Ed,
Taking your comment "How are you defining a half par hole? Is it just one that plays significantly easier or harder than its designated par? Or is it one where attempting to play the hole tee to green in a different number of strokes than regulation is a viable option? Seems to me the former is strictly a question of difficulty whereas the latter is one of design..." to the next step, I think integral to the definition is WHEN is the choice of playing the hole a viable option that defines it as a half-par. Let me give an example.
The 5th hole at Bethpage Black. If the good player hits a good drive that goes a bit left-of-center, they will be faced with an uphill blind second shot over trees. The smart play is to then lay-up down the fairway along the right as close to the end of it as possible, thus leaving a short 40+ yard wedge shot into the green.
Now, is this then a half-par hole by definition? Must the defining factor be a decision of how it is to be played before one tees off or can it be after? Is the definition of the half-par hole one of how to save par with smart plays and take bogey as the worst score?
Now I believe that the 5th on the Black is a true half-par hole because it bears the classic Tilly design features of various routes that he would have laid out in a drawing. The same for the 12th hole. On the other hand, the long tough par-4's numbers 10, 15 & 16 wouldn't be as they, despite being longer and more difficult than the 5th, only allow for a single DESIGNED planned play. In other words, if you looked at a design drawing of these holes it would have shown a SINGLE tee shot and a second shot drawn in.
So, doesn't the architect's design intent become the chief point of definition?