Monday, December 13, 2021

Wilderness Simulator Stats

Wilderness Encounters: Clear (log chart)

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:

Wilderness Encounter Simulator Stats

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:

Wilderness Encounters Simulator Log Charts

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)

11 comments:

  1. Sorry to ask this here, but when you use target20 do you use a floor of 1, for 1st level mages, for instance?

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  2. Replies
    1. There isn't any such specifier in OED (or OD&D or even 1E AD&D). That said, it's never come up, so I'm not sure if my tune would change if that ever starts happening.

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    2. ... Wait, let me give some more detail to that. My Judges Rules currently say to treat nat-1 as -10, and nat-20 as +30 (for both attacks & saves). That's to simulate how those odds in reality should taper off in asymptotic fashion.

      The 1E AD&D DMG actually does strongly recommend auto-fail on nat-1, and auto-success on nat-20, for saves, but not for attacks. In attack tables he has 5 repeated 20's to create the same tapering-off effect, and says it's "not necessarily undesirable" to have some enemies be unhittable.

      I'm dealing with some ramifications of those corner-cases in my Arena code at the moment. Not the best that I couldn't immediately remember what I had for a rule, I might need to streamline that further.

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  3. It would be fun to combine - 'survivability of treks in the wilderness' chains?

    http://cosmicheroes.space/blog/index.php/2021/12/26/arena/

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    1. Which you might have done already of course - some sort of not so random work, party going from A to B, with occasionally getting lost type algorithm?

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    2. Oh, neat idea! I'll put it on my list of stuff I'd like to do given time available.

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