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Don’t Trust a Hot Putter

I have written a lot about predicting putting performance. I’ve found that 1st round putting performance provides no information to predict 2nd round putting performance. I’ve found that players who improve their putting at the beginning of a season tend to retain little of that improvement going forward. I’ve found that putting improvements driven by making more long putts tend to disappear the following season because making long putts is largely¬†a matter of luck. I’ve found that putting performance over a quarter of the season provides almost no information on how well a player will putt in the next quarter of a season. All of these studies indicate that putting performance is highly affected by luck.

What I have not done is test the influence of very recent putting on one week of putting performance. If one believed that putting came in streaks – perhaps someone got “hot” or “in the groove” for a few weeks before returning to normal – you would expect very recent performance (prior week or prior month) to have a strong impact on putting performance in the current week’s event. As I’ll show, that is not the case. My results over several different methodologies again show that short-term putting is driven mostly by luck and that recent putting performance provides almost no information on how well a player will putt going forward.

Methodology
I collected the following data from 2011-2015 for all qualifying PGA Tour golfers: 1. their average putting performance in strokes gained versus the field over the previous three seasons (2008-2010 for 2011, 2009-2011 for 2012, etc.), 2. their putting performance in the month prior to every event they played, 3. their putting performance in the week prior to every event they played, and 4. their putting performance in each event they played. I ignored majors and Tour events outside the US for which strokes gained data was not available.

Once I had matched that data for every qualifying golfer for each tournament they played, I discarded any data points for which the player had not played the week before. These two samples of performance (played prior week and did not play prior week) were not different in a statistical sense. Each data point contains putting data from 1. prior seasons, 2. the prior month, and 3. the prior week.

Influence of the prior week
I had nearly 3100 pairs of tournaments to compare. Just comparing performance in the prior week to the current week yielded almost no predictive value (R^2 = .006). For every stroke better than the field a player putted in the prior week, they’re expected to putt 0.08 strokes better in the next week.

prior week to current SGP

Influence of the prior month
Using the same 3100 pairs of tournaments and comparing performance in the prior month to the current week again yielded almost no predictive value (R^2 = .006). For every stroke better than the field a player putted in the prior month, they’re expected to putt 0.09 strokes better in the next week.

prior month to current SGP

Influence of the prior three seasons
Using the same process and comparing performance over the previous three seasons to the current week yielded more predictive value (R^2 = .057). For every stroke better than the field a player putted over the previous three seasons, they’re expected to putt 0.91 strokes better in the next week.

priorseasons to current SGP

Combined model
Including all three pieces of data and predicting the current week resulted in the following equation:

Putting estimate = (0.02 * Prior week) + (0.04 * Prior month) + (0.86 * Prior seasons)

This indicates that when attempting to predict putting performance, how a player has putted in the previous few seasons provides about fourteen times more information than how they have been putting recently.

What this means for this week

Putting performance is almost entirely driven by how well a player putts in general, rather than any hot or cold streak in recent weeks. Looking at the field this week, Nick Watney sticks out as a guy whose poor putting has cost him recently. Of players with at least 6 rounds of putting data in 2015, Watney is 2nd to last despite being generally a fairly average putter by the numbers. Poor putting likely cost him at least a spot in the playoff at Torrey Pines on Sunday.

Kevin Streelman’s putter has also been cold to start the season – he’s putted about half a stroke worse than expected over his first four events. He’s wasted three strong tee to green performances at Kapalua, Waialae, and Scottsdale by putting poorly, and managed only a T30 as his best finish there.

Predicting Putting Performance by Distance

Mark Broadie’s research of the Shot Link data established a clear relationship between putt distance and % of putts made. PGA Tour pros make a very high percentage of their close putts, but only about half of their putts around 10 feet and only around one in six around 20 feet. Pros hole very few (~5%) of their longest efforts from 25 feet and beyond. That data on % of putts made for each distance now forms the backbone of the PGA Tour’s Strokes Gained Putting statistic where players are credited and debited for making or missing every putt from every distance. Over a single season Strokes Gained Putting is often an unreliable indicator of putting performance, particularly at the extremes and also for players who have putted much worse or much better than in previous seasons.

Putting performance is polluted by randomness; Tour players just don’t attempt enough putts over the course of the season to get an accurate picture of their underlying putting ability. However, to make accurate projections of putting ability, you need to know whether Graeme McDowell’s 0.9 putts gained this season represents more talent or more luck. I’ve broken down putting performance into four different distance buckets from the PGA Tour data: putts inside 5 feet, 5-15 footers, 15-25 footers, and putts outside 25 feet. The results show that putting performance is far more predictable and consistent at the short distances. Long putting is so noisy that it’s difficult to say anyone gains much of an advantage from their long putting over the long-term.

Inside 5 Feet:

These putts are almost always converted (average 96%). The spread in performance between 2011-14 was 93% to 99%. The spread in expected performance derived from weighting the previous four seasons is 94.3% to 97.8%. This indicates that we should expect every regular Tour player’s true talent from inside 5 feet to fall somewhere inside that 3.5% range. Based on an average of over 900 putts attempted inside 5 feet over a season, we should expect every regular Tour player’s talent in terms of putts gained or lost to fall between +0.2/round and -0.3/round.

The graph below shows the correlation between a three year average (2011-13) and 2014 performance for all players with qualifying rounds in all four seasons. The correlation (R=0.56) between prior performance and 2014 performance is strongest in this distance range.

inside5feet

5-15 foot Putts:

This length is either short birdie putts or par putts after a scrambling shot that are converted approximately half the time. The spread in performance between 2011-14 was 36% to 54%. The spread in expected performance derived from weighting the previous four seasons is 40% to 52%. Based on around 450 putts attempted from 5-15 feet over a season, we should expect every regular Tour player’s talent in terms of putts gained or lost to fall between +0.4/round and and -0.5/round. Compare that to the best putters on Tour gaining about 0.75 putts/round.

The correlation between three year average and 2014 performance is below. The correlation (R=0.53) is similar to that for the short <5 foot putts.

5-15 footers

15-25 foot Putts:

These length are normally longer birdies putts and are converted about 16% of the time. The spread in performance between 2011-14 was 8% to 26%. The spread in expected performance derived from weighting the previous four seasons is 12% to 20%. Based on around 225 putts attempted from 15-25 feet over a season, we should expect every regular Tour player’s talent in terms of putts gained or lost to fall between +0.15/round and and -0.15/round. There’s much less at stake from this range than the previous two, just because so few putts are attempted from 15-25 feet.

The correlation between three year average and 2014 performance is below. There’s not much of a relationship (R=0.28), showing that putting performance from this range is much more affected by random chance over a full season than the shorter length putts.

15-25 footers

Putts outside 25 feet:

These length are the longest birdie putts, often really lag putts just to get it close for par. The spread in performance between 2011-14 was 2% to 13%. The spread in expected performance derived from weighting the previous four seasons is 4% to 9%. Based on around 300 putts attempted from beyond 25 feet over a season, we should expect every regular Tour player’s talent in terms of putts gained or lost to fall between +0.1/round and and -0.1/round. Again, there’s very little difference in expected performance from this distance. Even the very best long putter on Tour will gain little from these putts – over the long term.

The correlation between three year average and 2014 performance is below. There’s almost no relationship (R=0.10), which means it’s almost impossible to predict how well a player will putt on these long putts. The top ten long putters from 2011-13 average hitting 7.6% of their putts (versus 5.5% average). They only hit 6.7% of their putts in 2014 – a regression of almost 50% to the mean.

outside25ft

The Big Picture:

This graph shows performance in all four ranges. The longer putts show little relationship to future performance, while the shorter putts do show a more consistent relationship. This means that players who gained a lot of putts last season based off their longer putts will start making putts at a lower rate, while those who gained a lot of putts based on shorter putts are better bets to retain that putting ability.

bigpicture

Most Improved Putters from 5-15 feet in 2014:

1. Graeme McDowell

2. Charley Hoffman

3. Billy Horschel

4. Justin Leonard

5. Michael Thompson

These guys have a better chance of retaining their putting performance into 2015.

Most Improved Putters from > 25 feet in 2014:

1. Rory McIlroy

2. Y.E. Yang

3. David Toms

4. Brendan Steele

5. Brian Gay

These guys look likely to regress in terms of putting performance, especially McIlroy who performed to career average on all other putts, but hit 8% more of his long putts – gaining almost a third of a putt per round over his career average.

Measuring the Signal in First Round Performance

After the 1st Round of the Deutsche Bank Championship a month ago, Keegan Bradley sat two strokes off the lead. Playing in front of the home fans, Bradley fired a six under 65 fueled by great putting (4.2 strokes gained) and a solid long game (2.3 strokes gained on tee shots and approach shots). At that point he looked in great shape keep it going and capture his first win of the season. However, he came out the next three rounds and shot 71-69-71 to finish T16. The culprit wasn’t his long game either; he gained 1.6 strokes on the field per round in the second, third, and fourth rounds, good enough to finish in the top ten for the event in strokes gained off tee shots and approach shots. No, it was the putter that let him down. After being hot in the opening round, he actually lost 0.4 strokes per round from his putting.

My question is: how common is Bradley’s experience? When golfers come out in the 1st round and play/putt very well, how often do they keep playing/putting well? What about when they come out hitting the tee shots and approach shots well? Does that carry over to the next day? Many around the game act like one round of performance is really meaningful (just look at everyone who advocated for playing Jordan Spieth and Patrick Reed after their Friday morning 5&4 win at the Ryder Cup), but does first round performance tell us anything about how a player will perform in the following round?

Looking at Putting:

I gathered round by round Strokes Gained Putting data from the twelve most recent PGA Tour tournaments (Travelers Championship through the Tour Championship). First, I checked how 1st round putting performance predicted 2nd round putting performance. That’s the first graph below, and the results show how player putted in the 1st round hardly sheds any light on how they will putt in the 2nd round (R^2 of 0.001). In fact, someone who putted as well as Keegan Bradley did in the above mentioned round would be predicted only to putt 0.2 strokes above average the following round.

rd1SGP v rd2SGP

Next I generated prior expectations of Strokes Gained Putting performance from the past several years of data. I’ve shown before that putting performance isn’t very consistent season-to-season, so I’m using performance from 2011 to 2014 to generate the prior. The below graph shows how well the prior expectation predicted 2nd round putting. The results still were not highly predictive – R^2 of 0.01 (performance round to round is highly variable in golf) – but the regression line produced tracks pretty closely with results. Players predicted by the prior to putt well generally putted well and those predicted to putt poorly generally putted poorly.

priorSGP v Rd2SGP

Finally, I tied both pieces of information together. The prior estimate proved way more predictive than just 1st round performance, but does 1st round performance have any information to add? I set-up a linear regression with the prior estimate as x1 and the 1st round performance as x2. The results indicated 1st round putting performance provides no extra information to predict 2nd round putting performance (the coefficient was indistinguishable from zero). If you have a good guess of how well a player will putt, you can safely ignore first round putting performance.

Looking at Long Game Performance:

The long game is tee shots and approach shots (drivers/woods/irons essentially). I gathered long game performance data from the same twelve PGA Tour tournaments for the first and second rounds. I then ran the exact studies as above just substituting long game data for putting data. The correlation between 1st round long game performance and 2nd round long game performance was higher than with putting, but still didn’t contain a lot of information (R^2 of 0.03). If a player plays four strokes above field average in long game strokes gained, they’re expected to play 0.6 strokes better in the long game in the 2nd round.

rd1LONG vs rd2LONG

There was also a higher correlation between my prior estimate for long game ability and 2nd round long game performance (R^2 = 0.10). Again though, the regression line tracks closely with the results. Top ten long game players (around +1.2 strokes or above) generally performed to that level in the 2nd round.

priorLONG vs. rd2LONG

Tying both pieces together indicated that there is a small amount of signal in 1st round long game performance. Combining the prior estimate with 1st round performance slightly increases the fit of the model. The regression equation suggests that you should weight your prior estimate at twelve times the strength of first round performance. This indicates that someone who is PGA Tour average in long game shots, but produces an elite round of 4.0 long game strokes gained, should be expected to play about 0.3 strokes above average in long game shots. That seems like a small difference, but it’s enough of a shift in talent to move a player from around 50th best in the world to about 30th best in the world.

The Takeaway:

Based on these results, it looks like 1. a single round of performance is much less predictive than an estimate built on past-performance and 2. the small amount of signal contained in single rounds is from performance on tee shots and approach shots. Putting results from one round provide no more information than was available before the round. On the other hand, golfers who play particularly well on tee shots and approach shots in a round should perform slightly better than expected the following round.

 

PGA Championship Preview

This week’s PGA Championship returns to Valhalla Golf Club, site of the 1996 & 2000 PGA Championships and the 2008 Ryder Cup. This tournament comes at a nearly perfect time as the major stars of the game have just been destroying everyone for the last month. Rory McIlroy won the Open Championship and WGC-Bridgestone, Justin Rose won at Congressional and at the Scottish Open, Sergio Garcia has multiple runner-up finishes, and Adam Scott is playing as well as he has in his career. If you ignore the question of whether Tiger will play or not, there’s still a ton of story lines this week.

The Course:

Valhalla is built out of parkland outside of Louisville, Kentucky. Playing from the tips it measures 7458 yards for a par of 71, longer than most courses the pros face week to week, but not notably long compared to recent PGA Championship courses. Water comes into play on around half of the holes – mainly in the form of a creek along the fairway or pools near the greens. The fairways aren’t wide and the rough will be penal, so I don’t think this is a course where you want to spray it around too much. At the same time, about half the fairways are lined only with rough and bunkers. That limits the danger of an errant drive.

Valhalla, then, is a long test. It will absolutely reward the best iron players, but most courses do. Outside of the eternal question of whether to lay-up or hit driver, it is a course that forces you into shots, rather than allowing for multiple options. The short par 4 4th could be set-up as a drivable par 4, but if not it’s a boring 3 wood-wedge hole. The par 4 6th hole’s fairway ends ~300 yards from the tee, meaning everyone’s going to be left with the same 200+ yard approach shot. The par 4 12th runs out of fairway around 300 yards as well, leaving everyone again hitting to around 275 to avoid hitting out of the rough off a down slope. The par 4 13th features an elevated island green, but will be a certain lay-up and wedge for every player this week.

The one hole that offers any choice in real strategy is the par 5 7th. It offers a split fairway – the left fairway offers a shorter route to the green, but the approach shot requires at least a 225 yard carry over water, while the right fairway adds 40 yards to the hole and will limit opportunities to go for the green in two. The long hitters would be out of their minds not to hit it left; it’s an obvious birdie hole going left, while going right will make it play much closer to par. There will be talk all week from the commentators about risk and reward with this hole, but there’s plenty of room on the left fairway and even an average hitter can carry a hybrid 225 yards. It’s a different story for the shorter hitters though. Guys like Furyk, Luke Donald, and even G-Mac may not have the stick to play left.

 

Contenders:

The four obvious names are Rory, Sergio, Adam Scott, and Justin Rose. They’re the four best in my ratings, the four best so far this year, and four of the six best in the last two months (Furyk, Fowler are the others). That’s as close to clear-cut as you’ll ever get in golf. Beyond them, this might be Furyk‘s best chance to win another major. He hasn’t been this high in my ratings since he won the FedEx Cup in 2010. Bill Haas hasn’t received any attention all year, but he’s in that second group of guys with ~2% chance to win. Further down, I’d be remiss if I didn’t pump up Francesco Molinari’s chances again. He’s going to be as good or better than a half dozen guys on the European Ryder Cup team, so it’d be nice to see him make it on merit.

 

Randomness of Long Putts:

Long putts are the most random element of golf. Pros hit about 15% of their 15-25 foot putts and face around seven putts of that length per round. Hitting an extra 5% of your 15-25 footers, even just from chance, will cut almost a third of a stroke off your score – enough to take a player from 100th in putting to 40th. The problem analytically is that putting from this range fluctuates wildly year to year for the pros; it’s common for a pro to lose or gain 5% between seasons. Ryan Moore finished 2nd on Tour in 2012 and 7th to last in 2013. Rickie Fowler finished 4th in 2011 and 2nd to last in 2012. John Merrick sandwiched an 8th place finish in 2011 between two well below-average ones in 2010 and 2012.

I averaged conversion rates from 15-25 feet for everyone on Tour between 2010 and 2013 and compared them to 2014. The results show performance even over multiple seasons regresses by 75% to the mean. That means if you’re the best on Tour one year, you’ll finish more like 50th on Tour the next season. In short, putting from 15-25 feet isn’t consistent at all year to year. Instead, aggregating performance across multiple seasons gives a much better indication of expected performance.

That’s a problem analytically because, as shown above, a hot streak can really lower a player’s score. Each extra putt sunk from 15-25 feet is worth 0.85 strokes gained. Taken to the extreme, Bubba Watson (12% average between 2010-13, 25% average this season) has gained around 0.75 strokes just from 15-25 foot putts. We have no idea whether that represents a genuine change in his putting ability or, more likely, just a hot streak. In fact, the three largest over-achievers in strokes gained putting this season (relative to recent seasons) are all in the top ten for over-achieving in putting from 15-25 feet (relative to recent seasons). That may indicate some regression ahead for Matt Every, Graeme McDowell, and Adam Scott (AimPoint though). Among trailers, Kevin Stadler could cut around 0.4 strokes off his scoring just by putting at his career average from 15-25 feet.