What do these stats tell you about design?

[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.

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.

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.