You can't theory craft when it fires.
No. But I wasn't talking about that. I was talking about using Innate Sorcery (2 free uses + 2 SP per subsequent use), which automatically confers advantage on all your spell attacks. Assume 5-7 encounters per day, that's 3-5 extra uses, 6-10 SP spent. The character you spoke of had 3 dice naturally, so they must be at least level 11. Two (almost three) Feats implies a Cha mod of at least +4, more likely +5. That means a floor of ~15 SP each day (11 from Sorcerer level, +4 from Sorcerous Restoration), leaving at least 5 hits of Empowered Spell without needing to dip into slots.
If we assume
roughly 4 rounds per combat, that's roughly 20-28 combat rounds, all of which you have Advantage on attack rolls. We would expect at least two crits in that span, since Advantage means you crit a ton. Even without that, though, spending your remaining 5+ SP on Empowered Spell even
without a crit is still potentially quite useful: each die has a 1-(7/8)² = 0.234375 chance of coming up 8, so even
without a crit, you are very likely to get at least one bonus die for every use of Empowered Spell. (Specifically, a
And you can innately choose amazing damage types like Psychic, Lightning, or Thunder, which are very rarely resisted or immune, without needing Transmuted Spell. Finally, if you're willing to go all in, you can couple
sorcerous burst with a slotted Quickened spell, albeit at the cost of more SP.
So, with one cantrip, 15-20 SP, and the kinds of adventuring days the books
explicitly tell the GM to run, more often than not you're getting 8+3d8 damage. From a cantrip and
one spent SP. And it's not like the "always use Innate Sorcery" strategy hurts you if you don't do this, since +1 to your save DCs is also really solid.
You might be able to work out how much it happens or average DPR.
Yes...that's...precisely what analysis is for. It doesn't
create the opportunities. It makes you ready to exploit them maximally when they arise.
What on earth gave you the idea anyone saw it as "you can
control when this completely random event happens"?
I've seen it happen and something just dies. Firebolt could be doing 6d10 on a crit vs 6d8.
Firebolt does both a minimum and a maximum of 6d10 on a crit if you are level 11-15, yes.
With 6d8, Empowered (since you choose it
when you roll damage), you'd expect to get at least one 8, meaning that it's not 6d10 vs 6d8, it's 6d10 vs 6d8+8 (and more likely 6d8+16). Now, technically you can't reroll all six dice...but you can reroll 5 of them and that should be enough, since you'd never reroll a natural 8.
Remember: every 8 isn't just 8, it's actually 8+1d8, or, on average, 12.5. With 6d8 and a 23.4% chance to explode,
not getting at least 6d8+8 is only 20.1% (=(49/64)^6); and the chance to get only one, not two or more, is only 37% (almost exactly).
So the typical return from an Empowered crit SB is (.201)(27)+(.37)(35)+(.283)(43)+(.116)(51)+(.0265)(59)+(0.00341)(67) = 38.25, approximately. The typical return on an Empowered crit
firebolt is 5(7.15)+5.5 = 40.75. So...yeah, it's less than half a die better than SB+Empowered, but it lacks the supreme flexibility (and resist/immune avoidance) of SB.
And, incidentally? It's exactly this sort of situation where the mathematical analysis is
useful. Because it lets us see, yes, we're taking a tiny hit (~2.5 average damage), in exchange for a huge benefit in flexibility. By knowing what we give up, we can reasonably say we know we're making a good trade.
I'm not good at working out rerolls and exploding dice. I know SH is better than fireball.
I'm going to assume that's a typo for SB. SB is definitely better than
fireball against a single target.
Fireball should not be used unless you have several enemies to fight. Your thread on
chromatic orb shows why that option is, in a certain sense, better for exactly two targets. (Said because it still costs a spell slot, while SB does not, and
fireball is innately AoE, so it's better if you are hitting 5+ targets, as CO cannot jump more times than the slot you spent on it, and thus
at best you can hit 4 targets with CO.)
Fireball hitting 4+ targets, even if half make their save, definitely blows SB out of the water, unless everything resists fire...at which point of course
fireball sucks, you're using a spell exactly in its worst environment (but if you're so comfortable dropping SP on Empowered, why not grab Transmuted and make thunderballs?)
