[BHoover]

Brian, what makes you say that they're "inherently subjective"?

I'm not sure where the term "shot values" originated. But if Golf Digest invented it as a category for rating golf courses, and they expect their rating system to function as any sort of source of truth, then quantifying the concept would make sense to add some shred of objectivity to their ratings. The definition they've chosen for the term also happens to lend itself to relatively easy calculation.

As for the question of why, I wouldn't personally bother with it. But the original post asks if they're tangible or intangible, and I think if you define shot values as Golf Digest does, then they're pretty tangible and wouldn't be hard to calculate using a measurement definition the same way that sabermetricians calculate things like VORP and Player Efficiency Rating. I personally would rather just play golf, but someone who gives a crap about trying to identify if some courses are objectively better than others might be interested in an objective measurement of shot values.

I have no answers. I just believe that rankings, shot values, course assessments, etc are subjective rather than objective. At the end of the day, it's about personal preference. Just my opinion.

[Tom_Doak]

Tom, do you really think it would be that hard to quantify? It seems pretty simple to me. An easy way would be to track a few hundred rounds from players with 10 handicaps or better, tracking the dispersion of clubs hit per player to distinguish between courses that only test short iron play versus courses that require some long/middle irons and woods. That would establish the "variety of shots" component of the equation on some level (admittedly slightly reductionist, but I'm sure a smarter analyst could come up with a more comprehensive equation).

Then, to establish the risk/reward side of the equation, you would track those same few hundred rounds and note whether players took the aggressive or conservative route on a given hole. You'd compare the score for those who take the aggressive route and succeed against the score for those who take the same route and fail, and against the score for those who take the conservative route. You'd also probably want to identify how many players take the aggressive route vs. the conservative. That sounds complicated,

Yes, it does 

   but it's really not. My industry uses far more complicated measurements to evaluate how successful teams are. In my head, the measure definition would look something like the following (and this is probably stupid, but a real analyst could knock out an equation that actually makes sense pretty easily I would guess. Joel Lahrman might have some ideas):

(aggressive-successful scoring average)                                                               (# of times aggressive line chosen)
______________________________        x     conservative scoring average    x   ______________________________

(aggressive-unsuccessful scoring average)                                                            (# of times conservative line chosen)

The implication being that a course that tempts aggressive play and has a wide variation in outcomes for players who take aggressive lines would have more risk/reward than a course that doesn't do those two things.

If you really want to take that much time to analyze 18 holes, knock yourself out, I'd love to see it.  But I think I'll stick to the way I've been doing things, in the meantime. 

[Jason Thurman]

Hey, like I said, I have no interest in actually doing it. I also don't have the knowledge necessary to do it correctly even if I did. But that doesn't mean it can't be done. I work with guys who write measure definitions all the time, and shot values are definitely tangible enough as a concept that they could write a way to measure them.

[JESII]

Jason,

I don't think that formula could work for more than a single person playing those hundreds of rounds. You have people at the same overall skill level that perform drastically different at each component of the game that there's no way to get them into the same formula and have the results mean anything.

Think about two comparable level tour players on the 13th tee at Augusta...One hooks it easily and the other slices it easily. Your "value" calculation for each individual would be drastically different and would result in an average that meant nothing to anyone.

In other words, I think shot values are, and have to be, purely subjective.

[Sean_A]

Jim

Your conclusion seems quite obvious to me.  Anytime someone suggests design principles/quality can be expressed mathematically, I am very skeptical. 

Ciao

[Michael Wharton-Palmer]

Shot values....To me you know them when you see them whatever your level of play may be.
To me those courses that consistently rank highest display tremendous shot value when you play them, that is not to say they are always Dye like in their penal nature but the player is rewarded for hitting good shots.
In terms of being able to measure such shot values I wouldnt really know where to start as they are so individualistic in their interpretation, which is why I say...You kow it when you see it

[Jason Thurman]

Jason,

I don't think that formula could work for more than a single person playing those hundreds of rounds. You have people at the same overall skill level that perform drastically different at each component of the game that there's no way to get them into the same formula and have the results mean anything.

Sure there is. Those same variances exist in the data we currently collect about courses. Differences in how people perform at different aspects of the game don't stop us from calculating scoring averages for a tournament field on a given course or hole, or GIR percentage for a given course or hole, and identifying meaningful trends that tell us something about how one course or hole compares to another. Those differences wouldn't stop you from having a metric that calculates shot values either.

Think about two comparable level tour players on the 13th tee at Augusta...One hooks it easily and the other slices it easily. Your "value" calculation for each individual would be drastically different and would result in an average that meant nothing to anyone.

For two players, that's true enough (though I don't understand how a hook vs. a slice would throw off my prototype "value" calculation as written, since it doesn't account for shot shape. Maybe it should though, so I still understand what you're saying). But that's why we'd need a large sample size to collect any meaningful data. In every data sample there are outliers and variances. With a large enough sample, those outliers and variances tend to regress toward a mean.

In other words, I think shot values are, and have to be, purely subjective.

Are you an analyst or statistician? I'm not trying to be an ass, I'm just asking. I'd love to hear the thoughts of someone who works with numbers and writes measurement definitions or does other analytics work. As I've mentioned, I work alongside quite a few analysts as a quality improvement consultant, but I'm more of a pretty face who helps end users understand what the numbers say. I don't write measurement definitions myself, so I'm no real authority. But shot values just don't seem difficult to quantify to me, at least on a rough level. I don't know whether it's really worth doing or not, but if someone devised a formula for measuring them I'd certainly be interested in seeing the results.

[Richard Choi]

Shot values....To me you know them when you see them whatever your level of play may be.
To me those courses that consistently rank highest display tremendous shot value when you play them, that is not to say they are always Dye like in their penal nature but the player is rewarded for hitting good shots.
In terms of being able to measure such shot values I wouldnt really know where to start as they are so individualistic in their interpretation, which is why I say...You kow it when you see it

So, Shot Value is basically the same as pornography?

[Sean_A]

Shot values....To me you know them when you see them whatever your level of play may be.
To me those courses that consistently rank highest display tremendous shot value when you play them, that is not to say they are always Dye like in their penal nature but the player is rewarded for hitting good shots.
In terms of being able to measure such shot values I wouldnt really know where to start as they are so individualistic in their interpretation, which is why I say...You kow it when you see it

So, Shot Value is basically the same as pornography?

...minus the happy finish and for some, happy start.

Ciao

[Michael Wharton-Palmer]

Richard...now when is Porn Porn and when is it simply someones interpretation or body art?
So the director is the golf course architect right!

[Josh Tarble]

I do think this would be a really cool thing to possibly calculate...I see it being something similar to Win Probability
http://www.advancednflstats.com/2008/08/win-probability.html

In that it could say "an 8 handicap has a par-probability of x%, when hitting this type of shot"  Advanced statistics are truly amazing in what they can help show.  I would think a busy public course could possibly utilize GPS to help track these stats.  The key would be gathering enough of a sample size for each handicap to find any conclusive data.  I do think it's possible to find a "shot value" for each shot of a course.  

However, I think it would really only be of any significance on holes where there are two or more distinct options...say #10 at Riviera or any split-fairway hole.  Otherwise it may be very difficult to calculate the difference of play within 5 yards of a bunker or play 20 yards.  There is certainly a difference of strategy in something like that, but the actual execution may be too miniscule to showcase.

On a related by separate point, I'm actually surprised the PGA Tour doesn't do something like this.  I know they track every shot, and there has to be some sort of conclusion that could be pulled from this data.  The NBA has required all teams to have a sportVUE camera system in their arena this year...it is seriously cutting-edge technology in the advanced metrics stage, and teams are touting the benefits already.
http://www.nba.com/2013/news/09/05/nba-motion-tracking-cameras-ap.ap

I think its really cool stuff, and am pretty surprised someone hasn't figured out the equivalent for the PGA Tour yet.  Sorry for the tangent, but I do think advanced metrics in sports like basketball and baseball are pretty sweet and would be interested to see something focused on golf.

[JESII]

Jason,

I don't think that formula could work for more than a single person playing those hundreds of rounds. You have people at the same overall skill level that perform drastically different at each component of the game that there's no way to get them into the same formula and have the results mean anything.

Sure there is. Those same variances exist in the data we currently collect about courses.

My point exactly. Course rankings are not objective. They are a collection of opinions.

The shape of the shot on #13 at Augusta matters because for me, the slicer, the tee shot is way more difficult than for the hooker so the value is higher. once we both get it down by the creek on the flat, the second shot is easier for me.

What good is it to me to study that hole based on the average of 000's of other players that do not play exactly like me? Does looking at a 4.8 scoring average make me feel like I should birdie the hole?

I don't disagree that golf stats can be incredibly interesting and helpful, but once they factor other players, they're less relevant to you individually.

[JESII]

For what it's worth, I agree with you that the term "shot value" is definable and is tangible...but only for the individual.

A particular shot value to you means absolutely nothing to me.

[Jason Thurman]

For what it's worth, I agree with you that the term "shot value" is definable and is tangible...but only for the individual.

A particular shot value to you means absolutely nothing to me.

I can understand that. There's probably also a cutoff handicap for really being able to measure them. I'm a high single digit player and I'm nowhere near consistent enough to evaluate the risk in a shot as an architectural challenge alone. There's risk for me in hitting a level wedge shot to a flat green with no hazards. Just by making a swing I'm risking a shank or chunk or skull. I'm just not a good enough ballstriker. My mishit risk is too high, if that makes sense.

I would think you'd need to focus any measurement of it on scratch players or better if you wanted actionable data, which might make it irrelevant for a lot of us. Even then, you'd still have certain players who are better at a certain "risky" shot while other players may struggle with what the numbers say is a "safe" shot. That's true in any advanced metric for athletics though. After all, the "corner 3" might be one of the most efficient shots in the NBA, but not if Kendrick Perkins is shooting it.

[DMoriarty]

Tom, do you really think it would be that hard to quantify? It seems pretty simple to me. An easy way would be to track a few hundred rounds from players with 10 handicaps or better, tracking the dispersion of clubs hit per player to distinguish between courses that only test short iron play versus courses that require some long/middle irons and woods. That would establish the "variety of shots" component of the equation on some level (admittedly slightly reductionist, but I'm sure a smarter analyst could come up with a more comprehensive equation).

Then, to establish the risk/reward side of the equation, you would track those same few hundred rounds and note whether players took the aggressive or conservative route on a given hole. You'd compare the score for those who take the aggressive route and succeed against the score for those who take the same route and fail, and against the score for those who take the conservative route. You'd also probably want to identify how many players take the aggressive route vs. the conservative. That sounds complicated, but it's really not. My industry uses far more complicated measurements to evaluate how successful teams are. In my head, the measure definition would look something like the following (and this is probably stupid, but a real analyst could knock out an equation that actually makes sense pretty easily I would guess. Joel Lahrman might have some ideas):

(aggressive-successful scoring average)                                                               (# of times aggressive line chosen)
______________________________        x     conservative scoring average    x   ______________________________

(aggressive-unsuccessful scoring average)                                                            (# of times conservative line chosen)

The implication being that a course that tempts aggressive play and has a wide variation in outcomes for players who take aggressive lines would have more risk/reward than a course that doesn't do those two things.

If you actually tried to apply your formula (or one like it designed to identify the same attributes) to a few golf courses or even golf holes, I think you might be surprised with the results.  I tried something similar a number of years back by looking how the pros played what most would consider a high "shot value" hole, Riviera No. 10.   It turned out that, 1) the variance in scores (risk/reward) wasn't really all that different between the two options, and 2) the range of scores was actually pretty narrow.

So does that mean that Riviera 10 isn't a great hole or a "high shot value" hole? Or is quantifying "shot value" quality more difficult that it would seem?

[Josh Tarble]

David that is probably true...most golf holes don't have too much difference between high and low scores.  

However if it was a real formula developed to identify "shot values" it would have some sort of standard deviation factor.  I'm not exactly sure how it would work, but a hole like Riv #10 surely has a higher deviation than other par 4s on the course.  That would factor in to the "shot value" in some form.

I also think it would take a crap ton of plays to find a meaningful sample size.  I would think it would have to be in the couple hundreds to thousands of plays.

[DMoriarty]

David that is probably true...most golf holes don't have too much difference between high and low scores.

My post wasn't too clear.  I think some holes DO have a relatively large distribution of scores compared to other holes. I just don't think that this relative difference is a very good indicator of the relative quality of the holes or of so-called "shot value."  I offered Riviera 10 as an example because it is generally considered to be an excellent hole - very strategic with clear choices and I would presume a high "shot value" - but I don't think it would identify as a good hole using a formula identifying a wide variation in scoring.

However if it was a real formula developed to identify "shot values" it would have some sort of standard deviation factor.  I'm not exactly sure how it would work, but a hole like Riv #10 surely has a higher deviation than other par 4s on the course.  That would factor in to the "shot value" in some form.

Because of the lack of a normal distribution and the "half-par" nature of the holes I'm not sure standard deviation would be the proper measure.  But if what we are really looking for a wide distribution of potential scores then I'm not so sure that Riv. 10 has a higher deviation. Here are the scores from Riv. 10 the year I checked (2004).  Sample size 442.

Eagles:     3  (0.68 %)
Birdies: 134  (30.32 %)
Pars:     265  (59.95 %)
Bogeys:   37  (8.37 %)
Doubles:   2   (0.45 %)
Others:     1   (0.23 %)

As you can see, the vast majority (over 90%) made birdie or par, only 8% made bogey, and less than 1% made worse than bogey or better than birdie.  The scores are tightly bunched around birdie and par, without many big or small numbers at all.  

I wish I had numbers from other holes, but I don't.  Nonetheless, I am not sure that this is the type of range of scores which would seem to be predicted by Mike Young's or Jason Thurman's suggestions or methodology.  I think that this is because what they are suggesting would underweight subtlety, overweight severe penalty, and ignore the role of expectation.  Generally, nothing horrible happens to a good golfer at Riviera No. 10, and surprisingly, not too much really great happens either (very few actual eagles.)  But good golfers expect birdies, yet there is far from consensus as to the best way to achieve birdie and well over half (68%) ended up likely disappointed.  In 2004 approximately 69% laid up.  I can't find the breakdowns of which route was more successful, but I recall that it was a fairly even split. (Even one of the three eagles was from 70 yards!)

ADDED:  I could be wrong if the comparison is just with holes at Riviera.  Thinking of the other holes, it isn't the kind of course that beats golfers over the head with extreme penalties such as water hazards, lost balls, unplayable rough, out of bounds, etc.   The whole course is more subtle than that, and exacts its due over time.   I am not sure the methodologies being discussed take that sort of thing into account.

[V. Kmetz]

It's always some tip of the hat to semantics when these terms like "Shot Value" rear their head and I apologize if I haven't read the thread thoroughly, and am stumbling over someone's previous idea.

For me, as in the template hole "examinations," there are many, many types of "Shot"...

1. "low runner"
2. "aerial drop"
3. "hooking flight, slicing flight, etc"
4. "blind faith - indefinite target"
5. "forced carry"
6. "don't go long"
7.  "over 'there' - use fortune of ground"
8.  "needs to be straight"
9.  "anything BUT left, anything BUT right, etc"
10. "a partial wedge off slopy ground"

and probably dozens more I can't summon right now...some might involves properties of a prevailing wind and some are included in those shots that are close to the green like pitches, chips and putts ("Long Putt Judgement" would be a prevalent "shot value" at Yale)

AND then there is "Value," which for me, can be

1. how much a player encounters, or an architect uses, one of the shots
2. how many different types of "Shots" are deployed (hence the review phrase: "Variety of Shot Values")
OR
3. how much the player and/or architect "likes" the types of shots they call for.
4. how exactingly (penalty to reward) a particular "shot" is presented to the golfer.

I don't see how anything to do with scoring has anything to do with it, and the latter discussion regarding Riviera #10 seems to be "off," as:

A. A short Par 4 is not a Shot Value, it may be a "Hole Value," but its the shots provoked (or commanded) within such a hole wherein lies the actual Value of a particular  Shot
B. Consequently, the entire hole is mislabeled to have a "High" or "Low" Shot Value

and what's being missed is

C: the real beauty of a great Short Par 4, is the coordination and readiness to hold differing "Shot Values" depending on the players comprehension of ability, to risk/reward.  

On Riviera 10, for some like elite and tour players, it's a "Bomb with Miss Left" and then, "delicate partial pitch out of rough" OR  "checking skid pitch to igloo top" for others.  But no matter what your abilities and execution, the hole carries "exacting" shot value for anything you plan.  Whatever you choose, you must do correctly, or otherwise have great fortune to achieve a 4 or better on the hole. Riviera 10 will not let you get away with indifferent play.  This is probably owing most to the green complex and its situation to topography, fairway hazard, and the distances achieved.  Regardless, the hole is brilliant because whatever shot Values the player deems are commanded from tee to green, the hole is ready to make an exacting test.

Perhaps that is the beauty and the applicable "Value" label of many short Par 4s...the Hole itself bifurcates (based on ability and command) into two types of successive value columns.  It's two (or more) holes in one hole presentation right from the peg being put into the ground.

cheers

vk

[Josh Tarble]

I'm going to have to do some serious math...but it doesn't really matter what the actual scores are. It would still be a comparison based on the overall average and the average of the alternative.  

For example, out of 100 plays there may have only been 5 eagles (5%). But let's say 50 aggressive plays resulted in 4 (8%) eagles and 50 conservative plays resulted in 1 (2%) eagle.  The aggressive play is 1.6 times more likely to result in eagle than the average and 4x as likely as the conservative play.

Obviously this is way simplified but I think this is how it would be calculated.  

The whole course is more subtle than that, and exacts its due over time.   I am not sure the methodologies being discussed take that sort of thing into account.

This is where it gets difficult. On many holes there isn't a clear decision and I don't know that would be taken into account.

[Josh Tarble]

For what it's worth, I agree with you that the term "shot value" is definable and is tangible...but only for the individual.

A particular shot value to you means absolutely nothing to me.

That may be the case, but what if, standing on the tee, you knew you were 15% more likely to make bogie by taking driver and 7% more likely to make birdie?

[Tom_Doak]

For what it's worth, I agree with you that the term "shot value" is definable and is tangible...but only for the individual.

A particular shot value to you means absolutely nothing to me.

That may be the case, but what if, standing on the tee, you knew you were 15% more likely to make bogie by taking driver and 7% more likely to make birdie?

That information would be terrific, if the "you" were really YOU, and not some mish-mosh combining the efforts of John Daly and Fred Funk.

The Tour's Shot Link data is excellent.  I thumbed through their data for the 10th at Riviera one year myself ... the best part was where they showed little dots for where every single drive landed on each day, color-coded to whether the player made eagle or birdie or par or bogey.  Perhaps the data was not conclusive about whether it was wise to lay up or not, but it was VERY conclusive about whether you were better off missing the tee shot to the left or the right.

I am starting to think, though, that the 10th at Riv is becoming more and more like the 12th at Augusta, where years of Tour lore are starting to make everyone play it the same way, and robbing the holes of their real value, which was to make stupidly aggressive players pay the price for their sins.

[Howard Riefs]

So, Shot Value is basically the same as pornography?

Who knew that Justice Stewart was a golfer...

[DMoriarty]

I'm going to have to do some serious math...but it doesn't really matter what the actual scores are. It would still be a comparison based on the overall average and the average of the alternative.  

For example, out of 100 plays there may have only been 5 eagles (5%). But let's say 50 aggressive plays resulted in 4 (8%) eagles and 50 conservative plays resulted in 1 (2%) eagle.  The aggressive play is 1.6 times more likely to result in eagle than the average and 4x as likely as the conservative play.

Obviously this is way simplified but I think this is how it would be calculated.

I think, though, that when we try to use the real numbers we might lose any meaningful distinction you are trying to make.  In the year I checked, there were only three eagles in 442 plays.  So instead of your 5% it was <1%.  305 layups produced one eagle (0.33%), while 137 attempt to get on or close to the green produced two eagles (1.45%).  So yes, going for the green made eagle almost 5X as likely, but that doesn't change that eagle was extremely unlikely either way.  (Buying two lottery tickets may technically double my chances of winning, but the reality is my odds are horrible with one or two tickets.)

LIke I said, I don't have the breakdowns for percentages for the other scores for each option (if I have time I will try and dig them up.)  I think they were fairly even for each option, but don't recall for sure.  But let's assume that in the aggregate, that golfers had the same chance of making birdie, par, bogie or double whether laying up or not.  Would that mean that this was somehow not a good hole?  That is the implication of the suggested methodologies above, isn't it?

[Jason Topp]

I am struggling to understand the terminology.  Golf Digest lists "shot values" in its ranking system as
"How well do the holes pose risks and rewards and equally test length, accuracy and finesse."

"Tangible" - means it has a physical dimension.  "Intangible" means the opposite.  I am not sure what that has to do with anything.  Golf courses are real so it seems to me that their shot values are tangible.

I read the Golf Digest definition as testing the a hypothetical three ball that consists of three players with equal handicaps, one of which is long compared to the others, one is more accurate and one has a better short game.  If they all have a reasonable chance of success on the particular course, the course should score highly in shot value.  

I am not sure it is a very useful criteria because most courses are adequate in this regard.  

[Ulrich Mayring]

Do you use all clubs in your bag and all shots in your arsenal?

That is the question I ask when judging shot values. Obviously, this is highly dependent on the individual player, but then again, everything connected to course evaluation / rating / ranking is.

Ulrich

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