To have a total of 30-40 on a sailor? Not many, probably average about 100 experts. You could get lucky and do it with 50, you could be unlucky and need more like 150.
If you mean to boost your sailors by another 30-40 ontop of the ~100 they have now, you're looking at much closer to 400-600 experts I reckon.
I don't know what variables affect the success rate, my experience includes the premium sub bonus. If maximum sailors is a variable then that might account for something, but personally I think it simply gets harder with every success. It's pretty hard to pin down the exact rate of success.
However, to answer wether you need more, that IS a pretty generalised question. You should read Norms repost of adalberts guide to ability here in the tips section. It isnt entirely up to date any more, but it does outline the basics of calcuating a sailors true ability with each stat.
Ability caps I know of;
Reload, which caps at 2.7m reload. You can consider 2.4m the cap for AA gunners.
Repair, which caps at 35m (shared across your entire crew, so every sailor contributes to this total cap).
Accuracy, which is 4706 x the sailors level +1,100,000 (it was only 1m, but the cap was increased and no one knows by how much, so I have assumed a roughly ~10% increase is enough. Most sailors have easily capped accuracy if they have capped reload, the exceptions are UK and USN sailors of certain class combinations, you'll have to investigate your gunners ability more indepth if this is the case).
Wether you have enough vets or not will depend on what ability that sailor needs. 100 is a nice, basic amount for most sailors. Gunners with full experts will easily cap their abilities eventually, but doing so earlier obviously requires the presence of vets. 100 will get you capped between 90-100 most nations, 200 gets you capped in the late 70s. Repair is one you have to figure out first, obviously most sailors dont contribute very much repair at all. But basically, you need to look at the individual sailors and their abities to decide if they have enough vets for your needs.