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I finally found a source for golf scoring distributions. Naturally, my first instinct was to use it to pick a fight.
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A couple take aways for me:I finally found a source for golf scoring distributions. Naturally, my first instinct was to use it to pick a fight.
The first graph is the most interesting to me.Broad view of how well par fits the various skill levels at large events. More details here:
2. At the most fundamental level (the definitions) they are based on exactly the same principle. Essentially, the score expected of an expert.A couple take aways for me:
1. The data support conventional thinking.
2. The criteria for defining disc golf par are different than for golf par.
We could discuss whether MPO should have been playing this short of a course at all. But, let's set that aside and look at how the methods in the PDGA Par Guidelines work.I played an event yesterday with some real live Par 2's. Shot the 2 lowest round scores of my PDGA career and won it as well- yay me! My feeling from looking at and playing the holes is there were 13-14 Par 2's along with 4-5 easy Par 3's. My 29 under for the day becomes right around even par. Curious to see what the Steve West Par-a-nator spits out. Possible par 3's imo in descending order of difficulty- 8,7,3, 17,14. (I did ace 14 though.) I have intentionally not looked at the hole scores to this point. Small samples with a lot of players spread out over a wide range of ratings with no players above 930 or so.
Merry has Little Lambs
If an "expert" is defined as a field of players within the same distance/skill range, and 20% are getting the lowest score in the distribution, it makes the case from my contention that a better way to set par would be "best reasonable score (BRS) + 1" for a distance/skill level where their BRS occurs at least say 5%(?) of the distribution on that hole. If 5% is too high for a reasonable eagle percentage, I'd be okay changing the proposed 5% threshold down to say 2% or 3%.I'm thinking about a possible refinement to my formula for setting par by scores.
I'm satisfied that my current method will not set a par that is too low. (It sets par so that every throw has at least a 76.7% chance of leading to a par score.)
Now, I'm considering something to make sure it does not set par too high. Here is what's happening.
TDs and course designers are finding ways to get more scoring separation. This presents a challenge to any method for setting par. The more the scores are smeared out, the less obvious which score is the "expected" one.
For example, say the "expert" on the hole gets a scoring distribution of 20%x2, 20%x3, 20%x4,20%x5, 20%x6. Per my method, this would be par 4 because only 73.6% of throws contribute to a score of 3 or better.
73.6% = (20%+20%)^(1/3)
The average is also exactly 4. So far, so good.
Here's the problem. There shouldn't be that many eagles. To get an eagle, a player needs to make one throw that does the work of three throws. Or, make two throws that do the work of four throws.
As an example, a 1000-rated MPO player can get par with 427-foot drives, so an eagle that results from good drives would require one 1281-foot drive, or two 854-foot drives, or three 711-foot drives. Not impossible (especially for a player rated higher than the 1000-rated "expert") but it should not happen 20% of the time by players at exactly the skill level of an expert.
The holes where I'm seeing these spread-out distributions seem to be water carries. Maybe some artificial islands.
Making the water carry and gaining two throws on the other experts doesn't mean the players who cleared the water beat "errorless play" by two throws, it means that a lot of experts are making the two-throw error of throwing into the lake.
What I'm thinking is that there might be some cap on eagles. To me, 20% eagles is too many. In the 20/20/20/20/20 example, this rule would kick in and set par to 3. If 40% are getting 3 or better, and half of those players are getting 2, is anyone going to think that the scores of 4 do not include an error?
Thresholds for low percentages are tricky. Maybe it shouldn't be a flat percentage, but a count of the actual number of eagles. For example, I could see ignoring one eagle from the experts, even if there were only 5 experts.
Or maybe we could look for a way to identify the scores that resulted from two-throw errors and discount that effect somehow.
Your thoughts?
Par is not: Expected score with errorless play plus 1. Just read the definition.If an "expert" is defined as a field of players within the same distance/skill range, and 20% are getting the lowest score in the distribution, it makes the case from my contention that a better way to set par would be "best reasonable score (BRS) + 1" for a distance/skill level where their BRS occurs at least say 5%(?) of the distribution on that hole. If 5% is too high for a reasonable eagle percentage, I'd be okay changing the proposed 5% threshold down to say 2% or 3%.
The unrecognized "flaw" (until recently) in setting par the way you've promoted incorporates higher scores in the distribution that include "errors" in the calculation. The proposed BRS+1 method works from the errorless play value (BRS), recognized by many as "scoring on a hole", with Par being BRS+1, not so much an error but just "not scoring" on the hole. Any scores thrown higher than par set via BRS+1 are a result of errors. Their distribution and percentages do not enter into the determination of par for that distance/skill level.
This raised my curiosity about how often a throw actually affects the final score. It relates to the poll I can't get rid of up there. I ran the numbers against a whole lot of scoring distributions. I found that almost 80% of throws are of a quality that they would lead to the player getting the most common score. About 10% are good enough or bad enough to lead to the player getting a score one higher or one lower than the most common score. And only about 0.3% are so bad or good that they lead to a score which is two higher or lower than the most common.The difficulty of determining par by an errorless rate on each throw, is that all errors are not created equal.
Some errors give the thrower a reasonable chance at a save, with not just an average subsequent throw, but an above-average subsequent throw. Some give a slight chance of a save, with a great subsequent throw. Some, particularly water carries, give no chance of save or recovery of that stroke.
Well, that's a part of what I was getting at with asking whether more information was required."Across all divisions that played that hole"? What divisions played it, and how many in each?
Ideally, you'd like data from just a specific player rating range. Less ideally, perhaps just a few of the top divisions (MPO, maybe MA1, etc.) My score and a 1020-rated pro's score shouldn't be in the same batch of data.
Well, that's a part of what I was getting at with asking whether more information was required.
The hole is clearly designed with the idea that certain divisions play the hole and others don't, because there is an alternative. As such, I only included data from the divisions that played it. I might add that there was a fairly even distribution of skill levels (so it's not like there were 2x 1020 rated players that got 3s 6 times combined and the next best was 960).
A scoring average and distribution is meaningless without context. Was the hole designed as a par 4 for the division of players with enough distance to reach it in 2 good throws for chances at a birdie 3? If so, then it's probably a par 4 for that distance/skill level if they're the ones getting 3s AND ideally the rest of the holes in that layout were designed for that distance/skill level.Hey, we just had a tournament with a redesigned hole. Said hole scored an average 5.69 across all divisions that played that hole, there were 6 3s on the hole (and no 1s or 2s) and the most common scores on the hole were a 5, followed by 6, followed by 4.
With just this information, would it be safe to say that the hole is a par 5? Or would more information be needed. Weather was not a significant factor, fwiw.