Kuchar for 2nd place.  Coming into the week, I talked about how the Sony doesn’t seem to punish guys who are wayward off the tee. Walker is the team captain of the wild-off-the-tee guys. Of course, you have to be able to bring it with the irons (Walker certainly can) and putt well (yup), but wildness is not penalized here.

What’s interesting about Walker’s performance is that he’s putted extremely well in the Hawaii events since returning to the PGA Tour full-time in 2008. Between 2008 and 2013, Walker putted about 0.3 strokes better per round in the Sony Open. In the four Hawaiian events since (two wins and a 2nd), he’s putted 0.8 strokes better per round. For the whole period (36 rounds), he’s exceeded his normal putting performance by over half a stroke. Perhaps that’s random noise or perhaps there’s some level of comfort with the bermuda grass greens at Kapalua and Waialae, but anytime you can start a tournament with a half a stroke edge each round, you’re a lot more likely to win.

This is his fourth win since the start of 2013 (tied with Patrick Reed for top on Tour). It propels him to 1st place in the FedEx Cup standings – a familiar position that he held from this point until Rory’s dominant run last summer. Walker’s also pretty much assured his place on the Presidents Cup team this fall. He’ll look to defend at Pebble Beach in a few weeks.

What I’m Looking At:

Before the tournament I was very interested to see how Luke Donald played this week – especially with his irons/wedges/short game. His struggles last season were all about how poorly he was playing inside 150 yards and the hope was that his return to Pat Goss was going to help him on that front. In his first start, the signs were promising. He finished T51, driven by a typically great putting performance. Donald will always be able to keep his head above the water with his best in the world putting. The rest of his game definitely showed up too.

He’s never hit driver well and didn’t this week. However, he was solidly above-average with his approach shots – despite this course offering few chances for the very short <125 yard shots he used to excel the most at. Despite hitting only 43% of fairways and losing nine yards to the field off the tee, Donald hit 71% of greens and was above-average on wedge shots, short and mid iron shots, and long iron shots for the week. So far so good.

Matt Kuchar’s performance was up to expectations this week. The long game looked fine and he putted out of his mind – especially on par putts. My numbers had his short game performance as average, but he managed to scramble successfully 83% of the time. That means he was money on short par putts all weekend. He has to be disappointed to have played so poorly on the weekend, but his game looks fine going into the California swing.

It was nice to see rookie Justin Thomas break-through with a top ten. He got a lot of attention from the broadcast crew for his absurd length off the tee (he easily hits driver 25+ yards past Tour average), but it looks like he was laying up off the tee with irons/hybrids often. That’s not that rare for the longest guys, and I wouldn’t be shocked to see him do it a lot this year as he’s feeling his way around the PGA Tour courses.

Putting Driven Performance Changes are Illusory

Last week I posted about how repeatable performance on different shot types was from season to season. Tee to green play is more repeatable than putting which is more repeatable than scrambling. That makes sense once you realize that golfers play 2-3 times more tee to green shots than meaningful putts in a round; there’s just more inherent randomness in a season’s worth of putts than in a season’s worth of tee to green shots. Golfers play even fewer scrambling shots resulting in even more randomness in a season’s worth of scrambling.

Last month I also examined how repeatable small samples (4-8 tournaments) of putting performances are, in the context of discussing why I expected Jimmy Walker’s performance to regress to the mean. That micro-study indicated that there was very little correlation between a golfer’s performance in a 4-8 tournament sample of putts and the following 4-8 tournament sample of putts. In the whole, performances in such short samples regress almost entirely to the mean.

Those two lines of inquiry led me to examine whether putting was more random than tee to green performance. I have always believed that improvements/declines that were driven by over-performance in putting were less real than those driven by tee to green over-performance, but I had never actually tested that hypothesis. The key question is whether changes in performance driven by putting are less persistent than those driven by tee to green play. That is when a golfer performs better over the first half of a season, and much of the improvement can be traced back to an improvement in his putting stats, will that golfer continue to perform better in the second half of the season? The evidence says changes in performance driven by putting are more illusory than changes in performance driven by tee to green play.


I gathered the tournament by tournament overall, tee to green, and putting performances of all PGA Tour golfers in rounds measured by the ShotLink system for 2011-Present. I divided those rounds into roughly half-season chunks (January-May 2011, May-November 2011, January-May 2012, May-November 2012, January-May 2013, May-September 2013, October 2013-Present). Each chunk included around 15-18 tournaments. I considered all golfers who recorded at least 20 rounds in consecutive half-season chunks.

To measure putting performance I used the PGA Tour’s Strokes Gained Putting stat and to measure tee to green performance I used my own overall ratings with putting performance subtracted out. This methodology is consistent with my measurement of tee to green performance in numerous recent work.

Half-Season Correlations by Shot Type:

First, I measured how repeatable putting and tee to green performance was between half-season samples, much like the full-season samples used in this study. I included all golfers with at least 20 rounds in consecutive half-season samples and compared each half-season to the half-season that directly followed, including 2nd halves to 1st halves of following calendar years. This yielded samples of ~800 golfers for both tee to green and putting. Graphs are below.

half tee to green

half putting

Tee to green performance was again more repeatable than putting performance. In the study linked above consecutive full-seasons of tee to green performance were correlated at a R=0.69 level. I found a correlation of R=0.62 between consecutive half-seasons, understandably less given the smaller number of rounds/shots played. The full-season correlation for putting was R=0.55. Half-season putting performances were similarly less correlated than full-seasons at R=0.40. Both these findings are consistent with the understanding that randomness between samples increases when fewer rounds/shots are compared. Most importantly, putting is less repeatable than tee to green play.

Persistence of Changes in Performance by Shot Type:

Next, I measured how persistent changes in performance are when considering putting and tee to green play. That is, when a golfer improves their putting over a half-season sample, how much of that performance is retained in the following half-season? If 100% of the performance is retained, changes in putting performance over a half-season entirely represent a change in true talent. If 0% of the performance is retained, changes in putting performance over a half-season entirely represent randomness. The same for tee to green play. My assumption was that a larger percent of performance would be retained for tee to green play than putting, meaning that half-season samples of putting are more affected by randomness than half-seasons of tee to green play.

To measure the effect, I first established prior expectations of performance for every golfer in my sample. I simply averaged performance in tee to green play and putting for the three years prior to the beginning of each half-season sample. For example, for the May-November 2011 sample, I averaged play between May 2008 and May 2011. This is not an ideal measure of performance, but it provides a consistent baseline for comparisons to be made.

I removed all golfers from the sample who had no prior performances. This reduced my sample to around 750 consecutive half-seasons.

The values I compared were the initial delta (Prior minus 1st Half-season) and the subsequent delta (Prior minus 2nd Half-season). Using this method I can find how persistent a change in performance is between to half-seasons. I did this considering putting and tee to green play. Graphs are below.

persist tee to green

persist putting

Changes in tee to green play were twice as persistent as changes in putting play, meaning golfers who improved their tee to green play retained twice as much of those improvements as golfers who improved a similar amount in putting. Golfers maintained around 60% of their tee to green improvements, but only 30% of their putting improvements. This indicates that putting performances regress more sharply to prior expectations than tee to green performances.

Are Putting Performances More Illusory?

Finally, I gathered the data from above to measure whether changes in performance driven by putting less real than changes in performance driven by tee to green play. I ran a linear regression using the initial delta for overall performance and the initial delta for putting performance as independent variables and the subsequent delta for overall performance as the dependent variable. In short, given a certain overall change in performance and a certain change in putting performance over the first half-season, how much of that overall change in performance is retained over the second half-season?

As the following table shows golfers retain much more of their improvement or decline when that improvement or decline occurred in tee to green shots than if it occurred in putting. The columns show improvements/declines in overall play (considering all shots) and the rows show improvements/declines solely in putting. The table shows that a golfer who improves overall by 0.50 strokes will retain only a quarter of their improvement if all of the improvement was due to putting (0.50), while they will retain over half of their improvement if none of the improvement was due to putting (0.00). The equation used to produce this chart is Subsequent Delta = (0.56 * Initial Overall Delta) – (0.28 * Initial Putting Delta).

delta comparisons


These findings should fundamentally alter how we discuss short-term changes in performance. I’ve already shown repeatedly that performances better than prior expectation will regress to the mean over larger samples. That idea is consistent across sports analytics. However, these findings indicate that the amount of regression depends on which part of a golfer’s game is improving or declining. Golfers who improve on the basis of putting are largely getting lucky and will regress more strongly to the mean than golfers who are improve on the basis of the tee to green game. Those who improve using the tee to green game are showing more robust improvements which should be expected to be more strongly retained.

The golfers who represent either side of this for the 2014 season are Jimmy Walker and Patrick Reed. I’ve discussed both in the past month, alluding to how Walker’s improvements were almost entirely driven by putting and how Reed’s were mostly driven by tee to green play. Based off these findings, Reed is more likely to retain his improvements over the rest of the season, all else being equal, than Walker.


All graphs/charts are denominated in strokes better or worse than PGA Tour average. Negative numbers indicate performances better than PGA Tour average.

Will Jimmy Walker Continue to Putt at an Elite Level?

I got some push-back from Chris Catena on twitter today about my contention that Jimmy Walker’s recent run of great play was driven by lucky putting. In that post, I showed that Walker had established himself recently as an above-average, but not elite putter (a strokes gained putting of around +0.25-0.30/round for the last five years). During Walker’s recent run ( Open through Northern Trust Open), he’s putted at a +1.20 level. That +0.9 strokes/round improvement is entirely what carried him to three wins in the last four months. I also contended that Walker continuing to putt at this level is very unlikely, simply because no one ever has for a full-season. Moreover, Walker’s best putting season (+0.46) and average putting season (+0.26 from 2009-2013) are far short of the kind of elite, sustained level of play we often see out of the golfers who lead the Tour in strokes gained putting. This post is to defend those claims in more depth and show why I think it’s very unlikely that Jimmy Walker will continue putting and playing as well as he has in the last four months.


Above is a graph of Walker’s strokes gained putting performance per tournament in every tournament the PGA Tour has data for since the start of 2012. The red dashed line is a linear trendline of his performance. It has basically zero (R=0.03) relationship with the passage of time, indicating that on the whole, Walker’s performance hasn’t improved over time. This is important to note because if we hypothesize that Walker changed something in his ability to putt, it clicked in only weeks after his worst putting stretch of the past 2+ years. Now, poor performance is certainly a motivator to change and try to improve, but a simpler explanation is that Walker got unlucky during the summer, and has been riding a combination of luck and improved putting since.

What Walker has done in the past 23 rounds on Tour isn’t unprecedented even during the 2013 season. I divided the tournaments in 2013 (Hyundai ToC to Tour Championship) into four quartiles with 7-8 tournaments in each quartile. I then found the golfers who had participated in 4+ tournaments in each bucket and averaged their SGP for each quartile. I gathered all golfers who had qualifying consecutive quartiles and compared them using Q1->Q2, Q2-Q3, etc. For Q4, I compared it to performance so far in 2013-14 from the Open to the Northern Trust Open. From all that, I had 365 pairs of quartiles where a golfer had played at least four tournaments during each quartile. A graph of of those pairs is follows.

pairs of SGP quartiles

There was very little relationship between a golfer’s performance in one set of tournaments and their performance in the following set of tournaments (R=0.04, indicating a tenuous at best relationship). I had 61 quartiles with a performance > +0.50, averaging 0.72. Those quartiles played to only +0.12 in the next set of tournaments. In fact, in only 12 of those samples of > +0.50 performance did a golfer again average > +0.50 the next quartile. None of the six samples of > +1.00 SGP had > +0.52 SGP in the following quartile. In short, we should be very skeptical of elite putting performances over fairly short periods of time.

Now, when I said that Jimmy Walker’s performance was largely driven by luck I meant the “largely” part. I think it’s extremely unlikely that all of his putting performance can be explained by variance alone. Jimmy Walker has +1.20 strokes gained putting/round in 23 measured rounds so far this season. The observed standard deviation between 23 round samples for PGA Tour players is around 0.35 strokes. That means if an average (+0.00) putter plays an infinite number of 23 round samples, 68% of them will yield an SGP average of -0.35 to +0.35, while 95% of them will yield an SGP average of -0.70 to +0.70. In short, there’s a ton of variation between 23 round samples. For an average golfer, it wouldn’t be shocking for them to putt extremely poorly or very well over 23 rounds. Plugging that standard deviation (0.35), Walker’s 2013-14 SGP (+1.20) and Walker’s five year SGP average (+0.26) into a Z-score equation yields a Z of 2.7 which indicates <1% chance that Walker’s SGP is entirely due to chance. That means there is some signal in all that noise.

But how much? I consider myself a Bayesian in that I think it’s very important to compare any observed performance to our prior expectation for that performance. Up until October 2013, Jimmy Walker was an above-average, but not elite putter. Since then, in 23 rounds, Walker has putted out of his mind. Surely we should consider Walker a better putter than we did in October, but how much better? Fortunately, there’s a simple equation we can use to estimate how the 23 round sample should change our expectation for him. It’s ((Prior Performance)/(Prior variance) + (Sample performance)/(Sample variance))/((1/Prior variance)+(1/Sample variance)). Basically, this equation tells us how confident, statistically, we should be about a golfer establishing a new level of performance based on how far his performance is from the prior expectation and how large of a sample we’re dealing with.

We know the prior performance and sample performance from the previous paragraph. The sample variance is simply the 23 round standard deviation from above (0.35) squared (0.12). To find the prior variance, I was forced to run some simulations as my data was limited. I know the variance for 100 round sample is around 0.025, so the prior variance for Walker over his >300 rounds in 2009-2013 must be no greater than that. Simulations indicated to use a figure around 0.02.

Plugging those values into the equation yielded a new expectation for Walker of around +0.40. That’s significantly higher than his five year average, but also much less than what he’s done recently. The equation is saying that Walker’s been much better, but that 23 rounds isn’t nearly enough to say that he should be expected to continue to putt at an elite level. If we had just seen Walker putt at a +1.20 SGP level for 80 rounds, we’d be much more confident in him continuing to putt at an elite level.

The tl;dr here is that extremely good SGP performances over small samples (~4-8 tournaments) sharply regress to the mean in the following 4-8 tournaments. Sustaining the kind of putting Walker has shown recently is unprecedented over a large sample of rounds from 2013-14. Moreover, the expected level of variance of 23 rounds is very large. It would not be abnormal for an average putter to putt at a top 20 or bottom 20 level over 23 rounds. Considering all that, we should expect Walker to putt better over the rest of the season than he did in 2009-2013, but not nearly as well as he has since October.

We Need to Talk About Jimmy

After his win at last week’s Pebble Beach National Pro-am, Jimmy Walker has run his 2013-14 PGA Tour record to 3 wins, another top-ten, only 1 missed cut, and 1st place in the FedEx Cup standings. Prior to his win at the Open in October, Walker was certainly a strong PGA Tour player, but not widely considered among the elite golfers in the world. His world ranking peaked at 59th after the Players Championship in 2013, but has shot to 45th after winning the Open, 32nd after winning the Sony Open, and 24th this week. All of a sudden, Walker is entering tournaments as one of the touted favorites. What I’d like to do is to show where Jimmy Walker has come from and why you should be skeptical that he should be considered one of the Tour’s elite players.

Walker emerged as a PGA Tour regular in 2008 after bouncing around between the Nationwide Tour and PGA Tour between 2004-2007. Initially, he wasn’t a particularly good player. My Z-Score ratings have him at +0.16 in 2008, +0.16 in 2009, and -0.08 in 2010. For context, 0.00 is set as the average of all players who play on the Tour (down to the lowest qualifier, past champion, and club pro who competes in a tournament) while around -0.10 is the average player who holds a PGA Tour card. His seasons reflected those underlying stats; he was forced to re-earn his card at Q-School in 2008 and finished outside the top 100 on the money list in each of the next two seasons. Up to the beginning of 2011, Walker was a 32 year old who had never won a PGA tournament. It was as likely as not that he would fall off the PGA Tour in the next five years at that point.

But then something changed. Walker posted his best season in 2011 by actual results and underlying performance. His -0.24 Z-Score was well above PGA Tour average and he recorded four top-tens (including at Pebble Beach, Riviera CC, and the Sony Open). He followed that success up with a -0.31 Z-Score and five top-tens (again at Pebble Beach and Riviera CC) in 2012. Entering last year, Walker had posted consecutive solid seasons, but certainly no one was touting him as someone due to win a tournament. In fact, in this Golf Channel article from 2012 his name isn’t mentioned among eight guys (including Jeff Overton, Charlie Wi, and Brendon de Jonge).

Statistically up to 2012, Walker was decidedly a bomber. His average driving distance rank was 45th between 2008-12, while his average accuracy rank was 181st. He showed little ability to consistently hit greens, finishing no higher than 116th in GIR from 2008-12. Mostly, he putted well – he averaged 0.18 strokes gained putting over that period, solidly above PGA Tour average.

With all that context, Walker’s emergence looked unlikely as 2013 began. However, he played even better in the first half of the season, continuing a streak of 25 straight made cuts from the 2012 John Deere Classic to the 2013 Memorial. That run included four top-tens (again at Pebble Beach). From the Memorial onward, he missed six of nine cuts, crashed out of both Majors he competed in, and failed to reach the Tour Championship. For 2013 as a whole, Walker posted a Z-Score of -0.46 (including his fall swing) which is roughly what is expected out of a top 20 player in the world. The he went out in 2014 and won twice in four starts.

So did something change for Walker in 2013 that he carried over this year? Or is he suddenly a different player this season? In 2013, he remained wedded to distance above accuracy with his drives, finishing ~25th best in distance, but outside the top 150 in accuracy. He also putted about as well as he did in the previous five years, finishing with an average strokes gained putting of 0.27. What did change was his ability to hit greens. This article claims that Jimmy changed his aggressive style to chase pars on par 3/4s. It’s possible to imagine a more conservative game plan for attacking pins would lead to more greens hit, but his average proximity in 2013 was two feet closer to the pin than in 2012. What we’re likely looking at instead is a general improvement in Walker’s approach game. He was hitting more greens and hitting it closer because he was playing his irons better.

In his eight 2013-14 tournaments, Walker’s stats (adjusted for field and course conditions) are basically exact copies of his 2013 performance in terms of driving distance, driving accuracy, and greens in regulation. In fact, the only major statistical indicators that are different are his scrambling (surged from 60% to 65% this season) and his putting (he’s gained an additional +1.06 strokes on the field each round due to his putting). Now, obviously scrambling well is a typical result of putting well. I examined his proximity to the hole after the scrambling shot for 2014 and prior seasons to see if he was hitting it closer. Instead, he’s actually hitting it around 2 feet further from the pin, leaving himself more difficult putts to earn his par. From that, all I can conclude is that his putting results are driving all of his improvement from 2013 to this new season.

That conclusion is all well and good, but is it realistic to expect him to maintain such a putting improvement? In short, no. Since the Tour started tracking shot-by-shot data in 2004, only one player (Ben Crane 2005) has maintained a SGP above +1.00 per round. Most seasons, the leader is around +0.90 and those leaders are players who are demonstrated elite putters (Luke Donald, Brandt Snedeker, Greg Chalmers, etc.) who have multiple seasons of near that level of play. Walker only has one such elite season (+0.46 in 2012). Right now his SGP for 2014 is based on only 19 recorded rounds. There’s a ton of room for randomness to creep in over such a small number of rounds. In comparison, he has over 300 rounds of prior play that show that he is an above-average, but not elite putter. Being a proper Bayesian, that’s not enough to convince me that he’s significantly better going forward. At most, I’d place him as something like a +0.30 to +0.40 putter, enough to be in the top 20 putters on Tour, but not nearly the +1.33 figure he’s sporting so far.

Now that doesn’t mean Walker isn’t going to continue to be a very good player. He didn’t receive nearly the recognition he deserved over the past two seasons when he was legitimately playing at a top-50 in the world level. His three wins, 25 tournament streak of made cuts, and -0.36 Z-Score from 2011 to present are fantastic achievements for a guy who didn’t look like he’d ever contend for anything as recently as 2010. He’s has to be considered a favorite to earn a spot on the Ryder Cup team as a bonus. But no one should expect him to continue playing like he has since October. His putting is likely being driven by a ton of luck right now and luck cannot be relied on to stick around. Going forward, he’s probably not going to be able to putt nearly as well as he has; that doesn’t mean he’s not going to be successful, just that he shouldn’t be considered one of the favorites in a field with Dustin Johnson, Webb Simpson, Bubba Watson, Jordan Spieth, and Matt Kuchar.

How He Won: Jimmy Walker (Pebble Beach Pro-am)

Jimmy Walker did it again. After taking home both the Open and Sony Open to begin his season, Walker burst out to a huge lead after round 3 and survived a pretty poor 4th round to win by one at Pebble Beach. I wrote about Walker in my Thursday post, noting that he gained a lot on the field with two hole-outs for birdie from far off the green – overall scrambling 5/5 on Thursday. He kept that up at Monterrey Peninsula and Spyglass Hill, finishing Saturday having successfully scrambled 15 of 16 missed greens. Even considering his poor 2/5 on Sunday he finished at 81% for the tournament. The field, over all four rounds and three courses, scrambled at 56%; Walker gained over 5 strokes on the field just through his scrambling.

Walker’s other conventional stats were strong as well. He hit 72% of his greens for the week (field hit 63%) and out-drove the competition by 8 yards.

Thankfully this is the last multi-course event of the season so a clearer statistical picture will be available for the winners going forward. This week in particular I have no idea how much putting factored into Walker’s success because we don’t have Strokes Gained Putting numbers or even shot tracker data for Spyglass Hill or Monterrey Peninsula. As I noted on Thursday, Walker’s putting wasn’t particularly notable. His SGP figure was 0.76, which is great on average, but fairly low for being one of the best rounds of the day. His success was mostly driven by the aforementioned two hole-outs and a slew of approach shots hit close. Then on Sunday he putted horribly (-1.51 SGP). Despite generating 3.9 expected birdies, he only converted 3 of them.

Walker’s main issue on Sunday was leaving his birdie putts too far from the hole. He birdied 3 holes and had putts for par on 14 more (#10 he was forced to recover from the fairway bunker which cost him a stroke). Of those 14 par putts, he left his on #1, #12, and #13 beyond 10 feet – making bogey on all three holes. He almost did the same on #18 when he needed to par to win outright, but kept his par putt to 5 feet despite rolling it aggressively past the hole.

I hope to have more this week detailing just what Walker is doing differently this year that he didn’t last year, but  I don’t think I’ll find much. Walker rated very highly in the Z-Score model last year (and had five top tens) despite really not getting any attention (probably because he missed 6/9 cuts to close the season). Walker is just the third player in the last ten years to win twice before arriving at Riviera (counting his fall win is unfair to the competition). Phil began 2005 with two wins in six events before winning twice more, while Mark Wilson began 2011 with two wins in six events before basically reverting back to the average player he was prior to that run. It’s anyone’s guess what Walker will do the rest of the season, but with 3.6 million banked already, he should make arrangements to be in Scotland at the end of September.