Steve, your definition of "errorless" is too similar to "perfect" for my tastes. "Errorless" play does not mean the best score possible. I think it's closer to the average than your version of "errorless" play.
Imagine a tight 350' hole with a ten foot gap 100 feet off the tee. "Errorless" play in your book would have someone hitting that gap and having a 30' putt, which would be an "error" if they missed.
That hole is not a par 2. It's still "errorless" play if they nick one of those trees, have an obstructed 75' "putt" that they put beneath the basket, and drop in for three.
I agree that par should not mean the perfect score or best possible score. You're forgetting an important part of the definition: "the score an expert disc golfer
would be expected to make on a given hole with errorless play".
I agree that hole is not a Par 2, because an expert player would not get a 2 often enough to be
expected to score it. Only about 10% of 1000-rated players would get through the gap and land close to the target. That's not a high enough proportion to "expect" that score. Even without the gap, only about 15% would get close to the target. That's still not enough.
I also would not define errorless play as how a player would play the hole if he knew he could do no wrong. The player will not expect that he could never miss the gap, and therefore decide to throw 360 degree run-up with a driver. Errorless play would involve making an adjustment to increase the odds of hitting the gap.
Let's say this hole was shorter so that without the gap it would be a par 2. At some point the gap is so small that errorless play would be to try something other than simply ignoring the gap and throwing for the target. With a gap that is small enough to change how players approach the hole, even a short hole can become a par 3.
Par will usually be very close to SSA. Throwing even par would produce a round rating of approximately 1020, vs. 1000 for SSA.
In fact, I've calculated that simply using SSA's with x.6 instead of x.5 as the cutoff for par comes very close to the definition of par for the vast majority of holes. For example, instead of rounding the SSA's in the range of 2.5 to 3.5 to par 3, assign a par 3 to the SSA's in the range 2.6 to 3.6.
I calculated this by looking at the score that the 37th percentile player scored on each hole, calling that par, and comparing that to SSA. The 37th percentile is where I think players can reasonably start expecting a score.
You could also get to the .1 approximate difference between rounded SSA and par by saying that 1000-rated players make about one error about every 9 or 10 holes. Or, roughly 2 per round. So, errorless play by a 1000-rated player would be about two throws better than average, or rated 1020, which is right in between cashing and winning.
Holes where par is not close to SSA are holes where errors produce large increases in score.
Let's look at your example of a par 3 hole. If that gap is turned into a double mando with no drop zone, the average score will go up as the 5's and 7's pile up. But, even if the average score gets above 4, it would still be a par 3. Players would still be approaching the hole expecting to get the first throw through the gap and the second throw close enough to putt. Par 3.
As an aside, I think your example of nicking a tree is more of a case of an error with not enough consequences to prevent the player from saving par.