Random Assignment Tables
Random Assignment Tables (RATs), also known as Random ('Mech) Allocation Tables, are provided in many BattleTech rulebooks and sourcebooks as a means for players to randomly generate plausible forces of multiple BattleMechs, vehicles or other units for a participating faction to play a given scenario. In lieu with the dice-rolling conventions of classic BattleTech (board game) the tables are typically presented as either a 2d6 or a 1d6 table, where each of the possible roll results (either 2-12 or 1-6) corresponds with a specific unit. It is possible for a specific unit to appear in several rows, if it is very widespread among the forces in question and thus more likely to appear in a given lineup.
RATs are typically of limited scope: They are usually provided for specific military units during specific campaigns or time frames. As such, they are a poor indicator for unit compositions outside of their specific scope. They also suffer from the inherent limitations of the 2d6 table that only allows for eleven entries with only six tiers of statistical probability between them (the lowest being 2.77%, or 1 in 36, for the results "2" and "12" each). Thus, they can only provide a very rough approximation for canonical force compositions of the units in question.
It has indeed been clarified that RATs are not actually meant to provide an accurate picture of what forces a given faction has available. Rather, RATs, while rooted broadly in what units would conceivably be available to a given force in a specific context, are tailored to provide balanced gameplay over statistical accuracy.
Technically, RATs from canonical products are fully canonical. However, their inherent inaccuracy as mentioned above marks them highly unreliable even beyond their random element; they are meant more as a game rule, as opposed to an accurate depiction of the BattleTech universe. Consequentially, while can be regarded as a rough guideline for historical force compositions in the absence of other information, they are trumped by virtually all other (canonical) information with regards to accuracy.
Faction Assignment & Rarity Tables
The Faction Assignment & Rarity Tables by Keith "Xotl" Hann are a notable fan project aiming to avoid the inherent lack of accuracy in RATs, by using a much finer d1000 resolution and basing the tables on in-universe production and availability data, with no gameplay or balancing concerns whatsoever.