  The main limitation of most ultracold chemistry studies to date is the lack
of an analysis of reaction products. Here, we discuss the first generally
tractable, rigorous theoretical framework for computing statistical
product-state distributions for ultracold reactions in external fields. We show
that fields have two main effects on the products of a statistical reaction,
by: (1) modifying the product energy levels thus potentially reshaping the
product distributions; and/or (2) adding or removing product states by changing
the reaction exothermicity. By analyzing these effects and the strength of the
formalism to distinguish between different reaction mechanisms in benchmark
reactions involving $^{40}$K and $^{87}$Rb species, we argue that statistical
predictions will help understanding product formation and control, and lead
developments to realize the full potential of ultracold chemistry.
