User blog:Sylvandyr/The math behind the Battle Arena

Overview
The Battle Arena uses a point system and a game-generated random range to determine the damage done by a dragon's attack. Each factor (type, rarity, and level) contributes a certain number of points, and these points are combined to determine your chances of scoring your main objective: a critical hit to defeat your opponent.

You may increase your chances of victory by maximizing your point total, but you are not necessarily guaranteed to win even with the same pair of battling dragons.

Attack Selection
Your dragon has the Bash, Magic, and Ultimate attacks. While damage fluctuates slightly according to a game-defined range, using the Ultimate attack guarantees a critical hit, which deals an incredible amount of damage to the enemy dragon.

If you do not wish to pay for the Ultimate attack, it does not matter whether you select Bash or Magic. While you may sometimes see differences in damage between the Bash and Magic attacks, this is actually due to the slightly random variance in damage as well as the occasional critical hit, which deals a significant amount of damage more than normal.

Point Distribution
Points are distributed differently depending upon the factors.

Type

Your dragon is assigned a type score based on how all of its colors compare to all of the enemy's colors. This is a straightforward additive process. Every type of your dragon is compared to each of the enemy dragon's types. For every strength that each of your dragon's colors has against the enemy dragon's colors, you gain one point. For every weakness, you lose one point.

Once your type score is calculated, you will receive points based on the following chart:

Rarity

Your dragon is assigned a rarity score based upon its rarity type. However, just because a dragon is "Super Rare" in the game doesn't necessarily mean that its rarity type is the same.

The following chart lists the different rarity types, the corresponding points awarded for that type, and the dragons that fall under that category:

Level

Your dragon is assigned a level score, which is calculated in the following manner:

Level of your dragon - Level of enemy dragon = Level score

Once your level score is calculated, you will receive points based on the following chart:

Determining Crit Bonus
Your point total is the sum of points from type, points from rarity, and points from level. This is mapped to your crit bonus (which increases your chance of a critical hit) as shown in the following chart:

Determining Attack Damage
Your attack roll is a random number determined by the game and is completely out of your control. It affects your damage, the enemy's damage, and whether or not your dragon will land a critical attack.

Damage is calculated in the following manner:

Your dragon's regular damage = 25 + (a random number between 0 and 8)

Your dragon's critical damage = 60 + (a random number between 0 and 100)

Enemy dragon's regular damage = 34 + (a random number between 0 and 15)

Rolling a critical attack allows your dragon to deal its maximum damage for that attack. A critical max is derived from the crit bonus with the following formula:

Critical max = 1000 * (1 - (1 - Crit bonus)^(1/3))

If your attack roll falls under the critical max, then your dragon will deal a critical attack. This means that the higher your critical max, the better your chances of rolling a critical attack. You are not guaranteed to roll a critical attack unless you use your dragon's Ultimate move, which will automatically grant you a critical attack regardless of any random factors.