What is the scientific term for the expectation, that a personal experience positively deviates from what first- or second-hand experience suggests?
Are you referring to the optimism bias from a social psychology perspective?

Your brain has a built-in optimism bias. The phenomenon is also often
referred to as &quot;the illusion of invulnerability,&quot; &quot;unrealistic
optimism,&quot; and a &quot;personal fable.&quot;
This bias leads us to believe that we are less likely to suffer from
misfortune and more likely to attain success than reality would
suggest.2﻿ We believe that we will live longer than the average, that
our children will be smarter than the average, and that we will be
more successful in life than the average. But by definition, we can't
all be above average.

Source: VeryWellMind