Asymptotic bounds for the affinity level for almost all Boolean functions

We consider the asymptotic behaviour of one of the parameters of the Boolean functions known as the affinity level. We show that almost all Boolean functions of $n$ variables have the generalised affinity level exceeding $n-\alpha\log_2n$, $\alpha>1$, obtain an asymptotic upper bound for the partial affinity level, consider the asymptotic behaviour of the affinity level for the quadratic Boolean functions.