Another Way to Quantify “Score-ability”

denny ritner

Eagle Member
Gold level trusted reviewer
Joined
Apr 27, 2008
Messages
870
Location
FLA
We hear the term "scoreable" used by many disc golf commentators in both live and post-production formats. I'm going to argue for an alternative method of using the data from which most commentators currently employ.

From my experience as a viewer it seems that most commentators use the relative ease of birdying a hole as its "score-ability". I suggest that birdie-ability may or may not correlate strongly with scoreability.

Birdie-ability depends on par. Score-ability has NOTHING to do with par. Players do NOT compete with par. Players compete with each other through THROWS.

I will suggest this definition:
"Score-ability is the likelihood that players of equal abilities will have different scores on a particular hole."

Let's consider a "tweaner" hole with a 3.5 average for a certain group of players with exactly 50% 3's and 50% 4's. The hole is obviously scoreable as there is a 50% chance that any two players will have different scores on the hole. If the hole's par were listed as 3, then commentators would describe the hole as very difficult. If the hole's par were listed as 4, then commentators would describe the hole as easy or "scoreable".

Again, score-ability has NOTHING to do with par.

Before I suggest one method of quantifying score-ability, let's consider which data to use. I have found, as I imagine many commentators have, that it's cumbersome to use hole stats following a cut in big tournaments. There's always the caveat that needs to be mentioned that the score distributions discussed have been drawn from a set of players with better abilities (at least on the weekend under consideration.)

Way back in the day when I designed and subsequently modified holes for a PDGA Major, I only used data from players rated 975 or higher. I chose that number as it reflected the average cash line from A-tiers of the day. Today, I would suggest only looking at data from rounds rated 1020 or higher for MPO divisions at DGPT events. (This was the cash line for the recent LVC.) Note that I said rounds rated, rather than player ratings. Player ratings reflect the past. Round ratings better reflect the present. Using this data set, commentators would have no need to qualify their post-cut commentary.

Once having established a standard for data sets, score-ability could be calculated in a number of ways. For convenience, I utilized the standard deviation of scores on a particular hole for all players who shot a 1020 or better rated round.

I analyzed the first round of the recent LVC. (I would have done more, but it's cumbersome to extract the data from the results page.) Holes 11 and 16 were the easiest, relative to par, but not the most scoreable in terms of variation in scores among the rounds rated 1020 or higher. Hole 10 was the most difficult, relative to par, but the second most likely to produce variation in scores.

Revisiting the choice of 1020+ rated rounds: it's more than simply to avoid the inconvenience of comparing pre and post-cut data. While the overall quality of play in DGPT events has taken a big jump up over recent years, there are still a number of players in the events who are not on the same level of play as the touring players. I wouldn't argue that these players should be dismissed at the level of course design, but for commentary purposes they may skew data on certain holes.

In the grand scheme, these thoughts are just a minor suggestion. As a viewer, I am extremely grateful to all the hard-working video crews. I get a lot of enjoyment from watching disc golf on my devices and feel that the hard work, especially from Jomez Productions, has made a very significant contribution to the recent growth uptick in the sport.

As a final note to those on the dgcoursereview forum: I am glad that the moderators afforded me some time off the forum to reflect on the nature of my postings. I had a very bad year last year with my online behavior. I was abrasive to many and abusive to some and I made the moderators' lives more difficult than they deserved. I am grateful to dgcoursereview for being a resource as a player. I cannot change the past, but I promise to do better in the future.
 
Oops, forgot this:
 

Attachments

  • Scoreability Summary Data.JPG
    Scoreability Summary Data.JPG
    107 KB · Views: 39
It may be futile to debate a made-up word like "scoreable". It's a bit like arguing slang definitions.

But I will say that if par is properly set, a birdie should be gaining at ground on more than half of the field.

Another example to ponder: If Hole A yields 30% birdies and 70% pars, while Hole B yields 30% birdies, 50% pars, and 20% bogeys, both are equally scoreable if birdie frequency is the only criteria. But Hole B has more effect on the competition.

Perhaps we should consider the most common score on each hole. The lower the percentage of all scores that it represents, the better.
 
...

I will suggest this definition:
"Score-ability is the likelihood that players of equal abilities will have different scores on a particular hole."

...

I think score-ability has been enshrined as "the chance of getting a birdie". And, whether players are competing against par or against each other, the answer to "Who won and by how much" is the same wither way. So we might as well keep it that way.

But, score-ability is not quite what denny is describing. What was described is something closer to the ability of a hole to sort the players of interest by skill. Giving out a range of scores is one part of that. (However, if a hole is really good at testing skills, players of equal abilities should have the same score on a particular hole, not different scores.)

Anyway, we already know how to measure how well a hole sorted players by skill: calculate the amount of information generated by the scores.

Scoring Spread Width measures the information contained in a single hole's scoring distribution.

Contribution to Scoring Spread Width of Total Scores measures how much of the information contained by the final total scores was added by the hole.
 
(However, if a hole is really good at testing skills, players of equal abilities should have the same score on a particular hole, not different scores.)

Perhaps a distinction between ability, and consistent performance of that ability.
 
You know someone's had a really bad week, when he can find imagine par as part of a party.
 
If a hole is really good at testing skills, players of equal abilities should have the same score on a particular hole, not different scores.

If that were the case, players would always shoot the same score on every hole, but even Calvin Heimborg isn't that consistent.

Scoring Spread Width measures the information contained in a single hole's scoring distribution.

Contribution to Scoring Spread Width of Total Scores measures how much of the information contained by the final total scores was added by the hole.

Sounds useful. How is that calculation made?


Another example to ponder: If Hole A yields 30% birdies and 70% pars, while Hole B yields 30% birdies, 50% pars, and 20% bogeys, both are equally scoreable if birdie frequency is the only criteria. But Hole B has more effect on the competition.

Perhaps we should consider the most common score on each hole. The lower the percentage of all scores that it represents, the better.

The summary table refers to David's quote. The flatter the probability distribution, the greater the score-ability of a hole. I would hesitate to use the word "better", though. The "how" of the distribution that is hidden in the numbers matters.
 

Attachments

  • Method Compariso.JPG
    Method Compariso.JPG
    69.2 KB · Views: 8
I would hesitate to use the word "better", though. The "how" of the distribution that is hidden in the numbers matters.

Indeed. Scoring spread (or whatever we call it) is only part of the design quality.

On one end of the spectrum, a hole that produces the same score 98% of the time is boring.

On the other hand, a hole through a forest with no clear route may produce a very side scoring spread, but that may reflect more luck than skill.

I suppose one way to measure it, might be to compare scores from different skill levels. If weaker players tend to score the same as better players, the hole is probably not very good at measuring ability.

Or perhaps it's just, as the Supreme Court once described another subject, just "I know it when I see it."
 
If that were the case, players would always shoot the same score on every hole, but even Calvin Heimborg isn't that consistent.

I think you meant each player would always shoot the same score every time they played a certain hole.

If a hole actually and accurately measured the ability of a player, that measure would not change much from day to day. Think of measuring the maximum release speed of the disc. Sure, the speed of a player's best throw will vary by a few miles an hour from day to day, but not by much.

But, hole scores are a horribly ineffective way to measure ability. We only give out a few different integers. That would be like using a radar gun that is only calibrated to the nearest 25 mph. If radar guns were as clumpy as hole scores, yes, you would want Calvin's maximum release speed to come out to be 75 mph (to the nearest 25mph) every time.
 
Sounds useful. How is that calculation made?

Select the players and rounds of interest. You would select the players who had a 1020 or higher rated round on a certain course.

Calculate the scoring distribution = number of times each score occurred, divided by the number of player-rounds.

Let's say this comes out to be frequencies of 30%, 70% on one hole, and 30%, 50%, 20% on another. Note that the actual scores don't matter, only how many of each there are.

Compute the log in base 2 of each frequency. For example, 50% is one divided by 2, or 2 raised to the negative 1 power, so the log in base 2 of 50% is -1. For any zeros, use zero.

30%, 70% begets -1.64, -.51.
30%, 50%, 20% begets -1.64, -1, -2.32

Multiply the logs by the frequencies. Again, for any zeros, use zero.

-1.64, -.51. begets -.52, -.36.
-1.64, -1, -2.32 begets -.52, -.5, -.46.

Add up the results.

-.52 + -.36 = -.88.
-.52 + -.5 + -.46 = -1.49.

Take the negative of these totals to get .88 and 1.49. These are the actual amount of information in each distribution, in bits. For comparison, a 50%, 50% distribution contains one bit of information.

To get scoring spread, which is more understandable, raise 2 to the power of these totals.

2^.88 = 1.84.

So 30%, 70% is like the hole gave out only 1.84 different scores. For comparison, this is less than the 2 different scores a 50%, 50% distribution would give.

2^1.49 = 2.80.

So 30%,50%, 20% is like the hole gave out 2.80 different scores. For comparison, this is more than a 50%, 50% distribution, but less than the 3 different scores that a 33%, 33%, 33% distribution would give.
 
One issue here, as already alluded to, is that language is malleable and definitions do not proscribe the usage of a word but rather reflect it. Saying "scoreable" should mean something other than how people generally use it is a little bit of a lost cause.

That said, I don't think scoreable, as it is used, is as devoid of competitive meaning as you seem to imply. Compare "scoreable" to the phrase "must get". Both imply a high percentage of birdies, but "scoreable" tends to imply that getting a birdie gains ground on the field, while "must birdie" implies that par loses ground to the field.

You may be looking for one word to represent the same idea, regardless of where the hole's par is set relative to the field's performance, but I don't think that is really necessary, nor desireable. Consider the phrase "tough birdie" or "tough hole". This conveys that par is a good score and may even gain ground, whereas the word "tweener" tends to convey that par is the expected score for most of the field.

Each of these words or phrases add some nuance to the information conveyed, and aee thus useful. If you want a word that is closer to what you are going for, I'd suggest "seperator" is closer to the mark. It tends to imply that this is where you can truly gain strokes on the field.
 
Scoring in golf is popularly recognized as shooting a birdie or better.

When traditional golf holes are designed for players within a distance/power range such that par is the most common score on each hole under normal weather conditions, every hole will also be realistically birdieable.

A birdie percentage from 10%-50% would appear to be the ideal range for every hole designed for a disc golf player distance/skill level. This provides a good variety of scoring opportunities and separation over 54-72 holes without needing natural or artificial penalty elements likely to reduce skill-based separation.

I believe most would consider a hole with less than 10% birdies for a skill level not "scoreable" nor providing enough separation, and greater than 50% as too scoreable/easy although still better than under 10% or none at all on holes where par on the hole is set one too low.

Steve likely disagrees but if a hole's design/length can't easily be tweaked for Elite events, IMO it's still better for players and spectators if par is set higher so there are 70% birdie 3s expected as a par 4 versus setting it as a par 3 resulting in 70% par 3s and no birds. There's probably little disagreement that its hole design needs to be improved.

Is a hole with a score of 3 at 70% being the lowest score thrown better for the game being considered a birdie or par? As TD you are sometimes "forced" to make the better choice overall. Imagine if the par 5 at Toboggan was set at the technically correct par of 4 so McBeth didn't get the -18. You don't necessarily want a player to earn -18 on a course with all soft pars. But I think that's still better than having even one "trap" hole where it's almost not possible to score without a 200' throw-in to kill the potential, if only rare, for a player to shoot the mystical -18.
 
Select the players and rounds of interest. You would select the players who had a 1020 or higher rated round on a certain course.

Calculate the scoring distribution = number of times each score occurred, divided by the number of player-rounds.

Let's say this comes out to be frequencies of 30%, 70% on one hole, and 30%, 50%, 20% on another. Note that the actual scores don't matter, only how many of each there are.

Compute the log in base 2 of each frequency. For example, 50% is one divided by 2, or 2 raised to the negative 1 power, so the log in base 2 of 50% is -1. For any zeros, use zero.

30%, 70% begets -1.64, -.51.
30%, 50%, 20% begets -1.64, -1, -2.32
....................................................................................................................................................................................................................
:confused::confused:

It's great that we have you with this grasp of statistics and the ability to show us with a psychedelic graph!
 
Scoring in golf is popularly recognized as shooting a birdie or better.

When traditional golf holes are designed for players within a distance/power range such that par is the most common score on each hole under normal weather conditions, every hole will also be realistically birdieable.

A birdie percentage from 10%-50% would appear to be the ideal range for every hole designed for a disc golf player distance/skill level. This provides a good variety of scoring opportunities and separation over 54-72 holes without needing natural or artificial penalty elements likely to reduce skill-based separation.

I believe most would consider a hole with less than 10% birdies for a skill level not "scoreable" nor providing enough separation, and greater than 50% as too scoreable/easy although still better than under 10% or none at all on holes where par on the hole is set one too low.

Steve likely disagrees but if a hole's design/length can't easily be tweaked for Elite events, IMO it's still better for players and spectators if par is set higher so there are 70% birdie 3s expected as a par 4 versus setting it as a par 3 resulting in 70% par 3s and no birds. There's probably little disagreement that its hole design needs to be improved.

Is a hole with a score of 3 at 70% being the lowest score thrown better for the game being considered a birdie or par? As TD you are sometimes "forced" to make the better choice overall. Imagine if the par 5 at Toboggan was set at the technically correct par of 4 so McBeth didn't get the -18. You don't necessarily want a player to earn -18 on a course with all soft pars. But I think that's still better than having even one "trap" hole where it's almost not possible to score without a 200' throw-in to kill the potential, if only rare, for a player to shoot the mystical -18.

You want 18 under to be possible? Fix the holes, don't break par.

Eighteen under only means something if it is truly eighteen throws better than expected.

As Ben Franklin might have said: "Those who would give up meaningful par, to purchase a little artificial excitement, will have neither."
 
I think you meant each player would always shoot the same score every time they played a certain hole.

If a hole actually and accurately measured the ability of a player, that measure would not change much from day to day. Think of measuring the maximum release speed of the disc. Sure, the speed of a player's best throw will vary by a few miles an hour from day to day, but not by much.

But, hole scores are a horribly ineffective way to measure ability. We only give out a few different integers. That would be like using a radar gun that is only calibrated to the nearest 25 mph. If radar guns were as clumpy as hole scores, yes, you would want Calvin's maximum release speed to come out to be 75 mph (to the nearest 25mph) every time.

There are a number of skills included in overall ability. Consistency being one of the most important.

If you had a 33' open flat hole, 2 players of equal ability, when competing, would get different scores often enough to gain or lose ground on their opponent.
 
Top