Dragon Dice® Rules

The Player Tools page includes statistics for each individual die to assist in seeing how well the die will roll in your army. For each die, the page will show you the percentage chance of rolling a favorable result for each roll type, as well as the average value the die will produce and the standard deviation in the die's results for each roll type. If you are not used to these statistics, they can be overwhelming. So we will start by explaining what these values mean and how they're derived. Then we will go into detail for which dice produce results.

We will explain Favorable, Average, and Standard Deviation. To demonstrate the calculations, we will reference a Leopard Rider and a Wolf Rider.

Calculating the percent (%) favorable is easy. You count the number of sides of the die that have an effect on a given roll and divide by the total number of sides of the die.

For example, Leopard Rider has an ID, two Rend faces, and a Melee face that counts towards Melee, for 4 total sides that count towards a Melee roll. The Leopard Rider has 6 total sides, which means 4/6 or 66.7% chance of rolling a favorable result during a Melee roll.

(% Favorable) = (# of faces that provide a result) / (Total # of faces)

Average is the average number of results a die will produce for a given roll. For Average, total the number of results on all faces of the die, and divide by the number of sides on the die.

For example, Wolf Rider rolling Melee has 6 total Melee results (2 ID, 2 Melee, and 2 Melee) and 6 total sides. 6/6 is 1, for an average value of 1 Melee result per roll.

Some dice, however, have rerolls and this affects the average. Leopard Rider has 13 total Melee results which would equate to 2.17 average results per roll, but rerolls increase this average. Fortunately, there is an easy formula for this.

(Average) = (Sum of results on the die) / ( (# of faces on the die) - (# of reroll faces) )

Leopard Rider has 2 Rend faces which cause a reroll on Melee. So sticking with Leopard Rider as our example, we get: Average = 13 / (6-2) = 13/4 = 3.25 Average

Standard deviation indicates the extent of deviation for a group as a whole. This effectively means you won't get the average value every time. Your results are going to deviate from the average by some margin. In our Wolf Rider example, you won't roll 3.25 every roll. You're going to roll 0 or 2 Melee results every time.

The Standard Deviation represents the spread of the results, with 66% of all rolls lying within +-1 SD of the mean, 95% of all rolls lying within 2 SDs, and 99% of rolls lying within 3 SDs.

Calculating Standard Deviation is more tricky. Here are the steps to calculate Standard Deviation. 1. Calculate Mean 2. For each number, subtract Mean and square the result 3. Work out mean of squared differences 4. Square root of that

So let's continue with our Wolf Rider rolling for Melee example and follow these steps. 1. Mean = (2+2+0+0+2+0)/6 = 6/6 = 1

2. For each number, subtract the Mean (1) and square it. (2-1)2 = 1, and (0-1)2 = 1. Our 6 numbers are now 1, 1, 1, 1, 1, 1.

3. Work out the mean of squared differences means to calculate the average the results from the previous step. (1+1+1+1+1+1)/6 = 6/6 = 1 This value also happens to be the variance.

4. Now we square root that result. sqrt(1) = 1

This gives our Standard Deviation of 1 for Wolf Rider rolling Melee.

However, the formula once again gets more complicated with rerolls. The steps are the same except for the following marked differences. 1. Calculate Mean with rerolls; dividing by (number of sides on die) - (number of reroll sides) 2. For each number, subtract Mean (except for reroll numbers) and square the result 3. Work out mean of squared differences, dividing by (number of sides on die) - (number of reroll sides) 4. Square root of that

Let's calculate this Standard Deviation for our Leopard Rider with the following faces: 3 ID, 3 Missile, 3 Rend, 3 Rend, 4 Save, 4 Melee

1. Calculate Mean with rerolls (3+0+3+3+0+4)/(6-2) = 3.25

2. For each non-reroll number, subtract Mean and square the result. For reroll numbers, square the result.

3. Work out mean of squared differences
(0.0625 + 10.5625 + 9 + 9 + 10.5625 + 0.5625) / (6 - 2)
9.9375

4. Square root of that
sqrt(9.9375)
3.15

SAIs can provide a complicated factor in determining these statistics. Some are easy. Fly is favorable and produces results for Maneuver and Save rolls. But other SAIs are not as straightforward. Ferry, for example, has an effect during non-maneuvers, but it doesn't provide any results for any roll where it has an effect. Smite provides results on Melee, but the results are not added to the Melee roll and are instead resolved outside of the phase when the rest of Melee damage is applied. SAIs like Trumpet affect other rolls, potentially increasing your total results significantly. But on its own it doesn't provide any results.

Here are the assumptions made for SAIs and how they factor into the statistics on the Dice Browser page.

Favorable: Any SAI that has an effect during a roll is considered favorable during that roll.

Average/Standard Deviation: SAIs that provide results on their own have their value added for Average and Standard Deviation calculations, regardless if the results are added to the roll, or resolved outside of it. So Smite produces damage on a Melee roll, so it is counted. But Trumpet doesn't do any Melee damage on its own, so its value is not counted.

In the table below, for all SAIs, they are noted as 'F' if they are Favorable for that roll but do not add their value to the roll. Or 'A' if they are favorable AND apply their results to what's being rolled for value to the Average and Standard Deviation calculations.

Here is an exhaustive list of all SAIs that reroll.

Double Strike Flurry Rend Stun Tail

Bullseye

Summon Dragon

none

none

Racial abilities and 8th Face ID doubling or Minor Terrain ID doubling will further affect these statistics. Currently these are not supported by the Player Tools but may be a part of a future enhancement.