Well, I'd hate to sound like a broken record, but... no, there isn't a system in place to influence the families you can build your draft around. 
To be fair, there is some manipulations made to provide a fair play experience : the first and last picks are always full of your class' cards, you will see a Rare (or more) in every pick, we make sure Infinites pop up at a certain rate, etc...
But as for families, such a Tofu, Wabbits or even Ghouls, we do not alter the draft to suit better with your already-drafted deck. They are random, appear randomly, and if you see a lot of a same family, it's because they were drawn randomly that way.
Of course, that doesn't negate a certain player agency. It comes down to you,: if you have one or more interesting tofus presented to you in your first few picks, then maybe you will start to consider all other tofus that come afterwards as more enticing than, say, a generic 3 AP wabbit or an Infinite that doesn't play well with your God. In the end, you may end up with a deck containing enough synergies to work together properly. A few families are particularly large: tofus, drhellers or ghouls are more likely to appear in spades than rats or vigilantes, so basing your deck around them is easier to do in draft.
And it goes without saying that cards do not have the same "value" in Draft as they do in regular play. I wouldn't really want to play a Minotoror in my decks, but in draft, if I need larger end-of-the-game creatures? I would consider it if the draft gives me one. At the same time, you wouldn't see me play Timekeeper unless I'm sure that I can amass enough AP in the deck to play it with ease... It's a completely different meta, in the end!
See message in context

To be fair, there is some manipulations made to provide a fair play experience : the first and last picks are always full of your class' cards, you will see a Rare (or more) in every pick, we make sure Infinites pop up at a certain rate, etc...
But as for families, such a Tofu, Wabbits or even Ghouls, we do not alter the draft to suit better with your already-drafted deck. They are random, appear randomly, and if you see a lot of a same family, it's because they were drawn randomly that way.
Of course, that doesn't negate a certain player agency. It comes down to you,: if you have one or more interesting tofus presented to you in your first few picks, then maybe you will start to consider all other tofus that come afterwards as more enticing than, say, a generic 3 AP wabbit or an Infinite that doesn't play well with your God. In the end, you may end up with a deck containing enough synergies to work together properly. A few families are particularly large: tofus, drhellers or ghouls are more likely to appear in spades than rats or vigilantes, so basing your deck around them is easier to do in draft.
And it goes without saying that cards do not have the same "value" in Draft as they do in regular play. I wouldn't really want to play a Minotoror in my decks, but in draft, if I need larger end-of-the-game creatures? I would consider it if the draft gives me one. At the same time, you wouldn't see me play Timekeeper unless I'm sure that I can amass enough AP in the deck to play it with ease... It's a completely different meta, in the end!
To be fair, there is some manipulations made to provide a fair play experience : the first and last picks are always full of your class' cards, you will see a Rare (or more) in every pick, we make sure Infinites pop up at a certain rate, etc...
But as for families, such a Tofu, Wabbits or even Ghouls, we do not alter the draft to suit better with your already-drafted deck. They are random, appear randomly, and if you see a lot of a same family, it's because they were drawn randomly that way.
Of course, that doesn't negate a certain player agency. It comes down to you,: if you have one or more interesting tofus presented to you in your first few picks, then maybe you will start to consider all other tofus that come afterwards as more enticing than, say, a generic 3 AP wabbit or an Infinite that doesn't play well with your God. In the end, you may end up with a deck containing enough synergies to work together properly. A few families are particularly large: tofus, drhellers or ghouls are more likely to appear in spades than rats or vigilantes, so basing your deck around them is easier to do in draft.
And it goes without saying that cards do not have the same "value" in Draft as they do in regular play. I wouldn't really want to play a Minotoror in my decks, but in draft, if I need larger end-of-the-game creatures? I would consider it if the draft gives me one. At the same time, you wouldn't see me play Timekeeper unless I'm sure that I can amass enough AP in the deck to play it with ease... It's a completely different meta, in the end!