Percentile Effect Stacking

People say that percentile effects stack multiplicatively, but what exactly does this mean? In other words, could someone break down the math for me so I can understand it? Thanks!

It's simple.

Let's say you have [Guardian] and [Aegis].

When you get attacked, the game goes 50% to block, and if it isn't blocked, you get another 50%.

50% x 50% = .25 + .50 = .75 = 75% chance to block.

Ah, so the second percent is a percentage of the first one? That's pretty simple. Thanks!!

Another way to think of it is from the perspective of a successful hit instead of a block.

Suppose you have two skills, one with 80% to block and the other with 40%. These aren't real, but it's more clear than using skills with 50%.

The first skill only lets 20% of attacks through [1 - 0.8 = 0.2]. Of those attacks, 60% also bypass the second skill [1 - 0.4 = 0.6].

The probability of a successful attack is then
0.2 * 0.6 = 12%.
Thus the blocking percentage is
1 - 0.12 = 88%.

I think the 50% one was clearer.

Now what about percentages that add time? **cough** shadowform **cough**

So, I activate a skill that says all spells recharge 33% faster [skill]Deadly Paradox[/skill] and then another skill that says all spells recharge 25% faster. [skill]Glyph of Swiftness[/skill].

In this case, I'm assuming that the recharge time of a 60 second spell under DP is now 40 seconds? and 25% of 40 with GoS is 10 seconds for a total recharge time of 30 seconds?

That is correct. Reduced recharge time usually can not exceed 50%, but those two effects achieve 50% reduced recharge.

Ok, now I have a question. I hope its ok to just latch on to this thread. Question: The two formulas deliver different results. It is not two different ways of getting the same answer (like alot of math is). So which one is technically correct?

Here is why I am asking. The half casting time (HCT) & half skill recharge (HSR) percentages on wands, staves and offhands may not be worth stacking.

Wand HSR 20% + Offhand HSR 20% so .20 * .20 = .04 + .20 = .24. So the 2nd HSR is only worth 4% to me?

or slightly better,
[1-0.2]=.8 and the ones that get past that weapon [1-0.2]=.8

0.8 * 0.8 = 0.64 so 1-.64 = .36 or 36% cumulatively (Gosh, I hope this one is the right one!)

Thank you so very much,

Eradis

ya messed up the first one, remember u continue calculating the misses, so ud be using the 80% chance to not cast/recharge so .8*.2=.16+.2=.36
so both are right.

Is there some calculating formula that isn't made obvious in the game you could point me to? Why on earth would 50% x 50% = .25 + .50? The 2nd applied block skill only adds half the amount of the first block spell? Why?

Because the first block skill blocks half the attacks coming in, the second block skill only has half the attacks to affect. 50% of half of something is 25%.

So lets say you are attacked 4 times. The first 50% block skill will mean that only 2 of those skills will get through. Now you need to calculate the second block skill. Since only 2 of the original 4 attacks can get through, then the second skill only has 2 attacks to affect. As it is also a 50% block, only 1 attack or 1/4 of the total attacks made, get through the second block, for a total of 75% of attacks being blocked.

You forgot to calculate that 4 of those 36% is where both trigger. For cast time, this means you achieve a quarter cast time than normal (therefore, 32% chance to halve recharge). Since recharges can't get better than half unless from a single skill, double 20% HRT will mean 36% chance to halve recharges.

You seem to be confusing 20% chance with 20% increase (or whatever).

In this case both the wand and the off-hand have a 20% chance (1 in 5) to halve the casting time of a particular spell. So, out of 5 casts, the wand will halve the casting time of one and the focus will also halve the casting time of one. Because they sometimes halve the casting time of the same one, this works out to roughly a 36% chance of having a casting time reduction. (20% of the time, the reduction is 75%)

To the 40/40 set question: yes even though they are called 40/40 sets, they actually only give 36%. Technically should be 36/36 sets lool.

This is also why taking multiple + crit % skills is retarded. I've seen it so many times, no you don't need WotM, and crit eye....

statistics

the guardian (event A) + aegis (event B) is a good example of the application of stats.
The % chance of both event A (0.5) and event B (0.5) occuring per attack is 0.5 * 0.5 = 0.25
Then you have the chance of event A occuring and event B not occuring and vice versa which is (0.5 + 0) OR (0 + 0.5) = 0.5
The total chance to block an attack considering all cases is then
(even A + event B occuring) 0.25 + (event A or event B only ) 0.5 = 0.75

i hope my stats is correct as its been a while

Ok... I get it now. That was alot of good information that I had really never thought about. Now I like my blue collector weapons a bit more than before, lol.

Thanks for all your input. I am more grateful than you will know.