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How Golfers Win

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How He Won: Brendon Todd at the Byron Nelson

Some quick stats from Brendon Todd’s victory this weekend:

On average, PGA Tour winners putt much better than normal on the weeks they win. Since the start of 2013, the winners putted 1.3 strokes/round better than normal. Brendon Todd putted 1.9 strokes/round better than he normally does, a massive 2.4 strokes/round gained on the field. That putting performance would rank 7th among 2013-14 winners behind Bill Haas (AT&T National), Tiger Woods (Arnold Palmer), Russell Henley (Sony), Jimmy Walker (Frys), Webb Simpson (Las Vegas), and Matt Jones (Houston).

On average, PGA Tour winners also play tee to green much better than normal. Since the start of 2013, the winners played 1.8 strokes/round better tee to green than normal. Brendon Todd is basically average tee to green normally and he played in 1.65 fewer strokes/round. That over-performance is fairly low for winners; since 2013, only Tiger Woods (WGC-Cadillac), Jonas Blixt (Greenbrier), Jimmy Walker (Frys), and Matt Jones (Houston) were worse tee to green. Todd joins Blixt, Zach Johnson (Hyundai T of C), and Travelers champ Ken Duke as the only two winners in 2013 not to hit more greens than the field. Todd hit only 60% of his greens compared to 62% by the field, as well as driving it six yards shorter than the field off the tee. This was not a tournament won with the driver, woods, or long irons.

His tee to green performance was almost entirely a result of his scrambling. I don’t have shot-by-shot scrambling data for the other 2013-14 winners, but Todd gained 6.1 of 6.5 tee to green strokes from his short game – including three hole outs worth over a stroke a piece. I suspect that is abnormal. Some level of scrambling over-performance is a necessity to win on Tour, but I’m referring only to short game strokes. Gaining over six strokes in that manner seems extremely high.

It’s important to note that short term performance in putting and scrambling is much more random than other tee to green play. Based on that, it’s unsurprising that PGA Tour winners over-perform by so much in their putting. In fact since the start of 2013 only Steven Bowditch (Texas) has won a tournament putting worse than the field; only four others have gained fewer than two strokes on the field through putting over the weekend.

Aging Curves for Scrambling and Driving Distance

In the past months I’ve posted about aging on the PGA Tour several times, including a general aging curve and an aging curve for putting performance. The general shape of the aging curve for PGA Tour players is a slight improvement from the early 20s to early 30s, followed by a period of relative stability through the mid 30s, and then a steady decline from the late 30s until 50. I assume from limited post-50 PGA Tour data and the paucity of Champions Tour golfers over 60 that aging continues to steadily erode a golfer’s game after 50. For putting, the curve was similar, but much less pronounced. Aging due to putting accounts for little of the improvement experienced in a golfer’s 20s and less than 10% of the decline experienced from the late 30s onward. The source of age-related improvement and decline is clearly some other part of a golfer’s game – either off the tee, the short game, or the long iron approach shot game. I’ve constructed aging curves for the first two components.


Aging Curve for the Short Game

I’ve calculated my own adjusted scrambling statistic previously which uses the PGA Tour’s scrambling stat as its base, but attempts to remove the influence of putting and difficulty of the lie to figure out which golfers play the ball into the best positions when they miss the green. I’ve described the calculation in this post. The spread in talent between the best and worst golfers each year by this metric is roughly a stroke. That is, the best golfers at scrambling gain half a stroke/round on the field and the worst golfers lose half a stroke/round. For comparison, the best putters gain nearly a stroke/round on the field and the worst putters lose nearly a stroke/round while the best golfers tee to green gain two strokes and the worst lose two strokes. Scrambling shots make up only 10% of a golfer’s strokes per round (6-8 strokes).

Unfortunately, this method does not include strokes where a golfer went for the green in two on a par 5, but missed the green. I estimate these shots comprise only roughly 1.5 strokes/round for the average golfer, though as many as two strokes for longer hitters and as few as one for shorter hitters. These shots are no different than scrambling shots on par 3s or 4s (besides scrambling for birdie rather than par), but the data just isn’t there to include them. So around 15-20% of the sample of short game strokes is missing. I’m confident this will not materially affect the results of this study.

I gathered data between 2008-2013 for which each golfer played consecutive seasons with at least 30 PGA Tour rounds. This resulted in 693 pairs of seasons to compare. As with prior aging studies, I used the delta method popularized by Mitchell Lichtman for use in baseball research. This method simply aggregates all improvements and declines between golfers at each age to see whether an age cohort generally improved or declined. From that data, a curve can be constructed.

Scrambling Aging Curve

That is not even a curve, but instead a steadily increasing trendline. The data indicates that scrambling ability increases linearly with age. Golfers under the age of 24 (34 seasons since 2008) performed around 0.05 strokes worse than the field average at scrambling. From there, golfers improved by around 0.01 strokes/season – a small amount, but one that indicates that experience on Tour leads to improvement in short game play. This finding runs contrary to any other aging study I’ve conducted.

I suppose it is not that shocking, however. Short game play involves a lot of technical skill – stance, position of hands, correct judgement of swing speed, club head position, etc. (in addition to strategy) – while not involving much of the physical strength that declines with age. Any golfer who can play on Tour can generate the proper amount of swing speed to play <50 yard shots. Not so much for the ability to generate the swing speed to hit 300+ yard drives or reach the green with 3 wood from 275 yards.

Compare scrambling here with the other component curves I’ve introduced. Putting generally declines slightly, while tee to green play (meaning all non-putting/scrambling strokes) improves only until around 27, stagnates until the mid 30s, and then sharply declines. I’ll discuss why I believe tee to green play stagnates around 27 next.

component aging curves

Aging Curve for Driving Distance

My catch-all category “tee to green” from above includes a wide array of shots: drives on par 4s/5s, tee shots on par 3s, going for the green shots on par 5s, long approach shots on par 4s/layups on par 5s, and short wedges on par 4s/par 5s. Some of those shots require a golfer to exert maximum effort to hit the ball near his peak ability (most drives/going for green shots), while most others require at least a full swing. In short, most of the shots contained in the “tee to green” bucket are going to be heavily affected by how much physical strength of golfer can exert. There are other factors certainly (strategy, precision, etc.), but physical strength is a large part of it.

The problem with that is the type of physical ability that combines body coordination with physical power – think driving a golf ball or hitting for power in baseball – begins declining as early as the mid 20s. This study from 2012 observed that while baseball hitters have tended to peak around 27, their ability to hit for power (home runs, doubles, etc.) has peaked at 25. I’ve observed the same phenomenon in golfers’ ability to drive for distance.

To measure the impact of aging on driving distance I gathered the Trackman data the PGA Tour has from 2008-2013. Typically the PGA Tour sets up Trackman on one hole per tournament to gather information about the club head speed, ball speed, launch angle, carry distance, etc. for the drive. I prefer using this data to measure driving distance because it places all golfers on an even surface. The hole is selected for whether most golfers will hit driver and the carry distance measures only distance in the air (removing the effects of firm or soft fairways. I gathered data for all golfers with qualifying number of Trackman readings (>20/year) from 2008-2013 (the extent of the data collected by the Tour). I used the same delta method as above to measure the increase or decline in carry distance between consecutive seasons. That yielded 696 pairs of seasons.

Carry Distance

This indicates that a golfer’s peak driving distance performance comes from age 25 and earlier. Golfers out-drive the field by 6 yards before the age of 24, declining to roughly average by age 35, and then decline heavily from that point onward – losing almost 20 yards to the field by age 48. This is the exact pattern suggested by the baseball power hitting aging curve above.

But What About…?

Now, at this point you may be wondering how a golfer can lose so much driving distance over the course of their career and still remain competitive. However, this aging curve doesn’t prove that every golfer ages similarly and it especially doesn’t mean that we should observe elite golfers losing so much distance. Elite golfers are elite because they have overcome many of the age-related obstacles that derail other golfers. This curve merely shows what we should expect out of the typical PGA Tour golfer. Very few golfers survive to have the type of career Davis Love III, Jim Furyk, or Phil Mickelson have had. That is a direct consequence of aging; a large number of golfers simply do not age well (whether due to injury, lack of commitment to practice, or general physical decline) and find themselves off the PGA Tour by age 40. Below is a graph of three golfers – two elite, top-ten-of-the-last-25-years types and one above-average player. It gives you an idea of how even very good golfers decline in driving distance.


Greg Norman was one of the best golfers in the world in the 1980s-90s; he won 20 times on the PGA Tour and 14 times in Europe, largely by relying on his superior distance off the tee. 1983 was Norman’s first season on Tour with reliable driving distance data. That year at age 28 he out-drove the field by 19 yards – equal in performance to Bubba Watson and Dustin Johnson currently. Norman continued to out-drive the field by large margins, but his advantage fell to 14 yards (’87-’89, age 33), 13 yards (’92-’94, age 38), and finally 2 yards (’97-’99, age 43). Norman’s game couldn’t sustain the massive drop in driving distance and he declined from one of the best players on Tour in his late 30s to one who didn’t win a PGA/European Tour tournament after 1997 (age 42). He was only a part-time player from that point.

Vijay Singh was a late-bloomer on Tour, not becoming a full-time member until 1993 when he was 30. He out-drove the field by 14 yards that season. Even at age 40 he out-drove the field by 16 yards as he rivaled Tiger Woods for the #1 ranking. However, in 2013 and 2014 Singh has been exactly PGA Tour average at driving – a decline of ~15 yards over ten years; exactly what the aging curve predicts between 40 and 50.

Stuart Appleby was a very good PGA Tour player by 2006, winning eight times and recording top 25 stroke averages in several seasons. He out-drove the field by 10 yards on average between ages 25-35 (1996-2006). However from 2006 onward he declined sharply, averaging only average driving performance between 2006 and 2013 – winning only a single tournament and basically being a non-factor on leaderboards.

Applying Driving Distance to Performance:

Driving distance is correlated strongly with performance. Mark Broadie’s work has shown that for every yard closer to the pin your tee shot lands, you save around 0.004 strokes. That looks small, but it suggests that the absolute best drivers are gaining roughly a 0.1 strokes/drive based on their distance. Applying the 0.004 figure to the above aging curve means we should expect a golfer to decline by 0.12 standard deviations between 25-35, another 0.12 standard deviations between 35-40, and twice that amount between 40-50. In all, a decline in driving distance explains roughly half of the decline in tee to green play. The component aging curve graph from above is reproduced with tee to green game separated into driving and non-driving shots (“Approach”).

comp with driving

This shows that approach shots exist in a middle-ground between the largely power based driving strokes (which begin declining by 25) and the precision/technique based scrambling strokes (which never decline). This makes sense as iron/wedge shots with a full swing combine both power and precision elements.

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.

Repeatability of Golf Performance by Shot Type

My main interest in analyzing golf is using past data to most accurately predict future golf performance. Inherent in that are the questions of how to figure out how much randomness is affecting the data and how to remove the effects of randomness from the data. The easiest way to find how much randomness is involved with data is to find the correlation between subsequent measures of performance. For example, in this post I found the correlation between a golfers performance in various samples of years from 2009-12 and their performance in 2013. Based on that, I concluded that using such basic methods produced a correlation of around 0.70 – meaning that in a subsequent season we can expect a golfer to repeat about 70% of their prior performance above or below the mean. I’ve achieved correlations slightly higher than that using more sophisticated methods and more detailed data, but an R of 0.70 should be viewed as the typical baseline for judging the repeatability of golf performance.

In this post, I attempt to find the repeatability of performance on different shot types using the same methodology as above. I will use Strokes Gained Putting to measure putting performance relative to the field, my own Z-Score measure minus Strokes Gained Putting to measure tee to green (driving, approach shots, short game) performance relative to the field, and I’ll use my own Scrambling metric (methodology here) to measure performance on only scrambling shots (a scrambling shot is the first shot following a missed green). I have not stripped these scrambling shots out from the tee to green measure; tee to green measures all non-putting strokes.

I gathered data for all PGA Tour golfers for 2008-2013 who had a qualifying number of rounds played (50). I then paired consecutive seasons for each of my three performance measures and graphed the correlations below.

repeat teetogreen

repeat putting

repeat scram

For all three graphs negative values represent performances better than the field. Values are expressed in standard deviations above or below PGA Tour average.

The measure that was most strongly correlated from season to season was tee to green performance. That makes intuitive sense as tee to green performance includes the most shots/round of any of my measures (roughly 40/round). In fact, tee to green performance is almost as repeatable as overall performance (R = 0.69 compared to 0.69 to 0.72 in the study linked above). This indicates that a golfer who performs well above or below average in a season should be expected to sustain most of that over or under-performance in the following season.

Putting was less repeatable than the tee to green measure, but skill still shows strongly through the noise. An R of 0.54 indicates that a golfer’s putting performance should be regressed by nearly 50% toward the mean in the following season (provided you only know their performance in that one season). I would mainly explain the lower correlation on sample size; golfers normally hit 25-30 putts/round, but many of these putts are short gimmes that are converted upwards of 95% of the time. The number of meaningful putts struck in a round is more like 15. This indicates that it takes a golfer over 2.5 seasons of putting to reach a season’s worth of tee to green shots. This suggests that putting is less repeatable from season-to-season than tee to green strokes, which indicates we should be wary of golfers who build their success in a season largely off of very good putting.

Off the three measures tested, Scrambling was the least able to be repeated (R =0.30). This indicates that performance on these short shots around the green is very random. It’s not atypical for a golfer to perform as one of the best 10% on Tour one season and average the next. Again, this is likely a function of sample size. A golfer hits only 6-8 scrambling shots/round (every time they miss a green). It takes a golfer around five seasons of scrambling shots to reach one season’s worth of drives/approaches.

There are two important caveats with this approach. These correlations explicitly measure only one season compared to the following season. Measures like scrambling and putting likely are more strongly correlated when several seasons are used as the initial sample. I intend to test this in a future post. In addition, this study only considers golfers who played consecutive seasons with >50 rounds/season. This leaves out a certain sample of golfers who played so poorly in the first year that they were not allowed to play >50 rounds the following season. These stats may be slightly more repeatable if those golfers were included.

An Aging Curve for Putting

In prior posts on the PGA Tour aging curve I’ve established that golfers tend to peak in their late 20s and sustain that peak for nearly a decade. They begin to decline, on average, in their late 30s and their skills degrade far below where they started in the early 20s. In short, golfers experience a small and steady increase in performance in their twenties before suffering a large and steady decrease in performance in their forties. However, all of those studies considered performance in the aggregate – driving, approach shots, the short game, and putting – which prevents deeper analysis of why golfers improve slightly before declining greatly. This post attempts to construct a typical aging curve for PGA Tour golfers’ putting games.

Initial Thoughts:

I anticipated that golfers would noticeably improve their putting games in their twenties; they would learn to read greens better and approach putts using a more optimal strategy gained through experience. I then anticipated that they would decline by age 40. This decline is suggested by the constant references to age-related putting yips. Because putting is not the main driver of performance differences between PGA Tour players, I expected that the age-related putting improvements and declines would be modest relative to overall gains (the general aging curve for overall performance shows a per year improvement of ~0.01 standard deviations from age 20 to 30 and a per year decline of ~0.04 standard deviations from age 38 to 50).


As with my prior aging curve work, I’m using the delta method which measures the change between Year 1 and Year 2. Mitchell Lichtman explains the concept in this article and a general Google search for delta method aging curve provides more information.

The major impediment to this study is the consideration of survivor bias. The only accurate measure of putting skill is the PGA Tour’s strokes gained putting (SGP) statistic. This stat is the same as I use in general for my overall performance analyses, except it’s denominated in strokes instead of standard deviations. However, the PGA Tour only gathers the data to calculate SGP in regular PGA Tour events (not majors, events outside the United States, events opposite other PGA Tour tournaments, or Tour events). This means that for golfers who played on the PGA Tour in Year 1, but not in Year 2, would not have an SGP measure to calculate the delta from. When I ended up forming my sample, roughly a quarter of seasons that qualified in Year 1 did not qualify in Year 2.

I included in my sample all golfers who recorded at least 30 measured rounds (rounds where the Shot Link system was available to calculate SGP) in both Year 1 and Year 2. The years used were 2008-09, 2009-10, 2010-11, 2011-12, and 2012-13. 1021 seasons met the criteria for Year 1, while 769 met the criteria for Year 1 and 2 and were included in the study used in the sample. These included seasons averaged a SGP of 0.02 (above-average) and averaged 69 measured rounds. 252 seasons did not meat the criteria and were discarded from the sample. These seasons averaged a SGP of -0.04 (below average) and averaged 54 rounds played. This suggests that on average those included in the sample were better putters and likely better golfers overall.


My results showed a very slight increase in putting skill in the twenties, followed by a steady decline beginning in the mid-thirties. A graph of the curve follows with a smoothed aging curve in blue. I smoothed the curve using a weighted average of the two years before and after the age in question.


What surprised me was the small size of the improvement and decline. Recall in terms of overall performance golfers improve by around 0.01 standard deviations each season between age 20 and 30. The overall improvement in putting performance up to a peak in the early thirties is equal to one season’s worth of overall performance improvement. Putting improvements are a very minor part of the age-related improvement of golfers in their twenties.

Similarly, the general age-related performance decline per season from the late 30s is roughly 0.04 standard deviations. The decline due to putting declines in total only 0.07 standard deviations. I can only conclude, again, that putting does not form a significant part of the age-related declines in golfers.

Further Discussion:

When I initially observed these results I guessed that survivor bias was distorting the results somehow. In my first foray into constructing an aging curve, I failed to properly account for survivor bias and my result was an aging curve that was largely flat until the mid-thirties before declining steeply. That graph looks a lot like the one linked above.

To test whether survivor bias was affecting my results I constructed another overall aging curve using only the golfers and seasons used for this study (in fact, I also only included the results from rounds played on ShotLink courses). The same sample of 769 seasons was used, using the z-score method to measure performance on all strokes. The graph this study produced is linked below, smoothed using the five year weighting method described above. In red is performance on all strokes, in blue is performance on only putting strokes, and in green is performance on non-putting strokes.


The overall performance looks almost identical to my aging curves that incorporated measures to eliminate the impact of survivor bias. Overall performance shows a small steady improvement the the early thirties followed by a steady decline from the mid-to-late thirties. More importantly, this graph shows the impact of putting on overall improvement and decline. In short, there is very little impact. Almost 100% of the improvement up to age 30 is due to non-putting strokes and over 80% of the decline experienced from age 39 to 50 is in non-putting strokes.

This suggests that putting performance changes very little during a golfer’s career. While overall performance declines by 1.50 strokes on average from peak to age 50, putting performance declines by less than 0.25 strokes on average over the same period.

This suggestion has interesting implications. Most importantly, do golfers who rely on their putting for success decline differently than golfers who rely more on their long game? I’ll try to answer that in a future post.

Review of Every Shot Counts – Mark Broadie

Mark Broadie’s Every Shot Counts: Using the Revolutionary Strokes Gained Approach to Improve Your Golf Performance and Strategy (2014) is the long-awaited full-length explanation of his strokes gained research. Broadie had published numerous academic papers discussing his strokes gained method and the PGA Tour has been showing the Strokes Gained Putting stat for a few years, so much of this material is merely rehashed from articles others have written or from his 2011 paper “Assessing Golfer Performance on the PGA Tour“. It’s well known that Broadie’s research has disproved putting as the most important part of the game and has elevated the long-game (driving and long approach shots) in its place, but where this book shines is in its lessons for applying this new knowledge to actually playing the game, whether you’re a pro, advising a pro, or an amateur.

Broadie spends the first six chapters basically explaining the strokes gained method. He covers why putting is overrated, why traditional putting statistics are worthless, and how the strokes gained method works. He then introduces strokes gained for the tee-to-green game. Broadie establishes that why the long-game is so important in separating elite pros from average pros, average pros from good amateurs, and good amateurs from 90 handicappers; in the process he shows why Tiger dominated golf so much in the last decade (he was good at everything, but the #GOAT at playing long approach shots). This part of the book is worthwhile for the more in-depth exploration of the strokes gained method, but if you’ve read his academic work feel free to skim it for the handful of insights.

Essentially, Broadie’s work is about how fractional strokes are so important in separating pro golfers. The best and worst golfers in a PGA Tour tournament are separated by 2.5 strokes/round. Most of that separation is manifested in things like hitting an extra green each round, driving the ball five yards further, leaving your shots from the sand a foot closer, and/or hitting a single approach shot within birdie range. His research argues for a strategy that considers all possible shots and outcomes of those shots, and selects the highest expected value play. In this recent interview, Broadie says that most golfers don’t play aggressively enough; they leave putts short of the hole, lay-up on par 5s, and hit woods/hybrids off the tee when they’d be better served hitting driver. Central to his work is the idea that being much closer to the hole is worth playing out of the rough/fairway bunker.

Broadie finally explores new ground the final three chapters, laying out how this new knowledge should be applied to all aspects of the game. In Chapter Seven, Broadie explores what the strokes gained analysis means for putting and how to figure out how aggressive to be on long putts. He explains that many PGA Tour golfers aren’t aggressive enough with their putting; they often purposefully don’t hit putts with enough force to get to the hole, ensuring that they miss the putt. There’s a lot of work in this chapter figuring out optimal aim points from different locations on the green; very interesting work for amateurs who are looking to improve their strategy on the green.

In Chapter Eight he explores how to optimize your long game to shave wasted strokes. Much of the chapter is spent on figuring out the proper way to target drives to ensure you miss the dangerous hazards (water, out of bounds), even if you are forced to play less from the fairway. This section would be very useful for amateurs who often find themselves wasting strokes off the tee by not being cognizant of where the dangerous areas of the course are. Broadie also spends this chapter detailing why lay-ups are typically a minus EV play – particularly notable this week after the way Patrick Reed laid-up so poorly down the stretch at Doral.

Chapter Nine is a detailed look at numerous different practice methods that use the ideas behind valuing each stroke and playing the highest EV game. I mainly skimmed these, but amateurs might find the lessons/games useful for improving their play.

I did pick up a few interesting lessons:

1. It’s well established that those who hit for more distance off the tee usually hit fewer than average fairways, but Broadie has actually found that longer players have a smaller degree of error in terms of how off-line they hit their shots. In fact, the only reason many long hitters hit fewer fairways is because when they do hit a shot with a larger than average degree of error, the increased distance cause it to fly/roll further off-line – into bunkers and the rough. Driving is basically a geometry problem where a smaller angle and larger hypotenuse can produce a larger miss.

2. Broadie introduces the concept of “median leave” in Chapter Five. The PGA Tour publishes stats showing the average proximity to the hole from approach shots, the rough, green-side bunkers, etc. However, Broadie argues we should use the median proximity instead because it’s not distorted by larger misses (like when you fly the green and leave it 50 yards from the hole). Median leave is simply the distance remaining to the pin after the shot divided by the distance to the pin before the shot. So a 150 yard approach to 18 feet would be a median leave of 4%. The best approach shot players have a median leave of 5.5% – equivalent to hitting it a median proximity of 29 feet from the average PGA approach shot (175 yards).

3. When discussing optimal driving strategy he explains the idea of “shot pattern”. Your shot pattern is all the possible results of each type of shot, considering the distance you can hit with a club, the degree of accuracy, and any spin/fade/draw/slice/etc. you can play. Golf is a game where each swing is essentially slightly random – a golfer might swing perfectly, contact the ball perfectly, judge the wind perfectly, and get the right amount of spin when he lands it on the green, but more likely his swing will be slightly off or he’ll mishit it slightly or the wind will push it offline a bit, or it will roll-out when it hits the green. The optimal golfer will know their 95% confidence interval for a 125 yard wedge shot, his average degree of miss when he hits driver, and all the possible results of an approach shot if the greens are firmer than expected. The optimal golfer will play their shots with all that understanding and avoid playing shots that are excessively conservative or needlessly risky.

All in all, it’s a worthwhile book if you’re interested in applying Broadie’s research to your golf game or at least interested in how a pro might apply it to how they work around a golf course. Broadie has plenty of evidence of some of the elite golf instructors already using this kind of stuff to help their clients excel. On the other hand if you’re just interested in the research itself, reading the literature I linked above is sufficient. His initial six chapters don’t provide a substantial amount of expansion on his earlier papers.

How He Won: Kevin Stadler (Phoenix Open)

Most posts here are focused on the macro-level of how to predict performance. That’s my main interest and the most valuable research in terms of the big picture of golf analytics. However, occasionally it’s nice to delve into individual performances and look at how golfers win each week. This week, Kevin Stadler finally broke through and won his first PGA tournament at the Phoenix Open. Stadler’s performance over the 2008-Present period has been approximately that of the 150th best player in the world, though he’s played much better in the last two seasons. Guys like that (even with famous fathers) rarely play their way into a 4th round lead at a tournament, so it’s nice to see Stadler break-through.

How he won is interesting though. This post detailed some quick stats on how PGA tournament winners putted during the 2013 season. The average winner gained ~1.5 strokes on the field each round due to putting. The winner normally gains 14-15 strokes on the field during the week, so putting normally accounts for at least 40% of the winner’s strokes gained on the field. However, Stadler totaled just short of 2 strokes gained due to putting for the entire week, while he finished 14.6 strokes better than the field in total. I don’t have detailed figures for other tournaments at my fingertips, but he must’ve far outperformed the field in all other phases of the game to finish so highly while putting (comparatively) poorly among PGA tournament winners.

TPC Scottsdale is a fairly easy course overall, with the field averaging 70.6 strokes/round for the week. The field averaged 301 yards off the tee (well above PGA average of 287 yards), hit 59% of fairways (slightly short of PGA average of 59%), hit 68% of greens (PGA average of 64%), and successfully scrambled 57% of the time (PGA average 58%). It’s clear that a combination of easy distance and little penalty for missing the fairway made hitting the green more likely.

Stadler as a player is definitely a much better ball-striker/driver than he is at putting or scrambling. He’s finished near the bottom in strokes gained putting in the last several years and he’s finished outside the top 100 in scrambling three of the last five seasons. In comparison, he’s been above-average in both driving distance and accuracy in the last few seasons, parlaying that and his approach shot skill into rankings of 33/26/8 in greens in regulation. We’re talking about a clear top top tier player from tee to green.

This week, Stadler simply played to his strengths, out-driving the field by 8 yards, hitting 9% more fairways, and using that great driving to hit 10% more greens than the field. His proximity to the pin was also 5 feet closer than field average. It helped that he successfully scrambled 12 of the 16 times he missed a green, which likely gained him something like 3 strokes on the field. However, his ability to put the ball in the fairway, further than most others, and then hit the green won him this tournament.

Digging deeper on his final round, I attempted to estimate his strokes gained for different types of shots. Prior work in this vein is here and here. I’m pretty confident in my numbers overall because 1) the course played roughly average in difficulty on Sunday and 2) my strokes gained on putts figure is within 0.3 strokes of the official PGA Tour number. My numbers show that three of Stadler’s best four shots on Sunday were approaches to the green – his approach to 3 feet on #14, his drive onto #17 green, and his approach to 4 feet on #9. In total he gained +2.1 strokes with his par 4/5 driving (14 shots), +1.3 strokes with his approach shots (4 shots), and +0.5 strokes with his par 3 tee-shots (14 shots), while he lost -0.4 strokes on 3 short shots around the green. I show his putting as having gained him no shots on the field in total.

I can explore this further, but it’s likely that Kevin Stadler played unusually well from tee to green for PGA tournament winners. His driving was superb in both distance and accuracy (a rare but potent combination) and he cashed in on those great positions by knocking his approach shots on the green and close.

The Intersection of Driving Distance & Accuracy

If you have ever watched televised golf I’m sure you have heard an announcer bemoan the wildness of a golfer’s drive. Tiger Woods and Phil Mickelson in particular seem to dogged by comments about how often they end up in the rough compared to the field.  However, I cannot recall hearing much talk at all about the distance golfers are hitting the ball. Now, a lot of that is due to it being easy to convey the advantage of hitting an approach shot from the fairway rather than the rough. We see the thick rough and remember the times golfers have been forced to pitch out into the fairway when they are behind obstructions. On the other hand, it’s difficult to convey the advantage hitting an approach shot from 20 yards provides to a golfer. However, that advantage is very real.

The 2013 ShotLink data shows that, on average, PGA golfers hit the green on 71% of their shots from 125-150 yards, but on only 64% of their shots from 150-175 yards. In his seminal Assessing Golfer Performance on the PGA Tour, Mark Broadie shows that, on average, a golfer will take 2.89 shots to finish a hole from 137.5 yards, but 3.00 shots to finish from 162.5 yards. In other words, driving the ball 25 yards further provides a substantial advantage in hitting greens and scoring low. There is certainly an advantage to avoiding the rough also. According to ShotLink data, golfers hit the green nearly 76% of the time from the fairway, but only 51% of the time when they missed the fairway. Birdies are 50% more likely when you hit the fairway versus the rough (21% to 14% of holes).

However, almost every golfer is forced to choose which skill – distance or accuracy – they want to attempt to excel at. Driving Distance and Driving Accuracy are strongly negatively correlated (R = -0.51), meaning that very few players perform well in both categories. For example, of the 216 golfers who exceeded 10 tournaments played or finished in the FedEx Cup top 200, Dustin Johnson ranked 1st in driving distance and 195th in driving accuracy. Rory McIlroy followed at 2nd in distance, but 181st in accuracy. Opposite those two, Russell Knox finished 1st in accuracy, but only 135th in distance, while Chez Reavie was 5th in accuracy, but only 159th in distance. As the following graph shows, only one of six PGA golfers exceed the mean for distance and accuracy (shown in red) and no one is +1 standard deviation from the mean in both distance and accuracy (shown in yellow).

2013 Driving Distance Accuracy Correlation

However, knowing that it is important to do both well, but difficult to do both well, is their one skill that predominates? To determine just how important each factor was to analyzing driving skill, I set-up a regression of driving distance and driving accuracy on a golfer’s greens in regulation (GIR). Because the courses played can vary in difficulty, I used my course adjusted stats which determines how much better or worse than field average a golfer performed each week in each stat. These adjust most slightly, but for golfers like Tiger Woods who typically play tougher courses than average the adjustment can be significant. I’ve attached a Google Doc of every PGA player to finish in the FedEx Cup top 200 plus anyone else with >10 tournaments entered showing these adjusted stats.

The results show that combining distance and accuracy predicts 50% of the variance in GIR (R^2=0.494). The p-values are highly significant and indistinguishable from zero, which certainly squares with the empirical stats provided in the second paragraph. To predict GIR, the equation is Y=(.00283*Distance in yards)+(.4418*Accuracy in %)-(.4429). Basically, hitting the ball an extra three yards is worth around 2% in driving accuracy, meaning a golfer should be indifferent to adding three yards of distance if it means giving up 2% in accuracy.

If a golfer was provided with the choice of being one standard deviation better than average in one skill and one standard deviation below average in the other skill there is almost no difference between being good at driving distance and bad at accuracy or vice-versa (63.9% for good at distance and 63.6% for good at accuracy). This shows that performing well at either skill is a legitimate path to success on Tour.

Using this equation, we can also calculate a Total Driving skill stat. The PGA Tour has such a stat, which they calculate solely by adding together a golfer’s rank in distance and accuracy. Mine simply ranks golfers based on their predicted GIR based on their driving distance and accuracy. The leader, Henrik Stenson, finished 8th in accuracy and 55th in distance, with a predicted GIR of 69.2%, meaning a golfer with average approach shot ability would’ve hit the green 69% of the time shooting from his average location. The worst golfer by this metric, Mike Weir, finished 213th in distance and 196th in accuracy, with a predicted GIR of 56.2%.

Tiger Woods, who is regularly criticized for his wayward drives, actually finishes 20th in Total Driving on the strength of his 34th ranked accuracy and 78th (above average!) accuracy. His predicted GIR was 66.6%. On the other hand, Phil Mickelson is also criticized for being wild with the driver, and he has been wild this season (58% accuracy; 163rd on Tour), but his distance has killed him nearly as much. He’s only driven it 288 yards on average (98th on Tour). As a result, he was the 149th best driver on Tour last year.

I’ve attached the predicted GIR/Total Driving stats in this Google Doc.

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