Much like weapon procs, coin flips are a binomial distribution. This weapon proc is a binomial with p = 10.4%. Coin flipping is a binomial distribution with p = 50%. The way to calculate the expected number of Heads, or the expected number of coins, is to note that for a binomial distribution, the expected outcome is equal to np - that is, with 10 coin flips, the expected number of heads is 10 * 0.5 = 5. To be specific, a single coin flip is a Bernoulli distribution with p=0.5, and flipping ten coins is a Binomial distribution with p=0.5 and n=10.
Whenever you flip a coin, or whenever you swing a weapon, the statistical word for what you are doing is "drawing a sample" from the distribution. If you flip ten coins, you have drawn ten samples, or sampled the distribution ten times.
There is a law called the Law of Large Numbers that says that if you draw enough samples, the mean of the samples will approach the mean of the distribution. 'Mean' is the word in statistics that means what most people think of when they think of the word 'average'. The mean of a Binomial(n, p) is n*p, which is why above we said that the expected number of heads after ten flips of a fair coin is 5.
The Central Limit Theorem is a very important theorem in statistics, and it is this theorem that must be the cause of your confusion. It says this: if you sample a distribution, the mean of that sample is is a normal distribution. This does not mean you can then substitute this for the original distribution! It's a completely different calculation.
Here's a longer explanation of the previous paragraph. Say you're sampling from the weapon damage distribution - you're getting hit by some mob. As you take successive samples - as the mob takes one swing after another - you can calculate the average damage taken so far. Those successively calculated averages, those are samples of a
different distribution. That
different distribution is a Normal distribution. It does not mean that the distribution (weapon swings) from which you are sampling and calculating averages is normally distributed.
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