Anyway, the most likely time to get an op-up IME are when you are travelling solo, in school holidays, on a weekend, and usually when travelling with status.
I can add a new data point to this discussion - one as recent as a few months ago!
I was on SYD-HKG, in super cheap Y (like $300) - non-upgradeable. I was in the taxi on the way to the airport looking at EF with growing depression as the blocked seats around me were disappearing at a rate of knots. When I got to the airport and checked in I was really surprised to see 1A on my boarding pass (instead of the 23K i had on my app). Suddenly the day wasn't looking so grim! So I asked the check-in lady what the reason could have been and she said, although the system doesn't tell her, she thinks the reasons were:
School holidays, completely oversold flight, PLUS, flights the day before had been cancelled so there were still some stranded PAX, plus I was traveling solo, PLUS I had the appropriate status.
Interestingly there were still about 4 empty seats in J
So thank you Qantas!
Tomorrow though I think I am going to suffer the reverse fortune.... flight has heaps of seats in Y and 0 in J so that upgrade (actually requested this time) is looking unlikely....
But to throw in a few more data points.... 25 years flying Qantas, at least 10 as WP, only ever got op-up a handful of times domestic, once international. On the other hand, I received many on other carriers (6+ on CX, 4+ on EK, 3+ on AA), based on my QF/OW status. Now, I know the die-hard Qantas fans will want to lecture me that the reason QF gives so few op-ups is because they are sooooo good at managing their loads and best ever airline in the world etc etc.... but maybe they are just not popular enough to be oversold that often. And I think they are just stingy when it comes to upgrades in general. I have seen them give preference to staff travel in J over on-departure points upgrades for rev PAX. I have seen them (overheard talking on the phone), conspiring to tell people "sorry completely sold in J" so that their friend waiting at the service counter on staff travel will get the empty seat.... I have seen them in J cabin, ask staff travel PAX their meal preferences first, before rev passengers.... mind you these examples are a few years ago and I do think that QF has changed their attitude somewhat, but I still think they have a mentality of keeping us (their customers) in line with the carrot/stick approach to the hope/dream/promise of an upgrade.....