I guess I should clarify ... The Rug was just an example. Say I found a creature that exists in 1e, 2e, or 5e that doesn't exist in 3.5e. If I wanted to convert that creature to 3.5, how might I go about it? I suppose I could like for stats on a similar 3.5 creature. But is there any technical method, e.g. mathematical formula, for conversion?
Yes, to a certain extent, there is. When 3e first came out, there was a fairly extensive guide on doing conversions and the underlying math of 3e monsters that was published in several places. It's worth noting however that there are two basic approaches, and the two will demand different things of you. Additionally, you might prefer to apply one technique when translating between two editions, and then another when translating between two different editions. For example, I'd tend to apply an equal HD starting approach then converting 1e to 3e, where I'd try for an equal CR approach when converting from 5e to 3e.
The basic starting point for converting a monster to 3e is to define its HD, it's size, and the type of monster it is. Once you define that, you can work out its basic properties.
From there, you can start working on more complex properties like ability scores and AC.
In 1e, ability scores were seldom precisely defined, but they sometimes were. If precisely defined, it's usually a simple matter of copying them over. Intelligence scores for a 1e creature were defined as a range, like 'low' or 'exceptional' which translates into a range of values. The missing values can generally be inferred according to the creature size. Now look at AC, and try to figure out what portion of the AC is set by size and dexterity of the creature, and what portion is set by armor or natural armor. In some cases in 1e its explicitly defined, and in other cases you'll need to make a best guess. Once you have defined how AC came about, you can fix dexterity to a particular score.
Once you have HD, monster type, and ability scores, you can set derived stats like Saving Throw, Feats and Skill Points.
In some cases working out HD is a little bit tricky because HD was defined differently in 1e or sometimes not defined in a creature entry at all. Many 1e monsters will have entries like HD 4+1 or HD 5+5. Occasionally you'll see, HD 10+40. The second number is bonus hit points, and in general is best treated as a marker of exceptionally good CON scores. I might treat HD 4+1 as being 4 HD plus 2 higher CON than average for its size class, like HD 5+5 might be 5 HD plus 4 higher CON than average for its size class. Some interpretation is necessary for the best results. In the case of a Dragon, Beholder, Golem, or a Fiend Lord, it's best to work out HD by starting with dividing the given hit points by 4.5 to work out the effective HD. A 10 HD ancient dragon is better treated in 3e as a 17 or 18HD monster than a mere 10 HD creature. A fiend lord with 133 h.p. implies a HD of around 30.
Feats and skill points need to be set somewhat subjectively according to the trope of the creature.
After that you start working on converting the creatures abilities. Spell-like abilities, gaze attacks, and sometimes breath weapons can usually be directly converted because many abilities are just defined in terms of spells. If not defined in terms of a spell-effect, use similar creatures as the template.
This methodology I've very briefly outlined here will get you really close, but doesn't necessarily make for the best translation. Sometimes you need to take in to account the limitations of the system you are working from. For example, whales in 1e have very high HD, and a much better conversion to 3.5e would give them lower HD than indicated for 1e, but very high constitution scores. Keep in mind though that when you bury HD like this, you risk making whales a very powerful creature to summon as summoning creatures is based on HD. So you have to think about balance in the new system as well.
It's also possible to define average ability scores, AC, HD, and so forth by CR - although in a much less tight range. I've seen lists somewhere. Sometimes when you are going for a conversion, the best approach is to try to match a targeted CR based on how difficult to defeat a monster is in a particular system. Sometimes its best to start with one method and then refine with the other. Unfortunately, there is enough different between systems that while you can get close to a rote method of conversion, using your judgment is normally required and what is a 'perfect' translation for one DM won't be perfect for another.
