Posts tagged ‘ShotLink’

September 13, 2011

Strokes Gained: PGA TOUR Golfer Performance

So what does Strokes Gained tell us about PGA TOUR Player Performance?

The PGA TOUR has recently begun publishing Strokes Gained – Putting statistics on its website.  The PGA TOUR has not yet however endorsed the Strokes Gained (SG) methodology for use beyond the putting green.  The PGA TOUR has however released the raw ShotLink data to a number of researchers.  Mark Broadie is one of these researchers and has performed extensive SG analyses of all facets of the golf game (i.e. drives, approaches, chips, sand shots, putts, etc).

Due to the circumstances outlined above, GolfBrains will use this entry to first present highlights of Broadie’s comprehensive performance analysis and then present GolfBrains’ own analysis of the putting data.

The summary of Broadie’s work below is not intended to be a substitute for the real thing.  GolfBrains highly recommends you read his paper “Assessing Golfer Performance on the PGA Tour (individual player analysis begins on page 16).  As mentioned previously, GolfBrains feels this is by far the best paper written on SG to date.

Broadie’s Strokes Gained Analysis
Broadie analyzed ShotLink data from the years 2003 through 2010.  He only included players with at least 120 rounds played during this period.  These parameters yielded a population of 299 PGA TOUR golfers which were included in the analysis.

Broadie’s analysis yielded interesting insights regarding which facets of the game separated the elite golfers from the average golfers.  Most notably, he debunked the “drive for show, putt for dough” myth.  Broadie concludes “the contributions to total strokes gained are 72%, 11% and 17% for the long game, the short game and putting respectively” (with “long game” defined as shots over 100 yards from the hole and “short game” defined as shots under 100 yards from the hole, excluding putts).

In addition to highlighting the importance of the long game, Broadie’s work shines a spotlight on the dominance of Tiger Woods during this period.  For the period, Tiger gained 3.2 strokes per round over the average tour player.  Over the course of a four round tournament, this suggests that Tiger is nearly 13 shots better than the average PGA TOUR player.  A comparison to the other top players during this period further highlights Tiger’s dominance.  Luke Donald, the sixth best player during this period only gained 1.55 strokes per round.  Said another way, there were only four players in the world (Jim Furyk, Vijay Singh, Ernie Els and Phil Mickelson) who gained at least half as many strokes per round as Tiger.  Jim Furyk, the second ranked player from this period, was over a full stroke behind Tiger at 2.12 SG per round.

Breaking down Tiger’s SG into its component parts, we learn that, similar to other PGA TOUR golfers, Tiger’s overall SG can be explained in large part by his long game.  Of Tiger’s 3.2 SG, 2.08 can be attributed to his long game, 0.42 to his short game and 0.70 to his putting.

The chart below, shows Tiger’s total SG and SG components by year.

GolfBrains Strokes Gained – Putting Analysis
Rather than relying on Broadie’s work, this section relies on 2011 PGA Tour Stokes Gained – Putting data as of September 12, 2011 for all 189 golfers reported by the TOUR.  As the PGA TOUR does not publish Strokes Gained measures for the short game or the long game, rather than comparing the various facets of the game, this section will compare Strokes Gained – Putting statistics with traditional putting statistics.

It has been stated on this blog before, but at the risk of being pedantic, GolfBrains will restate that traditional putting measures have the drawback of mixing several components of the game. Traditional putting measures are based on the number of putts per round or per green in regulation.  Therefore, players who hit approach shots closer to the hole will appear to be better putters than they actually are.  Let’s consider an example.  Golfer A has an average first putt distance of 20 feet from the hole while Golfer B has an average first putt distance of 30 feet from the hole.  On average, both golfers need 1.8 putts to hole out.  Traditional golf statistics will suggest that these golfers are equally adept putters.  The truth is, and SG reflects that, Golfer B is a superior putter.

First let’s compare Strokes Gained – Putting with Putts Per Round.  As shown by the scatter plot and accompanying linear regression line below, Strokes Gained – Putting and Putts Per Round are correlated.  The negative slope of the regression line indicates that as Putts Per Round decrease, Strokes Gained – Putting increases.  The coefficient of determination with a value of R = 0.543 suggests that 54.3% of the variance is explained by the model.  In layman’s terms, 54.3% of Strokes Gained – Putting can be explained by Putts Per Round.  This suggests that Putts Per Round is not without value; it explains over half of Strokes Gained.  However, on the flip side, it’s not a great statistics as it only accounts for half of a players putting performance.

This shortcoming is highlighted by the measures for Kevin Na and Alexandre Rocha.  Kevin Na’s 27.78 Putts Per Round is the second lowest total on the PGA TOUR.  Kevin Na is an excellent putter, but Strokes Gained tells us that he’s not as good as his Putts Per Round statistic suggests; there are in fact 19 better putters on the PGA Tour.  Conversely, Rocha is a much better putter than his Putts Per Round statistics suggest.  Ranking him in the 185th spot, Rocha’s Putts Per Round suggest that he is one of the worst putters on the PGA TOUR.  The truth is he is a better than average putter.  He gains 0.168 strokes per round by virtue of his above average putting.

Putts Per Green In Regulation (GIR) was introduced in an attempt to reduce the distortions inherent in the Putts Per Round statistic.  Traditional thinking suggests that those players who hit a lot of GIR at a disadvantage when it comes to Putts Per Round; a golfer who misses a green in regulation and is chipping onto the green is likely to have a shorter, and therefore easier, first putt than a golfer who hit the GIR.  Interestingly, a comparison with Strokes Gained – Putting suggests that Putts Per GIR is inferior to Putts Per Round in terms of explaining putting performance.  In contrast with Putts Per Rounds which explains 54.3% of putting performance, Putts Per GIR explains only 47.1%.

September 13, 2011

Future of Strokes Gained

Strokes Gained (SG) is still in its infancy.  While the groundwork was laid in 1964 with the Golf Society of Great Britain’s work at the Dunlop Masters Tournament, the modern era of SG was not ushered in until Mark Broadie published his 2008 paper, Assessing Golfer Performance Using Golfmetrics.

As alluded to in earlier posts, while the SG formula will not change, there is still much work to be done in terms of refining the Strokes To Go (STG) calculations.  While STG is primarily determined by (1) the ball’s distance to the hole and (2) the ball’s condition (i.e. tee, fairway, rough, recovery, sand, green), STG is also impacted by the unique characteristics of each shot.  Aside from distance and condition, unique shot characteristics which may impact STG are elevation changes, sidehill lies, wind conditions, the degree to which a green is guarded or unprotected, hole location, etc.

While the STG calculations will never be 100% accurate, as the amount and quality of the individual shot data continues to grow, GolfBrains expects that significant progress will be made to adjust STG to account for a shot’s difficulty beyond what can be explained by distance and condition.

There are two approaches researchers can take in their attempts to refine STG calculations:

  1. Identify and adjust for holes or greens which are less difficult or more difficult than average, or
  2. Identify and adjust for the unique characteristics of individual shots which make them less difficult or more difficult than average.


It is the opinion of GolfBrains that, when possible, methodologies which attempt to identify and adjust for the unique characteristics of individual shots are superior.

Why does GolfBrains believe that methodologies which attempt to identify and adjust for the unique characteristics of individual shots are superior?  There are three reasons:

Reason 1: Better Individual Shot Data – Methodologies which identify holes or greens which are more or less difficult than average run the risk of mixing several parts of the game together (one of the well documented shortcomings of traditional golf statistic).

Let’s consider a hole that is more difficult than average.  This hole is more difficult than average because it is a very difficult driving hole.  The approach shot and putting green are of average difficulty.  Methodologies which take the difficulty of the overall hole into account will understate the value of a golfer’s drive on this hole to the benefit of the approach shot and putts whose value will be overstated.

Proponents of this approach will argue that these shortcomings will likely even out in the long run so when analyzing data over the course of a tournament or season the results remain valid.  GolfBrains does not disagree that it will likely even out in the long run.  But SG is a tool designed to assess the value of individual shots!

Why is getting the value of each individual shot correct so important?  GolfBrains believes that within 10 years time SG and STG will be fixtures of golf telecasts.

While SG can be used to assess past performance, it also offers insight regarding what we can expect in the future.  Let’s say its Sunday and Dusting Johnson is in the clubhouse with a one stroke lead over Steve Stricker who is standing on the 17th tee.  SG can help us understand the odds Stricker faces as he attempts to catch Johnson.  SG can be updated in real time to reflect the now odds Stricker faces after his tee shot on 17 and each subsequent shot he hits.  Ever watch one of those poker shows on TV?  They’re not that great to begin with.  Now imagine watching one without the probabilities displayed.  It’d suck, right?  GolfBrains isn’t trying to suggest that golf telecasts suck (though they do tend to put GolfBrains to sleep).  GolfBrains is however suggesting that golf telecasts would be infinitely more interesting with real time insights offered by SG.

If SG is to fulfill its potential and become a metric used to measure a golfer’s past performance and predict a golfer’s future performance in real time, SG must be reasonably accurate at the individual shot level.

Reason 2: Better Understand the Game – While SG can be used to help golf fans understand what makes one player better than another, it can also be used to help golf fans understand what makes one shot more difficult than another.  The MIT Team’s attempt to control for the difficulty of various putting greens concluded that TPC Sawgrass’ #1 green was particularly challenging.  But that conclusion left GolfBrains wanting to know more.  Specifically, why is TPC Sawgrass’ #1 green so difficult?  Is it due to the green’s speed?  Its contours?  Its hole locations?

So, methodologies which attempt to identify and adjust for the unique characteristics of individual shots will not only yield more accurate insights into the value of individual shots, they will also help golf fans understand why one shot is more difficult than another.

Reason 3: More Accurate STG Measures For All Courses – Methodologies which identify and adjust for holes or greens which are less difficult or more difficult than average require a significant amount of shot data from these specific holes or greens.  This is ok if you play at Augusta National (if you play at Augusta, please feel free to use the Contact feature found at the top of this page to invite GolfBrains) for which there is ample data.  But what if a PGA TOUR event is being held at a new course for which there is no data?  Or what if you want to better understand your performance at the local municipal course at which you play?  Methodologies which adjust hole or green difficulty will not be of any help.  Related to Reason 2 above, methodologies which adjust for individual shot characteristics will offer insights regarding all shots on all courses.

September 12, 2011

Strokes Gained Contribution: Mark Broadie’s “Assessing Golfer Performance on the PGA TOUR”

Mark Broadie publishes “Assessing Golfer Performance on the PGA TOUR” in April 2010.

Not the most innovative paper. While Broadie formally introduces the idea of recovery shots (which is an important innovation) GolfBrains suspects that this was a behind-the-scenes feature of his earlier work with the GolfMetrics data.

You will not find a better explanation anywhere of what makes the best players on the PGA TOUR better than the rest.

If you’re going to read one paper on SG, this is the paper. It provides a clear introduction to the concept, doesn’t get too heavy into the math so as to scare away the average reader, and provides fascinating insights into what makes the best golfers in the world the best.

So as not to appear to be letting Broadie off easier than the MIT Team, GolfBrains must mention that it is not entirely satisfied with the course difficulty adjustments Broadie uses. Just as difficult greens have both difficult and easy putts, difficult courses have both difficult and easy shots. In order to more accurately assess the SG of each an individual shot, shot, not course, specific adjustments should be made. GolfBrains is however more willing to overlook this shortcoming as the course adjustments are not the centerpiece of Broadie’s paper whereas the putt adjustments are perhaps the most prominent feature of the MIT Team’s paper.

September 6, 2011

Strokes Gained Contribution: MIT Team’s “How to Catch a Tiger: Understanding Putting Performance on the PGA TOUR”

A team from the MIT Sloan School of Management (Douglas Fearing, Jason Acimovic, and Stephen Graves) published a paper titled “How to Catch a Tiger: Understanding Putting Performance on the PGA TOUR.”  Using ShotLink data, the MIT Team attempts to calculate Strokes To Go (STG) for shots beginning on the green (i.e. putts).  One of the major challenges the MIT Team faces in accomplishing its goal is controlling for (1) green difficulty and (2) golfer skill level.

The MIT Team attempts to refine the STG inputs to the SG formula.  When published, How to Catch a Tiger presented the most in depth attempt to adjust STG to account for the varying difficulties of greens and golfer skill levels.

This is an important topic.  As the basic SG formula is solid advances will come from refining the STG inputs.

Regrettably, it is the opinion of GolfBrains that the MIT Team missed the mark with its analysis.  Or maybe it would be more accurate to say that it hit the bull’s eye but was aiming at the wrong target.

Every green is unique.  On this much GolfBrains and the MIT Team agree.  However every putt on every green is also unique.  Unfortunately the MIT Team’s work does not address this nuance.

An example helps to illustrate the problem.  The MIT Team cites TPC Sawgrass’ #1 green as unusually challenging and Bay Hill’s #9 green as unusually easy (as far as PGA TOUR greens go).  The MIT Team therefore proposes that all putts of X feet on TPC Sawgrass’ #1 green are more difficult than all putts of X feet on Bay Hill’s #9 green.  This is not accurate.

The MIT Team attempts to downplay the significance of this problem.  The MIT Team looks at the relative difficulties of uphill and downhill putts (it does not look at other unique putt characteristics, most notably break).  It concludes that downhill putts are more difficult but suggests “if all golfers have about the same distribution of uphill versus downhill puts, we can safely exclude this feature and still argue that our putting metric is fair and unbiased.”  The MIT Team later suggests that “there is an insignificant difference in the distribution of uphill versus downhill putts for all golfers” and it is therefore not necessary to adjust STG for uphill/downhill or other unique putt characteristics.

This methodology yields accurate results when a sufficiently large sample of putts is examined but is lacking when one attempts to analyze any one individual putt.

Rather than attempting to determine which greens are difficult and which are easy, GolfBrains would have preferred the MIT Team look at what characteristics make individual putts difficult or easy.  GolfBrains feels that green speed (measured using a Stimpmeter), slope (difference in elevation between the ball and the hole) and break (the maximum distance, as measured by a perpendicular line, between the straight line formed between the ball’s starting position and the hole and any one point on the putted ball’s path) would be a good place to start.

September 6, 2011

Strokes Gained Contribution: Broadie’s “Assessing Golfer Performance Using Golfmetrics”

In 2008, Mark Broadie published a paper titled “Assessing Golfer Performance Using Golfmetrics.”  This paper analyzed the data Broadie collected using his Golfmetrics software.  This post will focus on the papers contributions to the Strokes Gained performance measure.  In a later post GolfBrains will evaluate the conclusions drawn from Broadie’s analysis of the data.

The Landsberger version of Strokes to Go (STG) to relies on complicated adjustments for a golfer’s performance standard and shot-specific correction factors (e.g. wind, slope, lie, obstacles, etc).  While it is important to adjust STG to account for shot difficulty, Landsberger did not offer any guidelines for shot specific correction factors.  As a result, it would be difficult to implement the Landsberger methodology in practice.

Broadie simplifies STG by setting a single performance standard (i.e. a scratch golfer) and uses actual shot data to compute STG (which eliminated the guesswork associated with shot specific correction factors).

This is the first paper to use Strokes Gained (SG) to analyze actual golfer data from tee to green. Previously SG was a theory that no one had tested with real data.  With “Assessing Golfer Performance Using Golfmetrics” Broadie shows that SG can be applied in practice.

In addition to the important advances in SG methodology, Broadie uses SG to provide the first insights into a golfer’s overall performance (remember, the GSGB insights were limited to putting).

This paper briefly introduces the SG concept and then jumps into the results.  This makes it an easy read and accessible to a broad audience.  It however leaves GolfBrains wanting to know more about the methodology.  For example, did Broadie account for Recovery Shots, a concept he introduces in his next paper, when analyzing the Golfmetrics data?  And do the STG calculations attempt to apply hole or shot specific adjustments to STG to account for varying difficulties? (GolfBrains suspects that the data set is not robust enough to calculate hole or shot specific adjustment factors but would love to know for sure.)

Broadie also uses the Golfmetrics data to perform a few analyses outside the scope of SG.  He introduces the concept of Fractional Remaining Length (FRL) and also attempts to determine if there is a correlation between length and accuracy.  GolfBrains is not as impressed with FRL as it does not distinguish between ending conditions (i.e. fairway, rough, sand, etc).  As measured by FRL, a shot that ends on the green 30 ft. from the hole is inferior to a shot that ends 25 ft. from the hole in a sand bunker.  Also, GolfBrains would have liked to see Broadie control for overall skill level when considering the relationship between distance and accuracy.  Broadie concludes “longer hitters tend to be straighter.”  GolfBrains suspects that this might be more accurately stated “better golfers are longer and straighter than inferior golfers.”  Let’s consider two groups of scratch golfers: one group that hits average drives of 250 yards and once group that hits average drives of 300 yards.  GolfBrains suspects that the 250 yard group would be straighter on average.

September 6, 2011

Strokes Gained Contribution: Technological Advances Yield Data

Strokes Gained was slow to develop due to a lack of data.  Recent technological advances in GPS, laser surveyor and computer technology have made the collection of the requisite data much easier.

There are now two data sets: ShotLink and Golfmetrics (GolfBrains considers the Golf Society of Great Britain’s database too small and limited to be of practical significance today).

ShotLink was introduced by the PGA TOUR in 2001 and has been used track every shot hit in a PGA tournament since 2003.  ShotLink relies on GPS technology.  Before a tournament begins a map of the course is made.  During the tournament lasers are used to record the ball position before and after every shot.  The ball position measurements are very precise with tee to green measurements within a foot of the ball’s actual location and locations on the green measured to within a centimeter of the ball’s actual location.  Together the course maps and beginning and ending shot locations provide the distance to hole and lie type data that the Golf Society of Great Britain (GSGB) manually collected in 1964.

In the context of advanced golf statistics there are two major differences between the GSGB and the ShotLink data.  Using GPS and lasers, ShotLink leverages technology not available to the GSGB which has yielded more accurate data.  More significantly, the ShotLink database is many times the size of the GSGB database.  The ShotLink database currently contains over 7,000,000 shots whereas the GSGB database has approximately 4,000 shots.

Golfmetrics is a software application created by Mark Broadie to capture golfer shot data.  Shot data is entered by golfers who click on a graphical representation of the hole they are playing to enter beginning and ending shot locations.  It “contains almost 40,000 shots representing about 500 rounds of golf from over 130 golfers on six courses in tournament and casual play primarily during 2005-2007.”

GolfBrains does not view either of these databases as particularly innovative.  The idea to collect individual shot data was previously put forth by the GSGB.  And neither the brains behind ShotLink nor Mark Broadie can claim responsibility for the technological innovations which made capturing this data possible.

While not the most innovative developments in the evolution of Stokes Gained, the importance of the data yielded by ShotLink and Golfmetrics cannot be understated.  It was 30 years after the GSGB landmark work that Landsberger’s paper was published and it would be another ten years before the next important paper on Strokes Gained would be published.  However, the availability of quality data would lead to a flurry of activity and four important papers would be published between 2008 and 2011.

As stated above, the importance of this data to the development of Strokes Gained cannot be overstated.  The ShotLink data is more accurate than the Golfmetrics data (laser surveyors provide a more accurate representation of beginning and ending shot locations than golfers clicking on a graphical representation of the hole).  Nonetheless Golfmetrics is important as it is the only dataset which includes amateur golfers and the inaccuracies of the individual shot locations likely insignificant when the data is considered in aggregate.

September 6, 2011

Stokes Gained: A Common Language

While some have contributed more than others, the development of the Strokes Gained methodology has been a collective effort for which no single person can take sole credit.  In subsequent posts GolfBrains will explore the contributions each has made.

Not all of the contributors have used the same terms to describe the same concepts which can be confusing.  To prevent this, when discussing the contributions GolfBrains will use the previously introduced terms Shots to Go (STG) and Strokes Gained (SG) in lieu of the contributors unique terminology.

Strokes to Go (STG)

  • Definition: The average number of strokes a benchmark player* needs to complete a hole.
  • Introduced By: MIT Team in their paper “How to Catch a Tiger.”
  • Synonyms: Average Number of Strokes to Hole Out (introduced by GSGB) and Fractional Par (introduced by Landsberger and used by Broadie in his earlier works)
  • Why GolfBrains Chose STG: While GolfBrains feels Average Number of Strokes to Hole Out is a better description, it is too wordy. Further, STG is more intuitive than Fractional Par.

Strokes Gained (SG)

  • Definition: The change in STG minus one.
  • Introduced By: While Broadie was the first to use Strokes Gained, much of the credit is however due to the MIT Team as their paper, focused on putting, introduced the term Putts Gained.  Strokes Gained is an extension of this concept.
  • Synonyms: Shot Value (introduced by Landsberger and used by Broadie in his earlier works)
  • Why GolfBrains Chose SG: GolfBrains actually prefers Shot Value.  SG suggests players are gaining strokes however, just as frequently players lose strokes.  From a mathematical standpoint this is not a problem as SG can assume a negative sign.  However GolfBrains believes from an intuitive standpoint, Shot Value which does not suggest players are gaining or losing strokes is better.  So why SG?  Because it seems the PGA TOUR has elected to use the SG terminology and, as most contributors are now using this terminology, GolfBrains does not want to make things unnecessarily confusing by backing a competing definition.
August 31, 2011

Advanced Golf Statistics

Measuring Golfer Performance
At first glance, it seems easy to measure a golfer’s performance.  A quick look at a golfer’s scorecard tells us the number of strokes he needed to complete each hole and to complete the round.  However the scorecard provides little insight into why a golfer performed well or performed poorly.

Explaining Golfer Performance
Advanced golf statistics attempt to provide insight into why a golfer performed as he did.  Which factors contributed to a golfer’s success?  Was it due to excellent tee shots?  Penalty strokes?  Poor putting?  A great sand game?  And how much did each of these factors contribute?

Importance of Advanced Golf Statistics
Advanced golf statistics offer the promise of greater insight regarding why golfers perform as they do.  There are a number of practical applications for this information:

  • Who is the best golfer in the world?  Who are the ten best golfers in the world?
  • Why is one golfer better than another?  Is it due to his driving ability?  His iron play?  His short game?  His putting?
  • Sunday afternoon, standing on Augusta’s 18th tee and trailing by one shot, what is the probability Tiger Woods makes birdie to force a playoff.
  • How can I, as a golfer, most effectively allocate my practice time to lower my scores?
  • How can I, as a golfer, improve my on course decision making to lower my scores?

In addition to these practical questions, advanced statistics offers us the chance to better understand the game we play and in the process satisfy our innate human curiosity.


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