What do these stats tell you about design?

[ssjfewp]

This is taken from 3 rounds of tournament play.

Hole 1 Avg. 3.285714286

2's - 30
3's - 154
4's - 60
5's - 20
6's - 2
7's - 0

Hole 2 Avg. 3.304511278

2's - 20
3's - 161
4's - 69
5's - 16
6's - 0
7's - 0

Hole 3 Avg. 3.372180451

2's - 22
3's - 152
4's - 67
5's - 21
6's - 4
7's - 0

Hole 4 Avg. 3.830827068

2's - 14
3's - 94
4's - 96
5's - 50
6's - 9
7's - 3

Hole 5 Avg. 3.169172932

2's - 36
3's - 163
4's - 56
5's - 8
6's - 3
7's - 0

Hole 6 Avg. 4.093984962

2's - 0
3's - 66
4's - 129
5's - 54
6's - 14
7's - 3

Hole 7 Avg. 3.281954887

2's - 26
3's - 156
4's - 69
5's - 13
6's - 2
7's - 0

Hole 8 Avg. 3.026315789

2's - 49
3's - 171
4's - 38
5's - 6
6's - 2
7's - 0

Hole 9 Avg. 3.109022556

2's - 50
3's - 157
4's - 43
5's - 12
6's - 4
7's - 0

Hole 10 Avg. 4.609022556

2's - 0
3's - 22
4's - 114
5's - 87
6's - 33
7's - 9
8's - 1

Hole 11 Avg. 3.360902256

2's - 26
3's - 142
4's - 78
5's - 16
6's - 4
7's - 0

Hole 12 Avg. 2.95112782

2's - 72
3's - 141
4's - 48
5's - 4
6's - 1
7's - 0

Hole 13 Avg. 3.740601504

2's - 0
3's - 118
4's - 104
5's - 40
6's - 3
7's - 1

Hole 14 Avg. 2.680451128

2's - 103
3's - 147
4's - 14
5's - 2
6's - 0
7's - 0

Hole 15 Avg. 3.766917293

2's - 15
3's - 96
4's - 105
5's - 37
6's - 13
7's - 1

Hole 16 Avg. 2.981203008

2's - 50
3's - 176
4's - 35
5's - 5
6's - 0
7's - 0

Hole 17 Avg. 3

2's - 49
3's - 171
4's - 43
5's - 3
6's - 0
7's - 0

Hole 18 Avg. 4.135338346

2's - 1
3's - 51
4's - 146
5's - 48
6's - 19
7's - 1

Here are the same stats using only the pro open field. The layout used was intended for pro's. This tournament included some of the best players in the world and had a combined average player rating of 991.

Hole 1 Avg. 2.901234568

2's - 26
3's - 40
4's - 12
5's - 3
6's - 0
7's - 0

Hole 2 Avg. 2.987654321

2's - 18
3's - 47
4's - 15
5's - 1
6's - 0
7's - 0

Hole 3 Avg. 3.086419753

2's - 15
3's - 48
4's - 15
5's - 2
6's - 1
7's - 0

Hole 4 Avg. 3.382716049

2's - 12
3's - 37
4's - 23
5's - 7
6's - 2
7's - 0

Hole 5 Avg. 2.913580247

2's - 22
3's - 46
4's - 12
5's - 0
6's - 1
7's - 0

Hole 6 Avg. 3.765432099

2's - 0
3's - 31
4's - 39
5's - 10
6's - 1
7's - 0

Hole 7 Avg. 2.864197531

2's - 19
3's - 55
4's - 6
5's - 1
6's - 0
7's - 0

Hole 8 Avg. 2.666666667

2's - 31
3's - 46
4's - 4
5's - 0
6's - 0
7's - 0

Hole 9 Avg. 2.802469136

2's - 30
3's - 42
4's - 6
5's - 1
6's - 2
7's - 0

Hole 10 Avg. 4.308641975

2's - 0
3's - 12
4's - 43
5's - 17
6's - 7
7's - 2
8's - 0

Hole 11 Avg. 2.901234568

2's - 20
3's - 48
4's - 12
5's - 0
6's - 0
7's - 0

Hole 12 Avg. 2.641975309

2's - 37
3's - 37
4's - 6
5's - 1
6's - 0
7's - 0

Hole 13 Avg. 3.345679012

2's - 0
3's - 57
4's - 20
5's - 4
6's - 0
7's - 0

Hole 14 Avg. 2.234567901

2's - 62
3's - 19
4's - 0
5's - 0
6's - 0
7's - 0

Hole 15 Avg. 3.271604938

2's - 10
3's - 44
4's - 23
5's - 3
6's - 1
7's - 0

Hole 16 Avg. 2.703703704

2's - 29
3's - 47
4's - 5
5's - 0
6's - 0
7's - 0

Hole 17 Avg. 2.790123457

2's - 26
3's - 45
4's - 9
5's - 0
6's - 0
7's - 0

Hole 18 Avg. 3.703703704

2's - 1
3's - 32
4's - 40
5's - 6
6's - 2
7's - 0

These numbers say a lot to me but I also know the course in and out. If you know which course this is from, please refrain from commenting. I'd like to know what stands out based on these numbers. Which holes should be addressed to improve the design based solely on these stats. Thanks.

[Cgkdisc]

The numbers are not useful for analysis unless they are normalized to a specific skill level of 1000 rating for Gold or 950 rating for Blue depending on what level the course was designed for. Check out this article for help: http://www.pdga.com/course-design-validation

[solomon.trenton]

par for the hole would be nice, I can guess the par from the average but...

[ssjfewp]

Chuckles,
I know that article well. The layout used was intended to challenge gold level players but knowing that blue and white level players were there, we didn't go all out. That's why I separated it by the pro field only and the entire tournament. We're seriously limited to what can be done but other pin positions and some other tees exist to accommodate those blue and white level players for recreational play. I understand these numbers don't paint a great picture but do they tell you anything about the design?

Thanks

[Cgkdisc]

You need to either use the scores from a set of those players with ratings between say 965 to 1045 who average exactly a 1000 rating. Or, you need the program that the DCGD course designers use to adjust the scores to produce a distribution for the equivalent of a 1000 rated pool. Otherwise, analyzing the data doesn't mean anything since you won't always get the same mix of players each event.

[ssjfewp]

I can do that but I may be missing the point. Why exactly 1000? Some of the ratings are likely inflated and they're ever changing anyway. Design according to the color scheme is nothing more than a reference point, right? You don't design for a specific rating...more of a range that falls roughly into those categories. I'm happy to do it but why doesn't the average rating of 991 not tell you enough?

[Cgkdisc]

Gold level is 1000 rating average and it's also the rating for the course SSA. All of the design data is referenced to that. Even though you always get a mix of player ratings at an event, the scoring spreads are based on specific ratings reference points of 1000, 950, 900 or 850 so you can look and see if the layout is suited for the gold, blue, white or red level as planned. If you look at spreads for a pool of 50 players averaging 1009 versus a pool averaging 991 like you have, they are both 9 points from 1000 but they average almost a half a skill level difference and the spreads will be different on each hole. Both sets of numbers either need to be mathematically adjusted to 1000 or you need to select scores only from a group of players who average 1000 exactly, not just the ones who shot well compared to their rating but everyone you can include and still have the average at 1000. It's okay, in fact desirable, to have more than one round of scores on the same layout from the same players if available.

[agent_peebody]

looks like a bunch of jibberish to me

[Cgkdisc]

looks like a bunch of jibberish to me
That "gibberish" is what helped tweak the Lemon Lake courses, as a group, to be one of the most balanced and fair set of holes at Worlds, based on player feedback.

[Steve West]

They tell me that there must have been an ace on both 11 and 17 in the second round, and some joker played only hole 15 in the first.

[ssjfewp]

Ok, this equals 1000

Hole 1 Avg. 2.818181818

2's - 26
3's - 28
4's - 6010
5's - 2
6's - 0
7's - 0

Hole 2 Avg. 2.893939394

2's - 17
3's - 40
4's - 8
5's - 1
6's - 0
7's - 0

Hole 3 Avg. 2.893939394


2's - 15
3's - 43
4's - 8
5's - 0
6's - 0
7's - 0

Hole 4 Avg. 3.257575758

2's - 12
3's - 30
4's - 19
5's - 5
6's - 0
7's - 0

Hole 5 Avg. 2.787878788

2's - 21
3's - 38
4's - 7
5's - 0
6's - 0
7's - 0

Hole 6 Avg. 3.696969697


2's - 0
3's - 29
4's - 29
5's - 7
6's - 1
7's - 0

Hole 7 Avg. 2.803030303

2's - 18
3's - 43
4's - 5
5's - 0
6's - 0
7's - 0

Hole 8 Avg. 2.651515152

2's - 25
3's - 39
4's - 2
5's - 0
6's - 0
7's - 0

Hole 9 Avg. 2.772727273

2's - 27
3's - 32
4's - 4
5's - 1
6's - 2
7's - 0

Hole 10 Avg. 4.196969697


2's - 0
3's - 12
4's - 35
5's - 14
6's - 4
7's - 1
8's - 0

Hole 11 Avg. 2.772727273

2's - 20
3's - 41
4's - 5
5's - 0
6's - 0
7's - 0

Hole 12 Avg. 2.560606061

2's - 36
3's - 24
4's - 5
5's - 1
6's - 0
7's - 0

Hole 13 Avg. 3.257575758

2's - 0
3's - 51
4's - 13
5's - 2
6's - 0
7's - 0

Hole 14 Avg. 2.181818182

2's - 54
3's - 12
4's - 0
5's - 0
6's - 0
7's - 0

Hole 15 Avg. 3.151515152

2's - 10
3's - 37
4's - 18
5's - 1
6's - 0
7's - 0

Hole 16 Avg. 2.651515152

2's - 27
3's - 35
4's - 4
5's - 0
6's - 0
7's - 0

Hole 17 Avg. 2.712121212

2's - 25
3's - 35
4's - 6
5's - 0
6's - 0
7's - 0

Hole 18 Avg. 3.606060606

2's - 1
3's - 30
4's - 30
5's - 4
6's - 1
7's - 0

[sgamerp]

looks like the stat tracker is off. but it also seems like peope give up after the first hole.

[ssjfewp]

Hole 1- 4's=10

[Kwick]

This hole seems a little too easy. A par loses a stroke on the field, which shouldn't be the case.

Hole 14 Avg. 2.234567901

2's - 62
3's - 19
4's - 0
5's - 0
6's - 0
7's - 0

[Cgkdisc]

Front 9 is solid gold where maybe just hole 6 could be toughened up. Consider adding around 100 ft to 14 and 50ish ft to 12. Hole 18 is pretty good but could be made a little less of a tweener with a little more length if possible in the 30-60 ft range. Hole 13 should maybe be shortened by as much as 100 ft. Overall, a pretty solid gold level layout from a scoring standpoint.

[Dave242]

13 & 14 jumped out to me as holes that need tweaking (both in your 991 avg data and 1000 avg data). Chuck's suggestion of length is OK, but of course you could do things with hole shape as well to force a harder line for shot-shaping (rewarding those who can do it and punishing those who can't).

[Cgkdisc]

Not sure how the routing works on these holes but I might look at 12 thru 14 as a group for potential changes in all three.

[Dave242]

Gold level is 1000 rating average and it's also the rating for the course SSA. All of the design data is referenced to that. Even though you always get a mix of player ratings at an event, the scoring spreads are based on specific ratings reference points of 1000, 950, 900 or 850 so you can look and see if the layout is suited for the gold, blue, white or red level as planned. If you look at spreads for a pool of 50 players averaging 1009 versus a pool averaging 991 like you have, they are both 9 points from 1000 but they average almost a half a skill level difference and the spreads will be different on each hole. Both sets of numbers either need to be mathematically adjusted to 1000 or you need to select scores only from a group of players who average 1000 exactly, not just the ones who shot well compared to their rating but everyone you can include and still have the average at 1000. It's okay, in fact desirable, to have more than one round of scores on the same layout from the same players if available.

I have not invested nearly as much time or effort into this as you (and others), but it seems to me you need to understand the spread of scores going into those averages.

For example, for determining the appropriateness of scoring spread for Blue level players on a Blue level course if you have scores from 5 players each from each 10-point range from the 880's to 1020's you have MUCH more meaningless data than if you have data from 75 players whose ratings are 945-955.

[Cgkdisc]

The formal range of player ratings for each level is +/- 25 points from those midpoints, i.e., ideally for gold 975-1024(+), blue 925-974, white 875-924 and Red 825-874. From a practical standpoint, I use scores +/- 35 from the midpoints, i.e. 965+ for gold or 915-985 for blue and the Hole Forecaster template adjusts their score distribution to the midpoint rating if needed.

[chrishysell]

Those scores tell me that no one aced. I didn't look any farther than that.

[Dave242]

I have not invested nearly as much time or effort into this as you (and others), but it seems to me you need to understand the spread of scores going into those averages.

Meant "ratings" (sort of obvious I guess).

.....and I agree that if you can use only stats from players within the 50 point window (ie 925-975 for Blue) that is best. That is the disclosure I would want from ssjfewp on his 991 & 1000 average (you need to provide the average and the spread).

That said, the 991 and 1000 tell exactly the same story......so I discard the notion that you have to normalize to 1000 (Gold) or 950 (Blue). If your group average is off by 20 points, that is 2-3 throws per round which equals 0.11 - 0.17 throws per hole. That is negligible for "rule-of-thumb" approach that goes into this sort of analysis. You will get that much variation (or more) day to day, event to event with a limited sample size (and that is all that is available data-wise for the vast majority of tournaments).

[Cgkdisc]

If you're gpoing to make the effort at all, you may as well do it properly. That's one of the differences among those who design professionally versus casually. A 0.11-0.17 shift in distribution can be enough on certain holes to make you consider changes versus not looking at that hole.

[Steve West]

This saves me a headache trying to figure out which scoring distributions are narrow. To the left is narrower.

So, 13 and 14 jump out as not doing much to sort out players. 18, 10, and 6 take a lot of shots to achieve the same results as some other holes.

However, I would prefer to base the analysis not just on the scoring distribution, but on the hole-by-hole scores of each player. That would tell me which holes contributed the most (or least) to the final ranking of players.

Short of that, I would rather look at the distribution of the total score of each player from all rounds for each hole.

[ssjfewp]

Good stuff. Thank you.

[Dave242]

If you're gpoing to make the effort at all, you may as well do it properly. That's one of the differences among those who design professionally versus casually. A 0.11-0.17 shift in distribution can be enough on certain holes to make you consider changes versus not looking at that hole.

Sounds like a circular definition there on a couple levels, Chuck ("properly" and "professionally".

[Cgkdisc]

It is when you and the Course Committee are charged as the "definers" by the PDGA.

[Dave242]

This saves me a headache trying to figure out which scoring distributions are narrow. To the left is narrower.

So, 13 and 14 jump out as not doing much to sort out players. 18, 10, and 6 take a lot of shots to achieve the same results as some other holes.

However, I would prefer to base the analysis not just on the scoring distribution, but on the hole-by-hole scores of each player. That would tell me which holes contributed the most (or least) to the final ranking of players.

Short of that, I would rather look at the distribution of the total score of each player from all rounds for each hole.

I really like this chart.

http://www.dgcoursereview.com/forums/attachment.php?attachmentid=6885&d=1282853421

My first reaction when I looked at it is that if you do an absolute spread you factor in situations like 3-putting. Those usually have more to do with a player than what the hole is doing to the player.

But then I looked at the data and your chart and it looks like you did some sort of spread based +/- X standard deviations......which gives a more clear picture.

[Steve West]

I really like this chart.

http://www.dgcoursereview.com/forums/attachment.php?attachmentid=6885&d=1282853421

My first reaction when I looked at it is that if you do an absolute spread you factor in situations like 3-putting. Those usually have more to do with a player than what the hole is doing to the player.

But then I looked at the data and your chart and it looks like you did some sort of spread based +/- X standard deviations......which gives a more clear picture.

The formula for Scoring Spread (a measure of the width of a scoring distribution) is:

2^(0-Sum(Pr(x)*log(Pr(x),2)).

Where

x is each score value (2, 3, 4, etc.).

Pr(x) is the percent of players who scored x.

log(Pr(x),2) is the log in base 2 of the percent of players
who scored x.

The part (0-Sum(Pr(x)*log(Pr(x),2)) is the bits of information in the distribution, or entropy value.

Raising 2 to the bits-of-information gives a number equivalent to the number of unique scores in the distribution.

For example,

(50, 0, 50, 0) produces a Scoring Spread of 2.00
(25, 25, 25, 25) produces a scoring spread of 4.00
(50, 25, 0, 25) produces a scoring spread of 2.82.

[Dave242]

Are you using "scoring spread" or "width of distribution" in the chart? I am confused now.....and see that the way I used the terms (somewhat interchangeably) in my post might have confused you since you do not use them interchangeably.

BTW, would not (25, 25, 25, 25) produce a scoring spread of 1.00 (rather than the 4.00 you list above)?

[DSCJNKY]

The formula for Scoring Spread (a measure of the width of a scoring distribution) is:

2^(0-Sum(Pr(x)*log(Pr(x),2)).

Where

x is each score value (2, 3, 4, etc.).

Pr(x) is the percent of players who scored x.

log(Pr(x),2) is the log in base 2 of the percent of players
who scored x.

The part (0-Sum(Pr(x)*log(Pr(x),2)) is the bits of information in the distribution, or entropy value.

Raising 2 to the bits-of-information gives a number equivalent to the number of unique scores in the distribution.

For example,

(50, 0, 50, 0) produces a Scoring Spread of 2.00
(25, 25, 25, 25) produces a scoring spread of 4.00
(50, 25, 0, 25) produces a scoring spread of 2.82.

Holy Sh!t.
DSCJNKY

[Billipo]

The stats tell me that someone might think disc golf theories are accurate to 9 decimal places.

[Steve West]

Are you using "scoring spread" or "width of distribution" in the chart? I am confused now.....and see that the way I used the terms (somewhat interchangeably) in my post might have confused you since you do not use them interchangeably.

BTW, would not (25, 25, 25, 25) produce a scoring spread of 1.00 (rather than the 4.00 you list above)?

I use "Scoring Spread" (capitalized) to mean this particular calculation, which is one measure of the more generic term "width of distribution".

Some people might use other measures of the width of distribution - like standard deviation, or the difference between the top and bottom scores, or the inverse of the proportion of players that get the most common score.

This chart uses Scoring Spread as its measure of width of distribution. I probably should have used that term, but I thought width of distribution might make more sense to all those casual readers of this thread.

Any set of scores that are evenly distributed will produce a Scoring Spread equal to the number of distinct scores. So, if 25 players get a 2, 25 get a 3, 25 get a 4, and 25 get a 6, the Scoring Spread is 4.

Calculation: There are four different scores, each of which is scored by one-fourth of the players. The logarithm (in base 2) of one-fourth is -2. The product of one-fourth and -2 is -.5. Add up four -.5's and you get -2. Two raised to the (0 minus -2) is 4.

Note that for the purposes of calculating Scoring Spread, it doesn't matter what the particular scores are, only the proportion of players that scored each.

The calculation of 2.82 is left as an exercise for the student.

[REDARMY]

i don't know how anyone can deduce design criteria without other factors thrown in: elevation/weather, etc...

[REDARMY]

The stats tell me that someone might think disc golf theories are accurate to 9 decimal places.

LOL :clap::clap:

yeah, way too much math for me.

[Billipo]

Seriously on the math side....

Disc golf courses are not constructed, but carved into the randomness of nature merely cutting down trees and using the terrain mother nature gives us until we loop back to the parking lot. I suspect this makes it virtually impossible to design the perfect course. Big difference between ball and disc golf!

Any effort been made to understand the fractal geometry work of Benoit Mandelbrot or various laws of nature and applying to disc golf course design or scoring analysis? Might be better at predicting numbers than arm chairing numbers....dunno.

[Steve West]

Well, that seems to be about all that we can squeeze out of those numbers.

Now, how about a course map, so we can discuss whether the numbers told us anything or not?

[ArcheType]

These scores tell me, that you didn't play in the pro division,

And want a reason to cry about the course being too hard for anyone who isn't a pro.