  We show that generic H\"older continuous functions are $\rho$-irregular. The
property of $\rho$-irregularity has been first introduced by Catellier and
Gubinelli (Stoc. Proc. Appl. 126, 2016) and plays a key role in the study of
well-posedness for some classes of perturbed ODEs and PDEs. Genericity here is
understood in the sense of prevalence. As a consequence we obtain several
results on regularisation by noise "without probability", i.e. without
committing to specific assumptions on the statistical properties of the
perturbations. We also establish useful criteria for stochastic processes to be
$\rho$-irregular and study in detail the geometric and analytic properties of
$\rho$-irregular functions.
