How often should I be meeting monsters?

Question

It looks like there are 3 conflicting stories in AD&D 2nd Edition about the meaning of the monster frequencies, common, uncommon, rare and very rare. I'm curious if I'm misunderstanding or, if not, which one should one use. My goal is to understand which of the conflicting rules is closest to the game designers intent in regards to game balance.

The Dungeon Master's Guide summarizes the meaning of the frequencies on page 98 with two different methods, the "2-20 Table" and the "Percentile Table". The Monster Manual (and Monstrous Compendium) describe frequency at the beginning of each book.

Summary

Here are the differing probabilities of the 3 methods. The explanation and source pages for each are below

$$ \begin{array}{lccc} \mathbf{Frequency} & \mathbf{2–20\text{ Table}} & \mathbf{Percentile Table} & \mathbf{Monster Manual}\\ \hline \text{Very Rare} & 9.37\% ±3\% & 3\% & 4\%\\ \text{Rare} & 21.89\% ±3\% & 7\% & 11\%\\ \text{Uncommon} & 27.08\% & 20\% & 20\%\\ \text{Common} & 41.65\% & 70\% & 65\%\\ \end{array} $$

The 2-20 Table

The 2-20 Table from Page 98 of the DMG

The list of frequencies and a dice role are shown in the 2-20 Table where the dice rolled are a d8 and d12 added together.

The resulting probability distribution of rolling a d8 and d12 can be seen on anydice. When you add up the probabilities for each frequency you get the results above.

Note : For Rare and Very Rare, the rolls of 4 and 18 are DM's choice. In these probabilities I've opted to assign one to rare and one to very rare. If one were to either choose rare for both numbers or very rare for both numbers, the resulting probabilities would shift around a bit (about 3% up or down).

Each probability is just the result of adding up the percentages shown on anydice for each number of that frequency. For example uncommon maps to the rolls of 7, 8, 14 and 15. Therefor 6.25% + 7.29% + 7.29% + 6.25% = 27.08%

The Percentile Table

The Percentile Table from Page 98 of the DMG

The Monster Manual Table

The Monster Manual Table from page 3 of the Monster Manual

The Monster Manual and Monstrous Compendium describe a table similar to The Percentile Table in the DMG. It's worth noting though that the Monster Manual and Compendium also have 2-20 tables for encounters with the differing probabilities above. The minor difference between the Monster Manual table and the DMG don't concern me so much, I'm wondering about the large differences in the probabilities between the "2-20 Table" and the other methods (28% difference for common).

Answer 1

The various methods of rolling up random monsters from a table aren't meant to be statistically precise, they're designed to make the table convenient and “good enough”.¹ The suggested table layout allows you to approximate the statistics in a way that's good enough without adding complexity. You can arrange them however you like, even, in order to create a table for a region where some creatures are more or less rare than they normally would be. (E.g., the Valley of the Drakes will probably have more dragons and such than their Monster Manual rarities would indicate, and so they'd be put into less rare “slots” in the tables).

The exact rarities are given as a convenience also, in case you want to devise your own methods. Again, you don't need to aim for perfection — instead you want to achieve usability. Variance of a few percentage points in either direction isn't going to suddenly make the appearance of monsters seem implausible, so don't over-optimise for precision. In reality they're just guides anyway, slapped down by a designer's “gut feeling” — and nobody expects that monsters will appear with exact, machine-like precision!

Note too that AD&D 2nd edition predates the concept of designing the system math around “balanced encounters”, so if you're assuming that the rarity statistics are critical for some kind of design reason and getting them wrong will break all kinds of things, they really, really aren't and it really won't. That's why you're seeing a variety of numbers — none are wrong, they're just side effects of the exact numbers not mattering. The numbers for the two table types are an accident of what makes for convenient, whole numbers for the two different rolling methods; the ones in the MM are more a matter of representing a fantastical ecology than anything to do with balance. I mean, given the right things on a random encounter table you can meet a dragon way too powerful to fight at 1st level, or a war party of 100 orcs. Fighting everything you meet is not the expectation in 2e, so balance is really not something to assume these numbers represent.

^{1. As in, “perfect is the enemy of good enough”!}