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Math question
falloutx23
Member Posts: 456
I'm looking for the formula on how often multiple procs happen. Let's say you have 3 doffs with a 20% chance of proc'ing, I know how to figure the chance of at least one proc'ing, but how do you figure two or three proc'ing? Thanx. Been to long since math class...
Post edited by falloutx23 on
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The easiest way is to look at the chance on not getting the proc.
So each of the 3 Doffs have a 20% chance and therefore each have a 80% chance of not procing. We can then multiply these non chances of procing together.
So in this case you would do: (0.8*0.8*0.8) = 0.512
So we have a 51.2% chance of not procing. Therefore we can just subtract this value from a 100%, to get the full chance of the proc. 100-51.2 = 48.8%
So with 3 doffs that each have a 20% chance to proc, would yield a combined probability of 48.8% to proc.
You can reference this: http://www.edcollins.com/backgammon/diceprob.htm
Thank you for the response, but this doesn't answer my question. I understand the formula for ANY of them to proc, but what is the formula for more than one to proc. what's the formula for all three to proc. thanx
Answers:
0 Proc: 51.2%
1 Proc: 38.4%
2 Proc: 9.6
3 Proc: 0.8%
Solution:
3 Proc = Proc Chance ^ 3
3 Proc = .2 ^ 3
3 Proc = .008
2 Proc = (Chance of 2 proccing * Chance of 1 not proccing) * Rolls
2 Proc = ((.2^2) * .8) * 3
2 Proc = (.04 * .8) * 3
2 Proc = .032 * 8
2 Proc = .096
1 Proc = Chance of 1 Proc - Chance of 2 - Chance of 3
1 Proc = (1-.8^3) - .064 - .008
1 Proc = (1-.512) - .064 - .008
1 Proc = .488 - 0.096 - .008
1 Proc = .384
0 Proc = Chance no Proc ^ 3
0 Proc = .8^3
0 Proc = .512
Ah. Now this is a rarity. You mutiply the fractions together for this. So if you have 3 Doffs each with a 20% chance to proc and you want to see what the probability is for all 3 to proc at the same time. Then you would do the following:
.2*.2*.2 = 0.008
Which is 0.8% chance.
For 2 Procs
EDIT: I found a better way to look at this: If you have 3 Doffs you have the following possibilities:
[Proc][Proc][NoProc] [Proc][NoProc][Proc] [NoProc][Proc][Proc]
We can also look at each of these probabilities therefore as 3x([Proc][Proc][NoProc])
Or 3x(0.8)(0.2)(0.2) = 0.096 Or 9.6% chance.
So with 3 Doffs each having a 20% chance to proc. We have a 48.8% chance of getting one or more proc. A 9.6% chance of two to proc. and a 0.8% chance of all three to proc.
Keep in mind that 48.8% includes the 9.6% and the 0.8%. Tank you esuzi for pointing that out.
I will let you know that there is a bug in the system. I have found that quite often, in the majority of procs in STO, that once one doff procs, all three doff's benefits are given.
So considering that, you really have a 48.8% chance of getting all three doff's benefits.
Basically you need to multiply the probability of the individual event by the number of combinations that result in that event.
if x is the proc rate, n the number of doffs and k the number of procs occuring it would be:
chance of k procs = (n choose k) * x^k * (1-x)^(n-k)
where (n choose k) = n! / [k! * (n-k)!]
so for 2 procs with 3 doffs having 20% proc rate, this would be:
(3! / [2! * (3-2)!] )* (.2)^2 * (1-.2)^(3-2) = 0.096 , 9.6% chance of exactly two procs occurring
for more on combinations:
http://en.wikipedia.org/wiki/Combination
TRIBBLE | -Show Me Your Critz-
Svarog | Veles | et al.
Thanx. Posted this while I was typing
How exactly these are calculated I don't know. I must have something to do with how much incoming fire there is within something like 1s of activating BFI.
There has been something strange going on with procs. I will give one example that I know of very well. If you have 3 Purple Security Officers as a Tactical Officer and you call your Security Escorts you will either get 2 Security Escorts or 8. You will never get 4 or 6. This means that if you proc any of the 3 Security Officers you get the full benefit. If you equipt one blue and two purple, things change. You will now get a mix that closer resemble of what is suppose to happen. The same thing occurs with Purple and Blue quality Doctors.
So it is a lot better not to mix the quality of the Doffs. That way if any of them proc, it is as if all of them proc.
If you want to test this for yourself, equip some purple Security Officers and run a test. They each should have 20% chance but you will either get 8 Security Escorts or 2. And it does split at about 45% ratio.
1proc=78.4%
2proc=43.2%(I think)
3proc=21.6%
I've done no controlled testing, but doesn't getting hit with VM buffed by three doffs feel like it procs closer to these percentages? Having at least one proc should happen less often than not, yet I find it rarely doesn't proc at least one.
Ah, well some Procs occur on a tick basis. I believe VM is one of those. There are several "ticks" that occur over a time period and each "tick" has a chance. For example: Sub system attacks with a beam has 4 beam hits and each has a sub system attack chance. Therefore 4 ticks. BFI I believe has a similar "tick".
Interestingly enough, 4 ticks on a doff with 20% nominal proc rate will give a effective proc rate of 59% for said doff. If i had to guess though, I would say maybe it rolls once for each eligible subsystem, which would be 3 "ticks" for the doff. This would give an effective proc rate of 48.8%. Assuming any individual doff could only proc once for simplicity, this would give a 86.58% change of at least one proc occurring, with the following breakdown:
0 Procs: 13.42%
1 Proc: 38.38%
2 Procs: 36.58%
3 Procs: 11.62%
TRIBBLE | -Show Me Your Critz-
Svarog | Veles | et al.