I played 100 public Mafia games using my cult save and recorded the results.
Bodyguard stops cultist conversion - OFF
Doctor stops cultist conversion - OFF
Doctor is notified of cultist conversion - OFF
Witch Doctor immune to detection - ON
No limits to witch doctor conversion
Cult converts every night
Cult can convert night immune roles
Mason Leader limited to 3 recruitings/killings
Sample size: 100
Cult win: 24
Town win: 49
Evils win: 27
Of the 24 games where Cult won...
Witch Doctor saved someone on n1 in 18 of them.
Cult successfully converted on n1 in 23 of them.
Witch doctor saved someone on n1 AND cult converted someone on n1 in 13 of them.
At least 1 cultist and the witch doctor survived n1 in 22 of them.
At least one Mason leader used all 3 of his charges in 9 of them.
Cult ended the game with an average of 3.9 members alive and 5.8 members total.
Of the 76 games where cult lost...
Cult failed to convert on n1 in 26 of them.
Cultist or witch doctor were killed on n1 by Mason leader in 17 of them.
Cultist or witch doctor were killed on n1 by someone other than Mason leader in 9 of them.
At least one Mason leader used all 3 of his charges in 37 of them.
Cult ended the game with an average of 3.3 members total (none alive, assuming tiebreaker means 0 cult alive).
Takeaways and Analysis:
If cult fails to convert on n1, it is virtually a death sentence for the cult.
If cult has approximately 4 members alive and approximately 6 members total, it is looking like a win.
Cult play is highly dependent on getting a good start. It seems that in order to get a "good" start, cult has to convert someone and save someone on n1. Anything less than that is an "ok" start. If there are less than 3 cult members after n1, it is a very bad start.
In short, the whiners and complainers have no basis for hating the cult save. Cult needs miracles to win a game. You're more likely to win as a SK than as cult.
These results are particular to this setup and will not apply to other setups.