Monday, April 27, 2015

Dungeons & Demographics, Pt. 2

In the last installment, we noted that throughout all three volumes of OD&D, depictions of groups of men assert that there will be a leader of about Name level for every 100 or so normal men-at-arms. We can get fairly close to this distribution by a (surprisingly) simple divide-by-two method from each level, starting at 0-level, which is equivalent to an exponential function with a decay rate of about k = -ln(2) ≈ -0.70.

Now let's go back to our Arena simulator (link1, link2), which runs combats for a several thousand dueling fighters as per slightly smoothed-out classic D&D rules, and compare. For this investigation I've done a few things. One: I've modified the simulator to start the combatants at 0-level (Normal Man), with a 1,000-XP requirement to reach 1st (Veteran). Two: I'll only look at the Man-vs-Monster duels, following the Monster Determination and Level of Monster Matrix in OD&D Vol-3, p. 10. Three: I'll end the analysis at character level 9 (Lord), because after that point the XP charts switch to a linear progression, which would not be following the same regression function as the levels up to that point. With a constantly-refreshed population of 10,000 fighters, after 200 cycles of combat this is what we get:

That table tells a scary story! Practically no one survives past the 3rd level. In this case, one lucky soul is still alive at 8th level. But there are no characters of Name level or higher in this population. Only 1 in 20 of this population is above the 0-level. While the OD&D description for Men says that every 50th man is 4th or 5th level, there are no such lieutenants or subalterns in existence in this group.

Keep in mind that this simulation is actually more forgiving than by-the-book OD&D, because I didn't implement any special abilities: no monsters with poison, paralysis, petrification, spells, blood drain, energy drain, charming, hit only by magic, etc. If we had included those surely the death toll would be even higher. Also: There's no aging-out, so that 8th-level survivor might be effectively a hundred years old or more. Let's compare the two populations side-by-side: on the left, the text descriptions that I'll call the "OD&D NPC Demographics", and on the right, the output of the Arena combat simulation using Vol-3 monster encounters, which I'll call the "OD&D PC Demographics".

Major conclusion: These populations are not playing the same game. They're not even remotely close; it's hopeless to even think about harmonizing them as-is. While the NPC population has a regressed level decay rate of about k = -0.60, the PC survivors from the Vol-3 monster encounters have a decay rate of almost twice that, over k = -1.00. Obviously if the first population has about 1-in-100 Name level leaders, and the second has none, then they are essentially contradictory.

This is not tremendously unique news, because we've pointed out in the past that the OD&D Vol-3 wandering monster tables are really far too tough (1st level characters have a 1-in-6 chance per encounter of a 4th-level monster like wraiths, gargoyles, lycanthropes, etc.) All later editions toned down those tables -- especially Gygax in AD&D, who arguably made the tables in the DMG too easy.

How can we interpret this for D&D? Perhaps we can best assert that, whatever the exact encounter tables, our PC's are playing "the most dangerous game", a much riskier and more desperate gamble in the dungeons and wilderness, where they might quickly win fame and fortune, but is most likely to end in hideous death. On the other hand, we can propose that our NPCs are following some entirely distinct path: a slower and steadier progression in experience among the army legions, guild halls, and colleges of magic. This latter progression is not so likely to result in death, but characters of a given level are likely to be much older than PC's of the same level. PC's will be gaining levels in just a year or so that NPC's take an entire life's career to obtain. We are reminded of Gygax's note on experience from AD&D DMG p. 85:
Note:  Players who balk at equating gold pieces to experience points should be gently but firmly reminded that in a game certain compromises must be made. While it is more "realistic" for clerics to study holy writings, pray, chant, practice self-discipline, etc. to gain experience, it would not make a playable game roll along. Similarly, fighters should be exercising, riding, smiting pelts, tilting at the lists, and engaging in weapons practice of various sorts to gain real expertise (experience); magic-users should be deciphering old scrolls, searching  ancient  tomes,  experimenting alchemically, and  so  forth; while thieves should spend their off-hours honing their skills, "casing" various buildings, watching potential victims, and carefully planning their next "job". All very realistic but conducive to non-game boredom!

Now, let's think about exactly how how far we'd have to bend the encounter tables in Vol-3 to create a PC population that resembles the distribution of the NPC population. What I usually do here as a zero-degree house rule is to modify the d6 on those tables (which determine level of encounter) by some subtracted number (minimum 1 in all cases). For example: with a -1 modifier the 0- or 1st-level characters cannot ever run into 4th-level monsters, at least. This modification bottoms out at a level of -5, which is equivalent to simply always taking a roll of "1" on those tables. Let's re-run the Arena simulator, again with 0-level entrant to the Arena, for each of those modified levels:

The best fit to our NPC population is the "Mod -4" table (most but not all encounters being at the minimum level possible on those Vol-3 tables), with a decay rate of k = -0.58. We might say that this much safer game is equivalent to what the NPCs in our campaign world are playing at.

As I've said before, in my own games I do modify the rolls on those encounter tables downward in a fashion similar to this. On the one hand, I wouldn't actually use the -4 modifier; that's both too repetitive and doesn't honor the higher-variance game that the PC's have chosen. At the moment I'm splitting the difference in half: applying a -2 modifier to those encounter level rolls, and it's feeling about right. The encounters now only ever vary from the PC/dungeon level by a maximum of ±1 level; but on a 6-level monster level scale as in OD&D, that still covers half of all the monsters in the book.

Further research required: Propose a system for assessing the XP gains by NPC characters, who are pursuing safer and more "professional" advancement than the dungeon-delving PCs.

Next time: A comprehensive system for establishing high-level character ability scores.

1. Have you factored in that PCs get xp for treasure? This greatly accelerates advancement, and the need to engage in combat.

1. Yes, for example, for 1st level monsters the simulator actually multiples the given XP by a factor of 20 to account for the expected treasure associated with such an encounter. See paragraph 2 and the link therein: http://deltasdnd.blogspot.com/2014/06/arena-man-vs-man.html

2. IIRC your simulation fights are one-on-one. The other thing to consider is that most fights aren't one-on-one but groups vs groups.

Given the idea of safety in numbers, and picking the fights properly (i.e. generally going after targets you can successfully beat or getting enough comrades to make it so), and good tactics you get a higher survival rate. You also get the slower advancement rate (XP spread out among group) for the NPCs.

I think that the group dynamics would make a difference in the survival rate of the NPC's, it certainly does for the characters.

1. True, but my best guess is that the party size is about the same as the number of monsters encountered at like level. For example, the last paragraph of Vol-3, p. 11 seems to imply at least types such as Orcs are meant to be at least as numerous as the party members (if not more so). So the 1:1 combats are my best model of those odds.

3. Yeah, I think team tactics and "combined arms" synergy between the classes, XP for treasure and the morale system might modify those numbers quite a bit. But the complexity of accounting for all that - not to mention factors like poison, level drain and the like that would make it more difficult - hurts my brain to think about it.

1. XP for treasure is definitely included in the Arena simulation. For example: XP for 1st-level monsters is multiplied by 20 to account for expected treasure, etc.

My zero-degree guess is that the monster special abilities would approximately counter-balance combined arms of a PC party. But you're right, that's just a best guess.

2. Oops, my bad for missing the XP for treasure inclusion!

4. Blackbox D&D has it as "The difference between a monsters’ level and a dungeon level should usually be no more than 2. (p68)"

However I think "balancing" encounters this way gimps the game, Encounter is not a synonym for combat, and having encounters with deadly foes should encourage players to run or negotiate or employ clever strategems. That won't happen if they know they have a good chance of winning a fight every time.

1. Well... I'm sympathetic. But I think I would want those to be "specially placed DM's choices" and not just standard occurrences. If 1 in 3 wandering encounters is 2-3 levels above the PCs (on a 6-point scale), that's pretty much automatic death over the long haul (as evidenced by these stats).

5. Interesting. I was not expecting that level of lethality.

I wonder if the heroes are, in fact, playing "the most dangerous game" or are, just perhaps, a cut above. What would the PC demographics look like if you were to use the ability and hit point distributions you proposed back on August 7 (http://deltasdnd.blogspot.com/2014/08/arena-ability-distributions.html):

Roll 2d4+10 for Str (most important), 2d6+6 in order (for Dex and Con), and 3d6 in order for the mental abilities. Zero level PCs should probably roll the d4 +2 (to closely simulate being slightly-above the zero-level d6) for hit points.

How would these PCs fare against the wandering monster tables?

1. Well... it's the other way around; those abilities are what's possessed, on average, by PCs surviving to the 4th level. You'll see that restated (as well as scores for other levels) in the next blog. PCs with average scores (~10) get usually mowed down before advancing level.

Now that's not hugely surprising, because it's in line with the experience of the earliest D&D groups. There were a lot of people who didn't even bother to name their PC's until they reached 2nd level or something (since the vast majority were in fact expected to die). Recall the "death statistics" published in Dragon #20 for one DM: over 600 PC deaths over 2-3 years of play: http://deltasdnd.blogspot.com/2009/09/death-statistics-in-d-1978.html

2. For people that don't like that level of lethality in the game, my response is always: don't mangle the system itself at low levels -- just start PCs at higher level (where additionally the boosted HP and abilities are justified for the survivability effect). At last report, even Gygax would start OD&D PC's at 3rd-4th level, which I certainly support as the cleanest way to declare someone a "special hero", if so desired.

6. Perhaps an additional datum is needed to propose the experience system for NPCs - how old the "name level" character ought to be. If we assume that our highly experienced ruler-type should be about, say, 50 (I am reminded of Henry's line in "Lion in Winter"), perhaps there's some xp-over-time progression that can be made to fit the curve already in hand.

1. Right, I agree that could be part of it.

2. I should point out that those figures are, of course, the ones I use for agricultural/pastoral societies, where division of labor insists that only a small portion of the population act as professional fighters. For societies I designate as hunter-gatherer, like, say, lizardmen, I assume that adult males and females both fight, so that about 50% of the total population fights. Of course, they also have a lower population density (about 1 person per sq.mi., compared to a rough-and-ready approximation of 60 per square mile for agricultural and pastoral "settled" societies).

3. Right, that makes sense.

7. For NPC advancedment this is an interesting training system from Bard Games The Arcanum. The game system is basically house ruled D&D so I think this could have some application.

"During periods of relative inactivity, characters of any profession should be allowed to gain experience points by engaging in study or practice. The amount of X.P. that can be earned through the undertaking of such activity is as follows:

- Studying/practicing without an instructor = 10 xp per day, per level.
-Studying/practicing at a school or university = 20 xp per day, per level.
-Studying/practicing with a Master = 10 xp per day, per level multiplied by Master's level of Ability.

1. Oh, interesting!