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How Math Works


Paranitis's Avatar


Paranitis
05.13.2012 , 12:06 AM | #1
I've noticed people complaining about the 20% or 10% Reverse Engineer chance, and then complaining they don't get something to happen within 5 or 10 tries.

Here's how math works, so you cannot complain:

You have an object that you want to RE. It has a 20% chance to cause you to learn a new schematic. You fail.
You have an object that you want to RE. It has a 20% chance to cause you to learn a new schematic. You fail.

If you take a 20 sided die, you have a 5% chance to roll any specific number. Just because you roll the wrong number, it doesn't mean that that wrong number is no longer available. It still means you have a 5% chance on your next roll to roll any specific number.

People are complaining and acting as if 20% chance means that if you fail 4 times, that the 5th time will work.

20% chance is not cumulative. It does not stack. It doesn't go 20% to 40% to 60% and so on.

That's why RNG is RNG.

If an item has a 1% chance to drop from a boss fight, and you've killed it 1 million times and it hasn't dropped yet, that doesn't mean it doesn't have a 1% chance to drop. It just means that every time you've fought it, you rolled one of the other 99% of numbers.

Tawreos's Avatar


Tawreos
05.13.2012 , 12:11 AM | #2
It is to bad that facts won't make a difference in whether people complain or not.
Make sure you tell someone you love them today, because life is short. Scream it at them in German, because life is also scary and confusing.

pokota's Avatar


pokota
05.13.2012 , 12:54 AM | #3
What I especially like is the belief many people have that if THEY are seeing a short-term 10% rate, then everyone else is, as well. If you're having bad luck, then somewhere out there, someone is having good luck. Only, no one posts when they have good luck. Just because it took 30 attempts to get that purple pair of shorts doesn't mean the function is broken. The smaller the sample size, the greater the deviation. It's quite possible to flip a coin five times and get five heads or tails in a row. Though, I'd imagine if coins had a flipping forum, we'd have people posting "these coins are broken" threads.

Whatever the rate is, it's a massive improvement over pre-1.2, so I'm content.

Just putting it out there, but I hit a critical on my first attempt crafting the Synth BoP bracers. That's a 100% success rate! Totally broken!

ImmortalAlien's Avatar


ImmortalAlien
05.13.2012 , 02:58 AM | #4
Random number game is random.

But this is a basic statistics and probability lesson. Dice and RNG's have no memory. Thus, the chance for each RE attempt is always 20%.

When looking at grouping RE attempts, for example 5 attempts, it's not "The probability of getting a successful RE is 100% in 5 attempts," it is actually, "The average theoretical probability of getting a successful RE in 5 attempts is 100%".

There's a difference. On average, a person gets a successful RE in 5 attempts. And, from experience, I'm usually successful every 3-8 attempts on items. Pretty close considering the small sample size each time

Yet, there's still the chance of going 30 in a row without any successful RE, and there's also the chance of being successful in the first attempt. It's all a part of the RNG. Both extremes usually offset each other.

If we took all the RE attempts from all the players in SWTOR, the average player should be having a successful RE every 5 attempts with little deviation. This is hardly guaranteed from happening every single time, though.

DataBeaver's Avatar


DataBeaver
05.13.2012 , 03:16 AM | #5
Quote: Originally Posted by Paranitis View Post
If you take a 20 sided die, you have a 5% chance to roll any specific number. Just because you roll the wrong number, it doesn't mean that that wrong number is no longer available. It still means you have a 5% chance on your next roll to roll any specific number.
This is true, but when we observe the series of rolls as a whole, we can do statistical analysis on it. For example, at 20% success chance and 20 tries, there's only a 1.15% chance that you didn't succeed at least once.

And since we are talking about humans here, all sorts of psychological factors come to play. When dealing with randomness, most people have a very strong bias towards an even distribution, even with sample sizes where it's unrealistic to expect it. If you ask a human to produce a random string composed of the letters A, B and C, you're likely to get something where no two consecutive letters are the same. An unbiased computer might produce something like CCBBBBCACAAA, but a human will likely think this is not very random.

Quote: Originally Posted by Paranitis View Post
If an item has a 1% chance to drop from a boss fight, and you've killed it 1 million times and it hasn't dropped yet, that doesn't mean it doesn't have a 1% chance to drop. It just means that every time you've fought it, you rolled one of the other 99% of numbers.
Again, statistical analysis. After 1 million kills and not getting the item you can conclude with 95% certainty that the item has a droprate of at most 0.0003%. If it had a 1% droprate, the chance of not getting any in 1 million kills is about 1 in 10 to the power of 4365. That's 0.000000..(a total of 4362 zeroes)..000001%. In other words, if you killed that boss 1 million times every second since the beginning of the universe, there probably won't have been a second where that item didn't drop at least once, since the universe is less than 10 to the power of 18 seconds old.

(I realize that this last part was probably meant as hyperbole, but hey, since we're talking math...)

Cleet_Xia's Avatar


Cleet_Xia
05.13.2012 , 04:50 AM | #6
My personal favorite is people claiming to have crafted and RE'd many hundreds of a specific item -

1) made from uber expenssive grade 6 mats,
a) that have very long gathering mission times, that have pretty poor yields even at max affection
b) typically not really "farm"able, without massive investments in time

2) requiring large quantities of those same mats

3) that have very long build times, when the most they can que up at a time is 30

4) and they supposedly did all that while spending credits on class skills, speeders & training, spaceship parts, while leveling an alt or two, browsing these forums, going to school/ working, & playing ME3/ CoD/ Skyrim/ and Hello Kitty.

TL;DR ~ It was B.S. before 1.2 & it's B.S. after 1.2
~Master Telagtun Telag of Lord Calypho~

Cerion's Avatar


Cerion
05.13.2012 , 09:20 AM | #7
Quote: Originally Posted by DataBeaver View Post
This is true, but when we observe the series of rolls as a whole, we can do statistical analysis on it. For example, at 20% success chance and 20 tries, there's only a 1.15% chance that you didn't succeed at least once.

And since we are talking about humans here, all sorts of psychological factors come to play. When dealing with randomness, most people have a very strong bias towards an even distribution, even with sample sizes where it's unrealistic to expect it. If you ask a human to produce a random string composed of the letters A, B and C, you're likely to get something where no two consecutive letters are the same. An unbiased computer might produce something like CCBBBBCACAAA, but a human will likely think this is not very random.


Again, statistical analysis. After 1 million kills and not getting the item you can conclude with 95% certainty that the item has a droprate of at most 0.0003%. If it had a 1% droprate, the chance of not getting any in 1 million kills is about 1 in 10 to the power of 4365. That's 0.000000..(a total of 4362 zeroes)..000001%. In other words, if you killed that boss 1 million times every second since the beginning of the universe, there probably won't have been a second where that item didn't drop at least once, since the universe is less than 10 to the power of 18 seconds old.

(I realize that this last part was probably meant as hyperbole, but hey, since we're talking math...)
One thing you're forgetting, and something I've been trying to address in these threads, is population size. Take the national Lottery for example. Each individual has something like 1 in 200,000,000 chance of winning. If you were the only one playing, you would most certainly die before winning the lottery. And yet someone does actually win the lottery...due to the size of the population participating.

So in your example, you could easily have 1 million players of an MMO kill a boss mob once. One of those players is likely to have scored the drop, just as 1 person in the US will win the Lottery even though the individual odds are ridiculously minute.

As it applies to SWTOR RNG, the size of the population means you will have individuals who have, through no fault of their own, ridiculously bad streaks. You cannot say who those individuals will be, but you are increasingly certain to have those individuals nonetheless as a population size increases.
Good will always triumph because Evil is lazy.

Cleet_Xia's Avatar


Cleet_Xia
05.14.2012 , 12:17 AM | #8
The lottery concept is true, some exceptionally long streaks of bad luck are going to happen. But how many threads have we seen here where someone was talking about not being able to get a proc from green to blue on a piece of lowbie gear? It's almost always someone trying to RE blue to purple for a piece of gear made from T6 mats. Who would continue crafting if a piece of lowbie gear requirred them to RE over 150 items for a blue proc?

There have been many posts on this forum from people claiming that it has taken them hundreds of RE attempts for several different paterns within a single craft, on the same toon. That's like "winning" the bad luck lottery ~ over and over. You obviously can't say that it has never happened, but what are the odds? And what are the odds that it would happen more than once? It's a pics or it didn't happen kind of scenario.

Granted there was a real problem worth complaining about with the "you already know that schematic" proc. Because it made it genuinely more difficult to get a specific purple patern for gear with a branching RE scheme.
~Master Telagtun Telag of Lord Calypho~

Ironcleaver's Avatar


Ironcleaver
05.14.2012 , 01:57 AM | #9
Law of Large Numbers
Bernoulli Trial
Online Bernoulli Calculator
  • 20% chance for schematic while REing (80% fail rate).
  • 25 attempts (or rolls of the dice) - online calculator limit
  • Can have Zero Successes
  • All can be successes,
Formula:
Code:
P(A) = ∑bi=a(ts+i)(p)s+i(1−s)t−s−i = ∑25i=0(25i)(.2)i(0.8)(25−i) = (250)(.2)0(0.8)25+(251)(.2)1(0.8)24+(252)(.2)2(0.8)23+(253)(.2)3(0.8)22+(254)(.2)4(0.8)21+(255)(.2)5(0.8)20+(256)(.2)6(0.8)19+(257)(.2)7(0.8)18+(258)(.2)8(0.8)17+(259)(.2)9(0.8)16+(2510)(.2)10(0.8)15+(2511)(.2)11(0.8)14+(2512)(.2)12(0.8)13+(2513)(.2)13(0.8)12+(2514)(.2)14(0.8)11+(2515)(.2)15(0.8)10+(2516)(.2)16(0.8)9+(2517)(.2)17(0.8)8+(2518)(.2)18(0.8)7+(2519)(.2)19(0.8)6+(2520)(.2)20(0.8)5+(2521)(.2)21(0.8)4+(2522)(.2)22(0.8)3+(2523)(.2)23(0.8)2+(2524)(.2)24(0.8)1+(2525)(.2)25(0.8)0
Result:
Code:
0.00377789318629571+0.02361183241434800+0.07083549724304400+0.13576803638250100+0.18668105002584400+0.19601510252713620+0.16334591877172800+0.11084187345224400+0.06234855381688725+0.02944237262043000+0.01177694904817200+0.00401486897140800+0.00117100344999400+0.00029275083649700+0.00006273228867600+0.00001150090324680+0.00000179700081000+0.00000023783834250+0.00000002642407900+0.00000000243335400+0.00000000018223590+0.00000000001075250+0.00000000000046000+0.00000000000001500+0.00000000000000000+0.00000000000000000 = 0.9999999998285
Probability of Success: 0.9999999998285%

So after 25 attempts we have a near 100% Probability for a schematic. Issues is, a lot of people are REing a lot more then 25 items, some upwards of 200 items and still get nothing. The Probability of REing even 100 items at 20% chance of success, chance of failure so insanly small it's infinitesimal.

Sure Probability is Probability though....... :-/

It's 4am and Im bored. :-/
╒═══╡My 3d Weapon Thread╞═══╛
"My eyes scream for the souls that bleed in my mind." ~ Ironcleaver

Cerion's Avatar


Cerion
05.14.2012 , 03:58 AM | #10
I don't believe you're using that linked calculator correctly. You're trying to discover the probability of zero successes. You need to enter zeros in both fields. At least 0 successes, and at MOST zero successes after 25 trials.

That gives you a probability of .0037778931 for one individual to have a bad streak of zero success after 25 trials. But given a population of 100k crafters, you'd expect something like 377 crafters to have streaks of zero success after 25 trials.
Good will always triumph because Evil is lazy.