How often do diquarks form? A very simple model

Starting from a textbook result, the nearest-neighbor distribution of particles in an ideal gas, we develop estimates for the probability with which quarks $q$ in a mixed $q$, $\overline{q}$ gas are more strongly attracted to the nearest $q$, potentially forming a diquark, than to the nearest $\overline{q}$. Generic probabilities lie in the range of tens of percent, with values in the several percent range even under extreme assumptions favoring $q\overline{q}$ over $qq$ attraction.