...
Another issue with what you suggest is that there are plenty of people in influential positions (who make signs, design courses, run parks etc) who have no good grasp on what a 1000 rated player is.....much less how 37% of 1000 rated players will score on a hole or a course. But, everyone knows how to measure 300'.
Well, those who are influential positions SHOULD have a grasp on what a 1000 rated player will score, or rely on someone who does. Every one of the members of the Disc Golf Course Designers group does. They are not that difficult to hire.
I know that won't always happen, so see below.
One thing to note, which I forgot earlier: the estimated SSA should be calculated without including expected penalties. "Errorless play" and all that. Besides, the 1000-rated player, if playing errorlessly, would play somewhat above 1000. So, par would naturally fall in between the cash line and the win line. That's where I felt it should be anyway.
Even if the decider is completely familiar with 1000 rated players, scoring averages, standard deviations, etc......what if the hole produces results that are 50% 4's and 50% 5's for 1000 rated players. Who is the arbiter to assign a Par value to that? If there is just one hole like this on a course, no big deal. But what if there are 6 or 7 such holes (including of course, 2.5 and 3.5 averages)?
Stop looking at averages. Average is not the same as errorless play. Average is errorless play PLUS errors.
I'll start with the case where you have results from actual tournaments of 1000-rated players. That's the easier case, because the definition applies directly.
50% 4s and 50% 5s would be par 4. Duh. If half the 1000-rates players get a 4, that's obviously the score an expert disc golfer would be expected to make on this hole with errorless play under ordinary weather conditions
If all you know is the average, you can't set par perfectly accurately. Take a hole that averages 3.5. It may be 50% 2's and 50% 5's. If so, it's a par 2. I don't know what heck went wrong with those 5's, but it certainly wasn't errorless play.
Or it may be 25% each of 2, 3, 4 and 5's. In that case, it's a par 3. Sure, it's possible to get a 2, but it crosses the line from "errorless" to "errorless and lucky" to get it, because only 25% of players got a 2.
So, for all these 6 or 7 holes with x.5 averages, just see which score covers 37% of the players. Fortunately, for the vast majority of holes, the 37% falls comfortably into a particular score. I haven't seen a lot of cases that are near the bubble.
Now, what to do before the before the course has been played? That's more difficult, because you're trying to estimate what par will be.
The crudest way would be to assign a par to each hole, based on length ranges. These ranges would be figured out by looking at a lot of tournaments hole-by-hole scores, assigning par and graphing them against length. I say "crude" but it would be a huge improvement over what we have now. At least everybody using the same ranges, and pars would be set on something approximating the actual (modified) definition.
If you somehow have access to only score averages of 1000-rated players, a crude (but still better than what we have) way is to set pars based on scores that run from (x-1).6 to (x).6. Anything that averages less than 2.6 is par 2, for example. The extra 0.1 above just rounding approximates the effect of errorlessness.
A step up would be to use the SSE formula. Set the total par for the course at SSE and allocate to each hole based on difficulty or length of hole. I'm not sure how OB and other penalties figure into SSE. I'd take them out if I could.
Better would be to use the Hole Forecaster, (with OB turned off) to calculate the total par for the course, and then allocate that total to individual holes based on estimated scores for each hole.
To my thinking at least, your definition fixes only a small part of the problem.
Well, it only fixes the definition, if that's what you mean. If it were universally adopted, which problems do you think it doesn't fix?