Which is better? Persistent spell or Empower spell?

[avatar-84]

In another topic is being explained that Persistent spell is more usefull than Heighten spell in most of cases.
Here i'd like to know if the same spell is capable to substitute even Empower spell other than Heighten spell in a sorcerer feats list.

The 100% of the damage is better than the 150%\2? Math said yes, but isn't so simple, what's your thought?

[udalrich]

Actually, empower is normally better for save for half spells. The reason is that you are often comparing 100% vs 150% or half of both.

For a spell like Fireball targeting someone without evasion, empower is strictly better on average. Forcing two saves does not compensate for the extra 50% damage.

When it is better is when the target has evasion and is probably going to fail the save. Persistent then makes it more likely that they fail and, since saving causes a bigger swing in damage, Persistent averages more damage. The break-even point is when the target can save on an 11 (50%), in which case both have the same average damage.

For the math, let p be the probability that the save is made and d be the average damage on a failed save. Let s be the fraction of damage taken on a failed save (normally 0.5, 0 with evasion).

Empower:
average damage = d*1.5*(s*p + 1-p)

Persistent:
average damage = d*(s*p*p + 1-p*p)

For p = 0.4 and d=100, the relevant numbers are
Empower: 120 or 90 (evasion)
Persistent: 92 or 84 (evasion)

For p = 0.6 and d=100, the relevant numbers are
Empower: 105 or 60 (evasion)
Persistent: 82 or 64 (evasion)

Persistent is good for save negates spells like Baleful Polymorph, where Empower is not useful and a higher level spell (or Heighten) has an almost as good effect. It is also useful against enemies with Evasion but bad reflex saves, although that tends to be a rare combination.

Empower is still an excellent feat for variable effects spells with save for half.