Tom,
I was thinking about that as I wrote, but what other way do we have to measure difficulty?
If we disregard par then all the toughest holes are the ones with the highest scoring averages - basically, the longest ones, the holes that are currently par-5's.
If it's the highest ratio of shots per yard, then the one-shot holes are always the toughest at about 1 shot per 60 yards, and two-shot holes are next at about 1 shot per 100 yards.
Of course, if we're talking about one- and two-shot holes, then we're basically talking about par.
If we're talking about "toughest holes to beat the average score", then we're just talking about any hole whose scoring average is 2.999 or 3.999 or 4.999. That seems silly because then the easiest holes would have a scoring average or 3.001 or 4.001 or 5.001.
If it's some hypothetical measurement of the margin of error allowed on each shot and the resulting difficulty of the next one, I don't think you'd learn anything different than if you just looked at the average score.
Which is tougher - a 400 yard hole with a 4.2 average, or a 500 yard hole with a 4.3 average?
Difficulty has to be judged relative to *something*. Holes are only easy or tough compared to what we hope or expect to score on them. Given that we can only score in full-shot increments, we generally hope or expect to score either a 3, 4, or 5 on any given hole.
"Difficult holes are those which present the greatest challenge to achieving the score that one could reasonably hope to achieve."
I don't find that definition significantly different from judging difficult holes relative to par.