I am aware that there were quite a few questions about the interaction between Alchemist's Fire splash damage and Burn it! feat. However I think one thing remains without an answer: what about critical hits? Normally you don't double the splash damage, and you would double the status bonus to the initial target but what about status bonus to splash damage in situations where you crit against the initial target? Does it double or not?
Splash damage doesn't crit; increasing it doesn't change this
Gaining a bonus to splash damage does not change the basic rules for it; the bonus is an increase to the splash damage, so it doesn't increase for (not-)critting by itself.
Lesser alchemist's fire deals
- 1d8 fire damage
- 1 fire splash
- 1 persistent fire.
Burn It! increases this (by the minimum of 1) to
- 1d8+1 fire damage
- 2 fire splash
- 2 persistent fire
Because the Status bonus for regular and splash damage do not stack (as outlined in my answer to another question), the primary target would only take 1d8+1 and 1 splash damage (or 1d8 and 2 splash damage, it shouldn't matter mechanically).
The critical damage would then be
- 2x(1d8)+2 fire damage*
- 2 fire splash*
- *totaling 2x(1d8)+3 combined fire + splash for the primary target
- 4 persistent fire
It you crit with an alchemist's fire while using the feat Burn It!, you would do 2*(1d8+1)+1 damages +4 persistent damages to the main target, and 2 damages to other creatures within a 5 ft radius.
Normally, an Alchemist's fire would do 1d8 damage to the main target, +1 persistent damage to the same target, +1 splash damage to everyone in a 5ft radius (including the main target).
Scoring a critical hit multiplies the damage by 2, except for splash damage that is explicitly not multiplied. This means to determine the damage to the main target you would roll a d8, multiply the result by 2 (which is not the same as rolling 2d8), and then add 1 damage for the splash (aka 2*(1d8)+1). Persistent damage is explicitly multiplied, so the main target would also take 2 persistent instead of only one.
The feat Burn It! adds damage to your bomb (in this case: 1 damage). As a status bonus it would not stack with other status bonuses, but in our case there are none. This damage is added before the crit multiplication, for a total of 2*(1d8+1)+1. Burn It! also adds 1 to the persistent damage, before multiplication, so the persistent total becomes 4.
About the splash dealt to the adjacent targets, consensus seems to be that Burn It! increases it but that it doesn't stack on the main target. Thus the other targets would take 2 damage. No multiplication here since splash damage doesn't multiply in case of crit.