Proc Statistics Help

A proc has a 10% chance of going off. There are a total of 5 procs. What are the chances that one proc goes off? What are the chances all of the procs go off?

WARNING: I bold names.

0.1 * 0.1 * 0.1 * 0.1 * 0.1 = 0.00001

So, 0.001% chance for them all to go off.



0.9 * 0.9 * 0.9 * 0.9 * 0.9 = 0.59049

So, 59.049% chance that NONE of the procs go off. Which means the chance for at least one (perhaps more) procs will go off will be 100 - 59.049 = 40.951%

Thanks for the math!

So 59% chance that none of them will go off, and 41% chance that one will go off. Basically no chance for them to all go off. So, on any given run-through of the 5 powers, none of the procs will go off, most likely.

This has really clarified some build decisions for me. The math seems to agree with my in-game perception of performance of these procs.

*makes notes on how to do the calculations*

Thanks you!

WARNING: I bold names.

But don't some procs have a greater chance to go off than just 10%?

For an alternative look at the situation, let's consider what happens if we average across a larger number of activations.

There are a number of different procs with a 10% chance to activate - alas, none of them (that I can find with a three second search) are simple damage dealt procs; I'll pick two examples here, and you can apply similar logic to whatever your actual case is.

Consider first Entropic Chaos: Chance to Heal. That's a 10% chance to recover 5% of your (unenhanced, I think) health. So, on average, each one returns half a percent of health per power activation; for five of them, that'd be 2.5% healed over whatever the time of your attack sequence is. For a blaster, at level 50, you'd be looking at about 30 hit points per five powers.

Consider second, Pounding Slugfest: Disorient Bonus. That's a 10% chance for a mag 2 stun for 10 seconds. Let's assume that your powers are slow, and across those five powers you average two seconds of activation time per power. (Why? Because it makes the math easier.) So - against something that can be stunned by a mag two effect, how much of the time is this up? Well, at any given point in time, the target will be not stunned if (and only if) all five prior procs failed to fire. This would be the 59% chance listed above. So, once you get rolling, your target is stunned 41% of the time. Or, in other words, chance of target not being stunned is .9^N, where N is the average number of power activations you can fit into ten seconds. Yes, this may not be a whole number; the formula works regardless.

How does this change against a lieutenant or boss? Well, step one: if the stun doesn't stack with itself, you're suddenly out of luck, as your mag two won't do anything.

Note that it probably doesn't stack, in which case the remainder of this post is an exercise in excessive math and can be safely ignored.

If it does stack, though... well, you need a mag three (lts) or four (boss) effect. Which means you have to have had the proc go off at least two times out of the last five. So... we know the chance of no procs going off. What's the chance of exactly one proc going off?
Well, for five powers, this would be .1*.9*.9*.9*.9 + .9*.1*.9*.9*.9 + ... - aka, the chance that the first proc succeeds and all the others fail, plus the chance that the second proc succeeds and all the others fail, plus, etc.
Or, more generally, N*.1*.9^(N-1)
In this case, it'd be about 33%. So, 33% + 59% = 92% that one or zero procs activate, and 8% chance that two or more activate. Adjust N as needed for your powers, and you can figure out how often, on average, you'd have an at least double proc.

[ QUOTE ]
But don't some procs have a greater chance to go off than just 10%?

[/ QUOTE ]

None of the Damage procs in this game are as low as 10% >_>

ToD is 15%, then most procs are 20% and some (Purples, and apparently PvP IO's in PvP) are 33%.

Yes, the procs I'm talking about are the Disorient procs (I didn't specify because my question was on the math and I didn't want other, potentially confusing, details).

I was weighing two options for my build: the 5 procs I've got now, or Damage/Recharge Enhacements that would provide another 10% or so of damage plus about 15% Recharge (both are taking ED into account).

Based on the above math, I'm ditching the Disorient procs in favor of the bit of extra Damage and Recharge. Especially considering those are of benefit 100% of the time, where the procs are of benefit significantly less (in fact, in any one set of 5 attacks, you could count on them not firing; to me, that's pretty bad. YMMV.)

In terms of practical play, they were really underwhelming. Their one and only charm was that Eagle's Claw would disorient a Boss 10% of the time (EC's Disorient+proc). Cute, but anything but reliable.

I can see using those procs on an Energy Melee character though, just to make its secondary effects even more ridiculous lol.

WARNING: I bold names.

[ QUOTE ]
Thanks for the math!

So 59% chance that none of them will go off, and 41% chance that one will go off. Basically no chance for them to all go off. So, on any given run-through of the 5 powers, none of the procs will go off, most likely.

This has really clarified some build decisions for me. The math seems to agree with my in-game perception of performance of these procs.

*makes notes on how to do the calculations*

Thanks you!

[/ QUOTE ]

You missed a key phrase in the 41% its 'AT LEAST one'.

Procs can and do fire independently, such that it is entirely feasible to get 2 or 3.