I've had a stab at trying to work out the probability of being successful in ballot. I anticipate that I've made some errors, but posting here so others can improve on it.
Selling notice says that 63% of the tickets allocation of 16626 are available to general supporters i.e 10474
I’ve assumed that there are 5000 who are on 7+ credits, so that leaves 5474 tickets for those in the ballot.
The next part of my calculation looks at how many will enter the ballot. I’ve assumed that it will be everyone who got a seat at anfield roma home match less away supporters, uefa officials, priority rights holders, hospitality, and those who are on 7+ credits.
(Priority rights holders and hospitality seasonal are identified in the selling notice as having a separate allocation of 4157 tickets. That does leave non-seasonal hospitality, but I’ve assumed (wrongly or rightly) that given hospitality pricing & availability they are a group unlikely to have gone to every European home game.)
So the number in ballot may be 54074 (anfield capacity) minus 2904 (away supporters) minus 3055 (uefa ticket semi-final allocation according to their rule book) minus 7000 (our hospitality size according to a Guardian article) minus 1500 (number of priority rights according to a Liverpool echo article) minus 5000 (supporters with 7+ credits). Assuming that all remaining supporters have 6+ credits (ie were in autocup or survived through the members additional sales) – which is a big assumption – then there would be 34615 persons in the ballot trying to access 5474 tickets.
This gives a probability of being successful in the ballot as 15.8%. i.e. Between a 1 in 6 and 1 in 7 chance of getting a ticket.