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The Math of Spellcasting

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Joined: 07 Sep 2006
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PostPosted: Sun Feb 24, 2008 1:21 am    Post subject: The Math of Spellcasting Reply with quote

Awright, y'all. Listen up now. There is some confusion as to how one should roll dice for their spells. I'm going to give you a few ways to look at it: an easy way, and a harder way.

Easy Way:
Each spellcasting class has a guideline to be followed for determining a spell's effect: LvLd5+bonuses for mages, sorcerers, and necromancers, and LvLd4+bonuses for clerics, shamans, etc. Voila: you have the effect of your spell. Pretty simple, hey?

Want to cast against multiple targets? Just divide the result by the number of targets.

Want to do more damage? Charge it up. Spend one round charging (and cast on the second round) to do 2x damage, or spend two rounds charging (and cast on the third round) to do 3x damage. In other words, you do 2x damage when you spend 2 rounds on the spell, or 3x damage when you spend 3 rounds on the spell.

You are a level 8 mage with +3 from intelligence and +3d5+3 fire channeling from some items (and your innate elemental channeling). Your fire spells thus do 8d5 + 3 + 3d5+3, or 11d5+6.

Congratulations. If you don't like math, stop reading here. You already know enough to cast perfectly legal spells.

Harder Way:
If you decide to do pretty much anything else with the dice, you're going to have to do some math to find out whether or not your spell is still within acceptable limits. You need to know the minimum, maximum, and average damage of your spell, and you need to keep it comparable to the min, max, and avg of a standard spell (like the ones described above). AVERAGE damage is representative of a typical casting, especially over the long run (i.e., several hundred castings). Let's look at how to figure these values out for a spell.

- Minimum damage: Assume you rolled all 1s, and add the result to your bonuses.
- Maximum damage: Assume you rolled the highest numbers possible with your dice, and add the result to your bonuses.
- Average damage: Assume you rolled the average result for all dice involved (see below), and add the result to your bonuses.
Finding the average result for a roll: with odd numbered dice, the result is the middle number (a d5 can yield 1, 2, 3, 4, or 5, so the average is 3), and with even numbered dice, it's halfway between the middle numbers (a d4 can yield 1, 2, 3, and 4, so the average is 2.5). The math for this would be (1+2+...+X)/X = avg of dX, but that's more work and the end result is the same.

Try to keep your average damage close (probably within +/-10%) to a standard spell's average damage. Your maximum and minimum damages can have a little more variance, but also try to keep them close. If you want your maximum damage to be significantly higher, the average damage should be proportionately lower (2x as much max damage should mean 1/2 as much average damage).

Okay examples, using the same mage as before:
Standard fire spell: 11d5+6 = minimum 17, maximum 61, and average 39.
Elaborate fire spell: 5d11+6 = minimum 11, maximum 61, average 36. This is actually slightly Worse, even though it looks nastier.
Misguided fire spell: 5d6+11 = minimum 16, maximum 41, average 29. Sometimes moving numbers around can actually weaken a spell.

Not okay examples, again with the same mage; any of these could get you shot if the sheriff were in the room.
Iffy fire spell: 11d6+5 = minimum 16, max 72, average 44. It's close and sort of within guidelines, but let's be frank: you're increasing the value of 11 dice while only reducing your bonus by 1. That's a bit like arbitrarily just giving yourself more bonus dice. Please don't do this.
A popular way to do it: d5+6 x d11 rounds duration = minimum 7, maximum 121, average 54. Average is 40% higher, maximum is 2x higher. They can't both be so much higher, regardless of the minimum being 10 points lower.
Another way I've seen it done: 11d5 x d6 targets = minimum 11, maximum 330, average 116. See how much of a problem it can be to just change a plus to a multiply?
A Crazy way to do it: 11d5+6 x dLvL rounds duration = come on, it's a standard spell with a random 1x-8x multiplier with no drawbacks. Minimum 17, maximum 488, average 176. Obviously, this is ridiculous.

I hope this helps give you a little more guidance to creating your own wacky spells. Just remember: keep their max, min, and average damage CLOSE to that of a standard spell, because they're called STANDARD SPELLS and GUIDELINES for a reason.

- blueSC
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