I though it seemed off...
You are correct. Fixed.
Cool, but I think you used the original numbers for the RP/neutral category:
71% good, 39% mixed/RP (generally your choice), 2% bad.
Recaculated the spell bombardment as a %.
It's a bit better than I thought. About 15% for pure dice spells, being better for smaller dice. Though since disintegrate and finger of death are half flat damage, it's only 6% for them.
I appreciate the effort, but those percentages only hold true as long as you are rolling a single die. Using d12s as an example:
1 die, 0.083 chance to roll maximum, 0.54 (8.3%) added damage
2 dice, 0.160 chance to roll at least one maximum, 1.04 (8.0%) added damage
3 dice, 0.230 chance to roll at least one maximum, 1.49 (7.6%) added damage
etc.
Now with d4s:
1 die, 0.25 chance to roll maximum, 0.625 (25%) added damage
2 dice, 0.438 chance to roll at least one maximum, 1.093 (21.9%) added damage
3 dice, 0.578 chance to roll at least one maximum, 1.445 (19.3%) added damage
etc.
Notice the gained damage slowly decreasing with each added die.
If you were to graph it, you would find that the added damage is asymptotic with that die size's average damage. No matter how many d4s you roll, spell bombardment with never quite add 2.5 average damage.
This design has a few consequences. Though the gain is greater with small dice if you are only rolling one or two, it becomes greater for larger die sizes when you are rolling three or more, as you can see in the above comparison. Though small dice gain a greater percentage early, that percentage falls off rapidly.
For an extreme demonstration, consider a vitriolic sphere cast at both 4th level and at 9th, ignoring the 5d4 damage added on the opponents' turns. At fourth level, it deals 10d4 (25) damage, with spell bombardment adding 2.359, a gain of 9.4%. At ninth, it does 20d4 (50) damage, and spell bombardment adds 2.492, or 5.0%.
A third-level fireball, 8d6 (28) damage, gains 2.686 from spell bombardment, so it is already gaining more, both in absolute terms and as a percentage, than a vitriolic sphere at 4th or at 9th.
[There is a caveat with this example, of course. Vitriolic sphere provides
two chances to trigger spell bombardment, which makes it a very good spell for WMS.]
Thus, the general rule of thumb is, raw damage being equal, the sorcerer should choose the larger die size if he or she will still be rolling at least three dice. There are only a few cases where it actually comes up practically, though.
The best possible average gain with spells that are currently on the sorcerer list is 3.707 damage from . . . some spell, I don't remember which, cast at ninth level using 13d8, unless you count a crit on a ninth-level chromatic orb, which would deal 22d8 (99) damage and gain around 4.25 from spell bombardment. And then there's its function of increasing the value of rerolls with empowered spell. Anyway, enough trivia.
Spell bombardment will, on average, no matter the spell being cast, add less damage, on the first instance of damage, than the dragon's +Cha feature or the evoker's +Int. However, the big advantage of spell bombardment is that it can add damage to
anything and add it more often, and several of the best damage spells at high levels are neither elemental nor evocation.