Arena – Man vs. Monster

Adding Monsters to the Simulated Arena of Battling D&D Fighters, So As to Assess Average Advancement and Ability Scores at High Levels

Background

Previously, I presented a simulation of a D&D gladiatorial "Arena", where we generated a random population of 10,000 original D&D fighters and paired them in battles to the death for a few generations, to see what kind of level, hit point, and ability distributions would arise (link).

Note that this gave rise to a fairly predictable system: Once one fighter graduated from 1st to 2nd level, almost all of their later fights would be against 1st level opponents (96% or more of the population), whom they would almost surely defeat and gain XP from (generally 10 xp × 20 prize factor = 200 xp), reliably increasing in level from that point on. This gave rise to a fairly smooth set of numbers in level and ability distributions over 1,000 cycles of combat (what we might guess as 250 years of arena competitions).

One limitation of that simulation was obviously that normal D&D does not predominantly battle PCs versus NPCs, but rather a regime of mostly nonhuman monsters. It would take additional programming work to add that capacity to the simulation.

New Method

At this point I've added modules to the Java program for the simulation to allow input of a variety of basic monster types and determination tables from CSV text tables. (As a side-benefit, this also allowed use of more exact class XP tables, which were previously approximated by a simple formula.) Now, each combat consists of a given gladiator (fighter) pairing off against a monster of a random level as determined by the tables in OD&D Vol-3, p. 10 (see below). The level of the NPC fighter is used for "Level Beneath the Surface", that is, as though the character were exploring a dungeon equal to their own level. Only the simplest melee-type monsters are included from the following tables: Kobolds, Goblins, Skeletons... and so on up to Superheroes, Lords, and Giants. The program doesn't currently handle any special abilities, so the gladiators do not face off against any monsters with poison, paralysis, petrification, energy drain, breath weapons, spell casting, etc. (For a listing of the specific monsters and game statistics used, see the file Monsters.CSV, linked at the bottom of this post). In order to better resemble standard D&D play, I changed the fighters' presumed armor from chain & shield to non-magical plate & shield (the exact type didn't matter when all opponents are equal in this way, but now it certainly does against predefined higher-level monsters).

Results

Here are some of the chief lessons from this exercise. (1) There is enormously more variation in the system: a 2nd level fighter can be paired off against anything from a Zombie to a Lord or a Giant. (2) The wandering monster tables in Vol-3 are far too dangerous for this exercise as written, and almost no one can advance beyond 3rd level with this system; for example, when one encounters a Lord or Giant at 2nd or 3rd level, that fighter is almost surely destroyed. (3) Experience awards are many times more variable; for example, killing a Giant gains about 5400 xp including prize award (compare to the predictable 200 xp from most fights in the old system). If a 2nd level fighter does manage to accomplish this (through a set of cosmically fortunate rolls, or abnormally low monster hit points, say), then that would be enough to jump over two levels immediately (if it were not capped at a one-level jump). This, then returns us to point #1: there is enormously more variation in the system.

So when I started this simulation at the old parameters (10,000 population, 2,000 cycles), the most common thing was for no one in the entire population to be above 3rd level at the end. But sometimes, there would be one lucky star who managed to graduate past the danger area, and then continued cruising to 10th, 20th, or even 45th level! Of course, anyone in that situation is clearly an outlier that can't tell us anything about overall distributions or ability averages.

Clearly I needed a much larger population (to get better data about higher levels), and a smaller cycle length (to prevent the lucky few from shooting off the end of the scale and becoming deities). The simulation runs below are thus done for a population of 100,000 and only 200 cycles (what we might guess as 50 years of real-life gladiator combat). Here are the results of that, confronting the "normal" random monster tables in OD&D:

As you can see, extreme violence is inherent in the system. Of the 100,000 population, only about 2% have survived to 2nd level, and less then a half-percent have made it to 3rd level or above. The numbers are flat and single digits from 9th-15th level, so that surely looks like random noise to me, and the ability score averages swing up and down without any pattern at that point (the NPCs got there through dumb luck, not any particular ability advantage). So this doesn't tell us much, and I don't think that we expect D&D character levels to be so intensely constrained as all that.

However, before I go on, I must call out the one figure who achieved 16th level in that particular simulation: What a character! Strength 17, Constitution 16, hit points 92, he's clearly the beefiest fighter in the list. And also: Intelligence 5, Wisdom 6, a drooling barely-aware moron (IQ 50?). Charisma 10, so not a completely dislikable sort. Even with those physical abilities, I'd say he could only get to this point through a whole gauntlet of insane (really, really dumb) luck along the way. What if the most powerful NPC fighter in your campaign world was this same, blessed-by-the-gods, illiterate mass of muscle? Call him "Arnold" or "Jean-Claude" or "Groo" if you like.

Anyway, this excursion into nonstop brutality against most of our gladiators is not exactly what I wanted. So I went looking for a simple way to re-interpret use of those tables (have solo fighters play against a lower dungeon level, lower monster level, etc.). The easiest way seemed to be this: simply subtract 1 or more pips from the d6 roll on the monster level determination table. In fact, that's what I already have noted for my games, so it seemed like an obvious choice.

As it turns out, subtracting 1 from the d6 die makes a fairly small difference; achieved levels might increase by about one, is all (perhaps 2nd level fighters get stomped by a Superhero or a Minotaur instead). Even subtracting 2 is not a lot different. Here's what happens when I subtract 3 from that initial die-roll (i.e., limit results 1-3 only): 

At this point, I think you at least start have something that looks like a potentially legitimate D&D fighter population: about 80,000 1st-level fighters, 14,000 (about one-sixth) 2nd level, a third of the 3rd level, a third of that 4th level, and then diminishing reductions after that. There is a clearly increasing pattern to the favored abilities (Str, Dex, Con) that we can use to gauge proper values for new PCs or NPCs -- advancing a bit more slowly than in the former Man-vs-Man case, which makes sense because the gladiators are not contending directly with each other (in which case those abilities are the only distinguishing factor), whereas now the overall luck in monster draw is more telling.

The other thing I like about this is that, very broadly, it replicates the figures stipulated by Gygax in OD&D Vol-2 for proportion of a group of men that are higher-level leaders (see: Bandits, p. 5, and back-referenced in other places). Consider the following comparison:

While not perfect, the numbers are about the right order of magnitude. (And they look better if we add in the simulation numbers at 3rd level and 7th level to complete the picture.) It suggests that this is a place where we can choose to throw our anchor for the population distribution, before assessing ability scores achieved by the selection method. (Note that the more we modify the die roll, the greater the advancement proportions become. If we subtract 4 from the level die-roll, numbers at higher levels increase, and form a better match for the AD&D numbers where Gygax somewhat inflated leader proportions. For brevity, I'll omit showing that comparison here.)

Before I conclude, I'll make a few points about the need to soften those wandering monster tables. I've long seen the need for that already in my own games (link1, link2), and the same was indeed carried out by all later writers, including Holmes, Moldvay, and Gygax himself in AD&D (arguably over-compensating in the DMG). Even though some writers have expressed positive views of how tough they are (see the comments under link2 above).

But I must emphasize how incredibly charitable I'm being in all my interpretations towards our NPC gladiators, even in the original simulation that massacres almost every one with fail. There are no monsters included here that have poison, paralysis, petrification, breath weapon, hit by magic, etc. (any one of which could destroy a lone fighter of practically any level). I've very gently interpreted monster statistics at every turn (see Monsters.CSV below); for example, all the giant animals are given just a single attack for 1d6 damage, white apes are given just 2 attacks (when it could justifiably be 4), NPC fighters are given no bonuses whatsoever for abilities, feats, or magic items, etc. Hit dice are all still 6-sided as per the Original D&D boxed set. There is no penalty to XP for battling creatures under your own level (which arguably would be worse for solo fighters, as opposed to parties that can gang up on one monster of like level for full XP). And yet for all that, the system is practically a sure-fire-killer unless we soften the initial roll for monster level (or the like) in each pairing.

Questions

What do you think of that? Is it what you expected when we switched from man-vs-man to man-vs-monster? Can you think of any more justifiable way of determining random pairings of D&D fighting gladiators versus monsters? Is it helpful for the game?

Want the data files and Java code used for the simulation? See here:

• Monsters.CSV
• Arena-v103.ZIP