Par Talk

[DG_player]

I've been refining my newest method (expectational par) which selects whichever par results in the highest expectation of normal throws underlying the scoring distribution. I'm comparing it to the Errorless method, as well as to the par people set for a hole, knowing its scores and stats.

That's where you come in – what par would you give these holes, and why?

For this test, I used all the Idlewild MPO players as "experts" so the course statistics from Udisc could be used without adjustment. So, we're setting par for the field here, not 1000-rated players. The average rating was 977, so it's about halfway between Gold and Blue.

For most holes, both errorless par and expectational par came up with the same par. Both came up with a total par of 65. I'll post stats for the holes where there are differences. For discussion. One at a time.

Hole 2, with 3=41%, 4=37%, 5=17%, 6=5% came out as par 4 using errorless, and par 3 using expectational.

Par 4 errorless implies the top 94% of throws were errorless, while par 3 would imply the top 74% of throws were errorless.

Using the expectational method, par 3 - with 26% errors - generated a higher chance of normal throws than par 4 with 6% errors, 23% heroes, and 3% double errors. 74% normal @ 3 vs. 70% normal @ 4.

Udisc stats were: Average = 3.89, OB=0.19, FWH=81%, c1 in 2=48%, c2 in 2=57%, Scr.=50%, Parked=17%.

This seems like an obvious par 4, it has a 3.86 average and median score of 4. Maybe slightly easy for a par 4, but still a par 4.

Once again I will raise the question I raised earlier. What is the logic behind going with the score that generates the most "normal" throws? Certainly a distribution that includes the full range of shots is more realistic than one that only includes errors and normal throws. Especially considering more traditional statistics support a par 4.

 

[Steve West]

This seems like an obvious par 4, it has a 3.86 average and median score of 4. Maybe slightly easy for a par 4, but still a par 4.

Once again I will raise the question I raised earlier. What is the logic behind going with the score that generates the most "normal" throws? Certainly a distribution that includes the full range of shots is more realistic than one that only includes errors and normal throws. Especially considering more traditional statistics support a par 4.

Choosing the par that results in the most normal throws is one candidate for the rule to select from several candidate pars.

Choosing the par that has a typical "full range" of throws is another candidate for the rule to select from several candidate pars. I'm not sure what ratio is correct. Should we pick the par that comes closest to implying equally as many errors as heroes? Or do players make more throws that cost them a throw than throws are as good as two normal throws?

Perhaps not all holes offer opportunities for a typical balance between errors and hero throws. My thinking is that betting on normal throws predominating is safer than betting that a hole will have a full range of throws.

 

[biscoe]

... because...?

drive leg leaves you outside of close range.

 

[DG_player]

Choosing the par that results in the most normal throws is one candidate for the rule to select from several candidate pars.

Choosing the par that has a typical "full range" of throws is another candidate for the rule to select from several candidate pars. I'm not sure what ratio is correct. Should we pick the par that comes closest to implying equally as many errors as heroes? Or do players make more throws that cost them a throw than throws are as good as two normal throws?

Perhaps not all holes offer opportunities for a typical balance between errors and hero throws. My thinking is that betting on normal throws predominating is safer than betting that a hole will have a full range of throws.

Your method is purely numbers driven. You don't look at the physical throw required based on the actual hole to determine what qualifies as errorless throw quality. Therefore if you're going to qualify a shot as "normal" you need to base it on whether or not it gets you close to the expected score. Clearly the expected score for this hole is much closer to 4 than 3 (3.86 average and 4 median), so how is it possible that "normal" throws are going to result in a 3, when 4 is the expected score?

 

[Steve West]

Your method is purely numbers driven. You don't look at the physical throw required based on the actual hole to determine what qualifies as errorless throw quality. Therefore if you're going to qualify a shot as "normal" you need to base it on whether or not it gets you close to the expected score. Clearly the expected score for this hole is much closer to 4 than 3 (3.86 average and 4 median), so how is it possible that "normal" throws are going to result in a 3, when 4 is the expected score?

Which kind of expected score is exactly what we're trying to figure out. More specifically, expected with errorless play.

Average score is one kind of expected score, but it includes errors. Average score without errors would be nice to have. That might be 3 on this hole. Can we figure that out from the Udisc stats?

The kind of expected score that is under scrutiny is based on the presumption that if par is the expected score, then par-quality throws should dominate, so the best par is the one which implies the most par-quality throws.

We'll try to see whether it works or not by looking at this and a few other holes where par is arguable.

 

[Cgkdisc]

Your method is purely numbers driven. You don't look at the physical throw required based on the actual hole to determine what qualifies as errorless throw quality. Therefore if you're going to qualify a shot as "normal" you need to base it on whether or not it gets you close to the expected score. Clearly the expected score for this hole is much closer to 4 than 3 (3.86 average and 4 median), so how is it possible that "normal" throws are going to result in a 3, when 4 is the expected score?

So if players average more than 0.5 penalties on a hole, should that flip the par towards the higher integer par because it's "normal" for the hole or be removed as an error and the par resolved to the lower integer?

 

[DG_player]

Which kind of expected score is exactly what we're trying to figure out. More specifically, expected with errorless play.

Average score is one kind of expected score, but it includes errors. Average score without errors would be nice to have. That might be 3 on this hole. Can we figure that out from the Udisc stats?

The kind of expected score that is under scrutiny is based on the presumption that if par is the expected score, then par-quality throws should dominate, so the best par is the one which implies the most par-quality throws.

We'll try to see whether it works or not by looking at this and a few other holes where par is arguable.

You might as well throw errorless out the window. It's completely undefined. You can't determine the definition simply by using statistics.

 

[Steve West]

You might as well throw errorless out the window. It's completely undefined. You can't determine the definition simply by using statistics.

So is "as determined by" for that matter. Rather than make a wild guess as to whether that means announced at the players meeting, on the scorecard, or in the caddy book, or in the TD's most private thoughts, I guess we could throw that part out the window.

I prefer to try out various working definitions to see if there is a practical benefit. The one I'm working on now for "expected errorless" is: a throw that does not increase or decrease the expected score.

Answering Chuck's question is also a step toward defining it.

 

[DG_player]

So if players average more than 0.5 penalties on a hole, should that flip the par towards the higher integer par because it's "normal" for the hole or be removed as an error and the par resolved to the lower integer?

If the majority of experts are throwing OB, I don't see how you could discard it from the expected score.

 

[Cgkdisc]

If the majority of experts are throwing OB, I don't see how you could discard it from the expected score.

Related question, Is it acceptable hole design if players are already starting the hole with the expectation of a penalty every other time they play it?

 

[brutalbrutus]

I got one that will make your blood boil a bit Steve...

I shot even par 54 at league last night and got 871.:gross: Got 938 on DGCR ratings, lol...


Side question, am I still considered a propagator even if I am not current but still have enough rounds to qualify?

 

[DG_player]

Related question, Is it acceptable hole design if players are already starting the hole with the expectation of a penalty every other time they play it?

If an expert is more likely than not to get a penalty, and still chooses to do so rather than take the "safe" route (assuming one exists), IMHO that would be a poorly designed hole (whether or not a safe route exists).

 

[Steve West]

If the majority of experts are throwing OB, I don't see how you could discard it from the expected score.

Right, but should it be included in the expected score with errorless play?

Or are you saying that if the majority of experts are doing it, then it becomes errorless?

 

[DavidSauls]

What if you have a long hole with multiple places to go OB---1st shot, 2nd shot, or 3rd shot. For each shot, OB is not expected, but you would expect most players to go OB at some point playing that hole?

 

[DavidSauls]

You might as well throw errorless out the window. It's completely undefined. You can't determine the definition simply by using statistics.

I'd love to see it thrown out the window, and out of the rule. My own philosophy is to ignore it, since I don't expect experts to make errors. (They do, of course, but those result in the unexpected scores).

Steve's trying to compare results to the pars that were set, as defined by the rule. So he's stuck with dealing with errorless, while that phrase is still in the definition.

Myself, I'm sticking with the expected score of an expert, and the ambiguity of two of those words. With less precision and more subjectively---looking at the scoring spread, average, median, mode, and perhaps the eye of a newt to see whether the TD's (or designer's) expectation was confirmed with the results.

 

[Steve West]

This seems like a good time to look at hole 16. (Hole 2 was in post 3256.)

Hole16 with 3=1%, 4=25%, 5=25%, 6=25%, 7=15%, 8=10% was par 5 errorless, par 4 expectational.

Par 5 errorless implies the top 87% of throws were errorless, while par 4 would imply the top 71% of throws were errorless.

Expectational par 4 implies 30% errors. At par 5 it would have been 25% errors and 14% heroes. 69% normal @ 4 vs. 65% normal @ 5.

Udisc stats were: Average = 5.61, OB=1.04, FWH=68%, c1 in 3=26%, c2 in 3=34%, Scr.=27%, Parked=13%.

 

[biscoe]

Distance says it is a par 5.

 

[Steve West]

Calculated Pars for the Am Worlds courses where there were enough rounds of data.

Bailey Road Park W-18
 Skill Rounds Sum 1 2 3 4 5 6 7 8 9101112131415161718192021
 Green=800 22  63 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
 Red=850   34  60 3 3 3 2 2 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3
                        
Bradford Park W-18
 Skill Rounds Sum 1 2 3 4 5 6 7 8 9101112131415161718
 Blue=950 149  53 3 4 3 3 3 3 3 3 3 2 3 3 3 3 3 2 3 3   
                        
Hornets Nest W-18
 Skill Rounds Sum 1 2 3 4 5 6 7 8 9101112131415161718   
 Red=850   14  69 3 4 5 4 4 3 5 3 3 5 3 4 3 5 3 4 5 3   
 White=900 55  66 3 3 5 4 4 3 4 3 3 4 3 4 3 5 3 4 5 3   
 Blue=950  66  61 3 2 4 4 4 3 4 3 3 4 3 4 3 4 3 3 4 3   
                        
Nevin W-18
 Skill Rounds Sum 1 2 3 4 5 6 7 8 9101112131415161718   
 Blue=950  86  62 4 2 3 4 5 3 3 3 4 3 4 4 3 4 3 3 4 3   
                        
Reedy Creek W-18
 Skill Rounds Sum 1 2 3 4 5 6 7 8 9101112131415161718   
 Green=800 23  58 3 3 3 3 3 4 3 3 3 4 3 3 4 3 4 3 3 3   
 Red=850   47  56 3 3 3 3 3 3 3 3 3 3 3 3 4 3 4 3 3 3   
 White=900 41  55 3 3 3 3 3 3 3 3 3 3 3 3 4 3 4 2 3 3   
 Blue=950  11  52 3 3 3 3 2 3 3 2 3 3 3 3 3 3 4 2 3 3   
                        
Renske Finals W-18
 Skill Rounds Sum 1 2 3 4 5 6 7 8 9            
 Red=850   12  33 4 3 5 3 5 3 3 3 4            
 White=900 14  29 3 3 4 3 4 3 3 3 3            
 Blue=950  18  26 3 3 3 3 3 3 2 3 3            
                        
Robbins W-18
 Skill Rounds Sum 1 2 3 4 5 6 7 8 9101112131415161718   
 Green=800 22  64 4 3 3 3 3 3 3 4 4 3 4 5 3 3 4 5 3 4   
 Red=850   36  59 3 3 3 3 3 3 3 3 3 3 4 5 3 3 4 4 3 3   
 White=900 42  56 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 4 3 3   
 Blue=950  48  52 3 2 3 3 3 3 2 2 3 3 3 4 3 3 3 3 3 3   
                        
Scrapyard/Idlewild W-18
 Skill Rounds Sum 1 2 3 4 5 6 7 8 9101112131415161718   
 Blue=950  16  55 3 3 3 4 3 3 4 2 3 3 3 3 3 2 3 3 4 3   
                        
Sugaw W-18
 Skill Rounds Sum 1 2 3 4 5 6 7 8 9101112131415161718   
 Green=800 21  60 3 4 4 3 4 4 3 4 3 3 3 3 3 3 4 3 3 3   
 Red=850   35  57 3 4 4 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3   
 White=900 45  54 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3   
 Blue=950  24  51 3 3 3 3 3 3 3 3 3 3 2 3 2 2 3 3 3 3

 

[jeverett]

I shot even par 54 at league last night and got 871.:gross: Got 938 on DGCR ratings, lol...

It's an aside, but you can request that Timg adjust the SSE for the course to get a more accurate DGCR round rating estimate for that round/course, btw.

 

[Steve West]

Different thought: The tournaments in Sweden always seemed to have pars that were "too high" because they always set par to be 1+the lowest score that a lot of people got. I nicknamed this method "Swedish Par". Now I know why.

A Chat With ESPN's John Buccigross

10 questions for the man who called McBeth's -18
...
5) What was your reaction when you first heard that a professional disc golfer shot 18-under par?

The Swedes have a system called "54." They teach, mentally, that is should be possible to birdie every hole and shoot 54. And that golfers should think that it is possible. That's what I thought of when I saw the 18-under.
...