Laboratory experiments of bacterial colonies (e.g., Escherichia coli) under well-controlled conditions often lead to evolutionary diversification in which (at least) two ecotypes, each one specialized in the consumption of a different set of metabolic resources, branch out from an initially monomorphic population. Empirical evidence suggests that, even under fixed and stable conditions, such an "evolutionary branching'' occurs in a stochastic way, meaning that: (i) it is observed in a significant fraction, but not all, of the experimental repetitions, (ii) it may emerge at broadly diverse times, and (iii) the relative abundances of the resulting subpopulations are variable across experiments.  Theoretical approaches shedding light on the possible emergence of evolutionary branching in this type of condition have been previously developed within the theory of "adaptive dynamics''. Such approaches are typically deterministic –or incorporate at most demographic or finite-size fluctuations which become negligible for the extremely large populations of these experiments– and, thus, do not permit to reproduce the empirically observed large degree of variability. Here, we make further progress and shed new light on the stochastic nature of evolutionary outcomes by introducing the idea of "soft'' trade-offs (as opposed to"hard'' ones). This introduces a natural new source of stochasticity which allows one to account for the empirically observed variability as well as to make predictions for the possibility of evolutionary branching to be observed, thus helping to bridge the gap between theory and experiments.