I don't think they're the most influencial, but they're literally my favourite games. Running away wasn't a super prominent tactic in them though, the majority of ghosts you had to fight- I think something like Clock Tower is more influencial on that front.
But yeah, they're literally all great with the exception of 5 which is a disaster in a lot of ways (Also Spirit Camera is meh but it's a spin off). Fatal Frame 3 is actually the best game ever
