Hole and Course Performance Statistics

[Steve West]

This is a spin-off from the "Multiple pins - why?/why not?" thread.

Here are the gaps Chuck was looking for in his quest to make sure all holes offer enough birdies.

Bottom Line: If we set the gaps so at least half the holes of that score offer 10% birdies or more, then no par 3 hole should average over 3.22, and no par 4 hole should average over 4.42, and it gets fuzzy after that but perhaps no par 5 should average over 5.33.

This does not mean that par should be adjusted higher when the average score exceeds these limits.

This means those holes should be wiped from the face of the earth. (Or made easier so as to bring the number of birdies up, or made harder so they are legitimately the next higher par.)

If the gaps were based on hole lengths, they would tell us that no holes should be between 445 and 500 feet long, nor between 830 and 990 feet long.

I must point out that ranges based on lengths or even average score would be far less effective than a straight-forward look at the number of birdies actually generated. If a hole doesn't produce enough birdies, change it. We have the data, we can do that sort of thing now.

 

[DavidSauls]

This means those holes should be wiped from the face of the earth. (Or made easier so as to bring the number of birdies up, or made harder so they are legitimately the next higher par.)

I disagree. I think there's a place for what I call "tough par" holes, where birdies are unlikely but bogeys a real danger.

I wouldn't want to play a whole course of them, and there's an argument that they create more separation in the bottom half of the field than at the top, but that doesn't mean they're not fun or challenging or both.

 

[Steve West]

I disagree. I think there's a place for what I call "tough par" holes, where birdies are unlikely but bogeys a real danger.

I wouldn't want to play a whole course of them, and there's an argument that they create more separation in the bottom half of the field than at the top, but that doesn't mean they're not fun or challenging or both.

I was awkwardly trying to semi-channel the school of thought that every hole should be birdie-able; to jiu jitsu the thinking away from "just add one to the lowest score".

If the goal of a course is to separate players by performance, it can be shown mathematically that a 10/70/20 (par 3) distribution is no better than a 70/20/10 (par 2), or a 20/10/70 (par 4). In fact, the non-conformist distributions actually contribute more, because - as you point out - they sort out a different, under-sorted part of the field.

But measuring skill is only one goal for courses. Another is fun. When at least two of the top designers take the stance that every hole should be birdie-able, that's proof that it is a good way to design courses.

However, it is not always good way to set par for holes that weren't designed that way.

So, I want to enable that design philosophy in a way that doesn't distort par.

An analogy might be training a dog. It can be done with treats or a shock collar, or a combination of both. The trainers who only use treats will be more popular with the dogs, even if adding the occasional shock might be more effective. But, a trainer shouldn't give out a treat when the dog doesn't do the trick.

 

[chevis]

I disagree. I think there's a place for what I call "tough par" holes, where birdies are unlikely but bogeys a real danger.

I wouldn't want to play a whole course of them, and there's an argument that they create more separation in the bottom half of the field than at the top, but that doesn't mean they're not fun or challenging or both.

yeah! just cuz chuck thinks there is a right to birdie every hole, doesn't mean he's right. par has a wide range. "par is the expected score" so you're going to end up with some hard/soft par holes.

 

[DavidSauls]

The "every hold should be birdieable" philosophy also runs into this: Even if a course is well-designed for its target skill level and every hold is birdieable for them, players who are below that skill level still play and enjoy it. Some of those holes will be "tough pars" for them /I]-- they may not birdie, but they still have to play well to save par. Those holes don't seem to dissuade a lot of players from enjoying that course.

 

[jeverett]

It was very interesting to see that local maximum at ~3.22! Just as a general design guideline, I've always assumed it to be roughly 3.3, so it's nice to have solid data suggesting it might really need to be a little lower than that. On the topic of this:

If the goal of a course is to separate players by performance, it can be shown mathematically that a 10/70/20 (par 3) distribution is no better than a 70/20/10 (par 2), or a 20/10/70 (par 4). In fact, the non-conformist distributions actually contribute more, because - as you point out - they sort out a different, under-sorted part of the field.

.. I think one big challenge for design is that while 10/70/20 is quite common "in the wild", 70/20/10 and especially 20/10/70 often don't actually exist on real holes. e.g. By the time a hole reaches ~50% 2's, it's pretty unlikely to produce 4's at all (if the target group is minimally 900+, anyway). So you're much more likely in that case to get 70/30, not 70/20/10. Similarly, by the time you're hitting 70% 4's, still producing 20% 2's is highly unlikely.. you'd likely see something more like 0/10/70/20.

 

[Steve West]

yeah! just cuz chuck thinks there is a right to birdie every hole, doesn't mean he's right. par has a wide range. "par is the expected score" so you're going to end up with some hard/soft par holes.

Sure, if you set the right par for every hole out there you will get some unbirdie-able holes. However, it is possible to design holes that do offer chances at birdie. If someone wants to design all holes that way, it wouldn't be a bad way to do it.

No one ever complains that Houck designs are bereft of unbirdie-able holes.

What we're looking for here is a way to codify how to design holes that always offer a chance at birdie.

 

[Cgkdisc]

Birdieability is not "Chuck's rule" but simply reiterating a game design fundamental in "golf". Scoring a "birdie" or better is how a player "scores" as an individual against the course. The player tries to score against the challenge on each hole in a course layout, not against other players. There are 7 or so different hole length guidelines in ball golf where players of that skill level have a realistic potential to birdie every hole (score) from that set of tees and potentially shoot par without a handicap that they can determine when playing longer tees. We could develop a similar set of hole length ranges for DG skill levels.

In any game design, the designer needs to specify how a player scores and how many points are awarded or subtracted for various actions in the game. In golf, shooting a birdie is scoring a point, an eagle scores 2 points. Shooting par is "not scoring" similar to scoring zero (shot on goal but not scoring) in many games. Earning penalties and/or shooting bogey or higher is scoring negative points. Again, this is individual scoring against the course, not comparative scoring in competition. It's weak game design from an individual standpoint if a player is prevented from a reasonable opportunity to "score" when playing a unit in a game designed for their skill level whether a hole in golf, a frame in bowling or a turn in darts, for example.

Consider commentary in some of our other threads regarding par. We've heard that many players intrinsically believe holes should be birdieable for their skill level. Note the resistance to having legitimate par 2s per Steve's calculations, i.e., you can't realistically birdie a par 2. Their underlying concept is that every hole should be birdieable for a field of similarly skilled players. Attendant to that underlying feeling is the idea that "par" should be their best expected score on a hole + 1. Of course, setting par this way would make every hole birdieable, but several holes would be 1 higher than Steve's criteria for par and also those "padded par" holes would likely produce too many (over 60%) birdies.

The concept of all holes being birdieable for a player (in the 10% to 60% range) provides potential "scoring separation" for that player and others at their skill level who can also reach those holes. However, we know that players of other skill levels higher and lower are also likely to play that course layout in competition. In which case, several of those birdieable holes for the layout skill level will either be too birdieable (easy) or not birdieable in relation to the par values set for that hole layout.

That's where incorporating skill-based elements in each hole design will produce good skill-based scoring separation regardless of player skill level. Otherwise, those who throw farther within the division will have a few holes where only they have a realistic chance at birdie. Even if they only get one or two in a round or event, it's an unfair competitive advantage when only they have the birdie potential.

Spectators and players have become more aware that birdies are how you score in DG when they see a string of blue cells in UDisc scoring whether watching competition or playing in leagues or recreationally. Confusing the issue for those following elite event scoring is the expectation that the goodness of a great round is measured by how many under par a player threw. For that under par number to truly be meaningful across all courses played in the DGPT, every hole should be birdieable in the MPO layouts and also in the shorter layouts for FPO. Otherwise, a -12 on a course where three holes were unbirdieable by the field is not considered "better" than a -13 on a course where every hole was birdieable and perhaps one or two eagleable. The idea of potential birdieability of every hole for a skill level provides a more consistent way for publicly comparing rounds. Of course, using round ratings is more accurate but less understood and more controversial.

 

[glassila]

In my area when someone says "holes should be birdiable" they really mean "holes should be EASILY birdiable".:wall:

I think a course should have 20% easy birdies, 60% tough birdies and 20% tough pars.

Easy birdie = birdie 40-50% of the time.
Tough birdie = birdie 20% of the time.
Tough par = par 60% of the time and very difficult to birdie.

 

[Cgkdisc]

The underlying factor for birdieability is reachability in regulation whether ball golf or disc golf. If a hole can't be reached in regulation with an accurate throw, it's not reasonably birdieable. So, the issue when looking at scoring stats on a hole for a division is whether birdies are distributed uniformly or to only the longest throwers. To make sure birdies are distributed uniformly among all players in the division, who have demonstrated they belong based on rating, the ideal design would only include hole lengths players could reach in 1 throw (par 3) AND no holes just a little bit longer that only the longer throwers can reach.

In other words, there should be a hole length gap between holes that most in the division can reach in one throw and hole lengths that most in the division can reach with two good throws (par 4s). That's the way to produce scoring in the division based more on skill than distance. Even by doing this, having excess distance/power over many in the division will still be rewarded if you can reach holes with rounder edged, more controllable discs than those who need drivers. But at least getting the hole length ranges set up well for a skill level, everyone has a puncher's chance to contend with better accuracy using drivers.

A simple way to achieve this ideal for courses would be to establish course levels based on reachable hole lengths for par 3s starting with 150' max, 200', 250', 300', 350', 400', 450' max. That's seven max effective hole length ranges for par 3s. Effective length takes into account elevation, water carries and doglegs. It will take some additional research to determine the min/max length ranges for par 4s in each level but that can be done. Same process to determine min/max length ranges for par 5s.

Once these length ranges are established, designers can design good holes for specific layout levels. Existing course owners can adjust their layout(s) on a few holes one way or the other if needed to meet a layout guideline. The beauty in this approach provides measurables (length) for designers to use without estimating how to design for a player skill level which is more abstract.

For players, they simply know that on this level of course layout, they have to be able to accurately throw 300' in order to have chance at birdies on the longest par 3 holes and to contend with others who have that distance range. In order to realistically contend on a 350' layout, they need to boost their accurate distance by 50ish feet or make sure they're competing with others who mostly have 300' distance like themselves. This has typically been the case for women and older divisions although playing layouts with several holes beyond your distance ability to reach them in regulation is more likely to lower your rating when players in other divisions can reach them.

 

[Steve West]

... Attendant to that underlying feeling is the idea that "par" should be their best expected score on a hole + 1. ...

I wish you would not keep rubbing up against the idea that par is the expected score plus one. Sure, that would be an easy big-bang way for all holes to be birdie-able, but resist the temptation to nudge popular thinking in that direction. It's wrong and would hurt the game.

"Best" and "expected" are usually different. They shouldn't be muddled together.

Saying par is the expected score plus one is just plain wrong. Par, by definition, is the expected score.

Saying par is the "best" score plus one is not as wrong. On holes where the best score is better than the expected score, par is best score plus one.

If, as your phrasing suggests, the best score is always expected, then par is the best score.​

"Reachable with a good throw plus two" is also problematic.

If reachable with a good throw means a player can expect to throw the disc within one-putt range, reach plus two will not match the definition of par.

If reachable with a good throw means a player can expect to throw the disc only to close range (where two more throws are expected to complete the hole), reach plus two may match the definition of par.

If reachable with a good throw means a player needs a better-than-expected throw to get within one-putt range, reach plus two may match the definition of par.​

You might claim you are standing behind one of the last two definitions, but we both know that if a player says they can reach a basket, they mean they will usually get all the way there with one throw. At least insert "exceptional" into the phrase.


Having said all that, I do support the idea of trying to find lengths so holes actually offer some real birdies. What bothers me is that the phrases you use indicate that you've not fully disavowed the idea that setting par as one more than the expected score is the way to make more birdies.

 

[Cgkdisc]

Note I didn't say a player's "Expected Score" but their "Best Expected Score" which "should" be a birdie with par set on that hole for that skill level for a field of players at that skill level. Perhaps "Reasonable Potential Score" would be a better term for what a player would think should be a birdie on a hole suited for their skill level.

 

[Steve West]

Note I didn't say a player's "Expected Score" but their "Best Expected Score" which "should" be a birdie with par set on that hole for that skill level for a field of players at that skill level. Perhaps "Reasonable Potential Score" would be a better term for what a player would think should be a birdie on a hole suited for their skill level.

The definition says "would be expected to make", not "thinks should be a birdie plus one". It's an important distinction.

You can color within the lines and still refine course design. Just say one better than par to refer to birdie.

If a birdie wasn't better than something, it wouldn't be improving the score, would it? It actually makes more sense - and introduces less confusion - to say every hole should reward better-than-expected play.

(Rather than say every hole should allow a player to score one less than something plus one.)

 

[johnrhouck]

Lots of important theoretical discussion going on.

Here's what would help me: would someone please name a hole or two that we would consider a "good" hole that almost never gets birdied. Talking about a real-life example might make the conversation easier. Thanks.

 

[Cgkdisc]

Lots of important theoretical discussion going on.

Here's what would help me: would someone please name a hole or two that we would consider a "good" hole that almost never gets birdied. Talking about a real-life example might make the conversation easier. Thanks.

It would be inconsistent to consider any holes "good" for a player skill level, if not birdieable, when you agree with the "reasonably birdieable for a player skill level" school of thought. But there are thousands of holes that many consider "good" whether being fun, aesthetically beautiful, challenging and many with decent scoring separation but the listed par has not been set so those holes are birdieable for some player skill/distance levels.

At the elite MPO/FPO level, Waco provides a good example where the pars on the holes have typically been set for a mix of blue & gold skill/distance levels, just above the skill/distance level for FPO and below the skill/distance level for MPO. The MPO & FPO hole scoring stats from the 2022 event provide several examples where simply changing the par on some holes would have made every hole birdieable for that player skill level. However, by following the PDGA par guidelines for a skill/distance level, the pars on several holes played by MPO should have been set lower to where they would not have been birdieable.

Hole 7 specifically touches on Houck's question regarding a "good" hole that's not birdieable. I believe Steve would say that par should have been set at 3 for MPO which would turn the 60% birdies into pars with no birdies thrown and the 36% pars would become bogeys. The scoring spread still remains the same and reasonably good. FPO played the same tee as MPO on hole 7, providing 36% birdies, 47% pars, and overall good distribution. With regard to the hole design, it was a reasonable challenge for players to execute getting out of the wooded chute off the tee, then landing a technical upshot over a gully.

From a design standpoint, moving the basket back 30 feet if possible, might have been an improvement so throwing cleanly through the gap over the gully is more rewarding. Moving back the tee for MPO if possible, may also have made the hole "better". But this was a hole design intended for blue level.

The ideal situation would be to provide layouts with 18 well-designed, reasonably birdieable holes for each player skill/distance level. However, an ideal layout where every hole is considered "good" and reasonably birdieable for skill/distance level X will have several holes that will turn out to be either too birdieable or not birdieable for the player skill/distance level above or below level X.

We're now faced with the key question, "Is it better to set the par on holes for those skill/distance levels above or below level X to where":
(A) Every hole is birdieable, even if the percentage is considered too high (>60%), or
(B) Par is set according to PDGA guidelines, even if that means some holes will not be birdeable?

Birdieability on every hole for a player skill/distance level is:
1. more fun for players (IMO) whether playing solo or in competition against the layout,
2. more easily understood by both players and spectators as "scoring" on a hole,
3. a metric to discuss/compare easy vs average vs tough holes,
4. a more understandable metric to design reasonably birdieable holes for a skill/distance level.
5. consistent with ball golf scoring design.

 

[Steve West]

Lots of important theoretical discussion going on.

Here's what would help me: would someone please name a hole or two that we would consider a "good" hole that almost never gets birdied. Talking about a real-life example might make the conversation easier. Thanks.

I'm not going to stick my neck out to call any hole good or not, but here is a list of candidates where a good low-birdie hole might be found.

From my list of holes with at least 20 rounds of MPO data in 2022, I selected the holes where:

tournament par agreed with guideline par,
the frequency of birdies was less than 2%, and
the scoring spread was greater than 2.00.​

 

[Cgkdisc]

Would increasing the par by one on each hole above have materially impacted their scoring and spread? Most look-like "easier" birdie holes where par has been "artificially" lowered so they appear more difficult, especially the second and third holes where the par was set more than 1 stroke below their average score (I know average score is not always "par" in Steve's calcs). I suspect on several of these holes, (sometimes artificial) aggressive OB was used to increase scoring spread and average.

Interestingly, Steve didn't include any holes that scored as legit par 2s (PDGA def) because none were set by TDs as par 2s for various reasons, one being non-birdieability as a par 2. But I'm thinking there are a few dramatic downhill and/or island holes where the scoring would indicate they are par 2s per PDGA def AND would also be considered "good" holes under some criteria other than scoring such as drama, aesthetics or scoring spread (likely from OB penalties).

 

[Steve West]

Would increasing the par by one on each hole above have materially impacted their scoring and spread? Most look-like "easier" birdie holes where par has been "artificially" lowered so they appear more difficult, especially the second and third holes where the par was set more than 1 stroke below their average score (I know average score is not always "par" in Steve's calcs). I suspect on several of these holes, (sometimes artificial) aggressive OB was used to increase scoring spread and average.

Interestingly, Steve didn't include any holes that scored as legit par 2s (PDGA def) because none were set by TDs as par 2s for various reasons, one being non-birdieability as a par 2. But I'm thinking there are a few dramatic downhill and/or island holes where the scoring would indicate they are par 2s per PDGA def AND would also be considered "good" holes under some criteria other than scoring such as drama, aesthetics or scoring spread (likely from OB penalties).

Has anyone actually ever heard of a case where a TD artificially lowered par?

For Fox Run 7, if there were no scores higher than bogey, the average would have been 5.62. A full 20% of the scores were double-bogey or worse. Yes, there was a lot of OB. But, there is nothing stopping any one from making three 350-foot open placement shots to get to 175 feet from the target for down in two more. That seems like a par 5 to me. Also, each throw had an 81% chance of contributing to a birdie score. That's lower than the average of 92%, but higher than the guideline cut off of 77%. A tough par 5, but still a large majority of throws were good enough for par. It's not hard to imagine that 19% of the throws on this long narrow fairway were not errorless.

For Hole 15 at the Sula Open, it's right on the bubble between guideline par 4 and par 5, and 24% of scores were double-bogey or more (which increased the average by 0.12). If the TD had set this as par 5, I wouldn't argue with that judgement. One the one hand, you would think a 1000-rated player could manage two 375-foot throws to get within 200 feet to get up and down in 4. One the other, those throws would be tougher on this hole because there are more obstacles actually in the fairway. Maybe three 250-foot putter throws that miss the trees to get within 200 feet for a 5 is good enough to keep up with the field. Either par is justifiable.

For both holes, perhaps there would have been lower scores if par was higher; because the players who think that the only good score is a birdie would have played safer. To me, those extra throws for going out of bounds by trying to get a birdie are fair punishment for not understanding that par is a good score and birdie is a better score.

I didn't include any par 2s, nor any other holes where par was different than guideline, because I wanted to separate the issue of "can an unbirdie=able hole be good?" from "was this par correct?". If we can find any good holes among this group, then we can say the answer is "yes"; so let's look here first. If we can't find any here, we can look among the par 2s and other holes where par was higher than guideline.

 

[Cgkdisc]

Par is no score at all, like a shot on goal that misses, where the course says, "Not this time. Try again on your next attempt to score (birdie)."

Here's where the PDGA definition for par fails the "game of golf" as an individual playing against the course with no one else around. On holes where pars are set per the PDGA definition such that some are unbirdieable, the player only knows that shooting par is a good score on those holes in reference to competitors at their skill/distance level, not the hole itself. However, in ball golf, the definition explicitly defines par in a way where the player knows a birdie on every hole is reasonably possible for players of the skill/distance level the tees are designed for. Competition scores are not required to identify whether par is "good" or birdie is "scoring" on various holes in normal weather conditions.

 

[Steve West]

Par is no score at all, like a shot on goal that misses, where the course says, "Not this time. Try again on your next attempt to score (birdie)."

Here's where the PDGA definition for par fails the "game of golf" as an individual playing against the course with no one else around. On holes where pars are set per the PDGA definition such that some are unbirdieable, the player only knows that shooting par is a good score on those holes in reference to competitors at their skill/distance level, not the hole itself. However, in ball golf, the definition explicitly defines par in a way where the player knows a birdie on every hole is reasonably possible for players of the skill/distance level the tees are designed for. Competition scores are not required to identify whether par is "good" or birdie is "scoring" on various holes in normal weather conditions.

You think "a good score on those holes in reference to competitors at their skill/distance level" is different than a good score on "the hole itself"? That's a concept I'm not capable of grasping. Explain the difference.

Show me in the golf definition of par where it says par is bad and/or birdies are guaranteed.

Or did the universal birdie-ability of golf come about by simply eliminating any holes where it was not possible to score better than expected?