Thread: Par Talk
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Old 07-06-2019, 12:04 AM
Steve West Steve West is offline
Par Delusionary
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Originally Posted by gdub58 View Post
As I said a few hundred pages ago, the question should not be focused on whether par is doing its job. The issue has always been whether the design of a hole creates a scoring distribution where a good par can be assigned. Your data simply shows that some holes can't have a good par because they are poorly designed.

As this thread has become little more than you displaying scoring data in a variety of ways, I would like to see you make suggestions as to how the hole design can be changed to make the scoring distribution more appropriate for a particular par. Those changes may be in conjunction with changing the par, or it can be a suggestion to make the hole harder or easier to bring scores in line with the current par. Doesn't matter either way. The goal should be to have a good scoring distribution around par.

So, I think the question is: "What is the range of scoring distributions that we would find acceptable?" Should we start with the notion that par should always be the most frequently achieved score, but no higher than 80%? Can we agree that the proportion of birdies should be at least 5%? 10%? And they should be no higher than say, 30%?

I'm just pulling these numbers out of the air, but I think those are the questions that we should focus on, and, once we come to a consensus on the distributions that make a well-designed hole, your analyses going forward should tell us how many holes fit the "well-designed" criteria.

There is no connection between “good” distributions and easy-to-set par.

For one thing, I’m only looking at the scores of exactly 1000-rated players. The perfectly performing hole would give a certain percent of 1000-rated players a lower score and the rest a score of one more. Either score could be the more frequent one. There is no need for a third score on the other side of the most frequent score.

Also, a hole that did give out a nice bell-shaped set of scores to the exactly 1000-rated players might give out the same bell shape to all players. That wouldn’t measure skill at all.

So, it is not possible to look at the scoring distributions I use to set par and see whether a hole is well-designed. Different kind of scoring distribution.

Even if we were to forget about par and look at scoring distributions across a range of ratings (or performances), there is no mathematical reason I know of which would tell us that a distribution of 10/60/30 is better than 60/30/10 or 30/10/60. They all chop the list of competitors into three ranked pieces of the same sizes. The number of different scores given across a range of skill levels matters, but not the ordering of the frequency of each score.

In fact, the interplay between various orderings of frequency will enhance the score-setting abilities of combinations of holes. Three perfect holes with 10/60/30 x 2, 3, 4 distributions will only give out 3 scores: 6, 9, and 12. But, three holes with the three different scoring distributions above would give out scores of 6, 7, 8, 9, 10, 11, and 12. The diversity is good, not any one particular nice-looking distribution.

Even if you prefer the bell-shaped curve for scores, a good hole would generate a shifting bell curve with the peak moving to higher scores as player skills get worse. At some points along this continuum, there will be a double peak, and at some points the second-most common score will be lower than the most common, and at other points the second-most common score will be higher than the most common one. It’s just not possible for a hole that measures skill to give a nice bell-shaped curve with a prominent peak in the middle to every different skill level.

Having said all that, I will take your suggestion that a good par should have some scores below and above it. Take it one step further – there should be just as many scores above par as below – and we get back to the idea that a birdie should count for just as much as a bogey. So, one test will be how well the pars do this.

As for figuring out how to adjust the hole to get a desired scoring distribution, that’s a few steps harder than computing par, so I’d only do that for specific holes on request. Anyway, it is beyond the scope of this thread. This thread’s goal is to assign the most useful par to every possible hole.
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