How often should I be meeting monsters?

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).

• Inconsistency? In AD&D2E? Where's my torch and pitchfork!? (Humor aside, I'm on board. I like weirdness like this, and I hope you get a reasonable answer. However, it might be useful to have some context: Are you trying to make your own encounter tables by the book or are you trying to use the encounter tables and you think they're wrong? That is, is this idle curiosity (which is totally cool) or is there a problem that needs solving?) – Hey I Can Chan Jul 29 '16 at 18:26
• @HeyICanChan Hehe, good point. Ya, my motivation is that I'm trying to write some tools (software) to help me generate monster choices for my games that I run. Currently my method for picking monsters is to read through the monster manual looking at monsters and at frequencies and just winging it. I'd much rather have some method to, given a specific locale, get monsters based on the frequency and probability that was intended (from a game balance perspective). – gene_wood Jul 29 '16 at 19:24
• @nitsua60 Ya, my background in the question probably obscures the question which I'd say is : "Given these inconsistent rules in the book (assuming that I'm not mistaken and they are inconsistent), which rule set is most consistent with the game balance intent of monster frequencies". My hope is that someone's read some Dragon Magazine article or knows more about the evolution of frequencies from 1st edition and D&D to know which one of the methods is the mistake and which one is the one the designers intended, specifically in regards to game balance. – gene_wood Jul 29 '16 at 19:27
• @nitsua60 Good idea, I've made your suggested changes to the question. – gene_wood Jul 29 '16 at 20:04
• Gene, I am not sure that probability that was intended (from a game balance perspective) is a correct assumption. – KorvinStarmast Jul 29 '16 at 21:27