Until recently, the algorithms and equations used in EarthBound have been shrouded in scary machine code and undocumented assembly code dumps. But luckily, a few awesome people have showed up to save the day and provide us with some very cool and interesting info. The following are how the game makes its decisions and/or makes its various calculations.
News:
MOTHER 2 / EarthBound Game Equations:
General Battle Equations & Algorithms:
Instant Wins
In some cases, when you get into a fight with a weak enemy, you automatically win without going into battle. This is based on your speed, offense, and status. Only the chosen four matter for this; NPCs such as Flying Man are not counted.
You can't instantly win in a red swirl or in a fight triggered by dialogue (such as a boss fight). If the number of enemies is greater than the number of characters who aren't unconscious, diamondized, paralyzed, nauseous, poisoned, and don't have a sunstroke or a cold (as well as 2 other statuses I haven't figured out), you can't instantly win.
In a black swirl, the highest speed among enemies is compared to the lowest speed among your current party members (even if unconscious). Each enemy's HP+defense is then compared to the lowest offense among your current party members (even if unconscious). If your party's stats are greater (not equal) in both cases, you instantly win the fight.
In a green swirl, your characters who do not suffer from the aforementioned statuses are sorted by offense in descending order, and the enemies are sorted by HP in descending order. In turn, each character "attacks" the first enemy which is still "alive", dealing exactly 2*offense-defense "damage". If every enemy is "killed" this way, you instantly win the fight.
Turn Order
At the beginning of each turn, each character has their speed adjusted by +/- 50% to determine the turn order. In the case of a tie, later characters act first, and enemies act before allies. If an enemy tries to steal, they will always act last.
Auto Fight
Paula and Jeff will always attack a random enemy. If Ness/Poo is not feeling strange or unable to concentrate, he will attempt to use PSI if applicable. The possible PSI commands for Ness and Poo in Auto Fight are used in the following priority order. As soon as an action is reached which is possible and fits the conditions, it is used and the rest are not considered. If both Ness and Poo use PSI, they will not target the same character. Lifeup Omega isn't considered to target anyone for this purpose. When more than one character can be targeted, the character with the lowest absolute HP has priority. A character is considered to be at low HP if his/her HP is less than 1/4 of maximum.
1. Lifeup Omega if more than one PC is alive and all have low HP
2. Lifeup gamma on someone with low HP
3. Lifeup beta on someone with low HP
4. Lifeup alpha on someone with low HP
5. Healing Omega on an unconscious character
6. Healing gamma on a paralyzed character
7. Healing gamma on a diamondized character
8. Healing gamma on an unconscious character
9. Healing beta on a poisoned character
10. Healing beta on a nauseated character
11. Healing beta on a crying character
12. Healing beta on a character who is feeling strange
13. Healing alpha on a character with a cold
14. Healing alpha on a character with sunstroke
15. Healing alpha on a sleeping character
If none of these options are available, Ness/Poo will attack a random enemy.
Run Away
The probability of successfully running away from a fight is (highest speed among PCs - highest speed among enemies + 10*turn number)%. Some enemies prevent you from running away regardless of your speed.
Calling for help
The odds of help arriving is (maximum number of enemy type - number of enemy type)/(maximum number of enemy type) * 205/256. (205/256 is probably an approximation of 4/5.) If the enemy being called doesn't exist in the current formation, help will not arrive. This is why there are formations with 0 of an enemy (such as 1 Skate Punk, 0 Pogo Punk, 0 Yes Man Junior).
General note about randomness
Whenever numbers are adjusted by +/- 25% or +/- 50%, the result follows a pyramid-shaped distribution. The number is more likely to be near the middle of the range than near either end, when considering intervals of equal length.
In some cases, when you get into a fight with a weak enemy, you automatically win without going into battle. This is based on your speed, offense, and status. Only the chosen four matter for this; NPCs such as Flying Man are not counted.
You can't instantly win in a red swirl or in a fight triggered by dialogue (such as a boss fight). If the number of enemies is greater than the number of characters who aren't unconscious, diamondized, paralyzed, nauseous, poisoned, and don't have a sunstroke or a cold (as well as 2 other statuses I haven't figured out), you can't instantly win.
In a black swirl, the highest speed among enemies is compared to the lowest speed among your current party members (even if unconscious). Each enemy's HP+defense is then compared to the lowest offense among your current party members (even if unconscious). If your party's stats are greater (not equal) in both cases, you instantly win the fight.
In a green swirl, your characters who do not suffer from the aforementioned statuses are sorted by offense in descending order, and the enemies are sorted by HP in descending order. In turn, each character "attacks" the first enemy which is still "alive", dealing exactly 2*offense-defense "damage". If every enemy is "killed" this way, you instantly win the fight.
Turn Order
At the beginning of each turn, each character has their speed adjusted by +/- 50% to determine the turn order. In the case of a tie, later characters act first, and enemies act before allies. If an enemy tries to steal, they will always act last.
Auto Fight
Paula and Jeff will always attack a random enemy. If Ness/Poo is not feeling strange or unable to concentrate, he will attempt to use PSI if applicable. The possible PSI commands for Ness and Poo in Auto Fight are used in the following priority order. As soon as an action is reached which is possible and fits the conditions, it is used and the rest are not considered. If both Ness and Poo use PSI, they will not target the same character. Lifeup Omega isn't considered to target anyone for this purpose. When more than one character can be targeted, the character with the lowest absolute HP has priority. A character is considered to be at low HP if his/her HP is less than 1/4 of maximum.
1. Lifeup Omega if more than one PC is alive and all have low HP
2. Lifeup gamma on someone with low HP
3. Lifeup beta on someone with low HP
4. Lifeup alpha on someone with low HP
5. Healing Omega on an unconscious character
6. Healing gamma on a paralyzed character
7. Healing gamma on a diamondized character
8. Healing gamma on an unconscious character
9. Healing beta on a poisoned character
10. Healing beta on a nauseated character
11. Healing beta on a crying character
12. Healing beta on a character who is feeling strange
13. Healing alpha on a character with a cold
14. Healing alpha on a character with sunstroke
15. Healing alpha on a sleeping character
If none of these options are available, Ness/Poo will attack a random enemy.
Run Away
The probability of successfully running away from a fight is (highest speed among PCs - highest speed among enemies + 10*turn number)%. Some enemies prevent you from running away regardless of your speed.
Calling for help
The odds of help arriving is (maximum number of enemy type - number of enemy type)/(maximum number of enemy type) * 205/256. (205/256 is probably an approximation of 4/5.) If the enemy being called doesn't exist in the current formation, help will not arrive. This is why there are formations with 0 of an enemy (such as 1 Skate Punk, 0 Pogo Punk, 0 Yes Man Junior).
General note about randomness
Whenever numbers are adjusted by +/- 25% or +/- 50%, the result follows a pyramid-shaped distribution. The number is more likely to be near the middle of the range than near either end, when considering intervals of equal length.
Bash/Shoot and Defend Equations & Algorithms:
Physical Attacks: Attacks are dealt with as follows:
1. Miss
Each weapon and NPC/enemy has a miss rate. Unarmed PCs have a miss rate of 1/16. Crying and/or nausea will increase this miss rate by 8/16. If the weapon misses, skip the remaining steps.
2. SMAAAASH!
With the Bash command or Bash-like enemy/NPC attacks, the probability of a SMAAAASH! is equal to guts/500 or 1/20, whichever is greater. If a SMAAAASH is successful, it deals 4*offense-defense damage, and skip the remaining steps. (Yes, even step 5.) This damage is still affected by defending if applicable. If the target had a physical shield, it will be depleted.
3. Dodging
The target has a (2*target speed - attacker speed)/500 chance of dodging the attack. If the enemy dodges, skip the remaining steps.
4. Damage
The attack will deal (attack level * offense - defense) +/- 25% damage. Bash, Shoot, and enemy/NPC projectile attacks have attack level 2, while Bash-like attacks can attack levels 1, 2, 3, and 4, depending on the attack.
5. Status
If the attack was Bash or a Bash-like enemy/NPC attack, the target will stop feeling strange if it was feeling strange.
Defend
Defending halves the damage taken from some attacks.
1. Miss
Each weapon and NPC/enemy has a miss rate. Unarmed PCs have a miss rate of 1/16. Crying and/or nausea will increase this miss rate by 8/16. If the weapon misses, skip the remaining steps.
2. SMAAAASH!
With the Bash command or Bash-like enemy/NPC attacks, the probability of a SMAAAASH! is equal to guts/500 or 1/20, whichever is greater. If a SMAAAASH is successful, it deals 4*offense-defense damage, and skip the remaining steps. (Yes, even step 5.) This damage is still affected by defending if applicable. If the target had a physical shield, it will be depleted.
3. Dodging
The target has a (2*target speed - attacker speed)/500 chance of dodging the attack. If the enemy dodges, skip the remaining steps.
4. Damage
The attack will deal (attack level * offense - defense) +/- 25% damage. Bash, Shoot, and enemy/NPC projectile attacks have attack level 2, while Bash-like attacks can attack levels 1, 2, 3, and 4, depending on the attack.
5. Status
If the attack was Bash or a Bash-like enemy/NPC attack, the target will stop feeling strange if it was feeling strange.
Defend
Defending halves the damage taken from some attacks.
PSI Equations & Algorithms:
PSI Rockin' Miss Rate: Ness's PSI Rockin' (or whatever you named your favorite thing) misses sometimes. The probability it'll miss is calculated by:
(((2 * target's speed) - Ness's speed) / 5)%
This will give you PSI Rockin's miss percentage. Say that Ness's speed is 50, and you're fighting a Spiteful Crow, which has a speed of 77 (taken from the EBDB). Plug in those numbers and calculate it out, and you'll see that PSI Rockin' will miss 20.8% of the time, on average, in that situation.
Flash
For each enemy it hits, it causes one of several effects, depending on which Flash you used.
Flash alpha
7/8: uncontrollable crying
1/8: feeling strange
Flash beta
5/8: uncontrollable crying
1/8: feeling strange
1/8: paralysis
1/8: instant death
Flash gamma
4/8: uncontrollable crying
1/8: feeling strange
1/8: paralysis
2/8: instant death
Flash Omega
3/8: uncontrollable crying
1/8: feeling strange
1/8: paralysis
3/8: instant death
Freeze
Has a 25% chance of solidifying the target
Thunder
Thunder randomly chooses a target, then tries to affect it. The probability of Thunder working is:
(number of enemies)/4
If Thunder kills an enemy and still has some shots left, this probability will not decrease. If Thunder hits an enemy with a PSI shield, the shield will be depleted.
Magnet
Magnet drains an amount of PP in the range 2-8 with a pyramid-shaped distribution. It can't drain more PP than the target has. Magnet Omega will ignore NPCs, while alpha merely fails due to lack of PP.
Offense Up
Offense up will fail if the target is a NPC. Otherwise, it will increase the target's offense by 1/16 of its current value, rounded down and capped below at 1, up to a maximum of 5/4 of the target's unmodified offense.
Defense Down
Defense down will fail with probability luck/80, or always if it targets a NPC. If it hits, it will reduce the target's defense by 1/16 of its current value, rounded down and capped below at 1, down to a minimum of 3/4 of the target's unmodified defense.
Healing gamma
Healing gamma has a 3/4 chance of reviving an unconscious character.
This will give you PSI Rockin's miss percentage. Say that Ness's speed is 50, and you're fighting a Spiteful Crow, which has a speed of 77 (taken from the EBDB). Plug in those numbers and calculate it out, and you'll see that PSI Rockin' will miss 20.8% of the time, on average, in that situation.
Flash
For each enemy it hits, it causes one of several effects, depending on which Flash you used.
Flash alpha
7/8: uncontrollable crying
1/8: feeling strange
Flash beta
5/8: uncontrollable crying
1/8: feeling strange
1/8: paralysis
1/8: instant death
Flash gamma
4/8: uncontrollable crying
1/8: feeling strange
1/8: paralysis
2/8: instant death
Flash Omega
3/8: uncontrollable crying
1/8: feeling strange
1/8: paralysis
3/8: instant death
Freeze
Has a 25% chance of solidifying the target
Thunder
Thunder randomly chooses a target, then tries to affect it. The probability of Thunder working is:
If Thunder kills an enemy and still has some shots left, this probability will not decrease. If Thunder hits an enemy with a PSI shield, the shield will be depleted.
Magnet
Magnet drains an amount of PP in the range 2-8 with a pyramid-shaped distribution. It can't drain more PP than the target has. Magnet Omega will ignore NPCs, while alpha merely fails due to lack of PP.
Offense Up
Offense up will fail if the target is a NPC. Otherwise, it will increase the target's offense by 1/16 of its current value, rounded down and capped below at 1, up to a maximum of 5/4 of the target's unmodified offense.
Defense Down
Defense down will fail with probability luck/80, or always if it targets a NPC. If it hits, it will reduce the target's defense by 1/16 of its current value, rounded down and capped below at 1, down to a minimum of 3/4 of the target's unmodified defense.
Healing gamma
Healing gamma has a 3/4 chance of reviving an unconscious character.
Pray Formulas & Algorithms:
Praying has one of several random effects:
5/16: subtle light, heals each PC by 1/16 of maximum HP, rounded down
2/16: warm light, heals each PC by 1/8 of maximum HP, rounded down
1/16: mysterious light, restores (5 +/- 50%) PP to each PC
1/16: golden light, heals a random living PC by the difference between their maximum HP and Paula's current HP
1/16: dazzling light, same effect as Rockin beta to a random enemy
2/16: dazzling light, same effect as Flash alpha to all allies and enemies
1/16: rainbow-colored light, revives all dead allies and enemies to full HP
1/16: mysterious aroma, put all allies and enemies to sleep
1/16: heaven rending sound, make all allies and enemies feel strange
1/16: heavy air, same effect as Defense down alpha to all allies and enemies
The mysterious aroma and heaven rending sound ignore resistance to Hypnosis and Brainshock respectively.
5/16: subtle light, heals each PC by 1/16 of maximum HP, rounded down
2/16: warm light, heals each PC by 1/8 of maximum HP, rounded down
1/16: mysterious light, restores (5 +/- 50%) PP to each PC
1/16: golden light, heals a random living PC by the difference between their maximum HP and Paula's current HP
1/16: dazzling light, same effect as Rockin beta to a random enemy
2/16: dazzling light, same effect as Flash alpha to all allies and enemies
1/16: rainbow-colored light, revives all dead allies and enemies to full HP
1/16: mysterious aroma, put all allies and enemies to sleep
1/16: heaven rending sound, make all allies and enemies feel strange
1/16: heavy air, same effect as Defense down alpha to all allies and enemies
The mysterious aroma and heaven rending sound ignore resistance to Hypnosis and Brainshock respectively.
Item Equations and Algorithms:
Bottle Rockets: The probability of an enemy dodging a normal bottle rocket is:
((2 * target speed) - Jeff's speed)%
Big Bottle Rockets and Multi Bottle Rockets try to hit the enemy 5 and 20 times respectively, at 120 power. Bottle rockets can work on any enemy if you have enough speed. Criminal Caterpillar and Master Criminal worm are too fast to hit without the Rock Candy glitch, and you can't increase Jeff's speed enough to hit Clumsy Robot by the time you can battle him. Anyone else can be hit by Jeff equipped with the Rabbit's Foot.
Bombs/Bazookas
Bombs and Super Bombs will deal (90 +/- 50%) and (270 +/- 50%) damage respectively to the target. They also deal splash damage to the characters or enemies on either side of the main target, with damage equal to:
((average damage to main target)/2 +/- 50%)
(Hungry) HP-sucker: has a luck/80 chance of failing against the target, and always fails if Jeff is confused and targets himself, or his HP is rolling down to 0. If it hits, it will suck HP equal to (target's maxHP/8) +/- 50%. This does not count as damage, so it will ignore Master Belch's immunity to damage. Jeff's new HP is set by adding the amount drained to his current rolling HP.
Insecticide/Xterminator Spray: has a luck/80 chance of failing against the target, and always fails if the target isn't an enemy or isn't an insect. They deal 100 +/- 50% and 200 +/- 50% damage respectively.
Rust promoter (DX): has a luck/80 chance of failing against the target, and always fails if the target isn't an enemy or isn't metallic. They deal 200 +/- 50% and 400 +/- 50% damage respectively.
Counter-PSI:unit fails with probability luck/40, and always fails against NPCs or when the target already can't concentrate.
Shield killer: fails with probability luck/80, and always fails (irrelevantly) if the target doesn't a shield or PSI shield.
Dragonite
This deals 800 +/- 25% damage to each enemy, and is fire elemental.
Big Bottle Rockets and Multi Bottle Rockets try to hit the enemy 5 and 20 times respectively, at 120 power. Bottle rockets can work on any enemy if you have enough speed. Criminal Caterpillar and Master Criminal worm are too fast to hit without the Rock Candy glitch, and you can't increase Jeff's speed enough to hit Clumsy Robot by the time you can battle him. Anyone else can be hit by Jeff equipped with the Rabbit's Foot.
Bombs/Bazookas
Bombs and Super Bombs will deal (90 +/- 50%) and (270 +/- 50%) damage respectively to the target. They also deal splash damage to the characters or enemies on either side of the main target, with damage equal to:
(Hungry) HP-sucker: has a luck/80 chance of failing against the target, and always fails if Jeff is confused and targets himself, or his HP is rolling down to 0. If it hits, it will suck HP equal to (target's maxHP/8) +/- 50%. This does not count as damage, so it will ignore Master Belch's immunity to damage. Jeff's new HP is set by adding the amount drained to his current rolling HP.
Insecticide/Xterminator Spray: has a luck/80 chance of failing against the target, and always fails if the target isn't an enemy or isn't an insect. They deal 100 +/- 50% and 200 +/- 50% damage respectively.
Rust promoter (DX): has a luck/80 chance of failing against the target, and always fails if the target isn't an enemy or isn't metallic. They deal 200 +/- 50% and 400 +/- 50% damage respectively.
Counter-PSI:unit fails with probability luck/40, and always fails against NPCs or when the target already can't concentrate.
Shield killer: fails with probability luck/80, and always fails (irrelevantly) if the target doesn't a shield or PSI shield.
Dragonite
This deals 800 +/- 25% damage to each enemy, and is fire elemental.
Status Equations & Algorithms:
Overwriting statuses
Some combinations of statuses can't coexist. When an effect tries to add a status to someone who already has a status of the same type, the one with the lower number wins. The statuses are:
Permanent statuses:
1. Unconsciousness
2. Diamondization
3. Paralysis
4. Nausea
5. Poison
6. Sunstroke
7. Cold
Special statuses:
1. Mashroomization
2. Possession
In-battle statuses:
1. Sleep
2. Uncontrollable crying
3. Immobilization
4. Solidification
Other statuses, such as feeling strange or being unable to concentrate, are stored separately from the other statuses and can coexist freely.
Diamondization
Uses the same resistance probability as Paralysis.
Sunstroke
Approximately every 20 seconds, if you're in a desert area and you don't have any permanent status ailments other than a cold, you have a (30-guts)% chance of getting a sunstroke, with a minimum of 1%.
Homesickness
Whenever you win a battle (but not an instant win), Ness has a certain probability of becoming homesick. The probability depends on Ness's level.
Level 1-15: 0/256
Level 16-30: 3/256
Level 31-75: 2/256
Level 76-99: 0/256
If Ness is homesick, he has a 1/8 chance of losing his turn in battle.
Sleep
A sleeping character can't do anything. A sleeping character has a 1/4 chance of waking up on his/her/its turn.
Immobilization
An immobilized character can't use weapons or items, much like being paralyzed. An immobilized character has an 85% chance of becoming able to move on his/her/its turn.
Solidification
A solidified character can't do anything. A solidified character will always become able to move on his/her/its turn.
Nausea and Poison
Nausea and poison deal 20 +/- 25% damage each turn in battle and deal 10 damage every 2 seconds out of battle.
Cold and Sunstroke
Colds and sunstroke deal 4 +/- 25% damage each turn in battle and deal 2 damage every 4 seconds out of battle
Some combinations of statuses can't coexist. When an effect tries to add a status to someone who already has a status of the same type, the one with the lower number wins. The statuses are:
Permanent statuses:
1. Unconsciousness
2. Diamondization
3. Paralysis
4. Nausea
5. Poison
6. Sunstroke
7. Cold
Special statuses:
1. Mashroomization
2. Possession
In-battle statuses:
1. Sleep
2. Uncontrollable crying
3. Immobilization
4. Solidification
Other statuses, such as feeling strange or being unable to concentrate, are stored separately from the other statuses and can coexist freely.
Diamondization
Uses the same resistance probability as Paralysis.
Sunstroke
Approximately every 20 seconds, if you're in a desert area and you don't have any permanent status ailments other than a cold, you have a (30-guts)% chance of getting a sunstroke, with a minimum of 1%.
Homesickness
Whenever you win a battle (but not an instant win), Ness has a certain probability of becoming homesick. The probability depends on Ness's level.
Level 1-15: 0/256
Level 16-30: 3/256
Level 31-75: 2/256
Level 76-99: 0/256
If Ness is homesick, he has a 1/8 chance of losing his turn in battle.
Sleep
A sleeping character can't do anything. A sleeping character has a 1/4 chance of waking up on his/her/its turn.
Immobilization
An immobilized character can't use weapons or items, much like being paralyzed. An immobilized character has an 85% chance of becoming able to move on his/her/its turn.
Solidification
A solidified character can't do anything. A solidified character will always become able to move on his/her/its turn.
Nausea and Poison
Nausea and poison deal 20 +/- 25% damage each turn in battle and deal 10 damage every 2 seconds out of battle.
Cold and Sunstroke
Colds and sunstroke deal 4 +/- 25% damage each turn in battle and deal 2 damage every 4 seconds out of battle
Stat Equations & Algorithms:
Level Up
When you gain a level, the increase of stats other than HP and PP is given by the formula:
Stat gain = ((growth rate * old level) - ((stat-2) * 10)) * r/50
r is given by one of the following:
* If the stat is vitality or IQ, and the new level is 10 or lower, r=5.
* Otherwise, if the new level is divisible by 4, r is a random number from 7 to 10.
* Otherwise, r is a random number from 3 to 6.
HP and PP are based on vitality and IQ respectively. HP tries to increase to 15*vitality, and PP tries to increase to 5*IQ normally or 10*IQ for Ness after Magicant. If either of these results in a gain of less than 2, the stat instead gains by a random number in the range 1-3 (HP) or 0-2 (PP).
When you gain a level, the increase of stats other than HP and PP is given by the formula:
r is given by one of the following:
* If the stat is vitality or IQ, and the new level is 10 or lower, r=5.
* Otherwise, if the new level is divisible by 4, r is a random number from 7 to 10.
* Otherwise, r is a random number from 3 to 6.
HP and PP are based on vitality and IQ respectively. HP tries to increase to 15*vitality, and PP tries to increase to 5*IQ normally or 10*IQ for Ness after Magicant. If either of these results in a gain of less than 2, the stat instead gains by a random number in the range 1-3 (HP) or 0-2 (PP).
