How exactly does Burn It! (and similar effects) affect splash and ongoing damage?

Question

The level 1 goblin feat Burn It! gives a status damage bonus to all spells and alchemical items that deal fire damage. It also gives a status damage bonus of +1 to all ongoing fire effects. How does that work with splash damage?

For example, suppose I'm a low-level goblin with the Burn It! feat, who really, really likes fire, and who has just come into a bit of money. I decide to blow it on an alchemist's Fire (Greater). It's got +2 to hit, and deals 3d8 fire damage, 3 persistent fire damage, and 3 fire splash damage. It's level 11, and Burn It! gives a bonus of a quarter of that (min 1) to base and splash damage. I spot two people I don't like standing next to each other, pitch it at one of them, and hit. Now, without the feat, it's pretty simple. The guy I hit takes 3d8+3 (base plus splash) and 3 ongoing. The guy next to him just takes 3 splash. With the feat... what happens? Does it affect the splash damage at all? If it does affect the splash damage, do I get the bonus twice on the main guy because I hit him with both base and splash? Does the ongoing damage get just +1 (for being ongoing fire damage) or the full bonus (for being fire damage from an alchemical device)? How is the actual bonus determined (given that the level is not evenly divisible by 4)?

there is a question that covers part of this from the playtest, but it appears that at least some of the rules text has changed since it was written, and it doesn't cover the full thing.

Answer 1

Burn It! increases your intital attack damage once (to each creature)

Burn It! provides a Status bonus to damage. Per the rules, you can only increase the damage of an attack by the highest of each typed bonus, once. Essentially, you do have bonus damage on your bomb and bonus damage on your splash, but they're not allowed to happen together so you only apply one.

Again like checks, you may also apply circumstance, status, item, and untyped penalties to the damage roll, and again you apply only the greatest penalty of a specific type but apply all untyped penalties together.

Splash is a trait of the attack being used, so it is not it's own damage instance and does not increase separately from the bomb damage. The status bonus can apply to everyone affected by the splash, because you are still only applying the bonus once.

It increases persistent damage less

The source of persistent damage does not matter. Persistent damage is a Condition that does not adopt traits or features from its origin. It is no longer an alchemical bomb, just persistent fire damage.

Number rounding

In Pathfinder 2e, all fractional numbers are rounded down unless otherwise stated.

You may need to calculate a fraction of a value, like halving damage. Always round down unless otherwise specified. For example, if a spell deals 7 damage and a creature takes half damage from it, that creature takes 3 damage.

Your example

• Level 11 bomb (3d8+3 splash and 3 persistent)
• Initial toss 3d8+5 splash (3+11*.25 = 3+ floor[2.75])
• Persistent 4 fire

Answer 2

Burn It! Applies to Each Damage Type

Bonuses of the same type to the same roll don't stack, but each damage type has its own roll and set of bonuses as described under the rules for damage:

1. Roll the dice indicated by the weapon, unarmed attack, or spell, and apply the modifiers, bonuses, and penalties that apply to the result of the roll.
2. Determine the damage type.
3. Apply the target’s immunities, weaknesses, and resistances to the damage.
4. If any damage remains, reduce the target’s Hit Points by that amount.

Splash and Persistent Damage

Damage types are only defined under a list that doesn't include splash or persistent damage, but they are distinct with specific damage amounts and behaviors.

Splash damage is combined with the initial damage for resistances and weaknesses, but this ability impacts neither of those. Persistent damage has been clarified as of the 3rd CRB printing to be both condition and damage. Both are damage caused by the alchemical bomb, so they would be increased by this ability.

The persistent fire damage of the bomb also qualifies for the second part of Burn It!, but only the largest status bonus applies.

Rounding

There's a general rule that fractions are rounded down unless specifically noted otherwise, so a level 11 alchemical bomb would gain a +2 status bonus to damage.

Greater Alchemist's Fire

So for a greater alchemist's fire:

• Target hit takes 3d8+2 fire damage, 5 persistent fire damage, 5 fire splash damage
• Target crit takes (3d8+2)x2 fire damage, 10 persistent fire damage, 5 fire splash damage
• Target missed takes 5 fire splash damage
• Adjacent takes 5 fire splash damage on Target being crit/hit/missed

Other Bombs

Burn It! gives a status bonus to damage, but it's not specific to any type of damage.

Fire fascinates you. Your spells and alchemical items that deal fire damage gain a status bonus to damage equal to half the spell's level or one-quarter the item's level (minimum 1).

Bombs that deal clearly different types of damage like a bottled sunlight would also have the other types of damage increased by this ability, so a lesser bottled sunlight:

• Target hit takes 1d4+1 positive damage, 1d4+1 fire damage, 2 positive splash damage
• Target crit takes (1d4+1)x2 positive damage, (1d4+1)x2 fire damage, 2 positive splash damage
• Target missed takes 2 positive splash damage
• Adjacent takes 2 positive splash damage on Target being crit/hit/missed