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This is a bit of a head trip but anyway, here goes:
The actions that a player takes makes it more likely that they are that type of player based on the new info we have from their actions!
Ok suppose you have a small sample of HUD stats on a player that says he is nitty . Now he 3bets you and barrels off every street. There's 2 possible explanations for this:
1) He really is a nit and has a monster hand
2) He is a looser player than we initially thought and is doing it with a wider range
Any related maths is a bit obscure, but the very fact that this action happened makes no.2 much more likely than no.1 because there's so few combos of hands that player type no.1 can take these actions with compared to player type no.2, who can do this with maybe 3x as many hands. If he folded pre-flop then that would make our assumption that he's a complete nit slightly more likely.
I guess it's a bit abstract but I think it ties in with not putting too much reliance on hud stats and what you've seen BEFORE . What happens now affects the info you had up to this point.
An easier example is an unknown shoves from the sb with 10bb into your bb . Before the hand you might think he doesn't know anything about nash and is only shoving "real" hands , maybe any Ax any broadway , any pair etc . Now the fact that he has actually shoved means that you should alter your perception of him because it's way easier for a player who shoves nash or an even wider range to shove than it is for a player who only shoves value hands to shove . So now with the limited info we have we can go with a new assumption that he's shoving a wider range than we first thought.
A mathematical example is:
Random Player in the sb with 8bb . We guess he's either someone who knows about nash and shoving light bvb and is shoving 80% of his hands in this spot . Or we think he may have no clue about shortstack play so as he'll only shove top 20% of hands.
You might guess and say well he's one type or the other so because of that I'll assume he's shoving 50% of hands because that's the mean of 20% and 80% . So if he shoves I'll call X% because I assume he's shoving top 50%
But once he shoves then that actually gives you a lot more info than you first had . The very fact that he shoved makes it much more likely that he is the player who knows about nash than the player who just shoves big hands . Because that player is shoving 4x as many hands as the other type. So now there's an 80% chance that the player is shoving nash and there's only a 20% chance that he's the nittier type.
So now you can say that 80% of the time he's shoving 80% of hands and 20% of the time he's shoving 20% of hands . So on average he's shoving 68% of hands , which means you can call a lot wider than you would against the 50% shoving range we calculated before.