Catch rate

Each species of Pokémon has a catch rate, a number out of a maximum of 255, that applies to all its members. 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, the type of ball being used, 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 by the following factors:

• The health of the Pokémon (relative to its full health), which can reduce the probability to ⅓× at full health.
• The type of Poké Ball, which can augment by some ×.
• The status of the wild Pokémon, i.e. 2× increase for sleep or freeze, and 1.5× for others.

The effects stack multiplicatively — for example, a 2× and a 3× will combine to be 6×. If the calculation ends up greater than 1, the wild Pokémon is assured to be caught.

The rarity of the Pokémon (i.e. how often it appears in the wild) is totally independent from its catch rate after it is encountered. Even rare Pokémon may have high catch rates, making them relatively easy to catch in battle, such as Nosepass (catch rate 255).

Transform will change a Pokémon's catch rate to that of the target, and is the primary purpose for the existence of catch rates for species that can not be found in the wild. However, in Generation V this is no longer true.

Exact formula

The exact formula in Generation III and onwards are based on three parts: determining the modified catch rate, calculating the "shake probability" and then performing "shake checks":

Modified Catch Rate

The modified catch rate, a, is calculated in Generation III and Generation IV is as follows:

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 (which may have been previously modified from the use of the Heavy Ball or Safari Zone modifiers),
• 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.

In Generation V, all divisions above are rounded down to the nearest multiple of 1/4096. Furthermore, two additional factors are multiplied into the above formula:

• The Dark Grass Factor: This factor, multiplied into the HP factor (3 × HP_max - 2 × HP_current above) and then rounded to the nearest multiple of 1/4096, depends on whether or not the battle occurs in dark grass (where Wild Double Battles may occur), and the number of Pokémon that have been caught in the Pokédex: if the battle is not in dark grass, this is 1. If it is, consult the following table:
• The Entralink Factor: Multiply by 1.1 if Capture Power ↑ is active, 1.2 if Capture Power ↑↑ is active, and 1.3 if Capture Power ↑↑↑, Capture Power S, or Capture Power MAX is active, and round down to the nearest multiple of 1/4096.

Multiplier	Number Caught
1	>600
3686/4096 (90%)	451-600
3277/4096 (80%)	301-450
2867/4096 (70%))	151-300
2048/4096 (50%)	30-151
1229/4096 (30%)	<30

If the modified catch rate is greater than 255, the Pokémon is automatically caught. In Generation V, a Critical Capture check is done regardless of whether the Pokémon is otherwise automatically caught.

Shake Probability

The shake probability, b, is calculated as follows in Generation III and Generation IV:

File:Catch formula 2.png

In Generation V, the formula is

b = 65536 / (255/a)^(1/4)

where all divisions and the fourth-roots are rounded to the nearest 1/4096, and the final value is rounded down to the nearest whole number.

Shake Checks

A "shake check" is done to determine whether the Pokémon is caught, and, if the Pokémon breaks free, the number of shakes that occurs before it does so.

Generation II

In Generation II, a check occurs to determine whether the Pokémon is caught outright, and shake checks are only used if this check fails to determine the number of shakes before the Pokémon breaks free. To perform a shake check, generate a random number between 0 and 255, and compare it against b. Do this three times or until the check fails, whichever comes first, to determine the number of shakes before the Pokémon breaks free.

Generation III onwards

To perform a shake check, generate random numbers between 0 and 65535, inclusive, and compare it against b; the Pokémon breaks free if the generated value is greater. In a standard capture, four checks are done, with the ball shaking for each passed check the first three times, and the Pokémon being caught if the last check passes. In a critical capture, only two checks are done.

Note that if a is 255 or greater, then b is 65535 or greater, and then the Pokémon is guaranteed to be caught.

Probability of Capture

Therefore, the probability p of catching a Pokémon in a standard capture, 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 21.2%.

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

Poké Ball effectiveness rates

Ball	Rate	Notes
Poké Ball	1×
Great Ball	1.5×
Ultra Ball	2×
Master Ball	255×	Never fails
Safari Ball	1.5×	Safari Zones only
Level Ball	1×, 2×, 4× or 8×	1× if the player's Pokémon is the same level as or a lower level than the wild Pokémon 2× if the player's Pokémon is at a higher level than the wild Pokémon but less than double it 4× if the player's Pokémon is more than double but less than four times the level of the wild Pokémon 8× if the player's Pokémon is of a level four times or more than that of the wild Pokémon
Lure Ball	1× or 3×	3× only if fishing
Moon Ball	1× or 4×	4× only if used on a Pokémon in the Nidoran♂, Nidoran♀, Clefairy, Jigglypuff or Skitty families
Friend Ball	1×
Love Ball	1× or 8×	8× only if used on a Pokémon of the same species as, but opposite gender of, the player's Pokémon
Heavy Ball	-20, +20, +30 or +40	-20 if used on Pokémon weighing less than 451.5 lbs +20 if used on Pokémon weighing between 451.5 lbs and 677.3 lbs +30 if used on Pokémon weighing between 677.3 lbs and 903.0 lbs +40 if used on Pokémon weighing more than 903.0 lbs
Fast Ball	1× or 4×	4× only if used on a Pokémon that run from battle or roaming PokémonWrong template. See Template:Sup/doc. 4× only if used on a Pokémon with a base Speed of at least 100Wrong template. See Template:Sup/doc.
Sport Ball	1.5×	Bug-Catching Contest only
Net Ball	1× or 3×	3× only if the target is a Bug- or Water-type Pokémon
Nest Ball	1× to 4×	((40 - Pokémon's level) / 10)×, minimum 1×
Repeat Ball	1× or 3×	3× only if target has been caught previously
Timer Ball	1× to 4×	((number of turns passed in battle + 10) / 10)×, maximum 4×
Premier Ball	1×
Luxury Ball	1×
Dive Ball	1× or 3.5×	3.5× only if divingWrong template. See Template:Sup/doc.Wrong template. See Template:Sup/doc. or surfing/fishingWrong template. See Template:Sup/doc.Wrong template. See Template:Sup/doc.Wrong template. See Template:Sup/doc.
Dusk Ball	1× or 3.5×	3.5× only if inside a cave or night
Quick Ball	1× or 4×	4× only if it's the first turn
Park Ball	255×	Never fails, Pal Park only
Dream Ball	255×	Never fails, Entralink only

Examples

Most legendary Pokémon have a catch rate of three. Assuming its HP is almost depleted and it is paralyzed, and Dusk Ball is used at night or in a cave, then the chance of catching the Pokémon with each ball is approximated by 3 * 3.5 * 1.5 / 255 = 15.75/255 ~ 6.2%, resulting in about 16 Dusk Balls required to catch the Pokémon on average.

If an Ultra Ball were used instead, then the chance drops to 3 * 2 * 1.5 / 255 = 9/255 ~ 3.5%, which amounts to about 28 Ultra Balls on average.

Critical capture

In Generation V, there is a chance of a critical capture, where the Poké Ball will only shake on the ground once before capture. When a critical capture occurs, the Poké Ball will pause in mid-air, shudder, and make a high-pitched whistling sound as it is thrown.

The probability of a critical capture depends of the number of Pokémon that has previously been caught in the Pokédex. First, compute the value of a (the modified catch rate), as above. Then, whether or not this value is less than 255 (above which the Pokémon is caught regardless of whether or not it is a critical capture), multiply this value by the following:

Species Caught	Multiplier
2.5	>600
2	451-600
1.5	301-450
1	151-300
0.5	31-150
0	<30

A random number is generated, and if it is less than the modified value, a critical capture occurs.

Critical captures make two shake checks instead of four, thus it appears to increase the odds of capture for Pokémon with lower catch rates (however, it also decreases the odds of capture for Pokémon with higher catch rates). However, a critical capture is not a guaranteed catch. It is possible for critical captures to fail.

Trivia

• Most legendary Pokémon have a catch rate of 3 because it assures that a is always at least 1. This might be because the final result for a is rounded down when it is calculated, and to have a catch rate of zero would result in an error when trying to calculate b.
• Some people claim to have discovered button combinations that increase a Pokémon's catch rate; this is merely idle thought, as there is no method to improve catch rates other than the methods described above.

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

This game mechanics article is part of Project Games, a Bulbapedia project that aims to write comprehensive articles on the Pokémon games.