The Value of Accuracy - Analysis of 2009 PGA Tour Results

[Anthony Fowler]

Commentators lament the fact that there is no longer a premium on accuracy on the PGA tour, and the USGA has instituted a costly groove rule change based on this premise.

The reason that commentators and the USGA feel that there is no value in accuracy is that fairway percentage does not correlate with success on the PGA tour.  Players who hit more fairways are no more successful than those who hit less (in fact they are slightly less successful on average).  However, this rudimentary observation is misleading because it fails to account for distance.  Distance provides a scoring advantage, but the further one drives the ball, the harder it is to hit the fairways.  We would really like to know if accuracy is correlated to success for a player that hits the ball a given distance.  To answer this question, I collected the stats of every regular PGA tour player from 2009.  To control for distance, I used multivariate regression.  I would be happy to discuss this methodology further if anyone is interested.  When controlling for distance, accuracy is highly predictive of success on the PGA tour.  The exact results are as follows.

If a player could improve his driving accuracy by 1 standard deviation (hitting 5% more fairways) while maintaining his same distance off the tee, he would:

Hit an extra 2% of greens-in-regulation,
make an extra $13,000 per event,
make the cut 7% more often,
earn a top 10 3% more often, and
win the tournament .5% more often.


Just for comparison, if a player similarly increased his distance by 1 standard deviation (an extra 8 yards per drive) while maintaing his same accuracy, he would

Hit an extra 2% of greens-in-regulation,
make an extra $24,000 per event,
make the cut 9% more often,
earn a top 10 4% more often, and
win the tournament 1% more often.

[note: a 1 standard deviation improvement would move a player from being average to being better than 2/3 of the players]

 
Just as an anectode, when controlling for distance Tiger was one of the most accurate drivers in 2009, while Phil and Padraig were well below average.

Given this data that the value of accuracy (when properly estimated) is almost as great as the value of distance, do you think the USGA may regret the great costs of changing the groove rule?  Are you convinced by this analysis that there is still a huge premium on accuracy on the PGA tour?  I think this data shows that the value of accuracy is alive and well in competitive golf and the claims about the "bomb and gauge" era are grossly overstated.  I look forward to any comments or critiques.

[Matt_Cohn]

OK, something here doesn't seem right to me. Increasing your driving accuracy by 5% means hitting slightly less than one more fairway per round. How can this possibly lead to hitting an extra two greens per round? Did you mean per tournament maybe?

[JESII]

I think it could just mean the player is overall more accurate if they are able to hit 5% more fairways...also, if the statistics are to mean 5% as in from 50% to 55% Driving Accuracy, that player is actually 10% more accurate than yesterday...but only 5% better on the scale.

Anthony,

Interesting findings...certainly supports the old adage of learning how to hit it far first and then learn how to hit it straight...



Is there any single initiative that would lend more value to accuracy than a determined goal of firm and fast golf courses every week?

[Anthony Fowler]

Matt, I apologize for the GIR problem.  Those lines should read "Hit an extra 2% of greens in regulation" which translates to about 1.5 greens per tournament.  I will make the appropriate change in the original post.  It's always good to make sure your results are plausible before reporting them.

Jim, by 5% more fairways, I mean that they will hit an extra 5% of the total fairways, so about 2.8 fairways per tournament.  The wording is a bit confusing because you could have read it to mean 5% of the fairways they were hitting before. 

Interesting findings...certainly supports the old adage of learning how to hit it far first and then learn how to hit it straight...

There is a tradeoff between distance and accuracy and players cannot disregard either one when learning to play the game.

Is there any single initiative that would lend more value to accuracy than a determined goal of firm and fast golf courses every week?

I don't know what single initiative would lend more value to accuracy.  My point with this post is to demonstrate that there already is significant value in hitting fairways.  I don't know what the optimal level is, but I'm not sure that the tour needs to worry about this.  It would be interesting to break this analysis down by event to see which types of courses put the highest premium on accuracy.  I'll let you know if I can get any leverage on that question.

[Anthony Fowler]

Since the units are somewhat confusing, I think it would be better to present the results in this way:

If the average player on tour improved his accuracy from 63.5 to 68.5% of fairways hit without giving up any distance he could expect
to earn an extra $330,000,
make an extra 1.7 cuts,
gain an extra .82 top 10s,
and win an extra .15 events in a given season.

If the average player on tour improved his distance from 288 to 296 yards without giving up any fairways he could expect
to earn an extra $600,000,
make an extra 2.2 cuts,
gain an extra 1.1 top 10s,
and win an extra .29 events in a given season.

[Anthony Fowler]

I've been thinking about the trade-off between distance and accuracy that Jim somewhat made reference to.  If you were a tour player, should you focus on adding distance or hitting more fairways?

My estimate is that adding 1 extra yard of distance will generate an extra $2000 per event.  In order to pick up the same amount with accuracy, a player would have to increase his fairway percentage by 1.1%. 

This is very close to the current trade-off curve between distance and accuracy on tour.  For every additional yard a player drives the ball, he gives up 1% of fairways hit.  This indicates that tour players are not systematically over-valuing distance over accuracy or vice versa. 

Obviously, the USGA is trying to alter the calculation with the new groove rule, but it is not clear that this is a necessary change. 

[Jim_Kennedy]

Anthony,
Lot of work you did.

If you average the accuracy and distance that the top ten players on the money list for '09 had as a group, it shows that they would have come in 88th place in accuracy and 68th place in distance.
Only one player, Kenny Perry, had equal numbers in both categories (49Acc/48Dist). Everyone else had a spread that was between 45 and 165 places in each category (Glover was 25Acc/70Dist; Mickelson was 179Acc/13Dist) with 6 placing better in distance, 3 placing better in accuracy, and one 'tie', Perry.

Not surprising, Tiger was 86th in accuracy and 21st in distance.

Outside of all the other factors that add up to money won, I think this shows that accuracy takes a back seat to distance, and this is what getting the players back into the fairway is all about.

I also think that the distance part of your work cannot be easily implemented, mainly because these players are at their limits and don't have another 8 yards in 'em.  That's a few more MPH of swing and ball speed, and even if a player tried to reach back for those extra bits it would likely cause him control problems.
 

[Anthony Fowler]

Jim, I will reiterate that that type of analysis can be misleading.  The best players in the world are long hitters, so they will naturally miss more fairways than the average tour player.  The important question is not whether the best players hit more fairways than others, but whether it is worth the while of an individual player to hit more fairways.  I think my previous analysis makes a strong case that players do have an individual incentive to hit more fairways.  Here are the top 10 players from the 2009 money list.  The number to the right of their name gives the pct of fairways they hit minus their expected fairway percentage based on their distance.  You can see that among these top players, 7 of them are more accurate than expected.  Further to the right is their relative rank on tour in this particular category.  These guys are much more accurate than their counterparts on tour who drive it the same distance.

moneylist      player        fwy% - expected           accuracy rank
1      Tiger Woods         4.8                           24
2   Steve Stricker         2.6                           55
3   Phil Mickelson        -6.6                           172
4   Zach Johnson         5.4                           13
5   Kenny Perry         5.5                           12
6   Sean O'Hair         0.2                           92
7   Jim Furyk                 3.2                           47
8   Geoff Ogilvy        -3.7                           152
9   Lucas Glover         5.6                           11
10   Y.E. Yang                -1.6                           127

[Ken Moum]

Jim, I will reiterate that that type of analysis can be misleading.  The best players in the world are long hitters, so they will naturally miss more fairways than the average tour player.  The important question is not whether the best players hit more fairways than others, but whether it is worth the while of an individual player to hit more fairways.  I think my previous analysis makes a strong case that players do have an individual incentive to hit more fairways.  Here are the top 10 players from the 2009 money list.  The number to the right of their name gives the pct of fairways they hit minus their expected fairway percentage based on their distance.  You can see that among these top players, 7 of them are more accurate than expected.  Further to the right is their relative rank on tour in this particular category.  These guys are much more accurate than their counterparts on tour who drive it the same distance.

moneylist      player        fwy% - expected           accuracy rank
1      Tiger Woods         4.8                           24
2   Steve Stricker         2.6                           55
3   Phil Mickelson        -6.6                           172
4   Zach Johnson         5.4                           13
5   Kenny Perry         5.5                           12
6   Sean O'Hair         0.2                           92
7   Jim Furyk                 3.2                           47
8   Geoff Ogilvy        -3.7                           152
9   Lucas Glover         5.6                           11
10   Y.E. Yang                -1.6                           127

Anthony, that's a nice bit of statisical analysis. 

The one thing I wonder, however, is how the relationship you show here compares to the balata ball days.

My theory--for some time--is that while long, straight  hitters have always been the game's best, today the balance of power has shifted from what it was in the 1940-1990 era. While your stats show that accuracy still means something, does it mean less than it did during that era?

If it does, then I still think action is required--because I believe that golf at all levels was a better game than it is now.

K

[Anthony Fowler]

Ken, that's a great question.  I am wondering the same thing.  Do you know where I can find the PGA tour stats that go back that far?  Just a few years of data pre-2000 and pre-1990 would be great.

[Jim_Kennedy]

All Tour stats for distance in 1980 show a disparity of 35.60 yards from top to bottom.
All Tour stats for distance in 2009 show a disparity of 53.00 yards from top to bottom.

All Tour stats for accuracy in 1980 show a high of 79.50 and a low of 50.00
All Tour stats for accuracy in 2009 show a high of 74.09 and a low of 48.02

You can glean what you will, but yardage has been given an advantage over accuracy since the balata days.
 

[Jim_Kennedy]

Anthony,

I think that trying to put accuracy back into the game is warranted.

Woods and Mickelson consistently rank near the bottom with numbers in the 140s, 160s, and 180s when it comes to accuracy, but they are in the single digits, teens, 20s, and 30s when it comes to distance. Their yearly money hasn’t dropped below 6th since 2003 (Phil).

Steve Stricker’s major improvement in accuracy came in ’06, ’07 and ’09. This is what it did for him. I think it’s also somewhat telling that his distance rank in 03 and in 09 are about the same, but his accuracy is much better, and so was the money.
           Acc.       Dist.     Money
’09       53          104         2
’07       97          146         4
’06       49          134        34
’05      197         129       162
’04      193         144       151
’03      190         109       188             
 
Zach Johnson is another…..
         Acc.       Dist.       Money
’09      10        143             4
’07        8        169             8
’06      26        145            24
’05      47          86            39
‘04      15        113            19
……his worst money year was his highest placement in distance, but his lowest accuracy.

I think what these numbers shows is that the long hitter (TW & PM) is already rewarded but the shorter player makes his money by becoming more accurate (SS & ZJ) as his distance may never increase. 

Therefore, leveling out the field reins in some of the advantage that the longer hitter enjoys, more in line with the 1980 numbers  shown in my previous post.

[Jim Nugent]

Anthony, on some courses accuracy is more important than others.  In U.S. Open type setups, e.g., I bet accuracy matters more.  At Torrey Pines, I bet it doesn't.  Same with Riviera: as I recall, the winners there often hit less than 50% of the fairways.   

But not all players play the same events.  They don't play the same courses.  Tiger, e.g., used to mostly play the toughest courses. 

Do you think you should make allowances for those two facts: that courses differ, and virtually none of the players play all the same courses as the others?

Related question, maybe: do you know how driving accuracy correlates with hitting par 3's in regulation?   

Cool analysis, btw.

[Mike Nuzzo]

Anthony
Cool data
What happens if you take Tiger and a few others out of your initial analysis?
Those are outliers and may have a bigger impact on the $.

[Cristian]

I wonder how many greens in regulation one shoud miss additionaly because of the new groove rules to elevate the importance of accuracy to the same level as that of distance scoring-wise in your calculations?

[Ken Moum]

Ken, that's a great question.  I am wondering the same thing.  Do you know where I can find the PGA tour stats that go back that far?  Just a few years of data pre-2000 and pre-1990 would be great.

There are season-long stats for most categories here http://www.pgatour.com/r/stats/. I think the ones you need go back into the 1980s.

Ken M

[Jason Connor]

Disclaimer:  Statistician is my day job (and too often, my night job).

My issue is the relevance of "When controlling for distance, accuracy is highly predictive of success on the PGA tour."

We all agree that we'd like to be straighter while maintaining length.

The more relevant question is to me is this:

Imagine a curve of Pr(Hit fairway) vs. Driving distance.  As driving distance goes UP, Pr(Hit fairway) will go down.

So the question becomes where is the optimal place to be on that curve?

The problem becomes that there isn't just a different answer for every player, there is  a different answer for every player on every hole.

Meaning the effect of distance on a short (but 2-shot) par four isn't much. We'd all be better backing off and making sure we hit the fairway.  But put us on a 440-yd par four.  There the optimal spot on the Pr(hit fairway) vs. distance curve is likely to be further to the right.

It's a complex model that would seem to require variables for both individual player and perhaps length of hole.

As it stands, while the analysis is interesting and informative, it doesn't seem to answer a real-life question.

[Anthony Fowler]

What happens if you take Tiger and a few others out of your initial analysis?
Those are outliers and may have a bigger impact on the $.

Definitely.  Woods, Mickelson, and Stricker are all over 3 standard deviations above the mean as far as earnings.  When we remove them, the results are more or less unchanged.  If anything, accuracy appears to be more important relative to distance.

Anthony, on some courses accuracy is more important than others.  In U.S. Open type setups, e.g., I bet accuracy matters more.  At Torrey Pines, I bet it doesn't.  Same with Riviera: as I recall, the winners there often hit less than 50% of the fairways.   

But not all players play the same events.  They don't play the same courses.  Tiger, e.g., used to mostly play the toughest courses. 

Do you think you should make allowances for those two facts: that courses differ, and virtually none of the players play all the same courses as the others?

At the moment, I am only looking at aggregated, season-long data.  It would be great to collect hole-by-hole, and event-by-event data to answer some of these additional questions.  Hole-by-hole data would allow us to control for the course and the player.  It would be great to see which courses place the highest premium on accuracy.

Related question, maybe: do you know how driving accuracy correlates with hitting par 3's in regulation?   

This is an excellent question.  Checking the correlation between fairways hit and par 3 performance would provide a reality check for our analysis.  It is possible that accuracy and distance are correlated to performance because the better ball strikers are better in other respects as well.  Perhaps straight drivers are also better iron players, so we would be falsely picking up some of their great iron play in our correlation.  I don't have GIR's for par 3's, but I do have the players' percentage of birdies on par 3's, 4's, and 5's.  It turns out that neither driving distance or accuracy are significantly correlated with birdies on par 3's, while they are correlated with birdies on par 4's and 5's, which is good.

Going from the most accurate driver to the least accurate driver (48 to 74% of fairways hit), controlling for distance, increases your probability of a birdie on a
par 3 by 0.7%,
par 4 by 3.6%, and
par 5 by 3.4%. 
The 0.7% effect on par 3's is not statistically distinguishable from 0, whereas the par 4 and par 5 effects are.

Going from the shortest driver to the longest driver (259 to 312 yards), controlling for accuracy, increases your probability of birdie on 
a par 3 by 1.1%,
par 4 by 5.5%, and
par 5 by 22%.

Once again the effect for par 3's is not statistically significant.  It turns out that distance is a big deal for birdies on par 5's, but this is something that the groove rule will probably not be able to change. 

Hopefully, this analysis suggests the correlation between accuracy and success is not driven by confounding variables.  The fact that the effect only arises on driving holes is reassuring.

I wonder how many greens in regulation one shoud miss additionaly because of the new groove rules to elevate the importance of accuracy to the same level as that of distance scoring-wise in your calculations?

This question does not have a straightforward answer.  A single standard deviation improvement in accuracy will have almost the same effect on GIR's as a standard deviation improvement in distance.  I think these estimates show that accuracy is already on a par with distance in terms of its importance for scoring (maybe with the exception of par 5 birdies).

[Anthony Fowler]

Disclaimer:  Statistician is my day job (and too often, my night job).

My issue is the relevance of "When controlling for distance, accuracy is highly predictive of success on the PGA tour."

We all agree that we'd like to be straighter while maintaining length.

The more relevant question is to me is this:

Imagine a curve of Pr(Hit fairway) vs. Driving distance.  As driving distance goes UP, Pr(Hit fairway) will go down.

So the question becomes where is the optimal place to be on that curve?

The problem becomes that there isn't just a different answer for every player, there is  a different answer for every player on every hole.

Meaning the effect of distance on a short (but 2-shot) par four isn't much. We'd all be better backing off and making sure we hit the fairway.  But put us on a 440-yd par four.  There the optimal spot on the Pr(hit fairway) vs. distance curve is likely to be further to the right.

It's a complex model that would seem to require variables for both individual player and perhaps length of hole.

As it stands, while the analysis is interesting and informative, it doesn't seem to answer a real-life question.

Jason, these are all great points.  As I said before, I am only working with aggregated, season-long data.  Obviously, the optimal point on the distance-accuracy tradeoff curve is difficult to estimate and different for every player and every particular situation.  I would love to collect hole-by-hole data for each player along with information about each hole and come up with a better answer to your question.

However, there are many people that do believe that there is NO value in hitting fairways on the PGA tour.  They look at the general statistics that Jim Kennedy described and say that fairways are not important.  This was more or less the logic used by the USGA in changing the groove rule.  For the purposes of ruling out that claim, I think the crude, aggregated approach does the job.  At least we can see correlationally that accuracy of the tee is highly predictive of success on the PGA tour when we include distance as an appropriate control.

Technical aside: Even if we did have all of that detailed data that we want, we still would have trouble exactly estimating the true tradeoff curve.  Accuracy and distance are not randomly assigned.  Instead, each observation represents an instance of the player attempting to optimize accuracy and distance in a particular situation.  This is the same problem economists run into when trying to estimate a supply curve.  Barring a good instrumental variable or randomized trials, it would be impossible to exactly tease out this curve for a particular player.  Nonetheless, I think my crude estimate is good enough to claim that accuracy is very important for scoring and tour players on average are doing a decent job choosing their optimal point along the curve (see my previous post on this).

[Cristian]

I wonder how many greens in regulation one shoud miss additionaly because of the new groove rules to elevate the importance of accuracy to the same level as that of distance scoring-wise in your calculations?

This question does not have a straightforward answer.  A single standard deviation improvement in accuracy will have almost the same effect on GIR's as a standard deviation improvement in distance.  I think these estimates show that accuracy is already on a par with distance in terms of its importance for scoring (maybe with the exception of par 5 birdies).
[/quote]

Mmm indeed the result of one standard dev. is 2% in both cases already, so the scoring difference must come mainly from average distance to pin. If we can establish that correlation, and we know the negative effect of distance to pin on average when firing from outside the fairway, then we could assess numerically the effect of the ruling on premium for accuracy. Anyhow it will be interesting to see the numbers change by the end of 2010!

[Jonathan Cummings]

I believe the PGA for years measured fairway drive length/accuracy for just one hole (usually a long par 4 or par 5) per round for a tournament.  (The ShotLink folks would set their gear up on just one hole).  That's where the drive accuracy/length stats were generated.  It is always a hole where everybody used driver and cranked it for everything they were worth.  I believe they have expanded that to more holes now.

For 40 years I have kept personal statistics on my own golf.  As an engineer I'm anal enough in my golf to track my own: fairways hit, GIRs, putts, putts for GIR, recoveries, penalties.... enough minutiae to put a cup of coffee to sleep.  I have built associated workbooks stuffed with convoluted macros that supposedly tell me where I stand year after year.  I perform one and two variable correlations with all data against the absolute for all stroke-play golfers - final 18-hole score.

There are only a few absolute I have consistently observed.  (1) I hit more greens, my scores goes down; (2) I putt less, my scores goes down, (3) I drive more accurately - no affect on my score.

JC

[Anthony Fowler]

There are only a few absolute I have consistently observed.  (1) I hit more greens, my scores goes down; (2) I putt less, my scores goes down, (3) I drive more accurately - no affect on my score.

Jonathan, this is very interesting.  I have just a couple questions.

Is it possible that you play on courses where the rough is not particularly penalizing?  PGA Tour and USGA events are held on penal golf courses with thick rough, so we might expect fairways to matter more for PGA tour players than for the rest of us.  Additionally, for those of us with less precise iron play than the pros, the rough will also not hurt our scores as much as it would for the pros.  If I would've missed the green from the fairway, it may not really matter whether I hit the fairway or not.

Does your fairway percentage correlate to your GIRs?  If so, then your regressions could be giving you a misleading result.  If fairways lower your scores by allowing you to hit more greens, regressing score on both GIRs and fairways will give you a zero coefficient for fairways because all of its effect is being picked up by the GIR variable.  If you have not already, try regressing GIRs on fairways and score on fairways with no other variables.  If fairways still appear to have no effect, that would be interesting.  I think we would have to conclude that 1. you are a superb player from the rough and trouble, 2. you do not typically play courses that place premium on fairways, 3. there is enough randomness in your game that you are unable to detect the effect despite your "anal" record keeping, or 4. there is not enough variation in your fairways hit statistic to tease out any effect (i.e. you always hit 13 or 14 fairways per round). 

In general, I would warn against assigning a narrow causal interpretation to any of your coefficients.  Your greens variable is highly predictive of score, but you had to drive the ball well to hit the green, so driving is already inherently present in that variable.  Your putts variable is a complex function of your ball-striking, chipping, and putting, and your putts per GIR is also a complex function of your ball-striking and putting.  So, even from your detailed data, it is difficult to say that your good scoring can be attributed to iron play, putting, and not driving.  At any rate, thanks for keeping such detailed records and sharing them with everyone.

[Jason Topp]

For those interested in some history on this subject I recomment "the search for the perfect golf swing" which has a chapter statistically analyzing this question. It concludes distance is more important than accuracy and the best way to improve is through improved iron play. I am not sure I agree with all of the conclusions but it is a very interesting read.

[BCrosby]

This is great stuff. I am not a statistician and don't follow some of the arguments.

But it is worth noting the extraordinary significance of fairly small changes in performance. Specifically, hitting 5% more fwys means hitting only .7 more fwy's during each round in a tournament. That's hitting only one more fwy for every 18 or so non-par 3 holes.

I find that amazing.

Bob  

[Jim_Kennedy]

However, there are many people that do believe that there is NO value in hitting fairways on the PGA tour.  They look at the general statistics that Jim Kennedy described and say that fairways are not important.  This was more or less the logic used by the USGA in changing the groove rule.  For the purposes of ruling out that claim, I think the crude, aggregated approach does the job.  At least we can see correlationally that accuracy of the tee is highly predictive of success on the PGA tour when we include distance as an appropriate control.

That is not the logic used by the USGA at all. There is Shotlink data that shows a very slight scoring advantage from the fairway, but that advantage is not enough to get the longest players to throttle back. Players taking the chance with a big swing/long drive get rewarded if they find the fairway, but players who take a chance with a big swing/long drive and find the rough are also rewarded because the aggressive nature of their grooves gives them a more than reasonable chance of being able to bring about a more controlled shot to the green than the situation should allow.

That distorts the balance between distance and accuracy, and that's what 'bomb and gouge' or 'flogging' is all about. It's also why the USGA has acted in the manner it did.

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