Let's say you read that Shattered Sun Supplies have a 10% chance to contain a Badge of Justice, and, excited, you go out and do enough dailies get 10 Shattered Sun Supplies. You open them all and find not a single Badge, or you find five badges. Do either of these outcomes mean the 10% drop rate is wrong? No! They do not! All a 10% drop rate means is that for each Supplies, there is a 10% chance that it contains a Badge. Random events have no memory, so no matter how many badges you get in the first nine Supplies, your chance to get a Badge in the tenth Supplies is still 10%. The traditional analogy is that if you flip a coin nine times and get heads each time, the chance of getting heads on the next flip is still 50%.
Now it is true that you will probably get a Badge in ten Supplies if the drop rate is 10%. If you're interested in how likely it is, here's the calculation to do. The chance of not getting a Badge in one Supplies is (100% - 10%) = 90%, or 0.9. Raise that to the tenth power, for your ten independent Supplies-opening events, and you get the chance of, ten times out of ten, not getting a Badge: 0.9^10 = 0.349, about 35%. So in fact, out of ten Supplies, you will get a badge (100% - 35%) = 65% of the time, about two thirds.
TL;DR version: A drop rate is a probability, not a guarantee.
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Reader Comments (Page 1 of 3)
4-29-2008 @ 6:09PM
Sebastian said...
Speaking of statistics, does anyone know of a good proc rate reference (per item)?
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4-29-2008 @ 6:11PM
Treima said...
You can lead a n00b to mathematics, but you can't make him learn.
Reply
4-29-2008 @ 6:57PM
BitterCupOJoe said...
Unfortunately, the human brain is not set up well for doing mathematics; it's evolved to be good at making a good decision correctly, rather than a perfect decision slowly.
4-29-2008 @ 6:18PM
drjonesac2 said...
Neat math! So if I open 30 supplies I have an approx 96% chance to get one?
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4-29-2008 @ 6:28PM
AlmtyBob said...
Correct
4-29-2008 @ 7:29PM
Simon Jia said...
no. your drop rate is still at 10%. Could it be 96%? of course, if you are lucky enough.
the easiest example to understand this (which is already in the post) is "flip a coin". Each time you flip it, you will always get 50% of chance for either the heads or the tail.
4-29-2008 @ 7:46PM
AlmtyBob said...
If you read his question as "If I open 30 SSO Supplies do I have a roughly 96% chance of getting one or more badges from that batch?" then he is correct.
To use your analogy, on the 4th flip of a coin, you're 50/50 to get heads. However, in 4 flips of a coin you've got a ~94% chance that one of the slips will have been heads.
Thanks for the condescending reply though!
4-29-2008 @ 6:22PM
Nathral said...
Stop trying to make me do math! I'm playing a game.
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4-29-2008 @ 6:23PM
Jp said...
Yay for math!
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4-29-2008 @ 6:27PM
Aranon said...
Thank you so much for this post. Probability in pretty much any game is terribly misunderstood (to "hot streaks" in sports, etc.)
The comments that kill me are "the drop rate must have been stealth nerfed! I haven't seen x in 10 runs!" "Oh yeah? I've sharded it 3 times in a row." That's random numbers for ya!
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4-29-2008 @ 6:36PM
aaronjay said...
I think every post needs a TL;DR version!!!
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4-29-2008 @ 7:29PM
Chris C. said...
agree
4-29-2008 @ 6:39PM
kellzea said...
im glad to see out of teh 1st 8 posts there is only one "duhhhh i dont like maffs" quote.
thx for the post, i enjoy probability. the fantistic symplisity of singular probabilities combined with the excruciatingly complex detail that probabilitiy mathematics brings makes for some very interesting thinking.
=)
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4-29-2008 @ 7:53PM
tk said...
"symplisity"
maybe you should have spent a few lessons in english as well as math.
4-30-2008 @ 9:45AM
Heenmor said...
The grammar police strike again....
in a math thread.... What is the world coming to?
4-29-2008 @ 6:47PM
Juneau said...
Maths. Yay.
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4-29-2008 @ 6:52PM
Atrix said...
Now I can't stop thinking about WoW when I do stats homework, thanks a lot >.
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4-29-2008 @ 6:53PM
tre said...
Ah, I remember learning about this the hard way in Vegas playing roulette...
...that being said, I have gotten TWO badges since I started doing the dailies...
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4-30-2008 @ 10:03AM
h8rain said...
You are one up on me. I have gotten like what 100(not been keeping track) of those supplies since those dailies started, and I have only gotten one.
4-29-2008 @ 6:54PM
Tekkub said...
I love the people in my guild that cry about a "bad batch" of prospecting... I just burn thru whatever I'm crushing and feel happy in the knowledge that, over the long run, I get raw blue gems.
People spend too much time looking at the small picture when it comes to droprates.
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