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  1. #1
    IncGamers Member Frostlion's Avatar
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    ilvl 63 drop rates, let's do this properly

    I've seen a few threads on multiple forums over the last months claiming that ilvl 63 drop rates for level 63 monsters are below the 16.3% that was the last reported figure by Blizzard back in summer 2012. Some of them have some numbers, but most claims are basically refuted by either "RNG" or "you only posted it because you noticed". So let's do this properly.

    My (alternative) hypothesis is that the drop rate for ilvl 63 magical items (blue, yellow, gold and green) is less than 16.3% in act 1 Inferno on MP1.

    To test this, I will collect the first 1,000 magical, rare, legendary and set items that drop in act 1 inferno MP1 runs and note their levels. Because the burden of proof is rather heavily on me to discredit a fact stated by a major game publisher, I will look for at least a 5 sigma confidence interval (that is: the chance that I happened to simply be unlucky in my drops must be less than 1 in 3.5 million).

    That means, if the number of ilvl 63 items out of 1,000 is less than 105, we will conclude that the drop chance is indeed below 16.3% (See 1). Otherwise, the number of 16.3% stated by Blizzard stands.

    I will be posting the results here when I am done, regardless of what they might be.






    1: Critical value where: ( [found fraction] - [expected fraction] ) / sqrt ( [expected fraction] * (1 - [expected fraction] ) / [sample size] ) = - [sigma]
    So:
    ([found fraction] - 0.163) / sqrt ( 0.163 * (1 - 0.163) / 1000 ) = -5
    ([found fraction] - 0.163) = -5 * 0.0117
    [found fraction] = -0.0584 + 0.163 = 0.1046
    Or 104.6 out of 1,000 items

  2. #2
    IncGamers Member Frostlion's Avatar
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    Re: ilvl 63 drop rates, let's do this properly

    First quarter (253 items found):

    ilvl 58: 13 (5%)
    ilvl 59: 4 (2%)
    ilvl 60: 56 (22%)
    ilvl 61: 90 (36%)
    ilvl 62: 72 (28%)
    ilvl 63: 18 (7%)

    Time for lunch!

  3. #3
    IncGamers Member Frostlion's Avatar
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    Re: ilvl 63 drop rates, let's do this properly

    Halfway (516 items found):

    ilvl 58: 25 (5%)
    ilvl 59: 10 (2%)
    ilvl 60: 109 (21%)
    ilvl 61: 186 (36%)
    ilvl 62: 137 (27%)
    ilvl 63: 49 (9%)

  4. #4
    IncGamers Member Frostlion's Avatar
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    Re: ilvl 63 drop rates, let's do this properly

    Over three quarters through (804 items found):
    ilvl 58: 43 (5%)
    ilvl 59: 17 (2%)
    ilvl 60: 151 (19%)
    ilvl 61: 287 (36%)
    ilvl 62: 222 (28%)
    ilvl 63: 84 (10%)

  5. #5
    IncGamers Member Frostlion's Avatar
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    Re: ilvl 63 drop rates, let's do this properly

    Final results:

    ilvl 58: 51 (5%)
    ilvl 59: 24 (2%)
    ilvl 60: 199 (20%)
    ilvl 61: 353 (35%)
    ilvl 62: 262 (26%)
    ilvl 63: 111 (11%)

    Although the number of ilvl 63 items is on the low side compared to the expected 163 items, it is within the range I set out in my first post. So based on this check, Blizzard's 16.3% drop chance stands.

    That said, it certainly is on the low side - in fact, if I'd chosen the slightly less harsh 4 sigma criterion (about 1 in 30,000 chance of a coincidence) anything under 116 items would have been enough to show a reduced drop chance. I'd be curious if anyone else repeated this check, what numbers they'd come up with.

  6. #6
    D3 Monk Moderator kestegs's Avatar
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    Re: ilvl 63 drop rates, let's do this properly

    I think you should run it again

    Nice work though, I think you had a really unlucky early steak, and you were constantly recovering from it.

  7. #7
    IncGamers Member Frostlion's Avatar
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    Re: ilvl 63 drop rates, let's do this properly

    Thank you for the kind comment.

    If it turns out that the drop rate is actually lower, at about 11% or 12%, running the test again wouldn't tell us anything, except "Hey, it's fairly low but not significant again!"

    If I were to do it again, I'd have to try a test with more power, i.e. a bigger sample size. Running the test again with 2,000 drops would have a 5 sigma border at under 12.2%, running it with 3,000 drops would have it at 12.9%. That would be interesting to do... if I have the time at some point. 3,000 drops to track is a lot.

  8. #8
    Administrator Flux's Avatar
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    Re: ilvl 63 drop rates, let's do this properly

    Interesting data, and I'm curious to see how it correlates (or not) with the find rates of various legendaries. Everyone reports a MUCH lower incidence of Mempos than Andy's hats, and people seem to assume it's because Mempos were made to be very rare drops, but maybe it's compounded by ilvl 63 hats having a vastly lower drop rate than ilvl 62 hats, due to a bug or intention?

    This doesn't seem to be universal; I've found as many or more lvl 63s than 62 and lower of some other item types, and given the (buggy and quirky) history of drop rates in earlier Diablo games, I can easily imagine some glitches in the code impacting what we see in the game. And no one ever knowing it since fans don't have the ability to crawl through the game code and find all the bugs, as they did in D1 and D2.
    --Flux
    The Diablo 1, 2, & 3 Wiki! (Under construction.)


  9. #9
    IncGamers Member AurelianZ's Avatar
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    Re: ilvl 63 drop rates, let's do this properly

    This is my data sample from 100 Act 1 runs on MP10, totaling 41358 items.

    The run is Fields of Misery -> Scavenger's Den -> Decaying Crypt

    Area\ilvl 58 59 60 61 62 63
    FoM 1024 440 2737 6130 4621 2799
    Den 416 185 1067 2416 1801 1145
    Crypt 976 359 2658 5636 4380 2613
    Totals 2416 984 6462 14182 10802 6557


    Area\ilvl 58 59 60 61 62 63
    FoM 5.77% 2.48% 15.42% 34.53% 26.03% 15.77%
    Den 5.92% 2.63% 15.18% 34.37% 25.62% 16.29%
    Crypt 5.87% 2.16% 15.99% 33.91% 26.35% 15.72%
    Totals
    5.84% 2.38% 15.61% 34.25% 26.09% 15.84%


    Here is someone else's sample from running a bot in Act 3 on MP0 http://i.imgur.com/jtVmaIY.png

    And here is yet another sample (just for rares) http://www.reddit.com/r/Diablo/comme..._ilvls/c8ahkwo

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