Heat Wave and Liquefier

Heat Wave (ヒートバーナー, Heat Banner) and Liquefier (ルークファイエル, Liquefier) are related Mars Psynergies featured throughout the Golden Sun series that are functionally identical but have different levels of power. They are among the strongest offensive Psynergies in the series and, up through Golden Sun: Dark Dawn, are only available to Warrior-style Mars Adepts.

Basic description
Heat Wave and Liquefier 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, Heat Wave resembles a charged horizontal blast of fire being shot directly at the enemy. In Golden Sun and The Lost Age, Heat Wave is resembles a sheet of flame. In Dark Dawn, Heat Wave is more concentrated, resembling a beam of fire.

Unlike Odyssey, which is similar in appearance to its predecessor, Liquefier looks vastly different from Heat Wave. A group of rings seem to go into the user, and after a sound like an explosion, a multitude of long shafts of fire stream out from the ground beneath his feet, disappear briefly, then rain down upon his target.

Damage Calculation
Elemental physical attacks such as Heat Wave and Liquefier 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

Heat Waves'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, Heat Wave 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 Heat Wave 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 + 33) * (1 + (150 - 50) / 400)
 * damage = ( / 2 + 33) * (1 + / 400)
 * damage = ( + 33) * (1 + )
 * damage = *
 * damage = 166

Therefore, a Heat Wave cast under these circumstances would deal 166 points of damage.

Availability
Heat Wave and Liquefier are exclusive to the Guard class series, and thus is unique to Garet and Tyrell. Both Adepts can only access the series if all set Djinn are Mars Djinn.

Both Heat Wave and Liquefier are learned at level 12. However, only Heat Wave is available at first: Many Psynergies are only available to the more advanced versions of a class, and Liquefier is no exception. What separates Heat Wave and Liquefier from most Psynergies is that Liquefier replaces Heat Wave. To access Liquefier, the appropriate Adept must have at least six Mars Djinn set, changing him to either the Champion or Hero class.

It should be noted that Liquefier is not introduced until The Lost Age, so in the original Golden Sun, even if he reaches the Champion class, Garet will only be able to use Heat Wave.

Analysis
General: Heat Wave's damage output is roughly the same as other elemental physical attack Psynergies like Ragnarok and Diamond Dust, but in practice Heat Wave's damage is slightly lower than Ragnarok due to the lower Attack multipliers of the Guard class series as compared to the Squire class series. Heat Wave 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, Heat Wave may be preferred over Unleashes due to its reliability. Liquefier, by comparison, may not be as practical as Heat Wave: Despite the increased damage output, Liquefier's high PP cost greatly reduces the number of times it can be cast, especially considering the Guard classes' low PP pool.

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 Heat Wave and Liquefier, 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 statistics 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 Heat Wave and Liquefier more feasible for long-term combat. Alternatively, players may choose to combine both approaches: Unleash several offensive Djinn, perform a Summon, then use Heat Wave and/or Liquefier to continue dealing damage while the Djinn are in Recovery.

By game
Golden Sun: Heat Wave will generally be learned by the time players must battle Saturos at Mercury Lighthouse. While useful on the Lighthouse's monsters, it is of little use in the boss battle due to Saturos's high Mars Resistance. Heat Wave will be more useful in the battle against the Kraken. However, by the end of the game, Heat Wave once again drops in usefulness, as the final bosses have high Mars Resistance.

Golden Sun: The Lost Age: Heat Wave and its upgraded form, Liquefier, are unavailable until Garet joins the party late in the game. By this time, there are few enemies that are weak to Mars; combined with Liquefier's high PP cost and the powerful unleashes available, both will see less use than before. However, Liquefier can be useful in the battle against a bonus boss, the Star Magician, which has a major Mars weakness that can be exploited.

Golden Sun: Dark Dawn: Heat Wave will be learned sometime while exploring the Ei-Jei region. Heat Wave is useful against both the monsters of Barai Temple and against the Ice Queen of the Harapa Ruins. Liquefier will be acquired in the Morgal region, and is useful against Blados. In general, changes to the Unleash system make the Psynergies a more reliable form of damage. Both are also a good weapon against the random encounters of the Great Eastern Sea. In addition, new methods of restoring PP reduce the impact to Tyrell's low PP pool.