Pokémon Crystal's capture formula (pret/pokecrystal)

A wild Pokémon's catch rate is its species' catch-rate byte, copied into wEnemyMonCatchRate when the battle loads it (45 for Bulbasaur). pokecrystal-capture/catch-rate

PokeBallEffect catches outright with a Master Ball or in the catching tutorial. Otherwise a ball's routine changes the catch rate: the Ultra Ball doubles it, and the Great, Safari, and Park Balls add half of it, each capped at 255. The Poké Ball has no routine and leaves it as it is. pokecrystal-capture/ball-modifier

{
 "kind": "ball-modifier",
 "ultra": "2C",
 "great": "C + floor(C/2)",
 "safari": "C + floor(C/2)",
 "park": "C + floor(C/2)",
 "poke": "C",
 "cap": 255,
 "master": "caught"
}

Cited by: Capture

Except with a Level Ball, PokeBallEffect scales the ball-modified rate $C^{\prime }$ by HP: $X=\max (\lfloor C^{\prime }(3M-2H)/3M\rfloor ,1)$ for max HP $M$ and current HP $H$. When $3M$ is 256 or more, both $3M$ and $2H$ are first divided by 4 (a quartered $2H$ of 0 becomes 1) and only each low byte is kept, so the formula breaks for max HP over 341. pokecrystal-capture/hp-term

{
 "kind": "hp-term",
 "maxFactor": 3,
 "hpFactor": 2,
 "quarterAbove": 255,
 "min": 1
}

Cited by: Capture

The Level Ball doubles the catch rate when the player's Pokémon is higher in level than the wild one, quadruples it when half the player's level is still higher, and multiplies it by 8 when a quarter is, capped at 255. It then skips the HP and status steps: its final rate is that multiplied catch rate alone. pokecrystal-capture/level-ball

{
 "kind": "ball-modifier",
 "levelBall": [
  2,
  4,
  8
 ],
 "cap": 255,
 "skipsHP": true
}

Cited by: Capture

Crystal adds 10 to $X$ for a sleeping or frozen Pokémon, capped at 255, and nothing for burn, poison, or paralysis: the test meant to add 5 for them reads a value the sleep-and-freeze mask has already cleared. Gold and Silver have the same code, and their disassembly notes that those three statuses were meant to rank between sleep and none. pokecrystal-capture/status-bonus

{
 "kind": "status-add",
 "sleepOrFreeze": 10,
 "burnParalysisPoison": 0,
 "intended": 5,
 "cap": 255
}

Cited by: Capture

The final rate goes into wFinalCatchRate, and one random byte at most that rate catches, so the chance is $(X+1)/256$ and a final rate of 255 always catches. This one roll decides the throw; the wobbles come after. pokecrystal-capture/roll

{
 "kind": "single-roll",
 "range": [
  0,
  255
 ],
 "catchIf": "Random() <= X"
}

Cited by: Capture

Computed, counting every value of the roll as equally likely: a Bulbasaur (catch rate 45) with max HP 100 and no status in a Poké Ball has a final rate of 15 at full HP, so 16 in 256 (6.25%), and 44 at 1 HP, so 45 in 256 (17.6%). pokecrystal-capture/chance

{
 "kind": "example",
 "catchRate": 45,
 "maxHP": 100,
 "ball": "poke",
 "status": "none",
 "fullHP": 0.0625,
 "oneHP": 0.1758
}

The ball's wobbles are drawn after the throw is decided. A caught Pokémon always gets three. On a failed throw, each of up to three wobbles happens with chance $p/256$, where $p$ is read from the first row of WobbleProbabilities whose catch rate is at least the final rate (63 for a rate of 1, up to 255 for 255). The table's comment gives nLeft/255 = (nRight/255) ** 4, so each $p$ is a fourth root, $p/255={(\mathrm{𝑟𝑎𝑡𝑒}/255)}^{1/4}$. The atlas reads that as the chance of passing one of four equal checks whose product is the catch chance; the comment doesn't say so. pokecrystal-capture/wobbles

{
 "kind": "wobble-table",
 "maxWobbles": 3,
 "rows": [
  [
   1,
   63
  ],
  [
   2,
   75
  ],
  [
   3,
   84
  ],
  [
   4,
   90
  ],
  [
   5,
   95
  ],
  [
   7,
   103
  ],
  [
   10,
   113
  ],
  [
   15,
   126
  ],
  [
   20,
   134
  ],
  [
   30,
   149
  ],
  [
   40,
   160
  ],
  [
   50,
   169
  ],
  [
   60,
   177
  ],
  [
   80,
   191
  ],
  [
   100,
   201
  ],
  [
   120,
   211
  ],
  [
   140,
   220
  ],
  [
   160,
   227
  ],
  [
   180,
   234
  ],
  [
   200,
   240
  ],
  [
   220,
   246
  ],
  [
   240,
   251
  ],
  [
   254,
   253
  ],
  [
   255,
   255
  ]
 ]
}

Cited by: Capture

Gold and Silver run the same capture code as Crystal: from the catch-rate load to the final roll, PokeBallEffect differs only in comments, and the wobble table is identical. pokecrystal-capture/gold-silver-same

About: Pokémon Gold and Silver Capture

Cited by: Capture