Arena v1.11: Man vs. Man

Returning to the Arena simulator one more time; recall that the initial motivation for this project was to analyze exactly what kind of demographics emerge out of actual D&D play -- in particular, frequency at each level, and average ability scores, hit points, etc. (See various prior posts.) This software module was then used as the kernel of the supplemental applications, MonsterMetrics and the Marshal (last few weeks). In particular, the observation that the natural Arena man-vs-man simulation produces demographics quite similar to the units of Men in Vol-1 (bandits and the like) allowed us to use it as a nice platform for that application. Let's return to that original usage here.

One thing that slightly bothered me about prior versions of the man-vs-man Arena is that I could discern the following phenomenon: There tended to be a character with halfway-decent ability scores who started out, got a slight advantage over the other fighters in the list, and then basically cruised from then on by beating up on all of the lower-level fighters they were matched against (which was necessarily everyone, because the initial run starts with a list of all 0-level fighters). They could reach an arbitrarily high level by just letting the simulation run long enough and wiping up the floor with enough 0-level fighters one was matched against. But does that reflect a reasonable campaign milieu? Would the highest-level fighter always be someone who would not have succeeded, if only they had entered the list at a later, more fully developed stage (with higher-level figures in the population)? Were we biasing the top-character's abilities downwards due to giving them a head start in this way?

The solution would be to implement character aging over time in the simulator. Even if one "Adam" like character rose to prominence early on, they should fade later, and let the population naturally achieve some kind of equilibrium, where successful fighters all have to fight their way up a ladder of already-present higher-level NPCs. This would then present a more realistic demographic distribution and ability score averages. I chose to implement the aging parameters for ability scores from the AD&D DMG, and also impose a loss of fighters levels every 2 years once one reaches Middle Age, similar to Gygax's writeup on Conan over the years in Dragon #36 (see last week's post). The results were ultimately quite satisfying.

In doing this, I had to explicate an explicit "clock" on the characters for the first time. When I first created the Arena, I had in mind something like the gladiatorial system in ancient Rome; that is, perhaps 10,000 gladiator in the entire country, battling seasonally; that is: maybe 4 times a year. It turns out in D&D terms that this is not frequent enough combat to generate high levels. With minimal combats, the NPC earns only a small amount of XP, before the aging process kicks in and the sink back down in levels. So I started increasing the fights per year, with the following results generated in terms of highest level attained in the population:

• 4 fights per year: max level 6.
• 6 fights per year: max level 7.
• 12 fights per year: max level 8.
• 24 fights per year: max level 9.
• 50 fights per year: max level 12.

Perhaps we might say that in "real life" (the first data point), the highest level achieved really is something like 6th level. But the 24 fights/year level does a better job of using the entire D&D level range, in particular the top levels for NPCs mentioned in OD&D (9th level Lords are reference as leaders for groups of Men in Vol-1, and Castles in Vol-3). That's a fight every two weeks, which starts to cast doubt on my assumption that everyone heals up between fights. On the other hand; if a high-level NPC smacks down a dozen or so 0-level mooks in a single encounter, that would fill their quota for a good part of the year.

Another thing I had to realize/adjust was this: Previously I'd used a lazy algorithm for level loss (as by undead), in which the XP was set to just 1 point below that necessary for the lost level (using the same code that would cap XP to prevent jumping levels on the upward climb). But here, that would result in an aging NPC apparently not ever losing a level, since they'd go down and then instantaneously back up again on the next fight. Therefore I also switched that code to match Gygax's rule in the AD&D DMG; XP now goes to the midpoint of the prior level after a level loss. Glad to be convinced of the necessity of that later rule.

Here's the results of the modified Arena man-vs-man program after those changes, letting it run for 500 "years". All fighters start out at age 18 and 0-level. Columns after "Num" all show averages for the given level:

I think that's a pretty attractive resulting population. Ability scores at the top level are broadly in line with what came before (not markedly higher or lower). As far as age goes, most low-level fighters are in their 20's, but the highest-level fighters are likely to be in their 30's or 40's. On this run of 500 years, there was one fighter who actually and kept fighting until he was killed at 76 years old; an outlier, but without historical precedent on Earth (one time on these simulations I've seen some grizzled warrior last until the age of 103, in line with Gygax's expectation that Conan would live until that age). All of this simply emerges organically from the mechanics involved, which I think is very nice; there is no enforcement of any maximum-age cutoff in the simulator.

A few other comments: Without the aging effect, obviously the NPCs involved can live arbitrarily long (hundreds of years), and so reach arbitrarily high levels (high teens and whatnot). Likewise, if we implement only the AD&D DMG ability score modifiers for age, we find that they make minimal to no impact on the overall demographics (again, NPCs wind up hundreds of years old and effectively of unbeatably high level). Only if we include the level-loss mechanism of Gygax's Conan does a realistic-looking population emerge. Generally what I see happening is that older high-level fighters sink from 8th to 9th level down to around 6th, at which point the earned XP sustains them against the next level loss, until at some point they get matched against a 7th-9th level opponent and they finally die by the sword. (Gygax suggested that Conan be reduced no further than 9th level, but this 6th-level point for an extremely venerable fighter doesn't seem bad to me.)

We might also consider classes other than the fighters used here. The Arena code also includes a slower level-loss factor for Thieves of one level every 4 years (again, similar to Conan's thieving ability at old age, per Gygax). I would assume that Wizards would not lose levels in the same way; we're all familiar with the trope of the bent-over, "wizened" figure, being in fact the most powerful/dangerous; although in this emergent system that would imply that they could live to any advanced age without limitation. Perhaps that's not a bad accident for our campaign.

Next time: The far more troublesome Man-vs-Monster case.