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So take this from someone taking AP Statistics – having to kill 120 Wither Skeletons is not an “extreme”, it is an average. There is a 2.5% chance per kill of getting a skull, meaning p=(.025). To calculate the average number of repetitions needed before achieving “success”, the formula is simply 1/p, or in this case 1/.025. Plug that into your calculator and it spits out 40. From there, it doesn’t take a statistics class to tell you that to get three, you multiply by three for (guess what!) 120. That means, the average player will have to kill 120 Wither Skeletons before getting three heads, leading me to the conclusion that you are either lucky or exaggerating. This isn’t really something you can dispute – these are well established mathematical formulas.
But hey, say you don’t believe me. Say you think I got the math wrong, even though this kind of probability is something I learned before statistics even expanded upon it. I built a quick calculator program on my calculator while I was bored in precalculus, then ran it for 999 trials (the max my calculator can take before no longer being able to run analysis). Here’s the coding, so you can be sure I didn’t cheat. It probably won’t make much sense to you, but I’m sure another programmer on the forums can confirm its validity, and I’ll comment it up and add actual names to the variables to make it easier to understand.

You probably didn’t understand that, so I’ll summarize what it does. It simulates the killing of a Wither Skeleton by giving a 1 in 40 chance of a “success”, and repeats that until 3 “successes” are achieved. It then stores the number of Wither Skeletons it took to get these three skulls in another location for further viewing, then runs again. I ran this program 999 times, simulating a random player going to get his three skulls 999 times. Here are my results:

So the mean was 119.45 Wither Skeleton kills needed. Don’t even try to tell me my math was wrong there now.

But I already knew that. I’m more interested in the standard deviation. Now, the Central Limit Theorem would normally cause the combined results of trials to be normal, especially with a sample size of 999, but unfortunately np = 3, which is less than ten. That means the left side of the normal model will be cut off, causing a right skew. That means the standard deviation isn’t useful for far-reaching calculations, and the SD can’t be calculated by regular methods. But we already have an approximate SD from our trials, so that should be almost dead-on accurate for our purposes, especially since independence is a certainty. So what does a standard deviation of 64.866 mean? Well, it means that when you go one standard deviation out in both directions, you have contained just about 68% of all results. Here’s a little table so you can visual what I mean:



But I said earlier that it can’t work quite as well in this case because np<10. We can still approximate, especially for the smaller sigmas. With a bit of math, we can find out that 1SD above the mean is 184.866, 2SD is 249.733, and 3SD is 314.599. With a bit more math, specifically, finding the area of everything else by taking (1-the other results)/2, we can find out the odds that a player might have to kill a certain number of Wither Skeletons to get his skulls.

Here are the results:

Odds that a player might have to kill above X Wither Skeletons to get all three skulls, according to the slightly-off normal model:

X=184: 16%
X=250: 2.5%
X=315: .15%

So that means 1 in 40 player will have to kill more than 250 Wither Skeletons to get their skulls. 3 in 2000 players (not unlikely at all considering the millions playing Minecraft) will have to kill more than 315, which is absolutely ridiculous. Some will have to kill more. If you’ve followed along with the math up to this point, you can do your own calculations as to how they might stretch out farther, but be warned that the normal model gets more and more inaccurate because np<10 as you go out farther. As I mentioned earlier, these might be a bit off because of the truncated normal model that causes a right skew. You can’t really call me out on that though, because what that would really mean is that for a manually placed normal model extending into the negatives the standard deviation would more than likely be even larger, meaning that unlucky players have to kill even more Wither Skeletons than is mentioned here. This of course means that many lucky players will have to kill somewhere on the range of 60 or less, but unlucky and lucky happen about the same amount of times, and with my way even the unlucky ones will be able to get it eventually with a bit of perseverance, unlike the obsession that would be needed if you wanted to get them just from Fotressses.So yes, some lucky players will be able to get enough materials to summon the Wither within an hour or so – it is really the same now. But do not even try to tell me any longer that needing to kill 120 is an extreme. It is the average, and needing to kill even half that would only happen to less than 1 in 5 players.

But let’s take a different approach, because I’m spending a lot of time applying what I learned in Statistics, and this is kind of fun. The Geometric model is even better for our purposes than the normal model, and even easier to use. It gives us a different perspective on how crappy the current system is as well.

So, if you have a TI graphing calculator, you can follow along. Hit 2^nd Vars, then go to the very bottom, where it says geometcdf(. That is the geometric cumulative distribution frequency, which you probably don’t understand. What is does is calculates the chance of an occurrence happening by the time a certain number of trials have gone by. So click it, then type in into the parentheses .025,120).That spits out .952075909, right? What that number means is that there is a 95.2% chance of getting at least one skull by 120 trials (note the at least). While that seems decent, that leaves us 4.8% of people, after having killed 120 Wither Skeletons, wondering if the info they got off the wiki on drop rates was wrong. You can plug in other values instead of 120 to see the chances a person will have received a Wither Skeleton Skull by the time they have killed that many Wither Skeletons.

But let’s remember that I’m not even suggesting a change of drop rate – I’m just suggesting that they are a bit easier to find, by moving them out of Nether Fotresses. Which means all this still applies even after my idea comes into play – all it means is that they will be easier to find, so you will be able to rack up these ridiculous amounts of kills.