Aetrimonde

It’s a double post today! In this post, I’m going to get into the design and balancing assumptions that ensure a “typical” attacker will hit a “typical” defender about 2/3 of the time. And, in the post that follows, I’ll be going over the related process of balancing damage against hit points.

Attack Mechanics

As a refresher on how attacks work: when you make an attack, you make a core roll, add an ability and potentially some other bonuses, and if the total is at least equal to the target’s defense against the attack, it hits.

In order to hit 2/3 of the time, a typical attack needs to hit when rolling 10 or greater on 2d10. So, a typical attack bonus needs to be 10 less than a typical defense.

Typical Attacks

I’m going to continue the assumption that a character has between +3 and +5 for their highest ability, which they use to make attacks with. Splitting the difference, this will make a typical attack bonus +4, and we should have a typical defense be 14.

I’m ignoring AC for the time being: that will be something of a special case to be tackled later. But we will want the other four defenses to be 14, on average.

Typical Defenses

I’ve already discussed in a couple of posts that there are four defenses, and each benefits from adding the higher of a pair of abilities. Before I delve into the exact formula, let me back up a moment and explain why this is the approach taken.

Abilities into Defenses

First of all, why have four defenses based on pairs of abilities? Why not one defense per ability? There are a couple of reasons:

• Many attacks thematically could be opposed by multiple abilities. A firebolt could be opposed by dodging it (Grace) or by throwing up an arm or a shield to protect yourself from the worst of it (Dexterity). A spell of compulsion could be opposed by having the self-awareness to recognize and ignore these external impulses (Wisdom) or by having the sheer presence of will that shuts the compulsion out entirely (Charisma). Giving characters the option to use either of these abilities in their defense makes narrative sense.
• Mechanically, having eight separate defenses spreads resources very thin. It’s not that odd to have a character with +5 as their high defense and -2 as their low defense, and this would create a 7-point gap between defenses just based on abilities, which could easily widen further based on various bonuses. This would create a situation where a character can virtually never be hit against one defense, and virtually never missed against another. Pairing up abilities reduces the spread of defenses and helps keep them in a range where there is almost always a meaningful uncertainty about whether an attack will hit.

Next: why the greater of the two abilities in each pair? Why not add both, or add the lesser?

• This is partly a narrative decision. If you could oppose an attack in two ways, you would naturally choose to do it in the way you’re better at.
• Also, these three options create different incentives for min-maxing:
  • Adding both abilities incentivizes having both abilities in a pair be equal. The diminishing returns from ability point costs means that it is cheaper to get +2 and +2 than +4 and +0, for example. This encourages homogeneity where smart characters are also cunning, wise ones are also charismatic, etc. it also has the same problem that having eight separate defenses does, in that there could be big gaps between highest and lowest defense.
  • Adding the lesser of the two abilities even further incentivizes having the abilities in each pair be the same, because there is no point in raising one ability above the other unless you have a particular use for it. It also means that a character will not necessarily have a high value in the defense that uses their highest ability, which feels wrong somehow.
  • Adding the greater of the two abilities allows characters to be, e.g., very charismatic but an absolute fool, or street-smart but uneducated, without compromising their defenses. This encourages more diversity of characters and roleplaying, which I am in favor of.

Defense Formula

With that settled, why does the formula of 10 + half expertise bonus + higher ability arrive at the average defense being 14?

I’m going to work from the assumption that a typical character has one of the balanced ability arrays laid out in the Why it Works post on ability generation. I’ll further assume that they put one of the four highest abilities into each of the four ability pairings, so that each of their defenses benefits from one of those high abilities.

The three arrays have high abilities of:

+3, +2, +2, +1
+3, +3, +1, +1
+4, +2, +1, +1

Note that, in all three arrays, the average of these abilities is +2. We could define defenses to be 12 + the higher ability from the relevant pair, averaging out to 14.

However, this omits the boosts from heritage, which (applied to two abilities from these four best) would raise the average ability to +2.5 and the average defense to 14.5.

Reducing the formula to 11 + the higher relevant ability brings the average defense down to 13.5. To get it back up to 14, we need to somehow give every character either +2 to a single defense or +1 to two of them. This can be a function of class, giving a slight increase to defenses that are appropriate for the class.

The last thing to do here is bring expertise into it. The expertise bonus is +2 at level 0, so setting the formula to 10 + half expertise + greater ability + class achieves the same result at level 0. As to why using half expertise is the way to go…I’ll leave that for a later post dedicated to level scaling.

Attacks vs. AC

I left attacks vs. AC for later, because this is going to be more complicated. As I hinted when discussing the purposes of Dexterity and Grace, the AC defense will be based on one of these two abilities, if a character is wearing light to medium armor. That means that the calculation of an Armor defense will include something other than those abilities, that being the protection afforded by the armor they are wearing.

There are three kinds of armor: light, medium, and heavy. Light armor allows adding the greater of Dexterity and Grace, medium armor the lesser, and heavy armor neither. Why set the armor types up like this, other than thematic reasons? It’s easiest to see if we look at the levels of AC that can be achieved with typical armors in each group:

AC	Leather Greatcoat (+2)	Maille Shirt (+3)	Scale Armor (+5)
14	+1 DEX or GRA	+0 DEX and GRA
15	+2 DEX or GRA	+1 DEX and GRA
16	+3 DEX or GRA	+2 DEX and GRA	Any DEX or GRA
17	+4 DEX or GRA	+3 DEX and GRA
18	+5 DEX or GRA	+4 DEX and GRA

As can be seen here, it’s possible to get 18 AC using light or medium armor. However, getting the highest AC in light and medium armor means investing a lot of ability points into DEX and GRA:

• To get 18 AC in a leather greatcoat, one needs +5 DEX or GRA. This costs 10 ability points and requires boosting the ability using heritage; virtually the only character who can afford to do that is one that would be DEX-based already, like a rogue. 17 AC is slightly more affordable at 6 points, and could be achievable for a non-DEX-based character, but would leave virtually no ability points for other important abilities.
• To get 18 AC in a maille shirt, one needs +4 DEX and GRA. In the best-case scenario (a character who can boost both DEX and GRA using their heritage), this costs 12 ability points. The only character for whom that could be worthwhile is a DEX-based character like a ranger or tactician focused on ranged weapons. 17 AC is slightly more affordable at 6 ability points, and actually works decently well for martial characters who want to switch back and forth between melee and ranged weapons…but even then, it leaves basically no margin for secondary abilities like CON or CUN.

I’m going to treat 16 AC as the typical AC, and not just because that’s the AC achievable with most heavy armor:

• It costs 3 to 6 points to get 16 AC in a leather greatcoat, depending on whether the character can boost the relevant ability. This is cheap enough to be achievable while also having a +4 in another ability.
• It likewise costs 2 to 6 points to get 16 AC in a maille shirt.

16 AC being typical means that the typical attack bonus vs. AC should be +6. How do we get the extra +2 (on top of a +4 ability)?

Most attacks vs. Armor will be made with weapons. We can give weapons a flat +2 bonus to attack rolls. Or, even better, we can give them a varying bonus to attack rolls, with +2 being the default but having some big, heavy weapons that deal more damage but have only +1 to attacks. Any other attacks vs. AC can have a built in +2 (or so) bonus to bring them up to par.

Deviations from the Assumptions

All of this depends on the initial assumptions about how a character’s abilities will be distributed. In practice, it won’t work out so cleanly: there will be characters that boost one of their low abilities, or that put two high abilities in the same pairing, and this will mean that they have lower defenses. And then there are Dexterity-based martial characters (most rogues, plus fighters, rangers, and tacticians focused on ranged weapons), who will find it easy to get their AC quite high, because they already have a high DEX. Is this a problem?

Not a significant one, I think. I’ve generated a bunch of characters to test out the math behind this balance point, and had some testers generate their own. And it seems that in practice, any character that isn’t purposely built as a joke is going to wind up with their defenses averaging no more than half a point below “typical.”

Aside from that, the guidelines I’ve developed for designing monsters mean that the monsters suffer from the same issues causing their defenses to be just slightly lower than the setpoint I aim for. So, even to the extent that this is an issue, it should affect both “sides” of the game equally.