Need Statistical numbers comparison


Advice


Ok, let's say there is an ability that allows you to roll an additional die -1 when you roll the maximum of any particular die, for weapon damage purposes.

So, if you roll 4 on a d4, you get to roll an additional d4-1 and add it to the original roll and that is your damage for the strike.

What would be the equivalent direct bonus enchantment (+1 to +5) that would work out to the same damage range?

Extended, what would be the equivalent direct bonus enchantment if the second d4 roll (modified by -1) rolls the max on the die resulting in +3 to damage) is able to be rolled as many times as is possible (basically until you don't roll the maximum on a die). What would be the equivalent enchantment bonus on this "greater" version of this ability?


For your first question, it depends entirely on what the weapon's damage die is:
1d2 = +0.250 average damage
1d3 = +0.333 average damage
1d4 = +0.375 average damage
1d6 = +0.417 average damage
1d8 = +0.438 average damage
1d10 = +0.450 average damage
1d12 = +0.458 average damage
More damage dice will multiply the increase in damage, but this still never really becomes powerful. And it still never increases your chance to hit. I wouldn't consider it more than a +1 bonus equivalent. It could help out Vital Strike builds a bit, which they definitely need, but there's not much else it's good for.

The math for the second question (the "greater" version) is a bit more complicated, and it has an interesting effect. The greater version has the same result with every single type of damage die: it adds, on average, half a point of damage per die. That includes the damage from the basic version, so you're barely gaining anything. You really don't want to make that a +2 bonus equivalent. In fact, I would just have this be the base ability, in which case it balances quite nicely as a +1 bonus equivalent.

Interesting idea.

Grand Lodge

If you allowed the second roll on a 4, average damage would be 2.875 on a hit. If you allowed the third die on a second 4, average damage would be 2.97. If you allowed a forth die on a third 4, average damage would be 2.99. The odds of getting a 4th 4 are less than one half of one percent so I didn’t bother to take it further.

The ability would be worth about ½ point of extra damage on an average hit.


Avoron,

Awesome, thanks for the analysis.

What happens on damage for weapons that have multiple die when it applies to each individual die:

Say the estoc, which is 2d4, or the greatsword which is 2d6?


Quintain wrote:

Avoron,

Awesome, thanks for the analysis.

What happens on damage for weapons that have multiple die when it applies to each individual die:

Say the estoc, which is 2d4, or the greatsword which is 2d6?

Just looking at it, I'd say it's still the same amount, just multiplied by how many dice you allow to be rerolled like this. And remember, it's not just 2d6 you need to worry about -- there's a lot of people who suggest greatsword wielders need to have Enlarge Person tossed on them, and that means 3d6.

You'll have to determine whether only one die can reroll, or all of them are eligible (in those rarer cases when more than one pops up). And if it's the latter, it just multiplies the actual damage involved by the number of dice. Which starts making it a bit more powerful on some weapons, like that enlarged barbarian's greatsword.

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