  Sufficiently clean geometrically frustrated (GF) magnets are the largest
class of candidate materials that may host quantum spin liquids (QSLs). Some of
them have been shown to exhibit spin-glass freezing, potentially precluding
QSLs, at the "hidden energy scale", which is significantly lower than the
microscopic energy scale of spin interactions. Here, we investigate the origin
of the hidden energy scale and its relationship to the $f$-ratio, the figure of
merit for the degree of frustration in GF magnetic materials. The available
experimental and numerical data provide evidence that GF magnets display,
universally, two distinct temperature scales in the specific heat, the lowest
of which is of the order of the hidden energy scale $T^*$. We argue that this
scale is determined by non-magnetic excitations, similar to spin exchanges in
chains of spins. The collective entropy of such excitations matches the entropy
of the ground states of the Ising model on the same lattice, which provides a
way to verify the proposed scenario in experiment. We further confirm this
scenario of the hidden energy scale by numerical simulations of spins on the
kagome lattice. As $T^*$ is a property of the clean GF medium, it leads to a
constraint on the $f$-ratio.
