13th Sage: Player Character Damage Math

Recently, a member of the 13th Age community who’s trying their hand at spell design asked if we had any resources to help with the math. We’ve written a lot about monster design, but haven’t really delved into classes; so for this month’s column, I’ll share the basic math behind figuring out how much damage characters should deal, for those of you who are creating your own character classes or variants.

Below, you’ll see the table we use when we’re figuring out roughly how much damage a spell, or an attack of a specific level, should deal. Three of the columns cover the target numbers for at-will, once per battle, and daily attacks. The last column indicates the amount of that damage that’s likely to come from the character’s ability score modifier—most attacks and spells add the ability score modifier, with a few exceptions. If it’s a normal attack that uses the ability score as a damage modifier, subtract the ability score modifier bonus from the target number to find out roughly how much damage needs to come from the dice.

A truly efficient designer would probably have created other columns, ones that show the target numbers that you’re aiming for, with just the average dice results. But I’ve always enjoyed doing the math on the fly, so today you get the columns the way I use them. No coddling!

Character level Target At-will damage Target 1/battle damage Target Daily damage Likely ability score modifier bonus
1 10 15 20 4
2 13 20 27 4
3 17 25 33 4
4 20 30 40 4
5 27 40 53 8
6 33 50 67 10
7 40 60 80 10
8 53 80 107 15
9 67 100 133 15
10 80 120 160 15

Multiple target math

There’s another significant piece of damage math related to attacks that have multiple targets.

If a character can make two (or three, or however many) separate attacks against any target they wish, it’s okay to simply split the damage in two (or three, or whatever)—because if the character wishes, they can focus all the damage on a single target.

But an attack that can’t be focused on a single target is different. Lots of attacks target 2, 3, 1d3, or 1d4 separate enemies. If we halved the damage of an attack that has two separate monsters as targets, that would be terrible for the player character, because what’s most important in combat is making attacks that take out enemies before they can attack you. Multiple attack rolls against separate targets do reduce the damage, but by less than you might imagine if you were spitballing. The same adjustments generally apply to damage dealt by monsters.

Here’s the math:

2 different targets (also 1d3 targets, since that averages 2): 80% normal damage

2.5 different targets (i.e., 1d4 targets, use it all the time): 75% normal damage

3 different targets: 70% normal damage

3.5 different targets (i.e.,. 1d6 targets): 65% normal damage

4 different targets: 60% normal damage

5 different targets: 50% normal damage

…And so on, though I can’t remember many cases of “and so on” coming up!

I hope this is helpful as you design new powers for 13th Age heroes. With another Bestiary on the way, they’ll need them!

4 Responses to “13th Sage: Player Character Damage Math”

  1. ruemere says:

    I would add two observations:
    1. I assume the average hit ratio assumed to be 0.75 (so I would multiply the values above by this parameter).

    2. If you want to find out if your combat is going to be fun or drag, total HP of the opposition, total average party damage, divide the former by the latter. If you get 3 or close, the fight is OK (about 3 rounds), if you have 5 or close the fight should be an epic finale or you risk running in to a drag.

    The value of three means that you players are unlikely to use dailies and recoveries, and there is little risk of anyone going down (because average monsters seldom exhaust PCs’ free recoveries within 3 rounds of combat).

    The value of five means that there will be close calls or missed rounds due to recovery actions. This will extend the length of combat, giving foes more time to act. In turn players will have to think more about resource management increasing length of individual turns. So, if you get five, either decrease number of monsters, decrease number of monster HP or make the game an epic finale.

    For in-between results, adjust the HP value down. Shorter fights mean more time for roleplaying, after all.

    NOTE: You don’t get more XP for the number of monsters killed by players :). So there is no need to keep the fights long.

    Regards,
    Ruemere

    • Ashley Walker says:

      Three rounds seem really short in 13A. I usually shoot for 5 or so, or else my players start wondering why I’m not giving them an actual challenge. Even so, half the time it doesn’t take as long as I think it’s going to.

      • ruemere says:

        The questions are whether you want every fight to be a challenge, and whether you need your challenging fights to be longer.

        My answer to the former is that a fight does not need to be challenging to be fun. To the latter, I would say that we can make a short and challenging fight. Finally, you can also go the third way, making a fight tough and challenging, but for such cases I would go with the epic finale as the constant teetering on the edge may be mentally draining.

        For a short and fun fight, consider a combat against a group of mooks on a board of a river barge hurtling toward waterfall of doom. You’re have a time limit, the fight is easy, you just need to make your fight really quick.

        For a short and challenging fight, consider (extreme example) double strength enemies with normal HP. Lots of damage at stake, but quick resolution.
        It’s alike a samurai showdown – first the staring contest, then a quick bout of strikes with the successful attacks littering the floor with the bodies.

        Regards,
        Ruemere

  2. Michael Keon says:

    This is great Rob, thanks for sharing! In regards to the last part of the article, about multiple target abilities, you say that it also applies to monster damage math. But when I’ve been designing my own monsters, or just modifying book monsters, I haven’t been scaling the damage for multiple target attacks in the way you describe (largely because this article didn’t exist yet), and so far its been working fine. It seems to me that while the PCs might face a fight with a single big monster where fireball is ineffective (and thus the scaling you describe is justified), the monsters will almost always have multiple PC targets to hit, and I often don’t play the monsters purely tactically where they gang up on one PC until that PC drops, so spreading damage around on PCs is better. Plus, if a PC drops below 0, any healing they get restores them to 0 first, so any damage below 0 is “wasted” unless the PC outright dies. So while your scaling makes a lot of sense for PC damage, should it really apply to monster damage the same way?

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