Question about the 3.5 spell point system variant

[jhawz]

Ok, so I have an epic level character with an intelligence score of 67, and I need to know what the bonus spell points are for an intelligence that high. The chart only goes up to 51. I've tried extrapolating based on all kinds of things, but I can't seem to grasp the right equations.

Help?

Thanks in advance!

[TuggyNE]

I hate to say it, but I've tried summed squares, integration, and polynomials, and I don't think there actually is any single equation or pattern that fits the whole chart.

The UA spell point variant is not what you might call a model of good design.

[jhawz]

Sigh. I was afraid of that. Thanks for the help!

[eggynack]

I hate to say it, but I've tried summed squares, integration, and polynomials, and I don't think there actually is any single equation or pattern that fits the whole chart.

The UA spell point variant is not what you might call a model of good design.
Oh god, why is it like that? It keeps fluctuating back and forth between an increasing difference, and a decreasing difference. I'm inclined to believe that there's some consistent pattern there, but I have no idea what it is. I'm probably going to spend a decent amount of time just staring at that thing.

Edit: I think I may have figured it out. Each level of spell is worth an increasing amount. First level spells are worth one point, second level spells are worth three, third are worth five, and so on. Then, you line it up with the regular bonus spells per day chart. It's just a hypothesis, because I haven't lined the charts up yet, but if it works you could just extrapolate based on the changes in the regular chart.

Double edit: I just ran a couple of comparisons, and it looks like it works. You have to go through the tedious process of figuring out what your regular bonus spells would be, and then add it all up. Actually, I think there's a formula for regular bonus spells per day, so you may be able to engineer that into a bonus spell points per day formula. I wouldn't know where to start, though.

Triple edit: Actually, it might not be all that bad. past the +9 intelligence modifier line, the increases should be pretty consistent.

[Flickerdart]

I remember someone on another board actually did figure out the numbers for how WotC calculated the spell points, but I can't remember where that's posted. I am reasonably certain that someone was making spell points for the Healer, which is what resulted in someone else posting the values...

[eggynack]

I remember someone on another board actually did figure out the numbers for how WotC calculated the spell points, but I can't remember where that's posted. I am reasonably certain that someone was making spell points for the Healer, which is what resulted in someone else posting the values...
I think that the numbers I posted work out. For example, if you have 18 intelligence and 3rd level spells, you'd normally get a first, second, and third level spell slot. It would add up to 1+3+5 spell points, which comes out to 9, which is the correct number of spell points. For another example, at 24 intelligence and 7th level slots, you'd get 2, 2, 2, 1, 1, 1, 1 as your bonus spells from int. That'd come out to 2+6+10+7+9+11+13 which matches the actual spell point count of 58. The only issue is that you have to figure out the bonus spells from intelligence under the normal system before proceeding. One good way to pull it off might be figuring out the differences from +9 through +18. After that, the difference between +18 and +19 should be the same as the difference between +9 and +10. I think that's how it'd match up, anyway. After that, you can probably work out a simple method of computing higher numbers. Probably, you'd just keep adding on the gains from a single +9 shift onto whatever the starting value is. It probably isn't too hard to work out.

[Ernir]

Actually, I think there's a formula for regular bonus spells per day, so you may be able to engineer that into a bonus spell points per day formula.
If I'm not mistaken, your number of bonus spells of a given level are:

max(1 + 0.25 * floor(key_ability_modifier - spell_level),0)

so if your idea on the bonus spell -> bonus SP conversion is correct, we can express the total number of SP in sum notation:

sum[on i from 1 to max_accessible_spell_level] max(1 + 0.25 * floor(key_ability_modifier - i),0)*((i-1)*2+1)

[TuggyNE]

If I'm not mistaken, your number of bonus spells of a given level are:

max(1 + 0.25 * floor(key_ability_modifier - spell_level),0)

so if your idea on the bonus spell -> bonus SP conversion is correct, we can express the total number of SP in sum notation:

sum[on i from 1 to max_accessible_spell_level] max(1 + 0.25 * floor(key_ability_modifier - i),0)*((i-1)*2+1)

Indeed! And I managed to get that into a nice Excel spreadsheet that appears to work. However, there are a couple of little glitches I've noticed so far; at +11 and +14, the printed 9th bonus spell points column is 2 or 3 points lower than the calculation. Not sure why this is.

However, assuming that's a printing error or the like, a score of 67 with 9ths gives you a solid 485 bonus spell points.