Monster Math: OD&D Giant Rats

How many hit points does a giant rat have? My friend Gus L. posted this fun illustration the other day, proposing that the open-endedness of OD&D implies the possibility of giant rats with 8 hit dice. He takes page 20 of Monsters & Treasure as evidence for this, that giant rats have at least 2 hit dice and hypothetically up to 20 (not just 8!):

This category includes giant ants and prehistoric monsters. Armor Class can be anything from 8 to 2. Hit Dice should range from 2 to anywhere near 20, let us say, for a Tyrannasaurus Rex. Also included in this group are the optionally usable “Martian” animals such as Apts, Banths, Thoats, etc. If the referee is not personally familiar with the various monsters included in this category the participants of the campaign can be polled to decide all characteristics. Damage caused by hits should range between 2-4 dice (2-24 points).

My initial thought was I disagree because a “giant rat” might not qualify as a large animal even if it’s large relative to other rats (the wolf, for example, falls under “small animals” with up to 1 HD; do we expect a giant rat to be bigger or smaller?), but this got me thinking more generally: OD&D is a highly-balanced wargame, isn’t it? There’s lots of creatures listed though barely explained in the rulebook(s). However, the dungeon encounter lists are organized by level from 1 to 6. This does not correlate with player-character level directly since the level of an encounter is randomly determined by the level of the dungeon, but we’d hope they’re at least internally consistent.

To satisfy my curiosity, I collected the hit points and armor class of every figure listed in the dungeon encounter tables. Then I calculated the “adjusted hit point” value of each figure based on how effective their armor class is (more granular and accurate this time):

AC	Avg. HP Adj.
9	100%
8	111%
7	125%
6	142%
5	168%
4	198%
3	251%
2	334%

Finally, I found the average of each in order to arrive at a pretty cohesive picture of what a typical figure looks like at each level. The results are weirdly consistent:

Monster Level	Avg. HP	Avg. AC	AAHP1	AAHP2
I	2.73	6.6	3.6	3.4
II	6.06	6.2	7.8	8.6
III	13.75	6.0	18.5	19.5
IV	14.64	4.3	27.9	29.0
V	21.54	4.5	42.3	42.7
VI	32.2	3.4	79.4	80.8

These are the sort of inscrutable variables:

• AAHP1: Average adjusted hit points, by taking the average of each monster’s individual adjusted hit points.
• AAHP2: Average adjusted hit points, by calculating it for the average hit points and armor class of each level.

Keep in mind that many figures listed are actually classed figures without an apparent armor class, so these were excluded from the calculation of average armor class. This results in AAHP2 being not necessarily reflective, although in the end it seems like there’s not much difference in hit points between classed and non-classed figures anyway. In other words, the results are extremely internally consistent! The average dragon has the equivalent of 99.4 hit points. Crazy stuff.

So, how many hit points does a giant rat have? Probably between 1 and 6, or even lower. The average raw hit points of a level 1 monster is about that of a goblin (~2.67), although when considering armor class they have the longevity of an unarmored figure with d6 hit points. The giant rat of AD&D has half a hit die and an armor class of 7, equivalent to the kobold with 2.5 adjusted hit points. This fits right at home with the level 1 monster table unless you imagine a human-sized giant rat with a whole hit die, and a lesser armor class to compensate (or not).

That being said, that's not the final word on what a giant rat should be. That's just a giant rat that would make sense to be a level 1 dungeon encounter. We should want bigger rats! Just like we should want better balance, too; good thing Delta already cracked that.

Addendum: Encounter Levels & Literary Critique

Gus L. asked about the range of hit dice at each encounter level, and here they are:

1. HD ½ to 1
2. HD 1+1 to 2+1, before zombies were changed from HD 2 to HD 1 in a later printing
   
3. HD 3 to 5+1
4. HD 3 to 6
5. HD 4 to 7
6. HD 7+

Keep in mind that these ranges correspond with increases in armor class, which is especially true between levels 3 and 4. Although their ranges of hit dice are about the same, level 4 sees a 2-pip increase in armor class that makes the figures much more formidable. This has predictable effects on the longevity of the figures listed at each level; look at the "adjusted hit points" values I found above, which reflect the impact of armor class. It's a difference of 10 "virtual" hit points.

Something to clarify, as well, is that although I'm using math to illuminate the text, my argument is not mathematical but literary. It's about how OD&D is not a cohesive, consistent text owing to multiple factors: it having two co-authors with different tendencies as well as visions of the game; its draft changing in various places during its development, but never towards cohesion; and the final work lacking rules, procedures, and statistics to explain things it explicitly mentions.

The "giant rat" falls victim to this incohesion. The specific context in which it appears in Volume III as a level 1 monster contradicts Volume II's explanation of "large animals" in general. We could read it as an exception relative to the other level 1 figures listed, more than HD 1, but that is a less obvious (and likely) solution than reading the contradiction as such. Of all the things that Gygax revised between OD&D and later revisions, the giant rat appears more like a confirmation of what is already apparent in OD&D, namely that it is a level 1 encounter figure with HD 1 or less.

This isn't about whether HD 8 giant rats are better than HD ½ "giant rats". I like Gus' idea way more! It's also not about whether AD&D (or B/X) was a completion or corruption of OD&D, or whether it best represents how Gygax originally intended D&D to be played. Both are bad books (by any definition) by bad people. Neither are how I really like to play, and I have no stake in defending a particular vision of D&D by Gygax or anyone else. Besides, late Gygax often disagreed with early Gygax; as Georgian philosopher Ioseb Jughashvili says, "both are worse!" This is not about arriving at a systematic understanding of OD&D (because one doesn't exist).

This is about OD&D as a complete mess of a text. This is about performing immanent critique of the text to see where its holes are, how it fails to be a system (mathematically, sure, but also in terms of literary meaning). It's about learning how its internal contradictions generate contradictory interpretations that manifest in later D&D as well as competitor books. Math is one tool, but it's secondary to (or an extension of) reading critically rather than assuming that OD&D as a whole is consistent.

One more thing. I checked one of the drafts of OD&D, called Beyond This Point Be Dragons. Giant rats are listed under the level 1 encounter table along with the other HD 1-or-less figures: goblins, kobolds, bandits, orcs, and centipedes. Like in the final OD&D, giant rats do not have an entry in the figure descriptions but, unlike OD&D, neither do large animals. This means that the "giant rat" entry was written in the context of the level 1 table, and the "large animal" description was written later and likely without consideration for giant rats. This is not evidence in itself, or at least I wouldn't accept it as such, but it confirms what is already apparent from that passage of the final text.