It depends on which "average pace" you're talking about. If you use a HR monitor and you run your long runs on the same course week after week, the average pace function, triangulated with your cumulative HR, can give you an excellent sense of what shape you're in.
My average pace on 15 mile LR's varies from 9:45 (early July, not really back in shape after spring season, high humidity with warm temps and sun) to, in exceptional cases, 8:10 or so. Now, in that latter run, I may run the last 6-7 miles at 7:30 pace, and I'm interested in THAT info, too, but the average pace over the entire run, combined with an average HR of 78% or so, tells me I'm in great shape and can run sub-7 for a half marathon.
If you're talking about average pace for a given mile: what's useful, once you've learned how to work with such figures, isn't just the rolling average pace figure--i.e., the rolling pace for THAT mile, and for each successive mile--but whether it's inching up or down, and how fast. You end up developing a feel for how fast you're actually going. If my average pace for an in-process mile is, say, 8:00 when I'm .5 miles into that mile and it's slowly inching down, then I'm probably running 7:45-7:50 pace.
Truth is, I don't worry about any of that stuff now. If I'm in the middle of a mile and I want to do some hard fartlek and want to know, after the fact, how hard I was running, I just start running hard and, a second or two later, click it over into a new mile segment, then click it off at the end. I'll do that, for example, when I'm running 8-10 times .12 hard, .12 easy (200 meter pickups, essentially). I'll go back later and discover that they ranged from 6:45 down to 5:50 pace. I don't see any reason on the roads (or trails) to get more precise than that. And in truth, the Garmin won't let me get any more precise. The "current pace" function just doesn't work very well.
But I've found that the actual distance (and of course the time, and thus the average pace) functions are extremely precise. And that's good.
I rarely wear the HR monitor these days. It turns out that one of the joys of longer runs for me is the freedom to think my own thoughts rather than continually be drawn in by "information." Technology is great, if used wisely, but in an of itself it doesn't necessarily improve the running experience in all conditions.