Par Talk

[Steve West]

That's not in the definition...

Thanks, that post helps me understand your position. I'll respond in detail later, but for now, I'll just address your analogy.

A more apt one would be to say that Chevy Malibus are not automobiles because neither the manufacturer nor the model name are mentioned in the definition of automobile.

 

[Doofenshmirtz]

Thanks, that post helps me understand your position. I'll respond in detail later, but for now, I'll just address your analogy.

A more apt one would be to say that Chevy Malibus are not automobiles because neither the manufacturer nor the model name are mentioned in the definition of automobile.

Not really. In fact, that is what is known as a false analogy because neither the model name nor the manufacturer are part of the definition of automobile. In stark contrast to your example, "expert" is a term that is part of the par definition. You are making up your own definition of expert.

So if the following is a definition of an automibilie: "a road vehicle, typically with four wheels, powered by an internal combustion engine or electric motor and able to carry a small number of people," then what you are doing with par is analogous to making up your own definition for "small number." Let's say that you decide that any positive, whole, rational number up to and including 3 is a small number, and any number above 3 or below 1 is not a "small number." Then you might conclude, using your definition, that any vehicle that is capable of carrying 4 or more people is not an automobile.

That is analogous to what you have done with SOCMOBR.

 

[roggenb3]

That is analogous to what you have done with SOCMOBR.

I think you and PM are the only people that take issue with defining an expert as a 1000 rated player.

Why? It seems like such a logical choice....
What is your definition of expert?

 

[lyleoross]

I think you and PM are the only people that take issue with defining an expert as a 1000 rated player.

Why? It seems like such a logical choice....
What is your definition of expert?

Because it doesn't give them what they want. If you define an expert as a 1,000 rated player you lose those easy birdies for average players. The trick is to convince yourself that par has an intrinsic value that fits what you want and isn't a contrived value built to give an outcome. In this case, that average players are expert players cause they gets lots of birdies.

 

[Steve West]

Not really. In fact, that is what is known as a false analogy because neither the model name nor the manufacturer are part of the definition of automobile. In stark contrast to your example, "expert" is a term that is part of the par definition. You are making up your own definition of expert.

So if the following is a definition of an automibilie: "a road vehicle, typically with four wheels, powered by an internal combustion engine or electric motor and able to carry a small number of people," then what you are doing with par is analogous to making up your own definition for "small number." Let's say that you decide that any positive, whole, rational number up to and including 3 is a small number, and any number above 3 or below 1 is not a "small number." Then you might conclude, using your definition, that any vehicle that is capable of carrying 4 or more people is not an automobile.

That is analogous to what you have done with SOCMOBR.

No, that's not a good analogy. Let's try another analogy.

Say we are talking about classifying cars as x-passenger vehicles, where x is defined as "how many people an automobile is able to carry".

I'm saying let's watch each model in use and take the maximum number of people we ever see riding around in it at the same time. Others might say let's measure the width of the seats and divide by 30 inches. Others might say it's however many people the engineer wanted it to carry. Others might say it's how many seat belts it has. Others might say find the cubic inches of the interior and divide by 4500.

We don't need to talk about the merits of each of these methods. The point is, all of these methods are based on, and did not ignore, and do not change, the definition.

 

[Cgkdisc]

The "Expert" in ball golf and disc golf depends on the skill level pars are being set for. In ball golf, the USGA has par standards based on effective hole distance for three experts - Men (typically blue or white tees), Women (Reds) and Juniors (Yellow) - all considered scratch golfers (0 handicap) for their "skill" category. The PGA defines an extreme standard for Tour level play (typically black) which primarily switches a few Men's par 5s to 4s.

Ball golf course architects have additional par standards for Senior Men, Senior Women and Recreational Men that are used for additional sets of tees when desired by the course owners. None of these additional tees have official par standards set by the USGA for handicapping. My assumption is that the USGA Men or Women standards are applied to these tees for handicapping purposes but not necessarily the par values.

Disc golf is duplicating the ball golf approach with multiple "experts" but our "experts" are in several skill levels simply based on rating ranges not age or gender. Our Gold level is equivalent to the 0 handicap Men's scratch standard in ball golf. Our other color skill levels with their own par guidelines emulate the additional "expert" standards defined by the USGA, PGA and course architects in ball golf.

 

[lyleoross]

The "Expert" in ball golf and disc golf depends on the skill level pars are being set for. In ball golf, the USGA has par standards based on effective hole distance for three experts - Men (typically blue or white tees), Women (Reds) and Juniors (Yellow) - all considered scratch golfers (0 handicap) for their "skill" category. The PGA defines an extreme standard for Tour level play (typically black) which primarily switches a few Men's par 5s to 4s.

Ball golf course architects have additional par standards for Senior Men, Senior Women and Recreational Men that are used for additional sets of tees when desired by the course owners. None of these additional tees have official par standards set by the USGA for handicapping. My assumption is that the USGA Men or Women standards are applied to these tees for handicapping purposes but not necessarily the par values.

Disc golf is duplicating the ball golf approach with multiple "experts" but our "experts" are in several skill levels simply based on rating ranges not age or gender. Our Gold level is equivalent to the 0 handicap Men's scratch standard in ball golf. Our other color skill levels with their own par guidelines emulate the additional "expert" standards defined by the USGA, PGA and course architects in ball golf.

I always get this confused. Typically, it seems we are talking about Pro events and elite events at that. So there wouldn't really be multiple experts, just two, that of FPO and MPO, correct?

What is an expert disc golfer, if we assume that it's the equivalent of a zero handicap, rated? It seems to be somewhere significantly below 1,000. In fact, it seems much more like our par is set for an Amateur player. That Amateur player might be considered an expert Amateur player, but he's likely to get his bottom kicked by most Pro players.

 

[Steve West]

First, errorless play goes out the window. You don't worry about errors - because you don't have the data for that. So, if someone nails a tree off the tee box on their drive, that and the subsequent throws go into your data. Arguably, this inflates SOCMOBR par, but who knows? Ultimately this doesn't matter to you because, as you've admitted, you're just trying to get to an arbitrary, and acceptable to you, number of birdies.

Most of that is pretty accurate. Since there is no way to use the data to determine which scores included errors, I have to settle for a method that comes up with the same score that we would get if we did know which scores did not have errors.

It seems self-evident that a significant majority of all throws made by experts are errorless.

While it is plausible that throws at the target end of the hole may have more or fewer errors than drives off the tee or approach throws or scramble attempts, we don't know that. (And anyway, we can't tell how much of each score was made in which parts of the hole.) So, the least speculative choice is to use the same percentage majority for all throws.

By closely examining "errorless" and making conservative choices, we get to the point where picking the scores that were a result of the best x% of throws is a practical way to come up with a number that seems very likely to be the same as the number we would find if we could pick the scores that were a result of errorless throws.

That is NOT ignoring the definition, nor coming up with a new definition. It is coming up with a formula that is the most likely to come up with the same number as the definition.

Second, you don't consult with the TD of the tournament to determine what the TD regards as an expert. You make up your own definition of "expert" with an arbitrary rating chosen solely for the purpose of reducing birdies to another arbitrary number that you deem appropriate. And, your definition of expert, isn't part of the current par definition.

Two issues here:

A. It's true that I do think that par would work better if all TDs used the same level of expert. It's true I also think that the 1000-rated player is the best choice. However, TDs are allowed to choose the 1000-rated player under the definition, so it's wrong to say I'm using a different defintion. I see your point that perhaps they think experts are rated 1025 or are players that can throw 500 feet or whatever. Those also comply with the definition. It's up to the TDs to decide whether their idea of expert is so much better than using a 1000-rated player that it outweighs the advantages of using a common standard.

B. My goal was never to reduce birdies to any particular number. It is to offer the means for TDs to be able to choose to set pars at a consistent level that works best. The number of birdies could still be very high if TDs wanted to adjust or select holes with a goal of more birdies. With any of the methods out there, on a soft course the experts could be getting 8-10 birdies per 18 holes, and the top players even more.

Additionally, you seem to ignore completely other documents when it suits you to do so and then reference them when convenient. For example, the design standards and par guidelines clearly link par to distance and foliage density, but you ignore that, insisting that par is not (or shouldn't be) tied to distance, but then discuss par for different skill levels which is, presumably, derived from those same supporting documents. If it's not, then you are simply giving different meanings to the word expert, something not supported by the definition. "Expert novice" anyone?

Again, two issues here.

A. I've made the point that par is not defined by distance in response to those who insist a score-based method can't be used because they say par is only a measure of distance. In other words, my point was that the definition does not preclude using scores to set par.

I've not argued the obverse: That distance-based methods can't be used simply because distance is not in the definition. Distance-based methods are valid and necessary.

B. I've always said that there is only one true par, and that is based on an expert. I view all the other "skill level" pars as something else. They don't fit THE definition, but they fit a definition where the only change is that "expert" is replaced by a player of another skill. Whatever that is, it is analogous enough that is makes sense to use the term "par" - if is it paired with a qualifier, such as "novice par".

(By the way, weren't you saying up there that TDs could choose whatever expert they want? Would you let them choose an Expert novice?)

Perhaps the worst part of what you do, .... without falsely claiming that TDs are "inaccurately" setting par.

I'll take all that as good advice. Thanks.

And until the design standards, par guidelines and par definition are all aligned and the PDGA decides who an expert is, your errorless and distanceless SOCMOBR analysis that uses its own definition of "expert" will always use a different definition of par than the one promulgated by the PDGA.

My method is a practical implantation of the definition. The PDGA par guidelines were calibrated to my method using a 1000-rated player as the expert. The Gold design guidelines are for players of over 969 rating which, as a group, average 1000. These three are as aligned as they can be given the goal of leaving the TD complete freedom to set par as they see fit.


Now, since you mischaracterized this whole thread as an attack on birdies, is that what you are really worried about?

 

[PMantle]

Because it doesn't give them what they want. If you define an expert as a 1,000 rated player you lose those easy birdies for average players. The trick is to convince yourself that par has an intrinsic value that fits what you want and isn't a contrived value built to give an outcome. In this case, that average players are expert players cause they gets lots of birdies.

I see you're still just making things up.

 

[PMantle]

Now, since you mischaracterized this whole thread as an attack on birdies, is that what you are really worried about?

What? That's all you're doing in here. Even your sycophants think so.

 

[Doofenshmirtz]

It seems self-evident that a significant majority of all throws made by experts are errorless.

So, the least speculative choice is to use the same percentage majority for all throws.

By closely examining "errorless" and making conservative choices, we get to the point where picking the scores that were a result of the best x% of throws is a practical way to come up with a number that seems very likely to be the same as the number we would find if we could pick the scores that were a result of errorless throws.

That is NOT ignoring the definition, nor coming up with a new definition. It is coming up with a formula that is the most likely to come up with the same number as the definition.

It's all speculation and you simply aren't willing to acknowledge that your are speculating. To what degree, you don't know because you don't have the data. Not that it matters.

A. It's true that I do think that par would work better if all TDs used the same level of expert.

We disagree on this at a fundamental level. Par already works as it should. It worked before the definition change. It works now. And it would work equally well if the definition was changed again to SOCMOBR for tournaments (though I'm pretty sure that would be widely ignored). It would work if EMBR were used for tournaments. All of these are equivalent in outcome and usefulness. Changing par relative to tournament scores doesn't make it work any better. I suspect, based on your prior writings, that you have real golf in mind when you choose how many birdies that you want (and you have previously admitted using your expert definition because of the number of birdies that result).

Let me offer an example. My wife sets her clock ahead so that she will get up early. She could just set the alarm to an earlier time. When she looks at the clock for time, she deducts the minutes she has set it ahead. I think that is a bit silly, but it works for her. I don't use her clock so I don't care. Less accurate/useful? Neither.

B. I've always said that there is only one true par, and that is based on an expert. I view all the other "skill level" pars as something else.

And yet, when I read the definition, it doesn't name you as arbiter of par. It names the TD. But you do like making up your own definitions. This is just one example.

(By the way, weren't you saying up there that TDs could choose whatever expert they want? Would you let them choose an Expert novice?)

We will likely never agree on many things. That a novice is not an expert is one of them. A TD can set par however they like but he cannot create "expert" novices by decree. The guidelines made some sense when par had a distance component. They are simply disconnected to the par definition at the moment. Novices do not play errorlessly. If SOCMOBR was used to set the "skill level" differences in the guidelines then the result makes sense due to the failure to account for errors. So do you think the majority of novices' throws are also errorless? Or does the red level "par" account for play that includes errors? Or did you just make it up, ignoring the par definition?

My method is a practical implantation of the definition.

I have no doubt that you believe that.

SOCMOBR is anything but practical. And you have substituted your definitions for all vague/ambiguous terms, making up your own par definition in the process.

Now, since you mischaracterized this whole thread as an attack on birdies, is that what you are really worried about?

You have admitted that SOCMOBR is for birdie reduction. You may call my claim that you are trying to reduce birdies a mischaracterization if you must, but birdie reduction it is.

I'm sure you have, or can come up with, a good explanation of why you should be entitled to define par however you like and then criticize others for not following your definition, but those explanations/rationalizations don't change what you are doing.

 

[Steve West]

We disagree on this at a fundamental level. Par already works as it should. It worked before the definition change. It works now.

[SARCASM]Sure, par works just fine, all the time.[/SARCASM]

Seriously, though, par is a lot better than when the thread started. The general trend is toward a more standard and appropriate par. All it takes to make par better is just a little bit of thought and effort. When that happens, TDs generally get to about the same result, because there IS an optimal level.

And it would work equally well if the definition was changed again to SOCMOBR for tournaments (though I'm pretty sure that would be widely ignored). It would work if EMBR were used for tournaments. All of these are equivalent in outcome and usefulness. Changing par relative to tournament scores doesn't make it work any better.

You're just wrong that changing par would not make it work better. It works provably better at some of the things par is supposed to do, when it is changed from a par that was not set at the appropriate level, or when it changed from a way that does not fit within the definition.

Sure, if you are in the camp that only cares about final results, then we don't need par at all, so any par will do nothing at all equally well.

However, if you want bogeys to be equal in impact to birdies, there is a very specific level that does that the best. If you want contender's to be able to have scores that don't vary much from par, that is a calculable level. Anything other than that level doesn't do that as well. If you want par to be consistent from round to round and course to course, then you want the level that will minimize the differences between scores and pars for a consistent skill level. All three of these optimal points happen to be the level at which everyone who has worked out a method of setting par has arrived at independently. Not just me.

Par has been improved. The awakening has already happened. See the biggest, best-run tournaments. They are leading the way. Now that players have a chance to experience better pars, they'll carry those expectations to other events. Now that the tools are available to set better pars, it's easy for TDs to do better.

If you want to dig in your heels and resist or reverse the change, you'll need to provide reasons why we should not continue to change. A steady steam of side attacks at any little flaw or inconsistency (real or otherwise) you think you find in tangentially related issues won't be very convincing.

I suspect, based on your prior writings, that you have real golf in mind when you choose how many birdies that you want (and you have previously admitted using your expert definition because of the number of birdies that result).

Your suspicions are wrong. I didn't even look at golf until I had developed my method. After it was done, I looked at how it would work on golf scores. I was surprised that it worked nearly perfectly. So it's got that going for it, which is nice for those who think disc golf par is not valid unless it is exactly like golf par. I'm not in that camp, but I can see the advantages.

But, did you think that if I admitted I had real golf in mind, you'd be successful in stopping and reversing any progress in improving par?

And yet, when I read the definition, it doesn't name you as arbiter of par. It names the TD. But you do like making up your own definitions. This is just one example.

Nobody has disagreed with any of this. How does it relate to what you are afraid is happening?

We will likely never agree on many things. That a novice is not an expert is one of them. A TD can set par however they like but he cannot create "expert" novices by decree. The guidelines made some sense when par had a distance component. They are simply disconnected to the par definition at the moment.

All methods of setting par are disconnected from the definition to some extent. If you want to attack any particular method of setting par on a purely theoretical basis, you could dismiss any or all of them. And yet, there are many methods that produce results that are good enough, and better than whatever a lot of TDs used a few years ago. The question is whether the game will be better off it they are used than if they are not.

Prove to us the game will be better if no one uses the guidelines.

Novices do not play errorlessly. If SOCMOBR was used to set the "skill level" differences in the guidelines then the result makes sense due to the failure to account for errors. So do you think the majority of novices' throws are also errorless? Or does the red level "par" account for play that includes errors? Or did you just make it up, ignoring the par definition?

The differences in the guidelines would be about the same no matter what method was used to generate them. Again, all well-thought-out methods agree on the general level where par should be.

Novices do sometimes make errorless throws. The extra errors that are made by lower skill levels are reflected in guidelines. The errors are not forgiven. What I mean is that it is actually less likely that a Novice will shoot Novice par, because they have more errors to not make.

But, what should we go back to instead? And why?

SOCMOBR is anything but practical. And you have substituted your definitions for all vague/ambiguous terms, making up your own par definition in the process.

Practical for generating pars for thousands of holes at a time, which was its primary purpose. Not practical at all for holes no one has played. Doesn't matter, that's not a reason to leave par as it was, because the other practical methods all produce similar results.



But, educate me, what is the correct way to deal with vague/ambiguous terms in a definition when building a practical method to implement it?

While you are at it, please describe "how par works now", so we know what exactly you are defending.

 

[lyleoross]

I see you're still just making things up.

So you're saying that basing par on a 1000 rated player wouldn't eliminate some birdies? Or are you saying that it wouldn't take away some of what you want? Given that there's are pages of comments here where you argue against it because it isn't what you want, I'd have to say the evidence is clear that you don't want it. Are you saying you don't want it even though your do but some greater moral value leads you to go against it?

In fact, I stated exactly what your position is. You don't want it cause it doesn't fit your perception of how it should be. That's okay, I'm stating my position of how I want it to be and why. The difference is that my position is always the same and your's changes as posters show your points don't have merit. I still remember the disc golfers get more birdies because they're better than ball golfers comments someone posted. Then after a while, you guys recycle the same points saying no one has addressed them. Intermittently you insert a you have no clue comment, a flat nope, or a your dumb has heck comment because no one gets it like you do.

 

[PMantle]

So you're saying that basing par on a 1000 rated player wouldn't eliminate some birdies? Or are you saying that it wouldn't take away some of what you want? Given that there's are pages of comments here where you argue against it because it isn't what you want, I'd have to say the evidence is clear that you don't want it. Are you saying you don't want it even though your do but some greater moral value leads you to go against it?

In fact, I stated exactly what your position is. You don't want it cause it doesn't fit your perception of how it should be. That's okay, I'm stating my position of how I want it to be and why. The difference is that my position is always the same and your's changes as posters show your points don't have merit. I still remember the disc golfers get more birdies because they're better than ball golfers comments someone posted. Then after a while, you guys recycle the same points saying no one has addressed them. Intermittently you insert a you have no clue comment, a flat nope, or a your dumb has heck comment because no one gets it like you do.

I don't want anything in particular, and you are still making things up.

your's changes as posters show your points don't have merit.

This is just an absolute lie. Oh, and I really do think there is something wrong with your though processes. There's no other explanation for the nonsense you keep posting.

 

[Steve West]

Play nice everybody.

 

[lyleoross]

I'm not being mean. The argument went from:

1) We get more birdies because we are better athletes than golfers
2) The disc golf rule is strokes plus two (it's been pointed out statistically that it doesn't fit the game we play, but the reply was, it has to be that way cause that's how it is done in golf and it was once written in our rules that way).
3) The ball golf guys do it this way.
4) Disc golf is easier than ball golf

BTW - given that golf has at least two methods they use, stokes + two, and distance, how is par determined there? I mean do the guys go out before the course is in and play in the empty fields?

Then round and round and just last week Doof rolled out, the Disc golf is easier idea again and wrote, "you still haven't answered this question," even though it had been answered before. Just a couple of weeks ago PM wrote that the standard way that all par gets laid out in golf is before the course is in the ground, even though we've gone through that before too. IIRC, even PM has posted things that show that par gets adjusted for different kinds of events. Then we come back to a discussion centered around adjusting par for every course, even though it's been stated numerous times the discussion centers around major events only, sort of like what ball golf does for majors and in certain situations.

I stand by what I wrote. The same old points keep coming up even after they've been answered.

Typically, in online debates, if you can't answer the point, you resort to name calling. That always seems to be where we end up.

 

[DavidSauls]

Par has been improved. The awakening has already happened. See the biggest, best-run tournaments. They are leading the way. Now that players have a chance to experience better pars, they'll carry those expectations to other events. Now that the tools are available to set better pars, it's easy for TDs to do better.
.

Plus, since this thread began, the PDGA has ditched the troublesome "two throws from close range." I have no reason to believe that this thread had anything to do with that....but I enjoy thinking that it might have, anyway.

Better par. Better definition. Progress.

 

[PMantle]

I'm not being mean. The argument went from:

1) We get more birdies because we are better athletes than golfers
2) The disc golf rule is strokes plus two (it's been pointed out statistically that it doesn't fit the game we play, but the reply was, it has to be that way cause that's how it is done in golf and it was once written in our rules that way).
3) The ball golf guys do it this way.
4) Disc golf is easier than ball golf

BTW - given that golf has at least two methods they use, stokes + two, and distance, how is par determined there? I mean do the guys go out before the course is in and play in the empty fields?

Then round and round and just last week Doof rolled out, the Disc golf is easier idea again and wrote, "you still haven't answered this question," even though it had been answered before. Just a couple of weeks ago PM wrote that the standard way that all par gets laid out in golf is before the course is in the ground, even though we've gone through that before too. IIRC, even PM has posted things that show that par gets adjusted for different kinds of events. Then we come back to a discussion centered around adjusting par for every course, even though it's been stated numerous times the discussion centers around major events only, sort of like what ball golf does for majors and in certain situations.

I stand by what I wrote. The same old points keep coming up even after they've been answered.

Typically, in online debates, if you can't answer the point, you resort to name calling. That always seems to be where we end up.

1) who ever said that is just crazy/ignorant.
2) not really worth discussing
3) That does have at least some merit. The problem with it has been pointed out repeatedly-putting in disc golf is WAY easier than golf, and lack of multiple tee pads.
4) It is WAY easier in every aspect.


I'll say it again since you didn't grasp it the other 8 times: Golf pars are predetermined. The course is, more likely than not, going to be a par 72 with two 5s and two 3s per side. Those pars will be based on distance, period. Those pars are never changed by anyone other than the USGA who holds one tournament per year for the various groups that qualify. The PGA Tour, The PGA of America, and the R&A never change par(3 of the 4 majors). When the USGA does it, it has nothing to do with statistics from past play. It is always to make two 5s into 4s to obtain a par 70. When they do this, they often leave a driveable par 4 which gets eaten alive by the players.

What points haven't been addressed?

Look, you've been wrong about everything having to do with golf. You have placed words in my mouth repeatedly that are totally false. You really should be banned.

 

[gdub58]

Par has been improved. The awakening has already happened. See the biggest, best-run tournaments. They are leading the way. Now that players have a chance to experience better pars, they'll carry those expectations to other events. Now that the tools are available to set better pars, it's easy for TDs to do better.

Pars haven't improved - hole design has improved. While this results in having more holes with assigned pars that are more in line with expectations, I think it is a reach to attribute this change to par-setting tools.

Your method doesn't set pars - it evaluates them. Looking at average scores and par percentages does the same thing. Adding graphs and arbitrary expected error rates may make some people see your method as more credible, but given that no method can account for differences in field composition, weather, and so forth it is pointless to argue for or against any particular approach.

What is abundantly clear is that the top tier tournaments have separated themselves in a way that has increased their standing and appeal in the disc golf community, and that is through better course design. Top pros are playing challenging courses with longer holes, more hazards, and trickier greens than ever. This provides a better experience for the spectators and allows these players to show just how much better they are than the rest of us - that's what any sport needs to have a viable pro tour.

As for par, we all have a good idea of what it means - the specific definition, filled as it is with ambiguous terms, doesn't provide any clarity even if you try to define those terms. Ball golf used to have specific guidelines for par (<235 yards = par 3, >470 yards = par 5), but changes in equipment and player conditioning made those obsolete.

It appears that disc golf is at least trying to follow ball golf in that there are par threes, par fours, and par fives. So far, thankfully, no par twos - short holes are being made more challenging with OB and other hazards. There are some "must birdie" holes, and some where getting a par will gain you a stroke on a large percentage of the field. That's the way it should be IMO. I also remain convinced that every hole should offer the possibility of a birdie for the 1000 rated player, even if that means increasing the par and turning it into a "must birdie" hole.

I think we as a community can take credit for showing the PDGA that par does matter to us and that we are willing to support a pro tour that looks different than a B-tier event played at your average local course. That said, at this point I don't think they need us to tell them that hole 14 should have been a par 3 instead of a par 4...

 

[DavidSauls]

Meanwhile, moving forward (heel-draggers, feel free to sit this one out)---

As par moves towards actually being the expected score on each hole, pondering what would make the best difficulty scale for a hole, or a course.

For the course as a whole, one simple one would be the difference between the total of the pars, and the 1000-rated round. Assuming you have enough rated rounds in good weather to nail down the SSA fairly well. So if the total of pars came out to 65 , and the average SSA 60.5, the course could have an difficulty factor of -4.5.

But perhaps it could be done for individual holes, too---if anybody was interested. Where par is the expected score, some holes are going to yield more birdies than bogeys (and above). Others, hopefully, will yield more bogeys. So while the expected score keeps pace with the field, some holes will give better opportunities to gain ground; some pose bigger danger of losing ground.

Would average score be the best number to use? It incorporates errors and bad luck and OBs, but then again, those affect the field as a whole. So a par 4 with an average of 3.8 might have a difficulty factor of -0.2; one with an average of 4.2, +0.2.

And the sum of the individual hole factors could be the course's factor, though that's probably not much different than calculating par vs. SSA.

Just thinking aloud, wondering whether, if par were the expected score, and we had enough numbers, we might produce some more interesting data from it. Nothing important; perhaps not even useful; but an interesting comparison of courses, and perhaps an interesting tidbit for spectators to know where the biggest opportunities and pitfalls lie.