Couple more random thoughts on the topic. Again, please remember that these are just tendencies:
Big woods bucks tend to have larger home ranges than farm land bucks. On the surface, one would believe that has everything to do with the farm land bucks having everything they need/want in small areas. No doubt that factors into it heavily, but I've seen the same when a property within the big woods setting is managed up and has everything a buck could ever want, far better than the surrounding area provides. Mr. Big still has the tendency to roam a bit more. I believe that's just because he can, with so much seemingly safe habitat surrounding the property, and because none of these settings have had what I'd consider a high density of mature bucks off the property. So, there's more competition between mature bucks on the ground and less off it. I'm not pretending to be right about the reasons. They're just the best I've come up with so far.
Mature bucks on high pressure grounds have a very strong tendency to have pretty darn small home ranges, even when they lack any other real buck competition. My belief is that it is because they have found that pocket that they feel safe in during daylight and really don't wander far from it...it appears to be their security blanket.
I don't believe most mature bucks try to expand their range during the rut. I believe the real reason in the overwhelming majority of cases are hot does that have home ranges overlapping his. She ventures into that overlap range and either her trail or her herself leads him off during the chase. In fact, I believe that many, if not most that just "take off" is really the result of a domino affect, where one either chases or is lead off by one's scent trail. When finished (either done breeding, she loses him or a more dominant buck claims her), he stumbles across another doe or her trail as he's heading back, taking him even further away. That happens 3-4 times during peak rut (which is easy to imagine with many does coming into estrus then), suddenly either his home range has been greatly expanded or it makes it appear that he just "took off looking for does." Sure, he "took off," but I believe that specific does caused him too. When you think about it logically (no, they can't think logically, but Mother Nature's system is nothing if not logical), it makes no sense at all for a buck to leave an area where he knows where are all the does are, and typically has more entering estrus than he can handle, to take off for an area he doesn't know at all. In fact, there's a laundry list of reasons why that doesn't make sense.
Just some random thoughts
P.S. The time I see most of the random roaming is really during post rut. At that time, odds are much higher that most does are done being bred within his normal range, but he is experienced enough to know that he wants more and that the odd late adult doe and some doe fawns are still out there to be had. At that point, it seems the urge to find those last few opportunities can outweigh all the downsides to leaving his home range. I personally rarely get pics of the "who the heck is he" bucks on the large properties during the rut. They're almost always post rut, searching for breeding scraps, or late season, being drawn in for food.