Hole and Course Performance Statistics

[Steve West]

MVP Open 2018 MPO

 

[Steve West]

Prodigy Disc Pro Tour - Lahti 2018

 

[Steve West]

I'm becoming less enchanted with the idea that larger scoring spreads of total scores always indicates less luck. There are some fluky things about it, and it needs hundreds of rounds of data to even hope to work.

I still like the basic concept of looking at how "well" a course allocated the scores it gave out, and comparing that to how well random assortments of those scores would have worked.

To measure how well a given sorting of scores worked, I'm now looking at the correlation of a single hole's scores to the total scores from all other holes.

For Pro Worlds, I looked at the total score from the first two rounds on each hole, now well that total correlated with the other holes, and how well that total did compared to all the two-round totals that would have come from scrambling the scores on that hole.

The way Brewster Ridge #10 handed out its scores was better than only 17.9% of all random assortments. At the other extreme, Fox Run #16 handed out its scores in a way that was better 99.8% of all random assortments.

Looking closer, we can see that BR #10 generally gave out lower two-round-total scores to players who scored higher on other holes, with a correlation of negative 9.7%. Random ways of handing out scores would not have a preference as to who gets higher scores, so they would cluster around zero correlation.

FR#16 generally gave out higher two-round-total scores to the players who got higher scores on other holes, with a correlation of positive 27.5%. Usually, random allocations don''t generate much correlation, so this hole beat random allocations 99.8% of the time.

If all the holes were allocating scores randomly, we would expect that some holes would fall toward the bottom of this measure, and some toward the top. However, 25 of the 32 holes had a positive correlation. There is only about a 1% chance of that happening if scores are only being allocated randomly.

 

[Steve West]

I was looking at the Idlewild stats and wondered why "typicality" mattered. So, I replaced it with "Sensitivity". Sensitivity measures the degree to which a hole gives lower scores to higher-rated players. The actual value is the ratio of the slope of actual scores (as a function of rating) to the slope expected of a wide-open flat hole of the same length.

 

[tbonesocrul]

Sensitivity measures the degree to which a hole gives lower scores to higher-rated players. The actual value is the ratio of the slope of actual scores (as a function of rating) to the slope expected of a wide-open flat hole of the same length.

For the Slope of the equivalent wide-open flat hole, is that based on data from real holes?

also by slope I'm assuming you mean slope of linear fit of player rating (x) vs score on hole

 

[Steve West]

For the Slope of the equivalent wide-open flat hole, is that based on data from real holes?

also by slope I'm assuming you mean slope of linear fit of player rating (x) vs score on hole

Yes and Yes.

 

[Steve West]

For some reason, I decided to calculate Hole Length Variety for 289 courses for which I have hole lengths. This is a measure of how many different lengths of holes a course offers. One hole is 100% "different" from another if the longer hole is as at least 20% longer.

The actual calculations involve taking the log to the base 1.2 of the ratios of the lengths of each hole to each hole, rounding to an integer and then count the number of different integers using the Scoring Spread Width formula.

Anyway, here are the results.

The average across all courses was 6.08, which is about like having an even spread of hole lengths from 208 feet to 518 feet.

Here are the hole lengths (shortest to longest) for the courses that had the most variety (8.53) and the least (2.97).

 

[ChrisWoj]

For some reason, I decided to calculate Hole Length Variety for 289 courses for which I have hole lengths. This is a measure of how many different lengths of holes a course offers. One hole is 100% "different" from another if the longer hole is as at least 20% longer.

The actual calculations involve taking the log to the base 1.2 of the ratios of the lengths of each hole to each hole, rounding to an integer and then count the number of different integers using the Scoring Spread Width formula.

Anyway, here are the results.

The average across all courses was 6.08, which is about like having an even spread of hole lengths from 208 feet to 518 feet.

Here are the hole lengths (shortest to longest) for the courses that had the most variety (8.53) and the least (2.97).

Blobby lookin' fellow, any significance to the seemingly weak positive correlation?

 

[Steve West]

Blobby lookin' fellow, any significance to the seemingly weak positive correlation?

Don't know for sure. Feel free to speculate. I'll start.

Some reasons for the positive part are obvious. There just isn't "room" to fit in different length holes if you don't have enough total length for really long holes.

The maximum variety would be achieved by making each hole 20% longer than the next-shorter one. Assuming no hole is shorter than 120 feet, to get 18 different lengths for all 18 holes would mean that the longest hole would be 2,662 feet long and the total length of the course would be 15,374 feet.

It think the maximum variety you could fit into a 3,600 foot course would be 5.96, or 9.64 for a 5,400 foot course, or 11.64 for a 7,200 foot course. (With no holes shorter than 120 feet.)

Similarly, the lengths of the longest and shortest holes put limits on the variety than can be achieved. That's why courses with more holes don't exhibit noticeably more variety. Between 200 feet and 600 feet you can only squeeze in about 6 different hole lengths whether you have 18 or 27 holes to do it.

As for the weak part, I think two things contribute. There may be others.

First, not many designers have been trying to get a lot of hole variety. Even if they had, it hasn't been measured before, and nothing can be optimized without accurate feedback.

Second, the most prolific designers have a philosophy of designing courses with "proper" hole lengths for a specific level of skill. That limits hole lengths to tight groupings around one-drive, two-drive, and (maybe) three-drive holes.

Similarly, the lengths of holes on local-player-designed courses probably all cluster around the length of the longest controllable drive by that player.

I'm not saying hole length variety is a goal in and of itself. I do think adding hole length variety is a good thing - if it is done within the constraints of the other goals for the course. For example, old-school designers could choose to make some of the holes at the short end of "proper" and others at the long end, or make an effort to find a place for that three-drive hole. Or include a zero-drive hole.

Personally, I design for the whole group of players that will be using a course. For me, increasing hole length variety helps make sure all users will have at least some holes "fit" for them. Also, so not all the holes are only good for my arm.

I also like to maximize hole length variety for an Ace Race. For those, the shortest holes should be putts anyway, so you can fit a lot of variety into 18 holes. If the shortest hole is 10 meters and the longest about 250 feet, you could have hole length variety of 11.64.

 

[Steve West]

I need a name for a new statistic. It's basically the inverse of standard deviation, to show how tightly packed the hole scores are.

I'm using "tightness" as a working name. (Maybe I've been watching too many Pitch Meeting vidoes.) However, that already means something when describing holes. (In fact, tighter holes will probably have less "tightness".)

I don't want to expand the name to Tightness of Scores Around... or anything that long. I want one word.

If it helps, two holes that would have very low values of this statistic would be:

Ledgestone Open 2015 / Eureka / Temp #6, and

2019 United States Disc Golf Championship / Winthrop University / Gold A #17.​

This statistic will not be one where bigger is always better. Two holes where the value would be doubly high would be:

Santa Cruz Masters Cup presented by Innova - National Tour / Delaveaga Golf Course / 7475 ft #2, and

2014 PDGA Professional Disc Golf World Championships / Blue Lake Park / Long Tees #9.​

Both of these have negative correlations to the scores of other holes in the course.

Any suggestions?

(Yes, Chuck, you can make a punny suggestion. I will ignore it.)

 

[biscoe]

bunching

 

[Cgkdisc]

SPART for Standard Par Thickness. Bigger SPART would mean scores are more tightly packed around your calculated par value if I understand what you're getting at?

 

[Steve West]

The leading candidates now are pithiness, succintness, and compactness. I want a positive connotation.

"Bunching" is what I call the tendency of random scores to create ties. Which is bad.

 

[Karl]

"Bunching" is what I call the tendency of random scores to create ties. Which is bad.

"Bunching" is what I call someone thowing their fist fowud when I have a code.

 

[keepitfun]

a few ideas for the compactness of scores

gridlock as in high performers and crappy performers are all stuck at same spot due to hole design
bottleneck where a better player is prevented from distancing from a lesser than due to hole design
socialist/communist haha as in we prevent the gifted from outperforming the challenged due to hole design

Hole Enables Lesser Players or HELP as in I was having a hard time keeping up with McBeth until I got to that stretch of HELP holes and I was able to hang around

 

[Steve West]

a few ideas for the compactness of scores

gridlock as in high performers and crappy performers are all stuck at same spot due to hole design
bottleneck where a better player is prevented from distancing from a lesser than due to hole design
socialist/communist haha as in we prevent the gifted from outperforming the challenged due to hole design

Hole Enables Lesser Players or HELP as in I was having a hard time keeping up with McBeth until I got to that stretch of HELP holes and I was able to hang around

Thanks, but that's not what this stat covers. What you are talking about is narrow scoring spread.

Compactness is when Paul gets a 3/3/4/4, and I get a 6/6/7/7.

Lack of compactness is when Paul gets a 2/3/4/5 and I get a 4/5/7/10.

 

[Cgkdisc]

It took awhile to coin a punny term but here goes with: Tighty-widey

 

[BionicRib]

The leading candidates now are pithiness, succintness, and compactness. I want a positive connotation.

"Bunching" is what I call the tendency of random scores to create ties. Which is bad.

Sorry to thread drift, but where would hole 4 at brp fit on the "bunching" meter?

 

[Steve West]

Sorry to thread drift, but where would hole 4 at brp fit on the "bunching" meter?

It's Hole and Course Performance Statistics, so that's not a drift at all.

444 has a good correlation to ratings and to the scores of other holes, as well as good scoring spread.

What happens is that all skill levels can get a 4 about half the time. But, the other half of the time their scores are very much reflective of skill. Only the best get 3s, and only the worst get 6s. Which works better than most holes.

 

[Steve West]

It's hole 3 now for most tournaments.