Keelhaul and Vicious Chop

Keelhaul (ヒャッホーチョップ, Hyahoo Chop) and Vicious Chop (ホットチョップ, Hot Chop) are related Mars Psynergies introduced in Golden Sun: Dark Dawn that are functionally identical but have different levels of power.

Basic description
Keelhaul and Vicious Chop are offensive, single-target Psynergies that are Attack-dependent, meaning characters with higher Attack ratings will deal more damage with these attacks. In addition, the caster's Mars Power and the target's Defense and Mars Resistance all factor into the damage dealt.

Visually, Keelhaul appears as the user launching a normal physical attack that knocks the target back a fair distance. Vicious Chop appears as the user launching a normal physical attack that is slightly delayed in midair before hitting the target, and knocks the target back a fair distance while a glowing red aura permeates the zone.

Damage Calculation
Elemental physical attacks such as Keelhaul and Vicious Chop use the damage dealt by the attacker's standard physical attack as the base damage to be later modified. The total amount of damage dealt by a normal physical attack is half the difference between the attacker's Attack statistic and the target's Defense statistic, as this equation shows:


 * base damage = (User's Attack - Enemy's Defense) / 2

Keelhaul's attack takes this base damage value and uses it in the following equation:


 * final damage = (base damage + bonus damage) * (1 + (User's Mars Power - Enemy's Mars Resistance) / 400)

To word this in prose, Keelhaul and Liquefier take the base damage of the user's normal physical attack, add a set amount of bonus damage to that, and then this result is modified by how much higher or lower the user's Mars Power is than the target's Mars Resistance. The difference between the user's Mars Power and the target's Mars Resistance is divided by 400, then 1 is added to this, resulting in what can be called the "elemental damage multiplier". This number is what the Psynergies' damage is multiplied by.

For example, if an Adept with an Attack rating of 300 and a Mars Power of 150 casts Keelhaul on a monster with a defense of 100 and a Mars Resistance of 50:
 * damage = ((Attack - Defense) / 2 + bonus damage) * (1 + (Power - Resistance) / 400)
 * damage = ((300 - 100) / 2 + 34) * (1 + (150 - 50) / 400)
 * damage = ( / 2 + 34) * (1 + / 400)
 * damage = ( + 34) * (1 + )
 * damage = *
 * damage = 167

Therefore, a Keelhaul cast under these circumstances would deal 167 points of damage.

Availability
Keelhaul and Vicious Chop are exclusive to the Pirate class series, and thus the series is unique to Eoleo. Eoleo can access the class when he has no or only Mars Djinn Set to him.

Both Keelhaul and Vicious Chop are learned at level 12. However, only Keelhaul is available at first: Many Psynergies are only available to the more advanced versions of a class, and Vicious Chop is no exception. What separates Keelhaul and Vicious Chop from most Psynergies is that Vicious Chop replaces Keelhaul. To access Vicious Chop, Eoleo must have at least six Mars Djinn set, changing him to either the Pirate King or Hull Reaver class.

Analysis
General: Keelhaul's damage output is roughly the same as other elemental physical attack Psynergies like Ragnarok and Heat Wave, but in practice Keelhaul's damage is slightly lower than Ragnarok due to the lower Attack multipliers of the Pirate class series as compared to the Squire class series. Keelhaul is roughly on-par with a mid-game Unleash (with the main difference of costing Psynergy Points instead of activating at random) and is more valuable the earlier it is acquired. Even in the middle and late stages of a game, Keelhaul may be preferred over Unleashes due to its reliability. Vicious Chop, by comparison, may not be as practical as Keelhaul: Despite the increased damage output, Vicious Chop's higher PP cost reduces the number of times it can be cast, especially considering the Pirate classes' low PP pool, though the cost is less than either Odyssey and Liquefier. It should also be noted that Vicious Chop's added damage is slightly lower than comparable Psynergies.

Vs. Djinn: Many, though not all, offensive Djinn use a damage multiplier instead of a fixed damage increase, in addition to the Power - Resistance multiplier. As a result, these Djinn have the potential to be much stronger than Keelhaul and Vicious Chop, especially in the later stages of a game when the Adept in question has a higher Attack rating. However, unleashing Djinn in battle places them in Standby, resulting in two main disadvantages. First, Djinn must be Set to affect a character's class; unleashing a Djinni may result in lower stats across the board, including Attack and Power, reducing the damage dealt by subsequent attacks. Second, a Djinni's effect cannot be used again until that Djinni is re-Set, which means either wasting a turn manually Setting the Djinni or using it to perform a Summon, after which the Djinn used must spend several turns Recovering before they automatically Set themselves. Either way, offensive Djinn cannot be repeatedly used as easily as Psynergy, making Keelhaul and Vicious Chop more feasible for long-term combat. Alternatively, players may choose to combine both approaches: Unleash several offensive Djinn, perform a Summon, then use Keelhaul and/or Vicious Chop to continue dealing damage while the Djinn are in Recovery.

By Game
Golden Sun: Dark Dawn: By the time Eoleo joins the party, the player will have access to enough Mars Djinn to allow Eoleo to enter the Pirate King stage of his class, giving immediate access to Vicious Chop. Due to changes to the Unleash system, Keelhaul and Vicious Chop are among the most reliable offensive options available to Eoleo, should he remain in his base class. While slightly weaker than Tyrell's Liquefier, Eoleo's Vicious Chop is less expensive and so can see slightly more use. It is particularly useful against the random encounters of the Great Eastern Sea, as well as the Star Magician and the Ogre Titans. New methods of restoring PP, such as Khiren Water and Ginseng reduce the strain on Eoleo's PP pool.

Cultural References
Keelhaul is a nautical term that refers to a punishment given to sailors at sea, where they were dragged under the ship's keel. The Psynergy itself, as well as the class it is unique to, likely references the fact that keelhauling eventually became associated with pirates.