User blog:Linathan/Mechanic Spotlight: Status Ailment Effect on Attacks

Status Ailment Effects are buffs that were introduced in the Dragon War batch, which included Arus, Belfura, Ragshelm, Shera, Priscilla, and Borgeus. Priscilla and Borgeus were the first units to utilize these type of effects.

These buffs add certain status ailments to all allies' attacks, allowing them to inflict the given status ailments with a fixed probability.

Let's take Magnazorda for example. Its SBB provides the following:

[Super Brave Burst] Meleg Drake (17 combo powerful Fire attack on all foes, boosts allies' BB gauge, additional attack at turn's end for 3 turns & adds Injury, Weak to attack for 3 turns ; Cost: 24 BC, DC: 17 BC)

Magnazorda gives all allies each a 10% chance of inflicting Injury and Weakness when attacking. This may seem low, but when using all six units to attack, the probability is significantly higher.

Statistics & Calculations
In a statistics standpoint, a proper way to calculate the probability that a certain event that combines a number of trials with a number of successes will occur is by using a binomial cumulative distribution. These type of distributions are discrete distributions of the number of successes in a sequence of a given number of independent yes or no experiments, all of which rely on a given probability.

There are three different variables when talking about binomial cumulative distributions: n, p, r. They each represent the following:


 * n represents the total number of trials, or the number of units attacking in this case.


 * p represents the probability, which is the value given for the provided status effect.

In this case, we want to find the probability that at least one unit will inflict status ailments because you only need to inflict the status ailment once in order for it to take effect. Because of this, our base formula is as followed:
 * r represents the number of successes.

1-binomcdf(n,p,0)

The r-value is 0 since we want to find the probability that none of the units succeed. The entire binomcdf function is then subtracted from 1 to get the "at least" effect.

Let's take Magnazorda as an example. Let's say that we attack using all six units with Magnazorda's SBB buffs applied.
 * n is set to 6, because we are using six units to attack.
 * p is set to 0.10, because that is the probability at which units inflict Injury.

By plugging those values into the formula, we get the following:

1-binomcdf(6, 0.10, 0)

Entering this into the calculator yields a value of 0.4685589998. This means that you have a 47% chance of inflicting Injury on your enemies. Not bad?

You can find binomcdf on TI-83 and TI-84 calculators by following these steps: What happens if only five units attack? Simply change the n-value to 5.
 * Press 2nd
 * Press VARS
 * Scroll down until you see binomcdf(

1-binomcdf(5, 0.10, 0)

Entering this into the calculator yields a value of 0.40951. This means that you have a 41% chance of inflicting Injury on your enemies.

Leader Skills
Leader Skills work the exact same way as the buffs provided by the units that are capable of utilitzing such effects. It is also important to note that status ailment effects provided by BB/SBB are stackable with Leader Skills.

Let's take Tora as an example. The following lists her Leader Skill and Super Brave Burst:

[Leader Skill] Epidemic God's Possession (High chance of inflicting a random status ailment when attacking & slightly absorbs HP when attacking )

[Super Brave Burst] Demon Thorn Imprisonment (18 combo Earth elemental attack on all enemies, adds Poison, Weak, Curse and Paralysis effect to attack for 3 turns & partial HP drain ; Cost: 22 BC, DC: 18 BC)

Let's only pay attention to Weakness. There's a 15% chance that each unit will inflict Weakness coming from both Tora's Leader Skill and Super Brave Burst. With those effects active, the probability becomes 30%.

Simply entering 1-binomcdf(6, 0.3, 0) into the calculator, given that six units are attacking with the effects active, yields a value of 0.882351. This means that there is an overall probability of 88% that you will inflict Weakness on enemies.

Random AoE Attacks
Random AoE attacks have set targets when used. For example, Eric's SBB already knows who to target the moment his SBB is activated. Eric's SBB description is as followed:

[Super Brave Burst] Demons and Angels (15 combo random Dark elemental attack on all enemies & adds Light element to attack and gradually recovers BB gauge for 3 turns; Cost: 20 BC, DC: 15 BC)

For enemies that have been targeted, the formula is still applied as normal. Each hit does not have a probability of inflicting status ailments when under the effect. Eric is still treated as one unit. Regardless of using six units that have random AoE attacks to attack, the n-value is still 6.

Conclusion
Understand the basics of binomial cumulative distributions and how I use them in Unit Spotlights like Tora, Fadahl, Xie'Jing, and more? It's fine if you don't, but it's important to understand that the probability is significantly higher when you have multiple units under the effect attacking.

Comment below on what you think about status ailment effects! Have you taken Statistics before? Leave them in the comments below!

Check out my list of analyses in [http://bravefrontierglobal.wikia.com/wiki/User_blog:Linathan/Spotlights:_Table_of_Contents! Spotlights: Table of Contents!]

Check out the Unit Spotlights of units that utilize status ailment effects on attacks:
 * Rose Empress Tora
 * Radiant Virtue Fadahl
 * Temptress Xie'Jing
 * Inferno Wings Magnazorda