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Old 01-08-2020, 02:15 PM
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Originally Posted by Steve West View Post
Avg hole performance = .502 and sd = .179
I don't think those are valid questions. You can't figure out which is the best football team by looking at individual player stats. If I were to compare performances of courses as a whole, I would look directly at scoring spread width of total scores for the two courses with the same set of players.
The question becomes how can this information which takes some effort to produce be used to improve holes/courses unless there's a way to connect the numbers to guidelines. For example, let's say the "worst hole" on Course A is -0.02 the course average is .62 which is higher than the .53 average on Course B whose worst hole came in at .25. Intuitively, one would think the -0.02 hole should be improved but maybe it's more important to bring up the hole average on Course B with several hole changes. Seems the next step is to tie these numbers into a way that guides the designer/TD to make improvements or stand pat.
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Old 01-08-2020, 02:37 PM
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I read some of your articles on the website. Your article on Scoring Sloppiness and Focus stood out and I enjoyed it a lot. I think it's a way to analyze if a hole is fairly distributing players (rather than over punishing some shots). If I can suggest an improvement, I think it'd be even better if you measured par 3s differently than 4s, and those both differently than 5s. Right now, you are (this is my rough understanding) measuring each hole based on sloppiness (which is the average difference of the absolute values of expected score minus real score). However, that's not quite a fair distinction since 5s offer more trouble than 4s which offer more than 3s.

For instance, let's say a tournament is comprised of mostly par players and one who always throws an average drive but lands off the fairway, then throws back onto the fairway. His or her score on a par 3 (assuming they make the putt) is 3 (throw off the fairway, throw back on, make the putt). However, on a 5 their score will be 7 (throw off the fairway, back on, throw off, back on, throw off, back on, make the putt). The sloppiness of the 3s on the course will be close to 0, and the sloppiness of 5s higher. I realize this is a very simple and idealistic scenario, but it is accurate and explains the difference well. Another way to see that this is true is to measure your results. I'm betting that the higher the expected score, the higher the sloppiness is. I think there's a better way to measure this.

A better way to do it might be scaling based on expected score. In another simplistic scenario, if the sloppiness of a score with an expected score of 3 ("expected 3") is 0.33, that would be equivalent to an expected 5 having a sloppiness of 0.55. While I think that might be better without seeing all your formulas and thinking about it as much as you have (but maybe not), i think there is still a better way).

I think a formula that scales between holes properly based on how disc golf is played is ideal. In other words, on a hole there are shots where the design intends for the golfer to throw a drive, some where it expects an approach, and some where the design expects a putt. You could scale differently based on expected score. The last shot is expected to be a putt, and half of the time the shot before that is also a putt. The shot before is expected to be an approach (or maybe a drive, depending on semantics and hole design philosophy, yada yada yada). Shots before approaches and putts are drives. Then you could assign an score based on the normal % of shots expected to go move the sloppiness indicator based on each of those(putts, drives, and approaches). The percentage of shots that move the sloppiness indicator is a poor way of saying how often that type of shot changes the sloppiness score (putts probably aren't changing it much since every hole has roughly the same challenge in putting, approaches offer a little more variety, and driving the most). Then, add those up and you have a number that scales based on the expected score appropriately.

To lay out my suggestion as simply as I can:
  • Let's say the last 1.5 shots of each hole are considered putts, the shot before that an approach, and anything before that a drive.
  • Let's also say that putting impacts sloppiness 25% of the time, approaches impact sloppiness 20% of the time, and drives impact sloppiness 30% of the time (all of these are rough guesses, more on determining that below)

So a hole with an expected score of 3 would expect 1.5 putts, 1 approach, and .5 drives, and the expected range of scores is from 2.275-3.725. (1.5 * .25 + 1 * .3 + .5 * .3) = .725. Add and subtract that to the expected score of 3 to get the range.

However, an expected score of 4 would have a different range (3.025 - 4.975). This would account for the greater range of scores as expected score increased.

To determine how many putts there are on an average hole, I think you could use UDisc's stats to look for the average # of shots within 20m. To determine how often a putt "changes sloppiness", you could look at how many times a player holed out without a shot within 60m, and add that to the amount of times a player 3-putted, then divide that by the number of holes played. That's not perfect, but close. That's not 100% accurate but it's in the right direction.

For approaches, i'm not sure. If you include it, my gut says it's 1 shot per hole. However, that's not accurate, so idk. maybe just ignore them for now since they aren't measurable? I also don't have any idea how to determine if they "change sloppiness" based on the current stats we have.

For average drives on a hole, it'd be the expected score - expected putts - expected approaches (if you use approaches), For sloppiness, you could use UDiscs "Greens in regulation". Take the percentage of the time that a player is not in regulation on a par 3, the percentage of the time they aren't in regulation on a par 4, and then on a par 5. Calculate the amount of expected drives for a par 3, 4, and 5 (based on the first sentence of this paragraph). Then weight those accordingly. Example: if UDisc says players hit greens in regulation on 80% of the par 3s, 65% of par 4s, and 50% of par 5s, and the expected drives on a hole are 2 less than the expected score (based on the formula above), then that leaves 1 drive on 3s, 2 on 4s, and 3 on drives (I don't think these numbers are accurate, but they make for easy math and therefore easier explanations). That would mean that (roughly) 80% of the time drives are average, and 20% of the time, a drive is increasing sloppiness. Again, this isn't 100% accurate, but it is in the right direction.

Why did I type all of this?
I think your ideas are great, and the graphs you've shown in this thread shed a lot of light, but I think you could be much clearer and more influential with simpler communication. Graphs only stick if people understand them easily, and yours are easy to understand once someone understands all the terms, understand how the scale works, etc. If you could boil your measures down to 1-2 numbers, you can design visual aids (graphs or otherwise) to grasp them easily, and I think Focus could be one of those numbers if you have a well thought-out formula. However, it has to be a well-thought out formula that scales appropriately to different courses and holes, and that's tricky (hence my ideas above). I think Focus is a great indicator of who has the hot hand on a given day. Essentially, it can answer "does this hole appropriately measure how well someone is playing right now?"

I think the other measure you should use is the correlation of ratings to scores on a hole, which is probably much simpler, but I haven't thought through it as much (and I'd like to read your ideas on it more when I have time). Those two could be simply plotted on a graph (one on the X axis and one on the Y axis). That would show holes/courses that fairly measure a players ability in a way that is easy for people to understand, and that would lead to better course design.

Thanks for reading all this.
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Old 01-08-2020, 02:38 PM
Steve West Steve West is offline
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Originally Posted by Cgkdisc View Post
The question becomes how can this information which takes some effort to produce be used to improve holes/courses unless there's a way to connect the numbers to guidelines. For example, let's say the "worst hole" on Course A is -0.02 the course average is .62 which is higher than the .53 average on Course B whose worst hole came in at .25. Intuitively, one would think the -0.02 hole should be improved but maybe it's more important to bring up the hole average on Course B with several hole changes. Seems the next step is to tie these numbers into a way that guides the designer/TD to make improvements or stand pat.
Use the numbers directly. Remember, they were all tested in mulit-course environments so the performances of the rest of the holes on the course isn't important. Improve the -.02 hole first. Better, improve them both.
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Old 01-08-2020, 02:43 PM
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Use the numbers directly. Remember, they were all tested in mulit-course environments so the performances of the rest of the holes on the course isn't important. Improve the -.02 hole first. Better, improve them both.
I think the trick is where to draw the line such that a number below X "must be fixed" and above X is "could be better."
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Old 01-08-2020, 04:38 PM
Steve West Steve West is offline
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If I can suggest an improvement, I think it'd be even better if you measured par 3s differently than 4s, and those both differently than 5s.
That’s logical, but I’m OK with the measure of sloppiness coming out generally higher for higher scoring holes. It reflects the reality you mention, which is more opportunities for trouble. Here’s why I didn’t do it that way.

To give higher scoring holes a pass would tilt the cost/benefit ratio. (Cost of more sloppiness/Benefits of higher scores.)

Also, par is not a reliable point of data. Often, it is not available. Other times it was set by questionable methods. (Par is not rounded average score. You don’t want to get me started on that.)

While increased sloppiness is associated with increased scores, there is no obvious grouping; no clear cutoff between par 2s and par 3s and par 4s and par 5s. See the top chart on page 3. You can’t even tell which of those average scores are associated with each par, let alone see any places to draw a line and say “this bunch is different than that bunch”.

Your idea of scaling according to score (instead of bunching by par) is closer to what I would do, if I thought the measure should be scaled to be “fairer”.

As for the idea of using the different types of throws. Well, I’ve never seen any evidence that players actually make three and only three distinct types of throws. Nor have I ever gotten any indication that it would be remotely possible to tease out “types” of throws from scoring data. Those UDisc stats are an arbitrary fun way to put throws in buckets. Even in that case, they are already up to, what, six types of throws? Anyway, lots of sources of scores do not use UDisc stats.

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Originally Posted by Ryan P. View Post
I think your ideas are great, and the graphs you've shown in this thread shed a lot of light, but I think you could be much clearer and more influential with simpler communication.
Thank you, and your point about communication is well-taken. That’s the reason I put stuff here and on my website. I’ll let some Carl Sagan of disc golf come along and popularize it. I’d rather make new stats than teach about old ones.

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Originally Posted by Ryan P. View Post
I think the other measure you should use is the correlation of ratings to scores on a hole, which is probably much simpler, but I haven't thought through it as much (and I'd like to read your ideas on it more when I have time). Those two could be simply plotted on a graph (one on the X axis and one on the Y axis). That would show holes/courses that fairly measure a players ability in a way that is easy for people to understand, and that would lead to better course design.
Correlation of ratings to stats doesn’t need me. Also, I avoid using ratings whenever I can. Partly because they are just another stat derived from scores. The unseen and unknown intermediate steps raise the possibility of polluting the information. But mostly because ratings are never available alongside hole scores. (Get on that, UDisc, PDGA Live, and Matrix.) So it’s a lot of extra manual labor.

Another thing I’m worried about is that if we always design to maximize correlation to ratings, we would always choose hole designs that are closest to the typical hole design that goes into most players’ ratings. We'd end up with nothing but 300 foot, par-3-for-all-skill-level, holes.
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Old 01-12-2020, 12:08 PM
Steve West Steve West is offline
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This chart is a bit surprising.

The x axis is how much the hole’s average score exceeded the average score of all other holes with the same players.

The y axis is how well the hole sorted those players out to increase the scoring spread width of total scores for the shared players.




I would have expected a stronger relationship between average score and the ability of a hole to sort players. Yet, it seems a hole does not need to generate high scores to have good sorting ability.

The best-sorting hole is the 942 foot long 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy Codorus State Park - Red – CSR 7223 #10 which gave players a score that was 2.83 throws higher than other holes those players played. No surprise there.

However, the second best-sorting hole was the 244 foot 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy Ship Rock Disc Golf Course – SR 6068 #5 which gave players a score that was 0.72 throws lower than the other holes.

While it looks like perhaps a high score is a way to avoid really poor sorting ability, I think that is an illusion caused by the lack of data points for really high score holes.
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Old 01-13-2020, 04:09 PM
tbonesocrul tbonesocrul is offline
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Originally Posted by Steve West View Post
This chart is a bit surprising.

The y axis is how well the hole sorted those players out to increase the scoring spread width of total scores for the shared players.
Are you saying the y-axis measurement is the ability of the hole to increase the width of the scoring spread?

Or the ability of the hole to increase the width of the scoring spread while also being able to sort players by rating.
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Old 01-13-2020, 05:44 PM
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Are you saying the y-axis measurement is the ability of the hole to increase the width of the scoring spread?

Or the ability of the hole to increase the width of the scoring spread while also being able to sort players by rating.
The y-axis is the ability to increase the scoring spread of total scores across players. Scoring spread is a measure of the information content. An increased scoring spread of total scores almost certainly indicates that the hole is giving out scores in a less-random fashion (and is giving out more different scores).

Less-random is not exactly the same as more-correlated to ratings. But they go together most of the time.

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Old 02-07-2020, 10:59 AM
Steve West Steve West is offline
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Here is another attempt to quantify the ability of courses to sort players by skill. For this one, I compared two courses by looking at the scoring spread of total scores for the players that played both courses. Whichever course had the larger scoring spread won that comparison.

To take into account "strength of schedule" I then calculated a Sorting Power factor which reproduced the actual wins. The formula for expected wins is 1/(1+10^(B-A)). Where A is the factor for the course in question, and B is the factor for the opponent. For example, Gold B would be expected to sort players better than Gold A about 72% of the time.

I don’t know that we can read anything into the actual value of the factor, other than bigger is better and if the numbers are close the courses have close to the same sorting power. For example, negative numbers don’t mean the course is sorting players backwards.

The courses that were included were those that had at least 5 comparisons to other course, with at least 16 players in common for each comparison.

I'm not sure that the courses that hosted primarily AMs (or FPO) can be directly compared to the courses that hosted MPO. Maybe they can; there was some cross-pollination. Anyway, the ranking within these subsets should be good.

Here are the results. My initial impression is that there might be something to these numbers.

3.65 = 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy/Quaker's Challenge at Pinchot State Park - QC-L/8222
3.07 = 2019 United States Disc Golf Championship/Winthrop University/Gold B
3.07 = 2019 DGPT Tour Championship/Hornets Nest Park/DGPT Championship MPO Layout; 18 holes; Par 63; 8,905 ft.
2.66 = 2019 United States Disc Golf Championship/Winthrop University/Gold A
2.36 = 2019 PDGA Professional Disc Golf World Championships/Lake Eureka/9647
2.24 = 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy/Heritage Hills Disc Golf Course - HH/10641
1.55 = The Rumble 2019 presented by Discraft and Clint's Draft House/West Lake/Long
1.33 = 2019 DGPT - MVP Open at Maple Hill/Maple Hill/Golds; 18 holes; Par 60; 8,500 ft
1.25 = DGPT - Discraft's Portland Open presented by Bevel Craft Brewing/Blue Lake/10,220 ft
1.18 = 2019 Dynamic Discs Glass Blown Open - National Tour/Emporia Country Club/MPO
1.14 = DGPT - Idlewild Open driven by Innova Discs & The Nati/Idlewild/DGPT MPO; 18 holes; Par 68
1.02 = DGPT - AbsoluteXtracts presents the San Francisco Open driven by Innova at Gleneagles DGC/Gleneagles DGC/MPO
0.93 = The Ed Headrick Disc Golf Hall of Fame Classic presented by REC TEC Grills - National Tour Finale/WR Jackson Memorial Disc Golf Course/Jackson Long - MPO ; 18 holes; Par 68; 10,485 ft.
0.86 = Santa Cruz Masters Cup presented by Innova - National Tour/Delaveaga Disc Golf Course/8209 ft
0.83 = DGPT - Discraft Ledgestone Insurance Open 2019/Lake Eureka/9,647 ft, MPO
0.79 = 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy/Ship Rock Disc Golf Course - SR/6068
0.75 = 2019 Texas State Disc Golf Championships Presented by Discraft/Spring Valley Golf & Disc Golf/Gold
0.72 = 2019 Canadian National Disc Golf Championships Powered By Innova Champion Discs/Hillcrest Farm Disc Golf Course/Hillcrest Long (Blue); 18 holes; Par 66; 7,314 ft.
0.71 = 2019 PDGA Professional Disc Golf World Championships/Northwood/Gold 9299
0.69 = European Open 2019/The Beast/European Open 2019; 18 holes; Par 64; 2,738 m
0.62 = The Majestic 2019/Blue Ribbon Pines Disc Golf Course/BRP Pro 27 holes, 10,160 ft
0.56 = The Rumble 2019 presented by Discraft and Clint's Draft House/Camden 2/Rumble
0.47 = Beaver State Fling presented by KEEN - National Tour/Milo West/8681
0.40 = 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy/Codorus State Park - Blue - CSB/6489
0.34 = 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy/Codorus State Park - Red - CSR/7223
0.27 = 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy/Coyote Hills - CH/5910
0.26 = 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy/Klines Run Disc Golf Course - KR/6260
0.22 = 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy/Muddy Run Disc Golf Course - MR/8687
0.12 = Discraft's CCR Open 2019/Burchfield Park - Devil's Den - Renegades Trail/MPO layout; 18 holes; Par 66; 9,154 ft.
0.10 = Santa Cruz Masters Cup presented by Innova - National Tour/Delaveaga Golf Course/8713 ft
0.09 = Southwest Funding presents the Nick Hyde Memorial powered by Hyzerbomb driven by Innova - Pro Weekend/Harry Myers Park/Gold
0.07 = DGPT - 2019 Great Lakes Open presented by DISCRAFT/Toboggan/Long; 18 holes; Par 62; 9,461 ft.
0.01 = 2019 Delaware Disc Golf Challenge - National Tour/Iron Hill/Gold (MPO) ; 18 holes; Par 69; 10,240 ft.
-0.56 = 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy/Codorus Township Park - CT/5490
-1.14 = Beaver State Fling presented by KEEN - National Tour/Milo East/8596
-1.25 = 2019 Dynamic Discs Glass Blown Open - National Tour/Emporia Country Club/FPO
-1.58 = 2019 Canadian National Disc Golf Championships Powered By Innova Champion Discs/Huck It Middleton Disc Golf Course/Huck It Longs - Hurricane Dorian Baker's Dozen; 13 holes; Par 44; 5,062 ft.
-1.69 = 2019 United States Women's Disc Golf Championships - presented by Spotsy Disc Golf Club and Driven by Innova Discs/Hawk Hollow/USWDGC - Pool A; 18 holes; Par 65; 7,999 ft.
-1.69 = 2019 PDGA Professional Disc Golf World Championships/Northwood/Blue 7677
-1.83 = 2019 United States Women's Disc Golf Championships - presented by Spotsy Disc Golf Club and Driven by Innova Discs/Loriella Park/USWDGC - Pool A; 18 holes; Par 63; 7,189 ft.
-1.84 = DGPT - 2019 Great Lakes Open presented by DISCRAFT/Toboggan/Short; 18 holes; Par 60; 7,986 ft.
-2.13 = 2019 PDGA Professional Disc Golf World Championships/Sunset Hills/7539
-2.36 = 2019 PDGA Amateur Disc Golf World Championships- Powered by Prodigy/Boulder Woods at Pinchot State Park - BW/4845
-2.59 = DGPT - Discraft Ledgestone Insurance Open 2019/Sunset/7,045 ft
-4.01 = DGPT - Discraft's Portland Open presented by Bevel Craft Brewing 2019/Blue Lake/8,980 ft
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  #60  
Old 04-17-2020, 12:18 PM
Steve West Steve West is offline
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A new paper focusing on just the ability to assign the scores to players, not the ability to generate a lot of scores.

http://www.stevewestdiscgolf.com/Cal...ng_Ability.pdf
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