Aetrimonde

In the post series on Unified Mechanics (first post here), I described in general terms how some core mechanics would work, but I didn’t attach all the necessary numbers to them. In this series, I’ll start hanging numbers on that framework to achieve a benchmark I mentioned in an earlier post: that a character should succeed at tasks they are competent but not superb at, around 2/3 of the time.

To start with, I will need to work out what a typical character’s abilities should look like, because those abilities will feed into everything else that I need to calibrate.

Ability Generation In Detail

I’ve already said that I intend Aetrimonde to run on a point-buy system for generating a characters’ abilities. That is, players will all “buy” their characters’ abilities with the same budget of points.

However, there is also a second component to ability generation, which is that a character’s heritage allows the player to increase two (of up to 3) preferred abilities by a further +1.

This post will walk through the calibration of both components.

Defining Ability Scores

To start, what range of values do we permit for abilities? And how do they map to real-world qualities, for comparison?

As an intuitive first step, let’s define 0 to be an “average” ability.

How many “steps” above average do we want to allow (at least for PCs)? Let’s say, for the sake of argument, that each +1 represents a single standard deviation from the mean in an ability. Assuming a normal distribution of abilities, that lets us work out, statistically, just how extraordinary having a particular score is.

Unfortunately, it means that by the time you hit +3 in an ability, you are already around one in a thousand; +5 would put you at about one in ten million. That’s quite rarefied: Aetrimonde is aimed at supporting a pseudo-Victorian setting, with a world population of about 1.5 billion, so there would only be around 150 people with +5 in a given ability in such a world. I’d like there to be more than 3 increments between an average person in the street and someone who is probably stronger than anyone else they’ll ever meet.

Let’s halve how much a +1 means, to only half a standard deviation. Then, ability scores would imply the following:

• +1: You are in the top third of the population.
• +2: Top sixth.
• +3: Top 1/16th.
• +4: You are one in 40.
• +5: One in 160.
• +6: One in 800.

Point-Buy Costs

I’m going to impose that a typical PC’s highest ability should be between +3 and +5, with +6 being out of reach for a PC. I’ll also impose the following goals on the array of abilities they can get:

• After the boosts from heritage, PCs should be able to get abilities of +4, +3, +2, +1, and four +0s.
• It should be possible to get two +4 abilities, after boosts, but this should mean you have basically no other positive abilities unless you also have some negatives.
• It should be possible to get a single +5 ability after boosts, but not also any +4s unless you have several negative abilities.

I think this can be accomplished using a quadratic cost function for positive scores, such that the cost of each successive ability increment gets larger and larger:

These point costs (for the positive abilities) are given by the formula C(a) = a(a + 1) / 2.

Assuming that a character gets their +4 and +3 by boosting a +3 and a +2, for maximum benefit, they need to buy a +3, +2, +2, and +1. This costs 6, 3, 3, and 1 points for a total of 13: an unlucky number, but also a magical one.

What else could be bought with 13 points?

• It’s enough for +3, +3, +1, which boosted becomes +4, +4, +1, and five +0s.
• It’s also enough for +4, +2, which boosted becomes +5, +3, and six +0s.

This looks like it will work: it’s possible to get several good abilities, or a pair of excellent ones, without any abilities going negative.

Limits of Min-maxing

Min-maxing means to maximize the strengths of a character and minimize its weaknesses: it’s a form of character optimization. In the context of ability generation, min-maxing means raising the abilities your character benefits most from, without creating glaring weaknesses. In practice, that means decreasing abilities that you don’t need so that you can spend more points on the ones you do.

Most Aetrimonde characters will have two abilities they care most about, followed by a third of less importance. They will want to raise these as high as possible, but they will also want to avoid having too many negative abilities, which would severely impact their defenses. Assuming a character puts their four best abilities into separate defense pairings (so that they have one of their better abilities contributing to each defense), they won’t have any glaringly weak defenses. But as we saw with Ragnvald, who needed high Strength and Constitution, that’s not always going to work out. The negative abilities will create a lot of other weaknesses too:

• Low Strength will mean a character can’t carry much, will have trouble defending themselves in melee, and will have trouble climbing, jumping gaps, or swimming.
• Low Constitution will give a character low hit points and resurgences.
• Low Dexterity is probably the least problematic, as it really only prevents a character from using ranged weapons effectively or engaging in subterfuge like picking pockets.
• Low Grace will give a character trouble crossing slippery surfaces or remaining hidden, and will make it hard for them to maneuver around enemies.
• Low Intelligence will make a character bad at a whole range of skills.
• Low Cunning will ensure a character always acts last and is often surprised.
• Low Wisdom and Charisma will make it hard for a character to engage in social skills.

So what does it take to get +5 and +4? The +5 needs to be boosted from a +4, and if the +4 is boosted from a +3, that costs 16 points. So the character would need to have three -1s, or a -1 and -2. If they wanted more than those two positive abilities, they would have to go even more negative, as well. One workable array is +4, +3, +1, +1, -1, -1, -1, -2, which certainly has plenty of drawbacks.

What about +5 and +5? The only way to get that is from two boosted +4s, which would take 20 points, requiring at least three -2s and a -1. As far as defenses go, the best array is probably +4, +4, +1, +0, -2, -2, -2, -2, which has major drawbacks in half of the abilities.

In other words, it’s possible to get a pair of very high abilities, but at the cost of some crippling weaknesses. Is this a good basis for a character? Only if the party as a whole can compensate for the weaknesses.

Suggested Arrays

Here are some possible arrays of eight abilities (before boosting) that are well-rounded:

+3, +2, +2, +1, +1, +0, +0, -1
+3, +3, +1, +1, +0, +0, +0, -1
+4, +2, +1, +1, +0, +0, -1, -1

I’m also going to include a note in the core rulebook suggesting that, at least for inexperienced groups, characters should not have any more than a single -1 ability, and no -2s.