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The formula for Pokémon damage is an algebraic formula to compute the range of damage an attack can inflict in the Pokémon series of video games. The formula has become complicated in the newer games, but has retained the same basic structure.
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The formula
The formula for Pokémon Ruby and Sapphire is:
<math>{ERSM \over 50}\left({AP \over 50D} \left({L \over 5} + 1 \right) + 1\right)<math>
- E = Effectiveness factor (0.25, 0.5, 1, 2, or 4) - Multiplier for the resistance of the defending Pokémon to the type of the attack used. Some types are immune to certain attacks, which can cause this value to be 0 thus negating all damage.
- R = A random number between 85 and 100, inclusive.
- S = Same Type Attack Bonus - If a Pokémon uses an attack that matches one of its types, this bonus factor is equal to 1.5; otherwise this is 1.
- M = Extra modifier - if certain conditions (commonly involving a Pokémon's Ability, a Ruby/Sapphire invention) are met, a further modifier is multiplied within the formula.
- A = (Special) Attack - The relevant value of the attacking Pokémon's power. Attacks in Pokémon are considered either physical or special based on their type; if the attack is physical, the Attack statistic is used, otherwise the Special Attack statistic is used. Water, Ice, Grass, Fire, Dark, Psychic, Electric and Dragon attacks are considered Special attacks; all others are physical. This value takes into account both the actual statistic and any moves that have modified its value.
- P = Power of attack used, as shown in the attack's description.
- D = defense / special defense - The defense statistic of the defending Pokemon. If the attack is physical, Defense is used, otherwise Special Defense is used. This, too, takes into account both the statistic and any value modifiers.
- L = Attacker's level - Between 1-100 based on the experience points of the attacking Pokémon.
Further explanation
Power vs. accuracy and PP
All attacks have a power value. In general, a more powerful attack will either be less accurate or have fewer PP (power points, the energy devoted to an attack and therefore the number of times it can be used before recharging) than a less powerful attack. As an example, Tackle is a Normal attack with a base power of 35, 35 PP and a 95% accuracy, whereas Thunder has a base power of 120, starts with 10 PP, and has a 70% accuracy (although using Rain Dance increases this accuracy to 100%). Multiplying the accuracy by the minimum and maximum results of the formula gives the average range of damage a move can inflict.
Effectiveness
The effectiveness of attacks varies depending on type resistance and weakness. Most of it is immediately understandable (fire is strong against grass, grass against water, and water against fire) but some are present more for gameplay balance and require a strech of the imagination to explain. (rock is weak vs. ground because rock is strong on flying types and ground moves don't affect flying types).
If a Pokémon has two types, its weaknesses can cancel out or present it with compounded weaknesses/resistances. Scizor, a Bug/Steel type, will have a compounded weakness to Fire because both Bug and Steel are defensively weak to Fire. Although Scizor's Steel side is weak to Ground moves, its Bug side is resistant to those moves, causing the weaknesses to cancel out and make Scizor defensively neutral to Ground-type attacks. Both of Scizor's types also afford it protection to Grass-type moves, making those moves only 1/4 as effective as they would otherwise be.
A fourth scenario is when one type of a Pokemon is immune to a certain type of move. In the case of Swampert, a Water/Ground type, because Electric moves don't affect Ground types Swampert will not take damage from Thunderbolt despite Water's weakness to Electric moves.
In short, weakness, resistance and immunity multiply the damage respectively by 2, 0.5, and 0. If the defending Pokčmon has two types, the two values are simply multiplied together. Therefore: weakness x weakness = 4; resistance x weakness = 1; resistance x resistance = 0.25; anything x immunity = 0.
Abilities
Every Pokémon in Ruby and Sapphire has an Ability; most available abilities affect statistics or damage during battle. For example, Blaze, Flash Fire, Guts, Hustle, Overgrow, Plus, Minus, Swarm and Torrent all increase the power of certain or all attacks by 1.5 under certain conditions. Blaze, Overgrow, Swarm and Torrent are all activated when HP falls below 1/3 of its full value, and only affect Fire-, Grass-, Bug- and Water-type moves, respectively. Conversely, Levitate causes the value of M to be 0 for Ground-based moves, as if the Pokémon was a Flying-type (and therefore the value of E would be 0), while Thick Fat causes M to equal 0.5 when the attack is Ice- or Fire-based.
Other considerations
Calculated attacks are those which disregard most of a Pokémon's statistics in damage calculation, instead dealing damage either by a set amount or based on a formula different than the above. These attacks include Bide, Counter, Dragon Rage, Fissure, Guillotine, Horn Drill, Mirror Coat, Nightshade, Psywave, Seismic Toss, Sonic Boom and Super Fang. Depending on the move, type weakness/resistance is ignored; Fissure, being a Ground attack, cannot work against Flying Pokémon, but Bide will work against all Pokemon despite its Normal type.
Critical hits are considered to "cut through" all statistic modifiers; the values of A and D become equal to the relevant statistics for this attack, without consideration for their modifiers.