Healing Hands

Elf hero “Healer” has ability “Healing Hands - Every individual in the army of the Healer may roll an additional 25% saving throw when suffering damage in combat.”

Fortunately, I have experience with table games like Dungeons & Dragons and understand what the “roll a saving throw” concept is. (Not everyone does.) But the “additional 25%” thing is still confusing. Does it mean;

a) If each individual has (for example) a 80% chance of destruction in a fight, then the Healer would reduce that chance to 55%? Or …

b) If an individual in the army is going to be destroyed, the Healer grants a second, 25% chance to not die?

I agree it is not clear what is meant, though I don’t believe it is the first one.
(Otherwise they would be OP and I will definitely bring them :wink: )

As for the second, how exactly do they get a 25% chance to avoid death?
Is it:

  1. When they are dying, there is a 25% chance they get another throw?
  2. Every fourth person is exempted from rolling the throw?
  3. Anything else?

I have always understood it to mean case b) in all cases where the living army wins the battle. So in your example above, where the individual has an 80% chance of destruction, only 75% of the time it actually dies. So the actual probability is 80% x 75% = 60% chance of a unit dying. (Assuming it is case b) that is the correct one!)

Now for battles where the dead overwhelm the living? We have two options there once again:

  1. The additional saving throw doesn’t apply, all units die
  2. The additional saving throw does apply, there is a secondary battle run by the 25% still living.

I’d assume option 1. is the one that happens, but this could still be clarified by someone (@JayKyburz please?)

Option 2 is indeed how it works. Any time the mortal army takes damage*, the following things occur:

  1. A mortal army wins a fight. Let’s say the army has 100 units in it to make the math easy.
  2. A “saving throw” value is calculated. In D&D land, this would be a “save DC” somewhere between 0 and 100. Each mortal in the army has the same percent chance to die. Let’s say it’s 60%, or “DC 60”.
  3. Each mortal unit makes their own “saving throw.” In D&D terms, they roll 1d100. If the result is less than the “save DC”, they are now “marked for death”. Otherwise, they live. On average 60 of the units are now “marked for death” from our 100 unit army.
  4. With a Healer in the army, each mortal that is “marked for death”, now gets to make an additional saving throw. This one is against “DC 75”, giving each one a flat 25% chance to get “unmarked”. Again, the math is easy: of our 60 expected casualties, 25% of them make their save (15 units).
  5. Any mortal units still marked for death (45 units) now die, and the rest live. Combat ends.

Note that battle odds in the game do not factor in the Healer’s ability! In practice, the quick rule of thumb for predicting a battle outcome with a Healer is to multiply the displayed expected loss percentage (“save DC”) by 0.75 (100% minus the bonus). In the case above, our original save DC was 60% * 0.75 = 45% losses at the end of the day.

This ability gets better the closer your battles are, because it’s always a flat 25% bonus. In your scenario with an 80% loss rate shown, the Healer brings that down to 60%, doubling everyone’s chance to live. If you go into a fight where you only barely win, so each unit has a 99% chance to die, then having a Healer in the army brings it down to about 75%, multiplying your survival odds by nearly 25!

By the way, this ability stacks (multiplicatively) with other units that have the same thing (not with multiple Healers in the same army—that doesn’t work). There are two: the Elves’ 5 Tree Friends and the Trolls’ 20 Turtle Warriors, each of which posses a monstrous 50% bonus save.

Multiplicative here means “the worse way”. If you have a Healer with your Tree Friends, they get the bonus saves sequentially, not added together. To estimate, you multiply the expected losses by both bonuses, e.g. deathRate x bonusModifier1 x bonusModifier2 = expectedLossPercent

It’s easy to see with an example: let’s say I’ve got 80 Tree Friends who are also receiving a Healer bonus save. They win a fight that shows 50% expected losses.

  1. Save DC = 50
  2. Bonus 1 = 50%
  3. Bonus 2 = 25%
  4. First round: 40 units are marked for death (50%)
  5. Bonus Save 1: 20 units are unmarked for death (40 x 0.5 = 20). 20 units still marked.
  6. Bonus Save 2: 5 units are unmarked (20 x 0.25 = 5). 15 units still marked.
  7. 15 units die. Combat ends.

This lines up with what we would expect by multiplying our saves together:

deathRate = 50%
bonusModifier1 = 0.5
bonusModifier2 = 0.75  # Remember; these modifiers are for how many DIE, not how many live!

bonusMod = bonusModifier1 x bonusModifier2 = 0.375  # expected loss adjustment from bonuses
expectedLossPercent = deathRate x bonusMod = 18.75%

80 units x 0.1875 = 15 dead units

Hope this helps!

*All this math only applies if the mortals win! If all mortals are guaranteed to die, none of them get a save.

This is actually true of either side. For instance, the Dwarf boss Ironhide has 2400 strength and a 100% bonus saving throw, meaning he always survives any battle where he gets to make a save. You can shoot him all day with 2000 strength ranged attacks (which would normally have an 83% chance to kill something with 2400 strength), and he’ll never ever die, unlike any other boss where you’d eventually get the kill. However, you can kill him with a ranged attack of 2401 strength, because he won’t get a chance to use his perfect save.

The same goes for melee. Usually it might be worth it to make a stand against a strong boss even if you can’t quite win, because a 90% chance to kill the boss may be worth it and you’ll usually get him. Not so with Ironhide—your army must be strong enough to actually win the battle in order to kill him. That 90% chance the game shows you is a lie.

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I didn’t know that’s how the Ironhide boss worked. I assumed the “100% bonus saving throw” was just an awkwardly-worded way to say it was immune to ranged attacks.