I’ve had 4 op-ups over the years. The most recent showed in the app around 36 hours before departure, because the flight the day before was cancelled (an A380), so lots of people getting moved up to accommodate irrops from the day before. Another was done as late as boarding at the gate, and the rest were early on the morning of departure, a few hours before getting to the airport.

Things like status, luggage, historic purchase patterns, number of passengers in booking reportedly have some impact. As datapoints: 3 of my upgrades were when I was silver, 1 as a bronze. 2 while travelling alone and HBO, 2 while flying with my husband and checked luggage. So while there are general rules, also plenty of exceptions that prove the rules. The one rule I’ve found to be consistent is op-ups only happen when they are least expected. Hoping for one seems to be the sure-fire way to rule yourself out. It is the sneakiest part of the algorithm