I pull out numbers from time to time in games, but it's something I constantly do behind the scenes to predict chance.
First off, we know if there's only one mafia party at work they are usually 1/3 the size of town or 1/4 the size of town. With games over 8 players almost always having 1+ 3rd parties.
So let's say we have a 16 player game. 4-5 players would be mafia with the chance of an additional 1-2 third parties.
So we've now created the possibility of 5-7/16 anti-town players.
That means we now have a 31-43% chance that each player is anti-town.
As a town player looking for mafia, you now can eliminate yourself from the list, leaving 5-7/15 anti-town players. Bringing your percentage chance of each player being mafia to 33-46%.
If you're a Vanilla townie, that's the best you can do until people begin to die (as each townie dies, the percentage increases and as each mafia dies the percentage decreases).
But, let's say that you are a Town Cop with suspicions of there being a God Father.
Night 1 you investigate Player A, he comes back as Town.
You can now be 93% certain Player A is indeed town assuming all players live through the first night.
1-(1/15)
Night 2 you investigate Player B after Player C is lynched and Player D dies the following day.
You can now be 92% certain that both Player A and B are town. (Notice the percentage drops a bit, that is because the Godfather is still alive, however the percentage is still going up faster for others)
1-(1/13)
With 13 alive, you can now be 45-63% that any OTHER player in the game is mafia over the mere 8% of the player's you investigated being God Father.
Now lets go into another role. A Town Watcher. Let's keep the same game on Day 3 now with 14 alive. Night two you watched player D die. But, there were three people to visit D in the night. One of which is of course the killer.
Ignoring the watch you would have a 38-53% Chance of randomly hitting anti-town with a lynch.
We will assume for this purpose that 2/3 of the ones to visit D in the night were town PR's and the other the killer. To randomly lynch in them is a 33% chance of hitting the killer.
However, if we eliminate these 3 from lynching others, we now have a 4-6/10 chance of hitting anti-town, or 40-60% chance. While by instinct you'd want to go after the killer, it may be wiser to instead go after anyone else.
Just some insight on different mafia math for town to up their chances of finding scum.