State-to-state cross sections for the collision-induced transitions of H+H2 (and isotopic analogs) have often been examined using quasiclassical trajectory calculations. The assignment of quasiclassical trajectory results to final rotational and vibrational states by histogram methods can lead to distributions for endoergic (upward) transitions that are rotationally or vibrationally hot when compared with quantum calculations or with experimental results. This effect is most pronounced near threshold for the transition of interest. Various histogram methods are examined to determine why they can lead to distributions that are hot. The application of detailed balance (microscopic reversibility) to cross sections calculated for the inverse of the endoergic transition results in distributions that are neither rotationally nor vibrationally hot; only those effects that can be attributed to the classical approximation of a quantum process remain.