Summon

Summoning Heroes is one of the key aspects of. To obtain more heroes to use in combat, they must be either summoned or received as rewards.

Summoning Basics
To obtain heroes, a player must first select a focus from which to summon. These focuses typically feature three or four different five-star characters and are often categorized by common skills or game origins. Featured heroes have increased drop rates, normally starting at 3%. Legendary Hero focuses are the exception where twelve heroes receive a base drop rate of 8%, though no other five-star heroes can be summoned.

The initial cost for summoning is five orbs. Once paid, players are brought to a screen with five randomly selected colored stones. It is possible that all five stones have the same color. The player can select any one stone as their first summon.

After selecting the first stone, subsequent stones cost less:

A total of 20 Orbs allows five summons - summoning any less than five heroes in one session increases the orb/hero cost.

Summoning Mechanics
In order to enter the summon screen, the player must first pay 5 orbs or none if it is their first summon for that summoning focus. Once the entry fee has been paid, 5 randomly generated color summoning stones will be selected. The player must then choose one stone to summon from. Any consecutive summons in the same session will be discounted. Five summons in the same session will spend 20 orbs while summoning individually will take 25. After the first selection the player can exit to try again if the color for the character they want doesn't appear. However this means they will not be able to take advantage of the discounted price.

Heroes do not have individual drop rates. When a hero is rolled, the rarity of the drop is selected first. Once the rarity is selected, it will randomly choose any character in the rarity. This gives every Hero in a given rarity the same chance to drop. A Summoning Focus may give a 5-Star Focus rate to Heroes already available at different rarities. This will give the Focus Heroes a better chance to drop as they will have multiple chances to be selected.

The procedure followed by the game to form a summoning session can be summarized step-by-step:
 * 1) Randomly select a rarity pool based on the given rarity chances.
 * 2) Randomly select a Hero from that pool. (Heroes within this rarity pool are selected completely randomly, any attributes they have such as color are not taken into account).
 * 3) Repeat this four times to form a full summoning circle.
 * 4) Hide the selected units behind an orb of their respective color.
 * 5) Allow the player to choose which orbs to get a Hero from.

General

 * 3% for 5★ focus units
 * 3% for 5★ units
 * 58% for 4★ units
 * 36% for 3★ units

General (4★ focus)

 * 3% for 5★ focus units
 * 3% for 5★ units
 * 3% for 4★ focus units
 * 55% for 4★ units
 * 36% for 3★ units

Weekly Revival

 * 4% for 5★ focus units
 * 2% for 5★ units
 * 58% for 4★ units
 * 36% for 3★ units

Hero Fest

 * 5% for 5★ focus units
 * 3% for 5★ units
 * 58% for 4★ units
 * 34% for 3★ units

Double Special Hero Focus

 * 6% for 5★ focus units
 * 60% for 4★ units
 * 34% for 3★ units

Double Special Hero Focus (4★ focus)

 * 6% for 5★ focus units
 * 3% for 4★ focus units
 * 57% for 4★ units
 * 34% for 3★ units

Legendary/Mythic Hero Focus

 * 8% for 5★ focus units
 * 58% for 4★ units
 * 34% for 3★ units

5-Star Rate Increase
There is a system in place that increases the chance to pull a 5-Star hero the more rolls that a player goes without one. Every 5 rolls that a player goes without a 5-Star hero, the rate to pull a 5-Star will increase by 0.25%. This increase will be added after the summoning session is completed. If the player hits 5 in a row in the middle of the summoning session, the next roll in the session will not have an increased chance. When there is a special focus, the rate increase will be split between the 5-Star and 5-Star focus chances so 0.25% chance added to each per 5 rolls. If a player goes without a 5-star for 120 rolls, the rate to pull a 5-Star hero will be raised to 100% for the next summoning session (when this happens, summoning from any of the five stones will result in a 5-Star hero).

Appearance rate increases only apply to the current summoning event and will not be carried over into the next summoning event.

Rate-increase examples: During a focus summoning event :
 * 5 times with no 5-Star: 0.5% total increase
 * 10 times with no 5-Star: 1.0% total increase
 * 15 times with no 5-Star: 1.5% total increase
 * 115 times without a 5-Star: 11.5% total increase
 * 5 times with no 5-Star: 0.25% total increase to both '5-Star' and '5-Star Focus'
 * 10 times with no 5-Star: 0.5% total increase to both '5-Star' and '5-Star Focus'
 * 20 times with no 5-Star: 1.0% total increase to both '5-Star' and '5-Star Focus'

Color Distribution
Different colors of orb appear at different rates because there are unequal numbers of units in each color. Different Summoning Focuses will also have different unit representation. For example, if a Summoning Focus has no colorless 5-Star Focus units, the chance of summoning a 5-Star colorless character will be reduced because the 3% Focus chance will not produce any colorless orbs. In the Brave Heroes summoning focus, the 5-Star Focus rarity did not skew the orb distribution because there was one Focus unit of each color. The chance of an orb being a certain color under this focus was as follows: Note that Green orbs appear less frequently because there are fewer Green heroes and Red orbs appear more frequently because there are more Red heroes as of August 31, 2017.

A common misconception is that the chance of summoning a 5-Star Focus unit from a given color of orb is the same as the base Focus rate of 3%. The 3% is true when summoning randomly, disregarding orb colors. However, because the game gives the player extra information in the form of the orb's color, players summoning exclusively one color will find five stars at different rates. Using the above Brave Heroes summoning focus as an example and given a 5-Star Focus rate of 3%, 5-Star rate of 3%, 4-Star rate of 58%, 3-Star rate of 36%, and no increased appearance rate, the chance of summoning a 5-Star Focus unit given that their orb color appeared is as follows: A sample calculation detailing the 3.95% chance for a green orb to contain can be found below.

As of the Brave Heroes focus on August 31, 2017, the unit distribution breaks down as such:

See Summonable Heroes for tables on which units are currently available in the pool (adjust for newly added heroes who do not appear on the chosen summoning focus, such as heroes not yet added to the pool).

Using P(event) to mean the probability of that event happening, it follows that:


 * P(5-Star Focus that is green) = 3% * 1/4 = 0.75%
 * P(5-Star that is green) = 3% * 14/80 = 0.525%
 * P(4-Star that is green) = 58% * 18/94 ≈ 11.1%
 * P(3-Star that is green) = 36% * 9/49 ≈ 6.6%

Given that the orb is already green because the player is chasing Ike: Brave Mercenary,


 * ≈ 0.75% / (0.75%+0.525%+11.1..%+6.6..%) ≈ 3.95%

Similar calculations can be done for the other Focus units.

Statistics
The tables below shows some statistics for the current summoning pool. Calculations are done using these appearance rates: Percentages are rounded. These tables assume the distribution of Focus Heroes is 1 for each color, the results may vary depending on the color ratio of focus units.

The meaning of each tab is explained:
 * Appearance rate: The chance to summon a specific Hero in a rarity pool in the next randomly selected orb, ignoring color. Multiply this number by 5 to get the chance that the specific Hero will even show up in a summoning session. This rate is independent of color distribution of units in other rarity pools.
 * Unit count: Number of units in a rarity pool with a color.
 * Rate | Orb Color: The chance to summon a specific Hero given that their orb color has appeared and is being summoned from. This rate is dependent on color distribution of units in all the pools.
 * Failure to appear: The chance that an orb color will not appear at all in a summoning session.