Musings on minting money on Malygos…and more

Transmute proc math

Wes of Capped by Cata today wondered whether transmute procs have been nerfed, seeing as he’s 0 for 21 for his 3 transmuters over the past week.

Wes, this is unusual but not crazy.  If (iirc) transmute procs occur 1/8th of the time, then you should expect, on average, about 3 weeks a year where you will get no transmutes.

Here’s the explanation:

Say the chance of not getting a proc is 0.875 (this is 100% less the 12.5% chance of actually getting a proc).

To figure out the chance of x attempts without a proc, simply keep multiplying the “no proc” percentage by itself, e.g.:

The chance of two “no procs” in a row is 76.5% (0.875 squared).

The chance of 10 “no proc” chances in a row is (0.875^10) or 26.3%.

The chance of 21 “no proc” chances in a row is (0.875^21) or 6%.

That’s just less than 1 in 16.  In a 52 week year, that would happen about 3 times.

So though it may be possible, Wes, that transmute procs have been nerfed, I’d say what you experienced was not unusual at all.

The good news is that the odds of you getting procs in all the remaining weeks of summer (through the end of August) are close to 75%.  I like your chances.


I’d have posted the comment on Wes’s site, but it doesn’t allow open posting.


  1. There is a certain amount of paranioa around the RNG. THAT is if the RNG is truly random!

  2. Actually, his chances for the remainder of the summer would not be what you pointed out as the RNG is reset with each new roll.

    Similar to saying the odds of rolling heads are higher because we have rolled tails 12x in a row – really, they are still 50 / 50.

    • @Clint -

      You are correct that the odds reset at each new roll, but that is not the issue here. I am not saying the odds are higher because he struck out. I am saying the odds are that high because they simply are.

      The method for calculating his odds of not “striking out” in any remaining summer weeks (i.e., 5 weeks of not striking out), is to calculate ahead of time the odds that he will get at least one proc each week.

      Per my post, we know the odds of “no proc” are approximately 6%; thus the odds of getting at least one proc are 94%.

      So the odds of getting a proc in all remaining summer weeks requires 5 independent events which have a likelihood of 94% each. The odds of them all going his way are 0.94^5, or 73.4%.

      I rounded to 75% for simplicity.

      I’m pretty sure on the math here, but I have been wrong before. Back to you.

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  3. Unfortunately , Clint is right,,,whatever the past is..the future is not dependent on it.
    The odds must be calculated in the beginning.
    If you have a 100 no procs…the odds of your next proc does not change.

  4. Nice post Midas!

    RNG is a bitch, no way around it. It’s a roll of the dice everytime, but your numbers seem fairly accurate, as I am normally a proc every other week or so…..around 1 in 12/14 seems about right to me.

    Keep up the great work!

  5. Well done Midas.

    Much more clear there.

    You’ve reset the clock and said the odds of proc for any 5 consecutive weeks are xx.

    Dont have Excel or a calculator in front of me but if it’s 94% for a week, then 94^5 should be correct.

  6. I have to say from my own experience, it helps if you don’t think about it too much. I do 10 transmutes per day, and I’ve gone as long as a whole week with 0 procs. It happens. Over time, it average out though. Sometimes you get boxcars, sometimes snake eyes. That’s just the name of the game. Obsessing over it will just make you crazy.

    I do like your math however.

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