How Damage is Calculated in Pokémon Red, Yellow, and Blue (RBY / Gen 1)
The battle damage formula in Generation 1 Pokémon (Red, Blue, Yellow, Green) is famous for its quirks, bugs, and unique mechanics. Unlike modern Pokémon games (Gen 2 through Gen 9) where Special Attack and Special Defense are separate statistics and damage uses a smooth 85%–100% distribution, Gen 1 executes mathematical integer division on the Game Boy’s 8-bit Z80-derived CPU.
The Unified Special Stat
In Gen 1, there was only one "Special" stat. It served as both your attacking potency with Special moves and your damage resistance against enemy Special moves.
Speed-Based Critical Hits
Critical hits were calculated directly from a Pokémon's Base Speed ($\text{Speed} / 512$). Fast Pokémon like Persian, Alakazam, and Tauros landed critical hits relentlessly.
The 39 Discrete Damage Rolls
Instead of continuous randomization, Gen 1 multiplied damage by a random integer $R$ from 217 to 255 inclusive, divided by 255, creating exactly 39 possible damage numbers.
Physical vs Special Move Classification by Type
Prior to Generation 4 (Diamond & Pearl), moves were not classified individually as Physical or Special. In Pokémon RBY, whether a move was Physical or Special was determined solely by its elemental type:
Physical Types (Use Attack & Defense)
Normal, Fighting, Flying, Poison, Ground, Rock, Bug, Ghost.
(e.g., Hyper Beam, Earthquake, Shadow Ball did not exist yet)
Special Types (Use Unified Special Stat)
Fire, Water, Grass, Electric, Psychic, Ice, Dragon.
(e.g., Surf, Thunderbolt, Blizzard, Psychic)
How Critical Hits Work in Gen 1: Level Doubling & The Stat Ignore Mechanic
In Generation 1, critical hits behave unlike any other generation:
- Level is Doubled in the Formula: Instead of multiplying final damage by 2.0× or 1.5×, the Game Boy formula doubles the attacker's level $(2 \times \text{Level})$. At Level 100, the formula calculates damage as if the Pokémon were Level 200! This results in roughly a 1.95× to 1.98× effective damage boost.
- All Stat Boosts are Ignored: A critical hit ignores the defender’s positive stat stages (e.g. +2 Defense from Barrier) and defensive screens (Reflect / Light Screen). However, a critical hit also ignores the attacker’s own positive stat stages! If you used Swords Dance (+2 Attack) and then scored a critical hit, the game ignores your +2 Swords Dance boost!
- High Critical-Hit Moves: Moves like Slash, Razor Leaf, Crabhammer, and Karate Chop use the formula:
Crit Rate = min(255, Base Speed × 8) ÷ 256.
For Persian (115 Base Speed), $115 \times 8 = 920$, capped at 255/256 = 99.6% critical hit rate!
Infamous Gen 1 Type Quirks & Programming Glitches
- Psychic Immune to Ghost Bug: Despite the game manual and anime advertising Ghost moves as the counter to Psychic, the Game Boy code incorrectly programmed Ghost attacks to deal
0×damage against Psychic types! - Bug and Poison Mutual Super-Effectiveness: In Gen 1, Bug moves deal 2× damage to Poison Pokémon, and Poison moves deal 2× damage to Bug Pokémon.
- Ice Neutral to Fire: Fire does not resist Ice in Generation 1. Blizzard deals 1× neutral damage to Charizard and Moltres.
- The 1/256 Miss Glitch: Every move in Gen 1 (except Swift) has an internal cap of 255/256 accuracy, meaning even 100% accurate moves like Body Slam or Earthquake can randomly miss with a 1 in 256 probability (~0.39%).