**Calculating Weapon Damage Part 1: Averaging Dice**

Before we can compare weapon damage we must first learn how to calculate weapon damage. To calculate weapon damage we must first learn how to calculate dice averages.

All weapons do damage based on some combination of dice so it’s important to understand how to average the results of the roll of the dice. To compare weapons we want to consider how much damage they will do over a large period of time. Boss fights can take several minutes with hundreds of swings. Because we would be looking at a large sample size (that means a large number of individual pieces of comparable data – in this case weapon damage calculated for each of hundreds of swings) we can express weapon damage as an average. This will give us an easier number to use in comparisons.

To calculate an average we need to consider all the possible rolls a dice can make and the chance of each occurrence. Dice conveniently have the property of equally rolling each number possible. This means that no matter how many times we roll a dice each number has an equal chance of being rolled. Furthermore, the larger the number of rolls (or rather the larger the sample size) the more likely it is that you will have a equal rolling of each number. Since we have a very large sample size we can simplify our calculations.

For each dice we can assume each number will come up an equal number of times. This means we can use the smallest possible sample size to calculate our average – that would be 1 roll of each number. To calculate the average number a dice can roll we will add each of the numbers together and then divide the sum by the number of rolls it would take to get each number exactly once. Let’s use the d6 as an example. Here’s how to calculate the average roll of a d6.

(1+2+3+4+5+6)/6 = 21/6 = 3.5

As you can see a d6 can roll each of the numbers 1 thru 6 and, as its name indicates, there are 6 possibilities that can be rolled. Now let’s look at some other dice.

D4: (1+2+3+4)/4 = 10/4 = 2.5

D8: (1+2+3+4+5+6+7+8)/8 = 36/8 = 4.5

D10: (1+2+3+4+5+6+7+8+9+10)/10 = 55/10 = 5.5

D12: (1+2+3+4+5+6+7+8+9+10+11+12)/12 = 78/12 = 6.5

Do you see the pattern? The average roll for a die is .5 higher than half the die number. This can be useful if you ever want to calculate other dice averages, but I’ve already calculated the main weapon damage dice. The main variation you’ll find in weapon damage is multiple dice like the falchion which does 2d4 damage. Since we know how to calculate average dice damage this is easy to calculate. Think of 2d4 as 2*[d4]. This means we can calculate 2d4 as 2*2.5 = 5.

If you have a topic or a build you’d like me to look at drop me an email (ddoepiceducation@gmail.com) or leave a comment. I am in no way guaranteeing that I will consider, reply to, or let alone read comments in anything resembling a timely manner (sorry, tiem is unfortunately not an infinite resource of mine until I am high enough level to cast time stop).

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To my understanding DDO dice are loaded, at least for spell damage you never roll a 1 (or 2?) – not sure if this applies to melee as well.

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