Wilderness Simulator Stats

One more reflection on the Original D&D wilderness encounter charts. Last week we were using some tabulated charts to decide between two possible rules interpretations, and one was clearly much nicer. But that was based on just looking at the average EHD (Equivalent Hit Dice) for each encounter type, which is maybe a little sketchy. Since I'm obsessive about these things, I wrote a simulator program that actually rolls up the individual encounters (varying the number appearing by psuedo-random dice), and I had it spit out a thousand random encounters for each terrain type.

Here's the statistics that get produced looking at those samples of size N = 1,000 for each terrain category. Note that this includes accounting for the sweep-attacks rule (high level fighters get one attack per level vs. 1 HD types), and also reduced numbers for the outlier groups of Gnolls, Cavemen, Treants, and Vampires that seem necessary based on our analysis last time:

As you can see, like we've said a few times, the danger levels across the different terrain types are a lot more constant than one might have guessed without inspecting closely. But of course, the various terrain types mostly feed into the same subtables, anyway. This is in stark contrast to encounters for different dungeon levels, which obviously represent a setting of increasingly dangerous tiers -- although note that the rate of encounter checks increases quadratically in bad terrain, so that does make for a significant difference in risk level. 

The mean EHD per encounter is close to 40 for any terrain, with a standard deviation around 27 or so; and the median is around 35 or something, with an IQR (interquartile range; comparable to standard deviation) around 30. The mean-higher-than-median indicates that the distribution is right-skewed, i.e., has a long tail to the right, with a number of very high EHD encounters occasionally occurring. In cases like this, it's sometimes interesting to take the logarithm of the data values (e.g., the general mean converts to log(40) = 1.6), and see if the distribution then looks like a normal curve. I did that below:

Okay: They're kind of normal? None of these actually pass a statistical test for normality (rejected at P < 0.0001). That's not too surprising, since it's not like the encounter design in OD&D has any kind of systematic consistency (nor would I argue for it to that extent). But it's at least kind of suggestive: a log-normal distribution is reflective of many natural biological and demographic processes, and these encounters are sort of in that ballpark, which is nice. There's significant variation in the encounters to make the D&D wilderness challenging and risky, but it's not a lunatic level of variation, where you can't even imagine half of the creatures surviving for a week in the presence of the other creatures.

So overall this doesn't change our conclusions from last week much at all -- or, in other words, it gives added support to those conclusions. These distributions feel kind of nice to me. For a party sized 8 (all fighters in our sim), an average level of 5th should stack up against the average EHD of 40 pretty well. Although rarely you'll have an encounter in the EHD 100+ range, and then you'd darn well better engage with the Evading rules. Or if you Arneson-ify the wandering numbers down to about 1/3 book values, and play with a 4-person party, then 4th level can be okay -- at least until you delve into the lair locations for that sweet, sweet gold treasure.

How do those simulated stats look to you?

Wilderness Encounter Sim Stats (ODS file)

Wilderness Encounter Sim on Github (Java code)

Sweeping Up the Wilderness

Last week I opened my personal journal on accepting sweep attacks (fighters getting as many attacks as levels vs. 1 HD targets) as a critical element throughout the O/AD&D rules, and my own game, and the effect they have on play. Today we revisit our analysis of wilderness encounter perils, in the context of including sweep attacks in the picture.

State of the Wilderness

Here's a recap. Back in 2019 I analyzed Wilderness Encounter Levels, and the overall distribution of danger on the OD&D outdoors tables. A first observation is that, on average, the different terrain types are actually pretty uniformly dangerous: we estimate they're roughly balanced for a 10th-level party (with a classically big size of 8 PCs, fighters only, and no sweep attacks). A second observation is that looking past the averages, the encounters have a very prickly distribution: lots of encounters at total 50 EHD or less; but also lots of encounters with EHDs in the 200s or higher. (EHD being "Equivalent Hit Dice", something a bit analogous to challenge ratings.)

In 2020, considering that problematic, I took a stab at considering Rescaling Wilderness Encounters; maybe dialing down some monster numbers to get things a bit more manageable -- possibly by Arneson's tactic in the First Fantasy Campaign (assume only about a third of any group is wandering outside the lair), or Moldvay's in the Basic D&D rules (drop humanoid numbers to around one-sixth the original). Here's a copy of the table I had there of EHD distributions for all encounters in the OD&D wilderness (note the logarithmic x-axis):

Now, as a statistician, you kind of hate to see that kind of bimodal shape in a graph -- the fact that there's not one but two upward spikes in totally different locations. (As noted: a whole bunch of encounters around 50 EHD total, and another big batch of upward of 500 EHD. The coin-flip of doom!) That usually suggests that you've got a problem with your polling process, in that you've likely munged together two totally different categories of things, and instead should be dis-aggregating and measuring them separately.

In this case, the distinction is easy to determine: the big batch of super-high EHD encounters is precisely all of the humanoid bands appearing in numbers of hundreds (men, goblins, orcs, dwarves, elves, etc.). All of those kinds of encounters have average EHDs of 150 to 300 or so -- whereas the median for the overall set is only about 40. Likewise, the wilderness encounter subtables that have lots of these types (Men and Giant-types, i.e., humanoids) have average EHDs of 120 to 200, while all other subtables (Lycanthropes, Undead, Dragons, etc.) only have average EHDs of 25 to 50.

Earlier in 2021, I looked at Monster Numbers Through the Ages, specifically for the canonical wilderness encounters, and considered them in relation to the status of sweep attacks in each of those editions. A discovery there is that in some ways the numbers were pretty consistent from 0E to 3E, and then disappeared from monster stat blocks after that.

Start Sweeping

So recently I added a switch to turn on sweep attacks in the Arena Simulator on GitHub, and last week I presented that it has the effect of reducing the effective power of 1-HD humanoids to about one-fourth their actual hit dice (on average; and of course this varies enormously by the exact level of classed fighter-type they're facing off against). At some point, I went to the wilderness data tables from before, and dropped in those modified numbers. Here's what the distribution of encounter EHD totals looks like now:

So: In one fell sweep, that solves the problem. The bimodal shape is gone, and now it kind of looks like a normal curve (after logarithmic scaling).

Some more details: The overall median is still around 40 EHD; but now the bands of humanoids have average EHDs in the range of 30 to 70 or so, that is, a much better match. Likewise, the subtable statistics become less jagged; mostly in the range of 30 to 50 on average (in other words, fairly spread around that 40 median). More on that later.

The difference in those two graphs is pretty much what single-handedly convinced me that if you're going to play an O/AD&D style, all other things being equal (like numbers appearing for humanoids), then it's pretty much a necessity to honor the classic sweep-attack rule.

Stones in the Field

But there are still a few exceptions: outlier encounters that have total EHD way outside the standard range of about 30 to 70. These are four specific cases that fall neatly into two classes:

• Creatures with summoning abilities. When these creatures are encountered, they can summon other allies to help them, multiplying their strength (vs. their book hit dice, if that's all you were looking at when balancing the encounter size). With the summons respectively doubling or tripling their power, the average total EHD for Vampires is 140, and for Treants it's 360.
  
  
• Creatures with 1 HD but a 2HD subtype. There are two humanoids with 2 HD, but are sub-types of a 1 HD primary creature class. Therefore they share the same high number appearing as the main type in the table (some hundreds), even though they're outside the range given for the sweep-attack rule. The average encounter EHD for Gnolls is 220, and for Cavemen about 310.
  

Let's be a little more specific about that latter category: In the OD&D Monster Reference Table, Hobgoblins and Gnolls share a single line jointly. The have the same AC, movement, % in-lair, treasure, and number appearing (20-200). But the hit dice entry says "1+1/2", i.e., Hobgoblins have HD 1+1, and Gnolls have 2. So while I'd interpret Hobgoblins as being in the range for sweep attacks, Gnolls would be out. In that regard, giving them the same numbers appearing seems to be a big mistake. This kind of gluing-together of types is in the tradition of Chainmail, where a lot of monsters were presented as tiny alterations of other classes. (In the past I've mistakenly said Gnolls were 1+1 hit dice in early drafts of D&D, but it turns out that was a typo in the later derived document called the Dalluhn Manuscript, so let's ignore I ever said that.)

Meanwhile, Cavemen don't appear in the table, rather being subsumed by Men, who have number appearing 30-300 and generally 1 hit die/man. But among the 9 different sub-types of Men described in the main text, Cavemen are uniquely noted as having 2 Hit Dice. (Actually, in the pre-publication draft of D&D, even that was ambiguous: the Guidon D&D manuscript says they "fight as 2nd level Fighting-Men", which could be interpreted a few different ways; when the LBBs were published, the entry was expanded to also say they "get 2 Hit Dice", apparently in response to some peoples' confusion. Thanks to Jon Peterson for personally answering a question about that.) Again, with this clarification, Cavemen stand outside the range of sweep attacks, but they still share the 30-300 number appearing like any other Men. 

Recall that up above I mentioned with sweep attacks, most of the wilderness subtables had average EHDs of 30 to 50. But I should point out that there's two notable exceptions: The Men (Mountains) and Giant subtables are both elevated up to around 90 instead, and that's entirely because those are the only tables with Cavemen and Gnolls (plus Treants) in them.

(Now, one might theorize that's evidence that 2 HD creatures should be in the range of sweep attacks, too. But there's even even more monsters on the reference table with 2 HD that have small numbers appearing: e.g., Zombies, Ghouls, Dryads, Pegasi. If we allow sweeps on them, then their EHDs plummet below the normal range, and you have an even worse problem. Also: most Horses and Mules are at the 2 HD level, and allowing whirlwind-slaughterhouse attacks against them just doesn't feel cool to me.)

So I do think that the numbers appearing in the four outlier cases are oversights and should be fixed. For Cavemen and Gnolls, following the idioms on the OD&D monster table, I'd recommend making their numbers 3-30 (as for skeletons/zombies), or 3-36 if you want to use Platonic dice, which of course you do, because you're a person of excellent taste.

Meanwhile for Vampires and Treants, I'd recommend lowering both to the smallest-appearing die of 1d4. This places Treant encounters at an average of about 80 EHD (still one of the highest), and Vampires at around 100 EHD (thereby making them the #1 most dangerous wilderness encounter). I'd actually make Vampires 1d3 if it weren't for the fact that it appears nowhere in the original table. Either way, this solves the eccentric subtables and related problems.

Wilderness Encounter Levels

All told, here's our revised estimate for encounter levels in the OD&D wilderness. Again, this assumes an eight-person, all-fighter party. When we started, we estimated that the tables present, on average, a balanced encounter for 10th-level PCs (with a huge amount of dangerous variation). By merely flipping on the sweep-attacks switch, our estimate drops to one appropriate for 6th-level PCs (and quite a bit more predictability in the danger, even you're still dicing for exact numbers in each case). What a huge difference that one rule makes! 

In both cases, this danger level is pretty consistent across all terrain types. Furthermore, if you make the adjustments to the monster numbers for the outliers I mentioned above -- even though that's only four entries -- they're influential enough to further drop the estimate down to 5th-level PCs. And that's pretty darned close to what many of our intuitions say (e.g., from the D&D Expert set rules) about what level wilderness adventures should be happening at in the first place.

One of my favorite things in the world is when two apparent problems cancel each other out, in that they're actually the mutual solution to each other. And for me, what appeared to be the bizarrely wonky variable danger of the OD&D wilderness encounter tables, and the mystery of whether sweep-attacks for PC fighters were really intended within the OD&D mechanics, is just such a satisfying case.

Just One More Thing

So sweep-attacks are the solution to the specific problem of big humanoid numbers in the wilderness. And yet separately, I'm still somewhat sympathetic to Arneson's idea in the FFC of having only around one-third of the given numbers actually show up wandering around in the wilderness (with the rest holding down the fort, or lair) -- applied universally to all monster types, not just humanoids. In some ways that cools the numbers for mythic monsters down to something more in line with what I have in my head for fantasy tales (what feels better: 4 dragons, or unicorns, or 1? 6 balrogs or 2? 8 giants or 3? 12 pegasi or 4?). And it also adjusts for the smaller standard (non-convention?) party sizes we might be dealing with now. If you reduce monster numbers appearing to 1/3 listed, and party size to 4 (instead of 8), then the average wilderness encounter in OD&D in fact seems to be balanced for 4th level PCs (exactly in line with the Expert rules expectation).

Appreciate any of your thoughts on that!

Wilderness Wandering Analysis 1.0.3 (ODS spreadsheet)