Hole and Course Performance Statistics

[Steve West]

This thread is for posting and talking about measures of how courses and holes perform.

 

[Steve West]

I'm trying out a new way to present measures of how each of the holes performed, relative to the other holes on the same course. See if this is self-explanatory.

 

[ElementZ]

Wouldn't "correlation to other holes" and "correlation to rating" be strongly correlated? I think you'd be okay with leaving one of these out. Really cool visualization though, Steve.

Just to see if I understand...taking #3 as an example...

It has a very low average (presumably a short par 3), yet has an above average scoring spread (variance?). Performance on this hole has a very strong correlation with other holes, which means it's predictive of total round score?

 

[ThrowBot]

All of the parameters seem pretty self explanatory to me, except the top one: "Average"
Is that the average of the hole's scores, and how does that average perform better or worse relative to other holes?

Also, question on "Correlation to Other Holes" ... How is that different from "Contribution" ?
(My understanding is that Corr. to Other Holes is a measure of how similarly a hole distributes scores to players, compared to the other holes on the course. And Contribution is how closely that hole distributes scores, relative to the total round. So those two parameters should track closely in my mind. But I see that they don't always match that closely. Am I off in my interpretations?)

Also, unless my interpretation is wrong for "Correlation to Other Holes", I think that's a dubious way to judge hole performance. A course that only tests a small number of skills will have very high correlation between all the holes...but that's also boring design, in my opinion. I would almost rather see holes that don't correlate well with each other, as long as other metrics of randomness/fairness are good (i.e. correlation to rating, contribution).

 

[Steve West]

Wouldn't "correlation to other holes" and "correlation to rating" be strongly correlated? I think you'd be okay with leaving one of these out. Really cool visualization though, Steve.

I'll probably leave out correlation to ratings, because ratings aren't always available at the same source as hole scores.

I like the five-pointed star because (at least in USA) it's a shape that people can instantly recognize as correct or warped. Good holes get a star.

So, I'm looking for a fifth number that represents what we want a score generating machine to do.

Just to see if I understand...taking #3 as an example...

It has a very low average (presumably a short par 3), yet has an above average scoring spread (variance?). Performance on this hole has a very strong correlation with other holes, which means it's predictive of total round score?

Pretty much.

Scoring spread is like variance, but not the same. It counts how many different scores were given out, but with fractional counts for rarer scores. Scoring Spread doesn't care about the magnitude of scores, so a hole that gives out 50/50 2s and 3s would have the same scoring spread as a hole that gives out 50/50 2s and 4s. Both holes divide the field into two equal parts.

 

[Steve West]

All of the parameters seem pretty self explanatory to me, except the top one: "Average"
Is that the average of the hole's scores, and how does that average perform better or worse relative to other holes?

Also, question on "Correlation to Other Holes" ... How is that different from "Contribution" ?
(My understanding is that Corr. to Other Holes is a measure of how similarly a hole distributes scores to players, compared to the other holes on the course. And Contribution is how closely that hole distributes scores, relative to the total round. So those two parameters should track closely in my mind. But I see that they don't always match that closely. Am I off in my interpretations?)

Also, unless my interpretation is wrong for "Correlation to Other Holes", I think that's a dubious way to judge hole performance. A course that only tests a small number of skills will have very high correlation between all the holes...but that's also boring design, in my opinion. I would almost rather see holes that don't correlate well with each other, as long as other metrics of randomness/fairness are good (i.e. correlation to rating, contribution).

It is just the average score. For all the stats, what is shown as a longer point is just bigger. Perhaps higher average isn't always better. However, generally the higher the average score the better the hole performs. Most of the time, most of the signs of a weakly performing hole can be solved by making the hole harder.

All of these stats are like components of good performance, or tools to use to get good performance. None are direct measures of a general concept of "good performance" (whatever that would be). That takes a lot more data and a lot more complicated formulas, and it would be less obvious how to change the hole to increase performance.

I share your concern about correlation. If we relied too heavily on it, we would end up with nothing but 320 foot hyzer throws. However, the variety of holes out there is so great that at this point, if a hole does not correlate well with other holes, it's most likely because of a bad design.

Contribution is a check on correlation. A hole gets a big contribution by non-randomly sorting out the players that the other holes did not sort out. If a hole has low correlation and a big contribution, that indicates it is properly testing a different skill than the other holes.

Conversely, a hole that has high correlation but low contribution is just being a yes-man to the other holes.

 

[teemkey]

I don't know if you want to take the plunge, but a measure of consistency over multiple rounds (when available) would be great.

Another interesting summary number would be the Q-function of the score distribution (i.e. the probability a score will exceed some multiple of the standard deviation, which would identify "disaster holes"). Or do you think scoring spread is sufficient?

 

[Steve West]

I don't know if you want to take the plunge, but a measure of consistency over multiple rounds (when available) would be great.

I do look at that when there are four or more rounds. For this chart I want to keep it to a straightforward scores-in stats-out function.

Another interesting summary number would be the Q-function of the score distribution (i.e. the probability a score will exceed some multiple of the standard deviation, which would identify "disaster holes"). Or do you think scoring spread is sufficient?

Good idea, thanks. I'll need to look at that. It sounds like it could be a check on scoring spread, to see if the hole is too loose.

 

[tbonesocrul]

Is there any way you could compare the scoring spread with and without penalty strokes? That might be interesting.

Also this is really interesting. I'm also curious more about the actual numbers/scaling methods.

 

[Steve West]

Is there any way you could compare the scoring spread with and without penalty strokes? That might be interesting.
...

That would be really easy - if I could get the penalty throws player by player, hole by hole. PDGA Live doesn't record them, and I haven't figured out any way short of going through each player and picking them out by hand from the UDisc stats. Ain't nobody got time for that.

 

[Steve West]

In the meantime, I've been cramming more info into the chart and re-scaled to better handle cases with negative values.

I also replaced Correlation to Ratings with Typicality which measures how well the holes scoring distribution matches the prototypical scoring distribution for a hole with the same average.

Usually, low scores of Typicality come from too many 3s or from an island hole with lots of 2s and 4s.

So here is San Francisco Open 2018 Gleneagles Golf Course MPO again.

and Santa Cruz Masters Cup presented by Innova - National Tour DeLaveaga Golf Course MPO

 

[sidewinder22]

In the meantime, I've been cramming more info into the chart and re-scaled to better handle cases with negative values.

I also replaced Correlation to Ratings with Typicality which measures how well the holes scoring distribution matches the prototypical scoring distribution for a hole with the same average.

Usually, low scores of Typicality come from too many 3s or from an island hole with lots of 2s and 4s.

So here is San Francisco Open 2018 Gleneagles Golf Course MPO again.

and Santa Cruz Masters Cup presented by Innova - National Tour DeLaveaga Golf Course MPO

Distance generally appears to make the star pointier.

 

[Steve West]

Distance generally appears to make the star pointier.

Definitely.

Since distance is almost always a limited resource, the art of design is to find the ways to make the star pointier without adding distance.

 

[Steve West]

2018 PDGA United States Amateur Disc Golf Championship on The Toboggan

 

[tbonesocrul]

That would be really easy - if I could get the penalty throws player by player, hole by hole. PDGA Live doesn't record them, and I haven't figured out any way short of going through each player and picking them out by hand from the UDisc stats. Ain't nobody got time for that.

I'll let you know if I get bored one day and manually work through a round. I thought I read you didn't include scores with penalty strokes when you do your par ratings, maybe there is something similar you could do with a scoring spread analysis?

 

[Steve West]

I'll let you know if I get bored one day and manually work through a round. I thought I read you didn't include scores with penalty strokes when you do your par ratings, maybe there is something similar you could do with a scoring spread analysis?

Do the Utah Open, or SC Masters Cup Golf course.

For par, I don't manually exclude scores with penalty throws. They just usually don't survive the crucible of taking only enough lowest scores to figure out what par should be. If there are enough penalty throws so that an expert cannot expect to avoid them, or if taking a penalty is the smart thing to do - such as teleporting to a very favorable DZ, penalty throws can be part of par.

I've never found a way to precipitate out ANY kinds of throws - drives, putts, or penalties - by just looking at scores, even if hole lengths and ratings are also available. I need a centrifuge, I guess.

 

[Steve West]

Beaver State Fling presented by KEEN - National Tour 2018 Milo McIver West & East

Beaver State Fling presented by KEEN - National Tour 2018 Milo McIver West & East

 

[Steve West]

DGPT - Discraft Ledgestone Insurance Open 2018 Eureka Temp A&B

 

[BogeyNoMore]

Thanks Steve! This sort of stuff is a DG Stat Geek's wet dream.
Hopefully people take this sort of data into consideration when designing new courses.

 

[BogeyNoMore]

...but I doubt many really will.
I don't think most "course designers" (in the loosest possible definition of the word), can really make sense of it.

I think the next step would be to take the really warped stars, look at those holes, and see "what attributes do those holes have that cause them to generate these unwanted results?"

If that can be summarized in a set of guidelines, sort of a "Do's and Dont's" of course design, perhaps we'd all benefit.

But I have a feeling, it's not so simple/easier said than done.