How much does ongoing damage add to the average damage when creating a monster?

GMing D&D 4e, I got used to creating new monsters and it's been quite simple so far with the guidance of the errata and observation of the Monster Manual 3 damage expressions.

But here is something I don't quite understand.

How much is ongoing damage worth?

Technically speaking, 2d6+9 = 4d6+2 (Average damage 16)

What if I wanted to change that 2d6+9 into Xd6+Y plus Z ongoing damage?

What would be the correct numbers to keep the same average damage?

In other words, how much damage is ongoing damage woth on the average damage of a power?

• Keep in mind that you can be a bit sloppy with ongoing because of two factors: 1) There's a lot of potential save granting powers and effects, especially if they have access to a leader which can stop the damage before it hits even once, and 2) Once they are already suffering from ongoing damage, hitting them again with the same ongoing damage won't do anything until they get rid of it, which means subsequent strikes against the same target will potentially lose that extra damage. Apr 8, 2015 at 2:45

The average damage from ongoing damage is approximately 181% of the damage.

The damage expression is an infinite series that converges.

Here are the first few terms of the series:

.45^Z^0 + .45*Z^1 + .45^2*Z + .45^3*Z....(.45^i)*Z

If we assume Z is 5, the first five terms are:

5+ 2.25 + 1.0125 + .455625 + .20503125 + .0922640625

Summing these we get: 9.015

Based on this WA page we get that the convergence of the damage is actually 9.09091. Ignoring the actual amount of the damage and isolating just the series of success odds, we get 1.818182.

If you want to be precise, you can use this number, but for back of the envelope monster calculations, you can use twice the actual ongoing number as your average damage number.

• That math doesn't take into account that under most circumstances, the PC won't get a saving throw before taking the damage once. As such, the expected equivalence ratio should be over 1. It may also be worth noting that ongoing damage is orders of magnitude better for monsters than it is for PCs, given the prevalence of NPCs with saving throw bonuses and their shorter expected lifespans. Apr 6, 2015 at 15:11
• @webbcode ack, I let myself forget that first turn damage is almost always a thing. I've corrected the math errors, it only changes where the series begins and the math means you use double(ish) of the number, not the actual number (which is what I thought it was, so I was surprised by this result...I should have checked my math again). Apr 6, 2015 at 15:13
• Yeah, I'm considering it pretty much twice the ongoing value and still think it's quite generous considering the comments on the question, but still, it was pretty well done math. Apr 23, 2015 at 8:47