Catch rate

Each species of Pokémon has a catch rate inherent to all its members. Catch rates are out of a maximum of 255. When a Poké Ball is thrown at a wild Pokémon, the game uses a formula based on its current health, any status effect it may have, and that Pokémon's catch rate, to determine the chances of catching that Pokémon.

Approximately, the probability of catching a Pokémon starts with the species' catch rate divided by 255. Then it is multiplied with the following factors:

• The health of the Pokémon (relative to full health), which can create a penalty of up to ⅓×.
• The type of Poké Ball, which can multiply up the probability by some ×.
• The status of the wild Pokémon, i.e. 2× for sleep or freeze, and 1.5× for others.

(If the multiplications cause this calculation to become greater than 1, then the wild Pokémon is assured to be caught.)

Exact formula

The exact formula:

File:Catch formula 1.png

Where

• HP_max is the number of hit points the Pokémon has at full health,
• HP_current is the number of hit points the Pokémon has at the moment,
• rate is the catch rate of the Pokémon,
• bonus_ball is the multiplier for the Poké Ball used, and
• bonus_status is the multiplier for any status ailment the Pokémon has (2 for sleep and freeze, 1.5 for paralyze, poison and burn).

Given this formula, the maximum value for a (if the Pokémon could have 0 HP) would be catch rate × bonus_ball × bonus_status. The minimum value for a (for a Pokémon with full health) would be ⅓ × catch rate.

If a is greater than or equal to 255, then the Pokémon is caught. If not, then calculate b as follows:

File:Catch formula 2.png

Then generate 4 random numbers between 0 and 65535, inclusive. If the random numbers are less than or equal to b, then the Pokémon is caught; otherwise the ball shakes n times, where n is the number of random numbers that are less than b. Note that b ≥ 65535 if a ≥ 255.

Therefore, the probability p of catching a Pokémon, given the values a and b calculated above, is:

File:Catch formula 3.png

The second expression for p may be expanded as follows:

File:Catch formula 3 expansion.png

Since (2¹⁶ - 1)⁴ ≈ 2⁶⁴, we can approximate p with the following expression:

File:Catch formula 3 approximation.png

The percentage error in this approximation approaches 0 as a approaches 255, and does not exceed 0.02%.

For a constant probability p, the probability P that a player can capture the Pokémon with no more than r tries is:

File:Catch formula 4.png

Note that this is the cumulative probability function for a geometric distribution. The expected value of r is 1/p, that is to say, on average, a Pokémon that can be caught with probability p will be caught with 1/p tries.

The inverse problem, the number of tries, r, needed to have a probability P of capturing a Pokémon is:

File:Catch formula 5.png

Trivia

• If the HP of a Pokémon to be captured is reduced to 1, usually by way of False Swipe or Tricking a Focus Sash onto it and using a move that would normally OHKO, such as Fissure, then only 2 would be subtracted from the part of the formula in the brackets. This makes it so that Pokémon with higher HP stats (such as Chansey) are easier to capture when their HP is reduced, despite low catch rates compared to others.

See also

• List of Pokémon by catch rate

References

• ポケットモンスター情報センター　2号館: ボール