There’s no real point in trying to work this out mathematically because there are too many variables, but if you really want to, then lets do some general estimates.
This year (2020) there are 468 SQ and 173 tickets from events. You also get 5 tickets per month from the shop, an average of 1 SQ per day from daily logins, 30 SQ for every 50 daily logins, and 3 SQ per week from master quests. That comes out to 1898. If we add a bit for bonding, interludes, and whatever else you might randomly pick up, then you’re looking at about 1950-2000 SQ equivalents in this year.
Now, lets take that 1950 and work out how many servants you can roll for before your probability drops below 50%. This is using cumulative binomial probability by the way.
1 servant = 98.96%
2 servants = 94.19%
3 servants = 83.29%
4 servants = 66.70%
5 servants = 47.77%
Going by pure statistics, you can probably target about 4-5 5* servants per year.
Having said that though, what Gou said is just generally a better idea. Don’t worry about the maths, roll as much as you think is reasonable.
What I personally do is look through the entire year and make a list of everything I want, then put it through a series of 3 criteria.
Roll criteria 1: Is it a strong support servant who will enable more playstyles or more efficient farming (e.g. Merlin, Skadi)?
Roll criteria 2: Is it a strong servant with a unique or fun role or playstyle for which I do not already have an applicable servant (e.g. Cleo, Hokusai)?
Roll criteria 3: Is the servant shortly before another servant that I want more?
Roll criteria explanations
Roll criteria 1 is the most important one. Strong supports always displace all other servants. Even if there is a servant that I was planning on rolling for, if I decide that I want to roll on a banner with a strong support shortly after it, then that servant gets removed from my roll list. An example of this is Reines. I was originally planning on rolling for her because she fills a similar role to Waver, but is a rider so can be used in rider boss challenge quests. When I failed to get Merlin last year though, he became more important than Reines, and since Merlin’s banner is only 2 months after Reines’, Reines was removed from my roll list.
Roll criteria 2 is different for me compared to a lot of other people, because I have very little attraction to waifu culture. Two examples for this are Hokusai and Eresh. Hokusai is a strong servant with an almost unique class who blends well with my already established roster. Additionally I like her stylistically (2nd ascension is better than 3rd ascension), so I decided to roll for her. Since I didn’t get her first time round, I’m also going to roll for her next year. Eresh on the other hand is a servant that I like stylistically, but doesn’t have a unique role in my roster. I already have Karna, and he is capable of doing most things that Eresh can do, albeit requiring more support. Because of this I did not roll for her, although before my Karna spook I was intending to.
Roll criteria 3 is fairly simple. If the servant is immediately before a criteria 1 servant, or a more important criteria 2 servant (Bradamante vs. Bennienma and Hokusai), I don’t roll.
I’d recommend doing something similar, and making your own roll criteria and shortlist. This year I’ve had 4 targets: Hokusai, Skadi, Jeanne D’Archer, and BBikini. Next year I currently have 3: Hokusai, Benienma, and Merlin. I have enough self discipline to not roll for anyone else, so this method works for me.