Wednesday, April 9, 2008

d20 Rethought: Balancing Magic

Magic in d20 rethought is already dependent on multiple ability scores and faces limitations parallel to those mundane combatants must deal with. The topic of this post is the raw number-crunching needed to make sure a system of skill-based magic is balanced. I've got not surefire approach in mind, so this will be done in a more stream-of-consciousness manner. (Note: this is a snapshot/transcript of the process, it doesn't really get into the numbers I eventually settle on. If those are what you're after then you'll want to wait a few more posts.

I'll start by theorizing that the three levels of a talent chain give a character to cast spells of that type at the same level as a D&D class's low, medium, or high spellcasting progression. Or, to put it differently: Take Healing Magic I and I can cast cure spells on par with a paladin of my level. Healing Magic II puts me on par with a bard and III on par with a Druid. Still confused? Here's the level at which each level of spell (from 1 up) can be cast by the three spellcasting progressions:

Low: 4/8/11/14/-
Medium: 2/4/7/10/13/16/-
High: 1/3/5/7/9/11/13/15/17

Note that this is giving us varying rates of progression, something that wound up being a problem with D&D 3.X. Let's keep this potential dilemma in mind while we go back and approach this from a more directly mathematical angle. For reference, all variables hailing from the start of the alphabet correspond to d20 results/modifiers/etc while variables hailing from the end of the alphabet will refer to non-d20 roll numbers like spell level. So:

A is the check result needed to cast a spell of level X. B is the amount A goes up by when X increases by one. C is the amount the second and third talent increases your check modifier by (assuming we keep the straight increase model). Using these variables, I can ask myself a few important questions.
-When a character can take 10 to cast a certain level of spell, how much higher level should he be *able* to cast? (Answer=10/B=Y, barring extraordinary circumstances involving crit successes and/or action points. I'd be fine with a Y between 1.5 and 4, therefore I want a B between 2.5 and about 7.
-At what level should a beginner (level 6, only the first talent, +1 mod for relevant ability) be able to cast? (Level 2 spells shouldn't be too far past the 50% mark, highest level possible barring crits/APs should be a max of 5. That means B can't be less than 3 and should probably be more like 4 or 5.

Now, this is giving us a problem. Because if we're going to make magic a skill like any others, then B's got be lower than 4 or 5. In fact, it might be ideal for it to be more like 1, since that means you can cast a new level of spell every two levels like in D&D. But with a d20's probability range that means he who can cast burning hands 50% of the time can cast Meteor Storm 5% of the time, and that's not acceptable.

Since magic's working differently already, we can make it something other than a skill and thus have it increase at a different rate- say ability+your full character level (instead of half). Combining that with a B of 3 and an A of 11 when X=1 means the low-level caster (Talent I, ability mod +1) has a 50% chance of casting an 8th-level spell and a 35% chance of casting a 9th-level one at 20th level. That's much too high-level for me, so let's adjust B to 5. Now that same level 20 character's got a 55% chance of casting a 5th-level spell and a 5% chance of casting a 7th-level one. The range is about right but the spell level isn't. Let's bump A up by 9- a level 1 spell's DC 20, level 2 is DC 25, etc. That means our level 20 character with a small knack for magic that he never really pursued is now capable of casting 5th-level spells with a 10% success rate and succeeds with level 2 spells 85% of the time. Range still strikes me as being too extensive- but then, this is the benefit of just a single talent. On the other hand, what if higher talents reduce B by one each but gave little or no extra bonus? The same level 20 character, with no changes except the other two talents (in other words, he'd still have invested three talents and nothing else- applied to other areas like lying or grappling, this would let him be as good as a focused mid-level character or a broken low-level one) would now cast a level 5 spell with a 50% success rate and level 8 at 5%. Meanwhile, they'd be casting 2nd-level spells at 95%. Throwing in a decent ability score (+4 instead of +1) and a feat (+3?) and you repeat all the previous statements while moving the spell levels up two notches. If the character's really invested in this area- supportive class features, some other ability that manages to stack- then you should be able to double that increase, at which point you're casting 6th-level spells with ease and have a 50% chance of pulling of a level 9. Considering we're talking one and only one school of magic (plus high-level spells will still cost you about 20% of your resolve points in a single go), that sounds about right to me.

So, now we've got a passable spread at high levels by saying that B=5-1 for each of the second two talents, while A=15+5X. How does it look at low levels, though? Will further tweaks be needed?

Well, let's say we've got a broken character meant to be as good with a particular talent chain as possible. He puts an 18 into the relevant score and gets another +2 bonus from his race. He selects a Skill Focus-type feat at 1st level that gives him another +3. And he plays a talent-oriented caster class that gives him the 3 relevant talents at 1st, 3rd and 5th level. At level 1 we're looking at a caster check modifier of 1 level +5 ability+3 feat, or +8 total. Whichever entry talent he selects, he can cast the fundamentals of magic from that school at a 45% success rate for level 1 spells and 20% for level 2. Flash forwards four levels and he'll have both the talents (meaning that the major difference between him at this level and at 20th level will just be the level bonus on caster checks). At this point, our level 5 character's +12 bonus on checks will let him cast 1st level spells with a 75% success rate and has a 15% chance of pulling off a 5th-level spell. Again, this seems pretty close to what I'm after.

For the record, this is not how I normally operate- extensive documentation like this has never been my thing, this would have likely been a half-page of scribbled tables and data sets with testing possibly being handled by an excel spreadsheet. Also, the math of the matter has since been altered (and improved) by my intention to include a max Result Cap on checks that can be temporarily increased but rarely bypassed. Either way, I hope this has been interesting and/or informative- and as always I'd love to hear your thoughts. Would you have approached this differently? Do you disagree with my judgment of the current system's odds as being balanced? Did I screw up my math? I'd love to hear what you have to say.

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