Are there websites that will try to calculate the probability of an upgrade for a particular flight and date?
I suppose the occupancy rate of business and economy class and other factors would help come up with a estimate. Eg as Star Alliance Gold, travelling alone, should I have a higher probability?
I'm wondering if there's anything out there for this kind of prediction.
Highly unlikely.
Most airlines have very strict and complicated rules about upgrades with insanely detailed pecking orders. A few years ago someone leaked an internal list from United that had over 30 different categories of passengers and their upgrade order. It depends on statuses, ticket price, fare class, upgrade instruments, employee status, business needs, etc.
Most of the rules and the underlying passenger data are not publicly available so it would be very hard to build a website.
Some airlines do publish upgrade lists on-check in day on their flight status page, so you can check where you are (if you indeed qualify) but that's obviously not available at time of booking. There used to be hack (also for United) to set your computer's date & time to the day of check-in and check the flight status and the current upgrade list would indeed appear. Still, how that changes between booking and flying is anyone's guess.
Another way is to count open seats but that doesn't take into account who else is already on the list.
Given all of this most passengers carefully plan and monitor their upgrade strategy for their specific case (airline, upgrade instrument, status, etc.). "Surprise" upgrades are exceedingly rare, so a website would have limited use.
This being said, one of the very few "surprise" upgrades I got was on Turkish Airlines from IST to BER landing me in a nice angle flat seat: Pre-boarding had been absolutely chaotic and I had been patiently waiting and helping a bit as the only passenger in boarding group one. Apparently the gate agent liked my attitude: when I scanned my Economy boarding pass, he ripped it up and printed me a new one for up front.
