# How do you calculate an average damage when damage is conditional on circumstances?

I'm trying to compare two rogue builds to each other. The first rogue is easy. It's a wood elf with a long bow in a wilderness campaign, doing 1d8+mod damage and always being hidden with SA damage. Fine. My second rogue however is a dungeoneering halfling who might use a rapier, or might use a short sword and a dagger in the off hand.

What I'm trying to figure out is how to calculate the average damage with five different possible scenarios in mind. Each scenario might be used depending on the circumstances: who's in the room, what obstacles are there, etc.

1. Shortsword(d6+3) + cunning action + SA(d6) (advantage) = (9)
2. Shortsword(d6+3) + dagger(d4) + SA(d6) (no advantage) = (7.5)
3. Rapier(d8+3) + cunning action + SA(d6) (advantage) = (9.9)
4. Shortsword(d6+3) + dagger(d4) (no SA available) = (5.4)
5. Shortsword(d6+3) + dagger(d4) + SA(d6) (advantage) = (11.25)

How do I figure out the odds of each of those 5 scenarios - just do average damage compiled then divided by 5? And how do I get a final reasonable number?

So does this become (9 + 7.5 + 9.9 + 5.4 + 11.25)/5 = 8.61 at level 1?

• Does the option you pick (from 1-5) just depend on the circumstances, or as you put it in the title, how you choose to roleplay at a given point? – doppelgreener Jul 10 '14 at 11:03
• Circumstances. Who's in the room, what obstacles are there, etc. – GMNoob Jul 10 '14 at 11:04
• Normally when optimising, you go for the modal scenario: which of these five is most reliable round after round? – Brian Ballsun-Stanton Jul 10 '14 at 11:14
• @BrianBallsun-Stanton the most reliable is the one with the lowest damage, because you can always not do things to your advantage, but it's also the least informative. It's also going to depend on DM. – GMNoob Jul 10 '14 at 11:21

There's no way to get the damage in a general case, as whichever actions you should choose depend on the circumstances and it's impossible to know the circumstances ahead of time.

You can calculate the damage amounts based on certain assumptions, though. For example, if you assume you'll have advantage about every other turn, just take the average of the damage you do when you have advantage and the damage you do without advantage.

This has the caveat that it relies on the accuracy of your estimate, but it's literally the best you can do. Try to get a good estimate on how often you'll use each of the options and weigh each option's average damage accordingly. For example, if you deal 10 damage every fourth turn and 8 damage otherwise, your average damage should be:

$$\left( 8 \times \dfrac 3 4 \right) + \left( 10 \times \frac 1 4 \right) = 6 + 2.5 = 8.5$$

So does this become (9 + 7.5 + 9.9 + 5.4 + 11.25)/5 = 8.61 at level 1?

Only if all the five different cases are equally common, which I don't think is likely. Without knowing the 5e mechanics very well yet, I assume some of these five options happen far more than the others, meaning they'll have a higher impact on your overall average damage per turn.

• So, I don't know where to put this, but I'll let you know what I did. I was able, from experience, to recognize how often I would usually grant advantage, (about 50% of the time) and how often a rogue would have a chance or desire to use a thrown weapon (about another 50% of the time) And how often all bonuses would align (about 5% of the time) and use those to calculate the damage. – GMNoob Jul 20 '14 at 17:59

It's impossible to tell this early in the game. Optimisation, like many other functionally academic activities, relies on the literature, prior writings establishing a research programme of common assumptions, language, and models-of-universe.

5e, being a wholly new mechanical framework, has none of this literature1. In prior editions, one evaluated different conditions based on which circumstance could be engineered to be the most common. It is wrong to average "uncommon" conditions without weighting them to their commonality.

For a rogue, it is reasonable to assume sneak attack if you are designing the rogue to be the fighter's "adjacency buddy". So long as you document your preconditions such that they can apply to other evaluations, any methodology will serve your purposes.

1 That is to say that the discussions which serve the purpose of peer review are beginning, but no compilation of those discussions, masterwork, or meta-discussions exist.

• Rogue gets SA with fighter adjacency, but not advantage. Advantage comes from hiding or one of the numerous other conditions. – GMNoob Jul 10 '14 at 11:41