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Posts with tag probability

[1.Local]: What alliances we have

Reader comments -- ahh, yes, the juicy goodness following a meaty post. [1.Local] ducks past the swinging doors to see what readers have been chatting about in the back room over the past week.

Tomorrow's the Big Day for one of WoW.com's own. Join us in congratulating Michael Gray and his bride Katherine on their marriage. It seems that this couple has been treading on geeky ground from the very start. Now, Michael has given us permission to share excerpts from the ceremony with the gang at [1.Local] here today. We've tucked in the wedding benediction at the end of this week's column ... Best wishes to the happy couple!

And now, on to the week's comment highlights.

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Filed under: Analysis / Opinion, WoW Social Conventions, Virtual selves, Features, Humor, [1.Local], Warcraft Movie

Math problem: Average winning roll

Here's a question that occurred to me while I was walking home from the subway recently: What's the average winning roll in a five-man group, assuming everyone rolls? That is, if you randomly chose five numbers between one and 100, what is the expected value of the highest one?

I know a bit of statistics, but I really don't know how to begin getting at that one. However, I do know how to write a script that will calculate the answer. (Yes, these numbers are only pseudorandom, but I did some limited testing with real random numbers (from random.org) and the results were the same. Besides, I'm pretty sure Ruby's Mersenne twister pseudorandom generator is good enough for testing distributions like this.) The average winning roll out of a group of five people is 82.8 83.8 83.3 (tested over many, many repetitions). Now can any mathemagicians tell me why?

The graph above, in case it isn't clear, is average winning roll on the y-axis vs number of people rolling on the x-axis, tested over 100,000 trials for each group (the relatively small sample size is why the first point is not right at 50, and probably why the curve is a little wobbly).

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Filed under: Analysis / Opinion, Instances

Some remarks on drop rates


I'm going to keep this relatively short, because a full discussion of probability could fill several college semesters. However, there is one misconception that some WoW players have that has been bugging me lately.

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.

Filed under: Analysis / Opinion

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