Catch rate

*Catch redirects here. For the concept of catching a Pokémon, see Caught Pokémon.*

Each species of Pokémon has a **catch rate** that applies to all its members. When a Poké Ball is thrown at a wild Pokémon, the game uses that Pokémon's catch rate in a formula to determine the chances of catching that Pokémon. Higher catch rates mean that the Pokémon is easier to catch, up to a maximum of 255. The formula also takes into account the following factors:

* The health of the Pokémon (relative to its full health)
* The type of Poké Ball
* Any status condition of the wild Pokémon

Certain other factors, such as the target Pokémon's level, may also factor in depending on the type of Poké Ball used or the generation.

Poké Balls that guarantee capture (the Master Ball) bypass the catching formula entirely.

## General capture method

The capture algorithms have three essential components: the modified catch rate, the "shake probability", and the "shake checks".

### Modified catch rate

The modified catch rate, *a*, is the catch rate after various factors such as weakening the Pokémon and using stronger Poké Balls are taken into consideration. A modified catch rate may never fall to 0 (that is, render a Pokémon impossible to capture), but it may cause the modified rate to fall below its original unmodified catch rate (such as from high health, Heavy Balls or Baiting in the Safari Zone).

### Shake probability

The shake probability, *b*, is a value that determines the probability that a single shake check passes.

### Shake checks

Shake checks are performed to determine whether the Pokémon will be caught or, if the Pokémon breaks free, the number of shakes that will occur before it does so.

## Capture method

### Modified catch rate

The modified catch rate, *a*, is calculated as follows:

# a

(
3
×
H

P

m
a
x

−
2
×
H

P

c
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r
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t

)
×
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b
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b
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3
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{\displaystyle a={\dfrac {(3\times HP\_{max}-2\times HP\_{current})\times rate\times bonus\_{ball}}{3\times HP\_{max}}}\times bonus\_{status}}

Where

* HPmax is the number of hit points the Pokémon has at full health,
* HPcurrent is the number of hit points the Pokémon has at the moment,
* rate is the catch rate of the Pokémon (which may be modified due to use of apricorn balls or actions in the Safari Zone),
* bonusball is the multiplier for the Poké Ball used, and
* bonusstatus is the multiplier for any status condition the Pokémon has (2.5 for sleep and freeze, 1.5 for paralyze, poison, or burn, and 1 otherwise).

The division is rounded down to the nearest multiple of 1/4096.

If a Pokémon could have 0 HP, the maximum value for *a* would be rate × bonusball × bonusstatus. For a Pokémon with full health and no status condition, and with a neutral ball used, the minimum value for *a* would be rate / 3.

*a* is capped at 255.

### Shake probability

The shake probability in Generation VI is calculated as follows:

# b

65536

(

255
a

)

0.1875

{\displaystyle b={\dfrac {65536}{\left({\dfrac {255}{a}}\right)^{0.1875}}}}

where the divisions and square roots are rounded to the nearest 1/4096

### Shake checks

To perform a shake check, a random number between 0 and 65535 (inclusive) is generated and compared to *b*. If the number is greater than or equal to *b*, the check "fails".

Before any shake checks are performed, the game checks to see if a critical capture may happen. If not, four shake checks will be performed, otherwise, only one shake check will be performed.

In a critical capture, the ball will always shake once, and the Pokémon will break free or be caught depending on the result of the shake check.

In a normal capture, the Pokémon is caught if all four shake checks succeed. Otherwise, the Poké Ball will shake as many times as there were successful shake checks before the Pokémon breaks free.

If *a* is 255 or greater, the capture will always succeed and no shake checks will be performed.

### Probability of capture

The probability *p* of catching a Pokémon—given the values *a* and *b* calculated above for each shake, then requiring all 4 shakes be passed—is approximately

(

b
65535

)

4

{\textstyle \left({b \over 65535}\right)^{4}}

, or simply

a

255

{\textstyle a \over 255}

. Due to rounding errors produced when calculating *b*, this approximation can be significantly inaccurate; for example, all *a* values greater than 200 yield the same *b* value, 65535, which results in a 99.994% chance of a successful capture.

For a constant capture probability *p*, the probability

P
(
r
)

{\textstyle P(r)}

 that a player can capture the Pokémon with no more than *r* tries is:

P
(
r
# )
1
−
(
1
−
p

)

r

{\displaystyle P(r)=1-(1-p)^{r}}

Note that this is the cumulative probability function for the random variable r, which has a geometric distribution. The expected value of the random variable *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:

# r

l
o
g
(
1
−
P
)

l
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g
(
1
−
p
)

{\displaystyle r={\dfrac {log(1-P)}{log(1-p)}}}

The divisions are rounded down to the nearest multiple of 1/4096.

## Critical capture

When a Poké Ball is thrown, a special type of capture that is much more likely to catch a Pokémon, called a **critical capture**, may occur. When a critical capture occurs, the Poké Ball will make a high-pitched whistling sound as it is thrown, then pause in mid-air, and shudder before it drops down to the ground, shaking only once on the ground before the Pokémon escapes or is caught.

The probability of a critical capture occurring depends of the number of Pokémon that have been caught in the Pokédex. First, compute the value of *a* (the modified catch rate) as shown in the appropriate section above. Then, multiply *a* by the appropriate multiplier from the table below.

 ≤30 | 0

Finally, divide the result by 6 and round down to the nearest integer. Call this final result *c*. A random number between 0 and 255 is generated; if it is less than *c*, a critical capture will occur. Overall, this means the critical capture chance ranges from 0 (if 30 or fewer species have been caught) to about 41.67% of the modified capture rate *a* (if over 600 species have been caught).

Critical captures only make one shake check instead of three or four, which means they are considerably more likely to successfully capture the Pokémon. The success chance for a critical capture is the fourth root of the success chance for a regular capture: if the regular success chance is 5%, the critical success chance will be around 47%, while if the regular success chance is 50%, the critical success chance will be around 84%. Given the rarity of critical captures, however, the Pokémon is always more likely overall to be caught with a regular capture than a critical one.

## Examples

If a Pokémon's HP is almost depleted, the chance of a single ball catching it can be approximated as

C
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C
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c
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≈

r
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b
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255

{\displaystyle CatchChance\approx {rate\times bonus\_{ball}\times bonus\_{status} \over 255}}

Consider a Pokémon with a catch rate of 3 (which is the case for most Legendary Pokémon) whose almost depleted its HP and is paralyzed.

If a Dusk Ball is used at night or in a cave (Ball bonus of 3.5), then the probability of capture per Ball is approximately

3
×
3.5
×
1.5

255

=

15.75
255

≈
6.2
%

{\textstyle {3\times 3.5\times 1.5 \over 255}={15.75 \over 255}\approx 6.2\%}

. This means that the average number of Dusk Balls required for capture is

1

6.2
%

≈
16

{\textstyle {1 \over 6.2\%}\approx 16}

.

If an Ultra Ball were used instead (Ball bonus of 2), then the probability of capture per Ball is approximately

3
×
2
×
1.5

255

=

9
255

≈
3.5
%

{\textstyle {3\times 2\times 1.5 \over 255}={9 \over 255}\approx 3.5\%}

. This means that the average number of Ultra Balls required for capture is instead

1

3.5
%

≈
28

{\textstyle {1 \over 3.5\%}\approx 28}

.

Alternatively, if a Timer Ball is used after the 10th turn, resulting in a Ball bonus of 4, the probability of capture per Ball is approximately

3
×
4
×
1.5

255

=

18
255

≈
7.1
%

{\textstyle {3\times 4\times 1.5 \over 255}={18 \over 255}\approx 7.1\%}

. This means that the average number of Timer Balls required for capture is

1

7.1
%

≈
14

{\textstyle {1 \over 7.1\%}\approx 14}

.

## Quotes

 1
 2
 3
 Caught

## Trivia

* The numbers 255, 4096, and 65536 result from the data types used. 255 is the highest number a byte can encode. 4096 is the amount of space a 12-bit integer can encode. 65536 is the amount of space two bytes can encode.