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View Poll Results: Which of these best describes Hole 18 at the Utah Open?
A par 2 where 38% of throws are errors, and 1% of throws are hero throws. 6 25.00%
A par 3 where 24% of throws are errors, and 33% of throws are hero throws. 16 66.67%
A par 4 where 16% of throws are hero throws, and 23% are double heroes. 1 4.17%
A par 5 where 37% of throws are hero throws, and 21% are double heroes. 0 0%
A par 6 where 16% of throws are hero throws, and 62% are double heroes. 1 4.17%
Voters: 24. You may not vote on this poll

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  #3981  
Old 11-21-2019, 06:37 PM
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Doofenshmirtz Doofenshmirtz is offline
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Quote:
Originally Posted by Steve West View Post
What would be the pros and cons of actually telling TDs after the fact what the pars should have been?
LOL.
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  #3982  
Old 11-22-2019, 06:02 PM
Steve West Steve West is offline
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Originally Posted by DavidSauls View Post
Might a lower rating also indicate that most holes yielded more birdies than bogeys, even if par were set correctly?
Yes.

For that reason, we cannot point to any one round here and say “this one was not based on 1000-rated play.” At least not any round rated above 970 or so.


However, not very many courses will have enough holes where birdies outnumber bogeys for this to happen. It varies by method.

Rounded Average score sets par so high that 61% of holes will have more birdies than bogeys. Which means that about one-third of courses will have enough holes with more birdies than bogeys so that there is a 50/50 chance the round rating comes out below 990. Multiplying all the probablities together, I calculate that 27% of courses that use Rounded Average would have a round rating below 990, and almost none would generate a round rating higher than 1030.

Mode sets pars low enough that only 42% of holes will have more birdies than bogeys. Just 0.2% of courses that use Mode would have a round rating below 990, while 19% would have a round rating above 1030.

For Standard par (which is what I’m currently calling my method with no hint of hubris at all) 52% of holes will have more birdies than bogeys, 5% of courses would have a round rating below 990, and 0.8% would have a round rating above 1030.

Note that the definition of “set correctly” comes into play. I don’t consider Rounded Average to be compatible with the definition. But, let’s be overly generous and assume all TDs were setting par based on Rounded Average for 1000-rated players. Of the 395 rounds, 107 rounds would be rated less than 990 based on chance and the generosity of Rounded Average par. What we actually saw was 318 rounds rated less than 990.

That still leaves 211 out of 395 rounds that where par was very likely not set based on the play of 1000-rated players – in other words, most of them.
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  #3983  
Old 11-22-2019, 06:47 PM
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Aren't round ratings, essentially, reflecting an average of averages?

Just as a bunch of more-easily-birdieable holes will tilt it, so will a course with enough OB strokes, so players can pile up multi-bogeys on some holes.
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  #3984  
Old 11-22-2019, 07:18 PM
Steve West Steve West is offline
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Quote:
Originally Posted by DavidSauls View Post
Aren't round ratings, essentially, reflecting an average of averages?

Just as a bunch of more-easily-birdieable holes will tilt it, so will a course with enough OB strokes, so players can pile up multi-bogeys on some holes.
Yes. As would a course with a lot of holes that have more bogeys than birdies. Both would increase the round rating for a score equal to par.
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  #3985  
Old 11-25-2019, 09:30 AM
Steve West Steve West is offline
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Rounds ratings of even par by TD. Open division, A-tiers, Majors, NTs, and Eurotour.

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  #3986  
Old 12-02-2019, 04:51 PM
Steve West Steve West is offline
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I had one more graph laying around.

Each black dot represents the score which was par for one round. The gold bar vertically aligned with the black dot represents the scores that fall between round ratings of 990 and 1030. The rounds are sorted left to right by the score that would get a round rating of 1010.

If all TDs set par based on the play of 1000-rated players (using any method), the black dots would mostly fall into the gold ranges.

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  #3987  
Old 12-14-2019, 01:28 PM
Steve West Steve West is offline
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I’ve been messing around with my data set after adding data points from 2018 and 2019. I now have 27,652 scoring distributions for various ratings.

This chart shows how Standard Par compares to Average Score. The blue grid lines indicate the outer edges of the range of scores or pars that would collapse into the nearest integer.

The white dots are a number which, when rounded, will collapse to the integer standard par. The higher up within a block, the closer that hole is to earning a higher par. A dot very low in the block means the hole barely qualified for that par.

For example, the column above the “Average Score” axis title contains the holes were the average score was between 4.5 and 5.49… – those that would round to 5.

The row to the right of the “Standard Par” axis title contains the holes where Standard Par would be 4.

The block where these two intersect contains holes that would have a rounded average score of 5, but a Standard Par of 4.



Now, who is going to be the first to find the island holes?
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  #3988  
Old 12-15-2019, 02:28 PM
Steve West Steve West is offline
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Here is the same kind of chart, except based on the idea that the most common score - Mode - should be par.

For the graph, I solved for the exact score which maximizes the quadratic equation for the frequencies of the mode and the scores one above and below it. For example, if the mode is 3, but there are almost as many 4s and not many 2s, the exact mode would be something like 3.49. This always rounds to the integral most common score. So, every dot between two horizontal blues lines would result in Mode par equal to the y-axis label.
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  #3989  
Old 12-16-2019, 11:01 AM
Steve West Steve West is offline
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And here is the graph based on the idea that par should be the lowest score which at least half the players get.

(I actually prefer a 42% threshold, rather than 50%. Which shifts the dots a little lower.)

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  #3990  
Old 12-16-2019, 12:53 PM
tbonesocrul tbonesocrul is offline
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Quote:
Originally Posted by Steve West View Post
I’ve been messing around with my data set after adding data points from 2018 and 2019. I now have 27,652 scoring distributions for various ratings.

This chart shows how Standard Par compares to Average Score. The blue grid lines indicate the outer edges of the range of scores or pars that would collapse into the nearest integer.
Is the Average Score just a naive average of the scores for a hole independent of player rating or Average Scores weighted to represent a 1000 rated player?
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