It is now well established that a power-law relationship exists between crystal strength and sample size. This scaling is remarkably robust for dislocated systems irrespective of a large number of various initial microstructural features. This indicates a fundamental origin that is insensitive, but not dismissive, of any particular dislocation mechanism. Here we show how this can be rationalized by a statistical approach that predicts the power-law exponent to be dependent on the universal scaling exponent for scale-free intermittent plasticity, as well on the leading order term of the underlying critical stress distribution (Phil.Mag. 2015, 95, 1829). We present an experimental verification across the nm and um size-regime of our model, which also gives insight into the underlying critical stress distribution of the deforming volume (ScriptaMater. 2015, 102, 27). The results are discussed in terms of dislocation structures at criticality and we propose further avenues to experimentally scrutinize the approach.