On the one hand, this is a spell attack, so from level 5 onwards it suffers from serious accuracy problems.
On the other hand, IF this is an opening move and the target lives long enough, the expected duration on the persistent damage is \~3.3 damage instances (IE on average they succeed on the save on round 3 after taking the third instance of damage, but sometimes it hits them round 4 as well). That gives an expected damage to a creature of \~**25** over 3 or 4 rounds (24 if rounding down to 3 rounds on the persistent damage).
For a 120 ft ranged spell from a second level slot, thats surprisingly good! It outdoes the melee heightened shocking grasp vs non-metal targets (and loses vs metal), outdoes heightened hydraulic push (but doesn't push), and is even approaching the raw damage of the overpowered (and PFS limited) Sudden Bolt... though that spell is all up front damage and half damage on a save, so its actual expected damage is higher than a spell attack.
Giving up the ranged aspect and using it as a magus spell, it outperforms many other options if used early in a fight. Solid single target burst damage.
In terms of scaling: level +2 hurts a bit, but in 2 levels it gains \~20.5 expected damage (9.5 if rounding to 3 rounds persistent damage). This is actually better scaling than many other spells! The 'standard' +4d6 is +14, 2d12 is 13. A fireball at level 4 is doing 28 to multiple targets and is a save spell, so will do much more to a group of enemies. An acid arrow will do \~45.5 to one target, if fired on turn 1, and if it hits.
It is very unfortunate that the persistent damage does not multiply on a critical hit - the 'critical' part of its damage scales poorly compared to other options (9/two levels instead of 14). Still, the spell benefits greatly from true strike like other attack spells.
So on balance, I'd say this is a useful spell for doing single target damage. Less useful for a fighter archetyping magus for massive crits because the crit part scales a little poorly.
But where it *really* shines is vs enemies with acid vulnerability. Then add that vulnerability multiplied by **4.3** to its expected damage (once on the initial hit, then 3.3 instances of persistent damage). There aren't too many of those enemies but it is very effective vs them.
Now here's where things get potentially interesting: the level 10 sorcerer feat Energy Fusion. This lets a character have half the damage the spell does be of a different energy type (acid, cold, electricity, fire, or sonic types, not good unfortunately) - there's no reason that 'half' doesn't include persistent damage! So using this feat a character can do that 4.3 weakness multiplier to any energy weakness!
The main issue with this is that because Energy Fusion is a single action metamagic, a character can't cast true strike on the acid arrow, so hit rates are bad. At this level a Shadow Signet can help the caster overcome this by targeting a weaker thing than AC. Because so much of the damage is coming from weakness, its also not important to use a top slot for this boosted acid arrow, so it can be an economical way to try for damage.
This is a deadly weapon in the hands of an NPC, but a middling tool for players. Persistent Acid Damage is in the top 5 causes of player deaths, but the value isn't high enough to do much more than rack up dying stacks and proc weaknesses (for the very few acid-weak creatures out there).
On the one hand, this is a spell attack, so from level 5 onwards it suffers from serious accuracy problems. On the other hand, IF this is an opening move and the target lives long enough, the expected duration on the persistent damage is \~3.3 damage instances (IE on average they succeed on the save on round 3 after taking the third instance of damage, but sometimes it hits them round 4 as well). That gives an expected damage to a creature of \~**25** over 3 or 4 rounds (24 if rounding down to 3 rounds on the persistent damage). For a 120 ft ranged spell from a second level slot, thats surprisingly good! It outdoes the melee heightened shocking grasp vs non-metal targets (and loses vs metal), outdoes heightened hydraulic push (but doesn't push), and is even approaching the raw damage of the overpowered (and PFS limited) Sudden Bolt... though that spell is all up front damage and half damage on a save, so its actual expected damage is higher than a spell attack. Giving up the ranged aspect and using it as a magus spell, it outperforms many other options if used early in a fight. Solid single target burst damage. In terms of scaling: level +2 hurts a bit, but in 2 levels it gains \~20.5 expected damage (9.5 if rounding to 3 rounds persistent damage). This is actually better scaling than many other spells! The 'standard' +4d6 is +14, 2d12 is 13. A fireball at level 4 is doing 28 to multiple targets and is a save spell, so will do much more to a group of enemies. An acid arrow will do \~45.5 to one target, if fired on turn 1, and if it hits. It is very unfortunate that the persistent damage does not multiply on a critical hit - the 'critical' part of its damage scales poorly compared to other options (9/two levels instead of 14). Still, the spell benefits greatly from true strike like other attack spells. So on balance, I'd say this is a useful spell for doing single target damage. Less useful for a fighter archetyping magus for massive crits because the crit part scales a little poorly. But where it *really* shines is vs enemies with acid vulnerability. Then add that vulnerability multiplied by **4.3** to its expected damage (once on the initial hit, then 3.3 instances of persistent damage). There aren't too many of those enemies but it is very effective vs them. Now here's where things get potentially interesting: the level 10 sorcerer feat Energy Fusion. This lets a character have half the damage the spell does be of a different energy type (acid, cold, electricity, fire, or sonic types, not good unfortunately) - there's no reason that 'half' doesn't include persistent damage! So using this feat a character can do that 4.3 weakness multiplier to any energy weakness! The main issue with this is that because Energy Fusion is a single action metamagic, a character can't cast true strike on the acid arrow, so hit rates are bad. At this level a Shadow Signet can help the caster overcome this by targeting a weaker thing than AC. Because so much of the damage is coming from weakness, its also not important to use a top slot for this boosted acid arrow, so it can be an economical way to try for damage.
This is a deadly weapon in the hands of an NPC, but a middling tool for players. Persistent Acid Damage is in the top 5 causes of player deaths, but the value isn't high enough to do much more than rack up dying stacks and proc weaknesses (for the very few acid-weak creatures out there).
Good range, good damage, fine for a 2 level spell slot.
Unimpressive single target damage on a spell attack roll with no rider effect. Terrible spell.