Some Pseudo Math for Dominance in the Social Network Dungeon Experiment

I’m a full fledged old school gamer so I haven’t used much of the newer mechanisms for encounter balancing. Still, the underlying math attempts to approximate an a metric for dominance levels of creature groups in a constrained environment.

The Challenge Rating (CR)

This is fuzzy math to determine how one creature may measure up against either another average party level and/or another creature. I stumbled on Kaww’s post describing Vorpal Tribble’s approach for determining CR of a creature on the fly.

#1. Divide creature’s average HP by 4.5 to 6.5.
4.5 for 5 HD or lower, 5 for 6-10 HD, 5.5 for 11-15 HD, 6 for 16-20 HD., 6.5 for 20-25 HD.

#2. Add 1 for each five points above 10 its AC is, subtracting 1 for every 5 below.

#3. Add 1 for each special attack (+2 to +5 or more if its got a decent number of spells in its spell-like abilities).

#4. Add 1 for each quality unless you deem it worthy of more. Add 1 for each resistance and 10 points of DR it has, and 2 for each immunity. Subtract 1 for each vulnerability.

#5. Add 1 for every two bonus feats it has.

#6. Divide total by 3. This should be its rough CR

I have a couple of issues with this. The first (#1) is the segmentation of the average HP calculation. While dividing by HD might be more elegant, simplicity is key so I will just use the average in the middle of 5.5.

Most of the games I play use descending not ascending AC so just invert #2. #3 is judgement call so to automate it, I’ll just use the raw number of special attacks. #4 will just use the number of special abilities. Designating one ability over another is complicated so roughly speaking they will just all be the same. My systems of choice have no feats so it will just be ignored. Others may choose to include it.

The simplified calculation is:

CR = (HP / 5.5) + 1 * (#Special Attacks) + 1 * (#Special Abilities)

This ignores AC for now. I will need to source a table that gives some indicator of descending to ascending armor class comparisons. Given the descending nature, I think one bonus CR per 3 points of AC below 10 (9) would work reasonably at first glance. So we could add:

CR += abs(10 – AC) % 3

Then divide it all by 3 per the original calculation.

CR /= 3

Apply this on a per creature basis then average for the group of creatures. This will give a baseline CR for the group. So now there is a rough CR for the creature(s) as a group. Couple that with the number appearing and you can begin to resolve the CR relationship.

CR is Non-Linear

Based on the explanations I’ve read, CR is a non-linear relationship. There is little explanation that determines how 1n CR = 2 CR(n-2) or 1n CR = 4 CR (n-4). There is probably an obvious calculation this non math guy is missing.

My buddy, Keith, came to rescue with a simple approximation

#Appearing * (CR^2) = Dominance Level (DL)

Dominance Level is similar to encounter level in some contexts. Both break down at the extreme of disparate levels. As a rough approximation, it allows for large numbers of lower level creatures to exist within the space of a far more dominant monster.

It is not a perfect metric as Keith explains:

For the moment, though, I would suggest when considering dominance use an exponential-based relationship. The square of the HD would be dead easy, but in D&D 3.x the CR is perhaps a better measure, and one creature of CR n is roughly equated to four creatures of CR n-4 (and two creatures of CR n-2).

By this math 8 CR 3 creatures might be considered roughly equivalent Dominance to a single CR 9 creature (and nowhere near the dominance of a CR 24 creature, 8*3=24 notwithstanding).

Squaring and adding, on the other hand, would give 8*3*3 = 72, while a single CR 9 creature would be 1*9*9 = 81… not so far off, really. For even lower-level creatures you might see 9 CR 1 = 9*1*1 = 9 vs. a single CR 3 = 1*3*3 = 9.

I’m not sure which works better. Nine CR 1 creatures against a single CR 7 creature can be a kind of even fight in the right circumstances (focused fire has some happy effects), but it’ll be touch and go and the CR 1 guys can expect a lot of casualties, possibly TPK. This suggests to me that a lower-CR creature could effectively hold dominance (the single CR 3 creature might be enough to balance them ‘socially’ — equal Dominance score). They could probably beat him if it came to a fight, but would it be worth the trouble and the possibly (likely) casualties?

Dominance Level

DL is not the end-all-be-all metric. It is one of many drivers within a simulated social network driven dungeon. The overall relationships including friendship will determine if one group tries to overtake another. On one hand, if you used it without consequence, the dominant groups would overrun the dungeon. However, those same groups are aligned with other groups or perhaps co-exist so they have no desire to overrun less powerful creatures wholesale.

Tags: affiliation, graph, random dungeon