re: How much influence do past games/trends have on this season?

I think it depends. If the teams are fairly even, then breaks can tip the difference from year to year.
If one team really dominates the other, then it is usually a physical and mental edge there.
In State's case, OM was 22-2-3 against State from 1947-73. That mental edge carried over for another 15 years or so. Now it is completely gone.
Bama won 36 out of 38 against us from 1958-1995. Obviously they have a big edge on us. Now from 1996-2007 we had some success against them 6-6. However since 2008 they have beaten us every year.
LSU is something like 25-5 against us since 1985. Some maybe mental but a number of those games especially through the 90's, State was the better team but lost the game.

OTOH, we had beaten UK seven straight before last year and I think it was mental with them.

So I think it depends on the teams involved and each situation can be different.