  Following Fisher, it is widely believed that randomization "relieves the
experimenter from the anxiety of considering innumerable causes by which the
data may be disturbed." In particular, it is said to control for known and
unknown nuisance factors that may considerably challenge the validity of a
result. Looking for quantitative advice, we study a number of straightforward,
mathematically simple models. However, they all demonstrate that the optimism
with respect to randomization is wishful thinking rather than based on fact. In
small to medium-sized samples, random allocation of units to treatments
typically yields a considerable imbalance between the groups, i.e., confounding
due to randomization is the rule rather than the exception.
  In the second part of this contribution, we extend the reasoning to a number
of traditional arguments for and against randomization. This discussion is
rather non-technical, and at times even "foundational" (Frequentist vs.
Bayesian). However, its result turns out to be quite similar. While
randomization's contribution remains questionable, comparability contributes
much to a compelling conclusion. Summing up, classical experimentation based on
sound background theory and the systematic construction of exchangeable groups
seems to be advisable.
