Catch rate

Each species of Pokémon has a **catch rate** that applies to all its members. When a Pokéball 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 Pokéball
* Any status condition of the wild Pokémon
* Any active Pass Powers (in Generation V), O-Powers (in Generation VI), or Rotom Powers (in Pokémon Ultra Sun and Ultra Moon)

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

Circumstances where capture is guaranteed—i.e. using the Master Ball and Park Ball, any Pokéball used on Kalos Route 2**XY**, Route 101**ORAS**, Alola Route 1 prior to the start of the festival in Iki Town**SMUSUM**, in the Entree Forest, in hosted non-event Max Raid Battles, or any Tera Raid Battle—bypass the catching formula entirely. Circumstances where capture is impossible (e.g. against unidentified ghosts in the Pokémon Tower) also bypass the capture formula and prevent capture even if the ball used would otherwise guarantee capture.

## Capture method (Generation I)

The capture method in Generation I differs significantly from those of later generations. To determine whether a Pokémon is caught or not, the steps below are performed. If, at any point, the Pokémon is caught or breaks free, the steps following that point are not performed.

1. If a Master Ball is used, the Pokémon is **caught**.
2. Generate a random number, *N*, depending on the type of ball used.
	* For a Pokéball: 0 to 255.
	* For a Great Ball: 0 to 200.
	* Otherwise (Ultra Ball or Safari Ball): 0 to 150.
3. The Pokémon is **caught** if...
	* It is asleep or frozen and *N* is less than 25.
	* It is paralyzed, burned, or poisoned and *N* is less than 12.
4. Otherwise, if *N* minus the status threshold (above) is greater than the Pokémon's catch rate, the Pokémon **breaks free**.
5. If not, generate a random value, *M*, between 0 and 255.
6. Calculate *f*:
	* f
	=

	⌊

	H

	P

	m
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	x

	×
	255
	×
	4

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	×
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	⌋

	{\displaystyle f = \left\lfloor \dfrac {HP\_{max} \times 255 \times 4}{HP\_{current} \times Ball} \right\rfloor}

	, where the value of Ball is 8 if a Great Ball is used or 12 otherwise. The minimum value of *f* is 1 and its maximum value is 255.
7. If *f* is greater than or equal to *M*, the Pokémon is **caught**. Otherwise, the Pokémon **breaks free**. In practical terms, lowering the target's HP to 1/3 of its maximum will guarantee capture with a Pokéball, while lowering it to 1/2 will guarantee capture with a Great Ball.

If the Pokémon broke free, the steps below are performed to determine how many times the ball will shake.

1. Calculate *d*:
	* d
	=

	⌊

	c
	a
	t
	c
	h
	R
	a
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	e
	×
	100

	B
	a
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	⌋

	{\displaystyle d = \left\lfloor \dfrac {catchRate \times 100}{Ball} \right\rfloor}

	, where the value of Ball is 255 for the Pokéball, 200 for the Great Ball, or 150 for other balls.
2. If *d* is greater than or equal to 256, the ball shakes three times before the Pokémon breaks free.
3. If not, calculate

# x

⌊

d
×
f

255

⌋

s

{\displaystyle x = \left\lfloor \dfrac{d \times f}{255} \right\rfloor + s}

, where *s* is 10 if the Pokémon is asleep or frozen, 5 if it is paralyzed, poisoned, or burned, or 0 otherwise.
4. If...
	* *x* < 10: the Ball misses the Pokémon completely.
	* *x* < 30: the Ball shakes once before the Pokémon breaks free.
	* *x* < 70: the Ball shakes twice before the Pokémon breaks free.
	* Otherwise, the Ball shakes three times before the Pokémon breaks free.

This algorithm thus has several unique properties that do not apply in later generations:

* The number of times a Pokéball shakes before failing to catch a Pokémon is a rough approximation of the Pokémon's catch odds.
* If a Pokémon will break free, a given combination of ball plus status condition plus HP will always result in the same number of shakes. This means that, if a given number of shakes is observed before the Pokémon breaks free for a given combination of these values, if the ball is ever observed to shake more times with the same combination of values, the Pokémon will be caught.
* Under certain circumstances, a Great Ball is more effective than an Ultra Ball. In particular, Pokémon with high catch rates, no status conditions, and above ½ HP may guarantee capture with a Great Ball but fail to do so with an Ultra Ball.
* The effect of reducing HP diminishes with lower catch rates, and the effect of inflicting status diminishes with higher catch rates. Regardless of catch rate, reducing the HP does not increase chances of capture at less than ½ HP with Great Balls, and ⅓ HP with other balls.
* Inflicting a status ailment gives the player a flat additional chance (from 4.6% to 16.6%) to catch the Pokémon regardless of all other factors, making certain Pokémon easier to catch in Generation I than they are in later generations. For example, a sleeping Mewtwo with full HP may, on average, be caught in about six Ultra Balls in Generation I, but from Generation II onwards exactly the same circumstances would require an average of about 64 Ultra Balls, over ten times as many.
* Due to the nature of the algorithm, Ultra Balls will only perform better than Great Balls on Pokémon whose capture rates are above 55 and below 200 in Generation I. Ultra Balls increase the overall chance of capture by as much as 20% in comparison to Great Balls for Pokémon near the center of that range.
* Assuming the current HP of target Pokémon is less than or equal to ½ HP for Great Balls and ⅓ HP for Ultra Balls, Ultra Balls increase the overall chance to capture by 10% or more in comparison to Great Balls for the following Pokémon:

- *Metapod, Kakuna, Pidgeotto, Raticate, Fearow, Arbok, Sandslash, Nidorina, Nidorino, Clefairy, Jigglypuff, Golbat, Gloom, Persian, Poliwhirl, Kadabra, Machoke, Weepinbell, Graveler, Haunter, Exeggcute, and Rhyhorn.*
### Approximate probability

The following calculation will give the exact probability of catching a Pokémon whose catch rate is at most a specific value. It will give results which are too high if the catch rates are more than this, but it remains a useful approximation. Specifically:

* For a Pokéball, it is exact for Pokémon with a catch rate of at most 230;
* For a Great Ball, it is exact for Pokémon with a catch rate of at most 175
* For an Ultra or Safari Ball, it is exact for Pokémon with a catch rate of at most 125.

C
a
p
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e
P
r
o
b
a
b
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≈

p

0

p

1

{\displaystyle CaptureProbability \approx p\_{0} + p\_{1}}

where

p

0

=

s
t
a
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s
A
i
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b
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M
o
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1

{\displaystyle p\_{0} = \dfrac {statusAilment}{ballMod+1}}

* *statusAilment* = 12 if poisoned, burned, or paralyzed, 25 if frozen or asleep, 0 otherwise.
* *ballMod* = 255 if using a Pokéball, 200 if using a Great Ball, and 150 otherwise.

and

p

1

=

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a
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e
1

b
a
l
l
M
o
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1

×

f
1

256

{\displaystyle p\_{1} = \dfrac {catchRate+1}{ballMod+1} \times \dfrac {f+1}{256}}

* *f* is defined in the above section for the capture method.
* *catchRate* (given as an integer value) is stated on each individual Pokémon's article.

### Safari Game

The Safari Game has additional mechanics exclusive to the Safari Zone; these modify the Pokémon's catch rate before any other multipliers:

* If bait is thrown, the Pokémon's catch rate is halved (and rounded down), a random "eating counter" between 1 and 5 is generated, and any "angry counter" is reset;
* If a rock is thrown, the Pokémon's catch rate is doubled and a random "angry counter" between 1 and 5 is generated, and any "eating counter" is reset.

At the end of every turn, the counters are decreased by one. If the "angry counter" hits zero, the Pokémon's catch rate is reset.

## General capture method (Generation II onwards)

The capture algorithms in Generation II and onwards have three essential components: the modified catch rate, the "shake probability", and the "shake checks". Generation II handles shake checks slightly differently than the later generations.

### Modified catch rate

The modified catch rate, *a*, is the catch rate after various factors such as weakening the Pokémon and using stronger Pokéballs 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, Baiting in the Safari Zone, or the dark grass penalty in Generation V). In Generation III and Generation IV, the modified catch rate may never fall below 1.

### 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.

In Generation II, whether a Pokémon will be caught is determined before any shake checks are performed, and shake checks are only performed if the Pokémon is not caught.

## Capture method (Generation II)

### Modified catch rate

The modified catch rate *a* is calculated in Generation II as follows:

# a

m
a
x

(

⌊

(
3
×
H

P

m
a
x

−
2
×
H

P

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)
×
r
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i
f
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d

3
×
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P

m
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⌋

,
1

)

b
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s

s
t
a
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s

{\displaystyle a = \mathrm{max}\left( \left\lfloor \dfrac{(3 \times HP\_{max} - 2 \times HP\_{current}) \times rate\_{modified}}{3 \times HP\_{max}} \right\rfloor, 1 \right) + 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,
* ratemodified is the catch rate of the Pokémon modified by the ball used, but no less than 1 and no more than 255,
* bonusstatus is the modifier for any status condition the Pokémon has (10 for sleep or freeze, 0 otherwise).
	+ bonusstatus was intended to equal 5 for paralyze, poison, or burn, but due to a glitch, the game skips this check.

If 3 × HPmax > 255, then both 3 × HPmax and 2 × HPcurrent are halved twice (and rounded down after each division) for use in the formula, as the values used are unsigned 8-bit integers. If the latter product is 0, it is set to 1 instead.

If the Pokémon's HP is 342 or greater, the 3 × HPmax value will be truncated and the subtraction may underflow, giving bizarre results and even making it possible for the game to freeze; however, no such Pokémon can be legitimately encountered in-game.

*a* is capped at 255.

The Apricorn balls apply changes directly to the Pokémon's catch rate, but due to various glitches, many of them do not work as intended. These balls were fixed for Generation IV.

### Shake probability

The shake probability *b* is determined from the table below, depending on the value of *a*.

### Shake checks

First, a check is performed to determine whether the Pokémon is caught at all. A random number between 0 and 255 is generated, and if this number is less than or equal to *a*, the Pokémon is caught.

Shake checks are only performed if the Pokémon is not caught. A single shake check consists of generating a random number between 0 and 255 and comparing it to *b*. This is done at most three times, but if the number generated in a given shake check is greater than or equal to *b*, no further shake checks will be performed. The number of times the ball shakes is the same as the number of shake checks that were performed. The table is essentially a very low-precision lookup table with numbers corresponding to the shake rate in later generations, so ultimately, aside from rounding errors (very bad ones in this case), the shake and capture rate remain similar between Generation II and the formula later used in Generation III.

## Capture method (Generation III-IV)

### Modified catch rate

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

# a

3
×
H

P

m
a
x

−
2
×
H

P

c
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3
×
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×
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b
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s

b
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×
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s
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s

{\displaystyle a = \dfrac {3 \times HP\_{max} - 2 \times HP\_{current}}{3 \times HP\_{max}} \times rate \times bonus\_{ball} \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 Pokéball used.
* bonusstatus is the multiplier for any status condition the Pokémon has (2 for sleep and freeze; 1.5 for paralysis, poison, or burn; 1 otherwise). Due to a bug in Pokémon Ruby and Sapphire, if the target Pokémon is afflicted with bad poison, no catch bonus is applied. This was fixed in Pokémon FireRed, LeafGreen, and Emerald.

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.

The formula is slightly different when applied to the Apricorn balls in Pokémon HeartGold and SoulSilver|s}}. The modifiers for these balls are applied directly to the Pokémon's catch rate, rather than in the formula. In this case, bonusball is always 1, and the catch rate cannot go higher than 255. This means that for Pokémon whose catch rate is already 255, such as Rattata, the Apricorn balls do not make the capture any more likely than a regular Pokéball.

For Shadow Pokémon, their base catch rate is determined separately, usually being higher than the normal catch rate for their species.

### Hoenn/Kanto Safari Game

In Generation III, a different formula is used to calculate a Pokémon's modified catch rate during a Safari Game. The modified catch rate is calculated from the Pokémon's "catch factor". The catch factor is initialized as:

c
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F
a
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b
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=
max

(

⌊

r
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12.75

⌋

,
1

)

{\displaystyle catchFactor\_{base} = \max \left( \left\lfloor {rate \over 12.75} \right\rfloor, 1 \right)}

The Pokémon's catch factor can be modified by the player's actions.

* In Pokémon Ruby, Sapphire, and Emerald, going near the Pokémon increases the catch factor by 4, then 3, then 2, then 1.
* In Pokémon FireRed and LeafGreen: bait halves the catch factor (rounding down, to a minimum of 3); rocks double the catch factor (to a maximum of 20).

The modified catch rate is calculated as

# a
c
a
t
c
h
F
a
c
t
o
r
×
12.75

{\displaystyle a = catchFactor \times 12.75}

As a quirk, throwing one bait at a Chansey at the start of an encounter will actually *increase* its catch factor, as its base catch factor is 2.

### Great Marsh and Johto Safari Zone

The Great Marsh and Johto Safari Zone also have mechanics that modify a Pokémon's catch rate. At the start of the encounter, the "catch" (and "escape") stages are set to 0. Then:

* Throwing bait will raise the catch stage by 1.
* Throwing mud has a 90% chance to lower the catch stage by 1.

This can modify a Pokémon's catch rate to a between 0.25× and 4× its base rate.

### Shake probability

The shake probability is calculated as follows:

**Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://mathoid-facade/v1/":): {\displaystyle b = \dfrac{1048560}{\sqrt\sqrt{\dfrac{16711680}{a}}}}**

The divisions and square roots all round down to the nearest integer.

### 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".

Four shake checks are performed. The Pokémon is caught if all four shake checks succeed. Otherwise, the Pokéball will shake as many times as there were successful shake checks before the Pokémon breaks free.

In Pokémon Colosseum and Pokémon XD: Gale of Darkness, the Pokémon breaks free after shaking once if the first or second check fails. Otherwise, the Pokéball will shake as many times as there were successful shake checks before the Pokémon breaks free. A different message will appear depending on if the first or second check fails, despite the Pokéball always shaking at least once.

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
o
g
(
1
−
p
)

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

## Capture method (Generation V+)

### Modified catch rate

Generation V follows the formula in Generation III-IV, with all divisions above either rounded down to the nearest multiple of 1/4096, or subject to standard rounding to the nearest multiple of 1/4096, rounded up at 0.5. Internally, this is represented by the modified catch rate now ranging from 0 to 1044480 (255×4096), with the HP factor

3
×
H

P

m
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−
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{\textstyle 3 \times HP\_{max} - 2 \times HP\_{current}}

 above being multiplied by 4096. However, there are three alterations, and in Generation V specifically, the modified catch rate formula is:

# a

⌊

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{\displaystyle a = \Biggl \lfloor \dfrac {3 \times HP\_{max} - 2 \times HP\_{current}}{3 \times HP\_{max}} \times 4096 \times darkGrass \times rate \times bonus\_{ball} \Biggr \rfloor \times bonus\_{status} \times passPower}

* HPmax is the number of hit points the Pokémon has at full health.
* HPcurrent is the number of hit points the Pokémon currently has.
* darkGrass only applies if the battle is taking place in dark grass, and is, as below, depending on how many Pokémon are registered as owned in the Pokédex. Result is subject to standard rounding, rounding up at 0.5.

 < 30 | 1229/4096 (~0.3)

* rate is the catch rate of the Pokémon.
* bonusball is the multiplier for the Pokéball used. Result is subject to standard rounding, rounding up at 0.5.
* 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). Notably, sleep and freeze's multipliers were boosted from 2 to 2.5.
* passPower is 1 if no Capture Pass Power is in effect, 1.1 if Capture Power ↑ is in effect, 1.2 if Capture Power ↑↑ is in effect, or 1.3 if Capture Power ↑↑↑, S, or MAX is in effect. Result is rounded down.

Some lit indoor areas will not give the Dusk Ball its boosted multiplier, even during the night.

If the modified catch rate is 1044480 or greater, the Pokémon is guaranteed to be caught (but a critical capture check will be performed anyway).

# b

⌊

65536
×

a
1044480

4

⌋

{\displaystyle b = \Biggl \lfloor 65536 \times {\sqrt[4]{\dfrac{a}{1044480}}} \Biggr \rfloor}

### Shake checks

Generation V's shake checks work essentially the same as those of Generations III and IV.

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

In a normal capture, the Pokémon breaks free without shaking if the first check fails or after one shake if the second check fails. If the third check fails, the Pokémon breaks free after **three** shakes (not two).

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.

## Capture method (Generation VI)

In Generation VI games, on the first route where a player can catch wild Pokémon (Kalos Route 2 in Pokémon X and Y or Hoenn Route 101 in Pokémon Omega Ruby and Alpha Sapphire), wild Pokémon will never break out of a Pokéball thrown at them.

### Modified catch rate

The modified catch rate is essentially identical in all respects to Generation V, except that Capture O-Powers give a 1.5×, 2× or 2.5× boost rather than 1.1×, 1.2× and 1.3×. The formula to calculate the modified catch rate in Generation VI is:

# a

⌊

3
×
H

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−
2
×
H

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3
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4096
×
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G
r
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s
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b
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⌋

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{\displaystyle a = \Biggl \lfloor \dfrac {3 \times HP\_{max} - 2 \times HP\_{current}}{3 \times HP\_{max}} \times 4096 \times darkGrass \times rate \times bonus\_{ball} \Biggr \rfloor \times bonus\_{status} \times passPower}

Where all the factors are identical to Generation V, save for

p
a
s
s
P
o
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r

{\displaystyle passPower}

 instead now being used by the Capture O-Powers, as mentioned above.

### Shake probability

Unlike Generation V, the shake probability in Generation VI is calculated as follows:

# b
65536
×

(

a
1044480

)

0.1875

{\displaystyle b = 65536 \times \left( \dfrac{a}{1044480} \right)^{0.1875}}

### Shake checks

The Generation VI games perform four shake checks again, like Generations III-IV. Critical captures function like in Generation V, with only one shake check being performed for a critical capture.

The change to the formula for the shake probability is designed to counteract the change in the number of shake checks: the odds of success for a normal capture are the same in Generation VI as in Generation V, barring small rounding errors. Since each shake check is more likely to succeed, however, critical captures are more effective than before.

## Capture method (Generation VII)

Generation VII re-introduces the Heavy Ball as an obtainable item, and with it, the added (or subtracted) modifier applied to the Pokémon's species catch rate. The formula for the modified catch rate in Generation VII is:

# a

⌊

3
×
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−
2
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3
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4096
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⌋

×
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{\displaystyle a = \Biggl \lfloor \dfrac {3 \times HP\_{max} - 2 \times HP\_{current}}{3 \times HP\_{max}} \times 4096 \times darkGrass \times rate\_{modified} \times bonus\_{ball} \Biggr \rfloor \times bonus\_{status} \times passPower}

In Pokémon Sun and Moon only, if *ratemodified* is negative, it is instead set to zero; this has the side effect of making Beldum and the Guardian deities impossible to catch in a Heavy Ball in these games. In Pokémon Ultra Sun and Ultra Moon}} onward, *ratemodified* is instead set to 1, making those Pokémon available for capture again.

As with Generation VI, the only factor that is different is

p
a
s
s
P
o
w
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{\displaystyle passPower}

, only being used by Roto Catch, which is 2 if it is active, or 1 otherwise.

Notably, unlike Pokémon HeartGold and SoulSilver, the Apricorn balls (aside from the Heavy Ball) now apply their bonuses to

b
o
n
u

s

b
a
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l

{\displaystyle bonus\_{ball}}

, instead of directly to the catch rate.

### Let's Go, Pikachu! and Let's Go, Eevee!

Pokémon Let's Go, Pikachu! and Let's Go, Eevee! uses a completely different catching mechanic and, as a result, also has a completely different formula:

# a
1.25
×

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1.85

×
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×

10000

100
−
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100

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C
P
1

4

×

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r
y

{\displaystyle a = 1.25 \times \sqrt[1.85]{rate} \times players \times \sqrt[4]{\frac{10000}{\frac{100-prev}{100} \times CP + 1}} \times \left(\frac{bonus\_{ball\_1} + bonus\_{ball\_2}}{players} \times bonus\_{early}\right)^\frac{3}{2} \times \sqrt{bonus\_{technique} \times bonus\_{berry}}}

Where:

* *rate* is the catch-rate of the species of Pokémon;
* *players* is the number of players;
* *prev* is the number of previous Pokémon of the same species previously captured, up to a total of 100;
* *CP* is the Combat Power of the Pokémon;
* *bonusball1* and – if used – *bonusball2* are the multipliers for the ball used;
* *bonusearly* is set to 1.5 if the player has not yet reached Viridian Forest, and then to 1 afterwards;
* *bonustechnique* is set to 1.5 for a Nice Throw, 2 for a Great Throw, and 2.5 for an Excellent Throw;
* *bonusberry* is set to 1.5 if a Razz Berry is used, 2.25 if a Silver Razz Berry is used, and 4 if a Golden Razz Berry is used.

The shake chance is

# b

65535

a

5
16

{\displaystyle b = \frac{65535}{a^\frac{5}{16}}}

, and the game performs four shake checks in the usual manner.

Additionally, the value of

a
¯

=

a

p
l
a
y
e
r
s
×

b
o
n
u

s

t
e
c
h
n
i
q
u
e

{\displaystyle \overline{a} = \frac{a}{players \times \sqrt{bonus\_{technique}}}}

 determines the colour of the capture ring:

* For

a
¯

<
32

{\displaystyle \overline{a} < 32 }

, the ring is red.
* For

32
≤

a
¯

<
64

{\displaystyle 32 \leq \overline{a} < 64 }

, the ring is orange.
* For

64
≤

a
¯

<
128

{\displaystyle 64 \leq \overline{a} < 128 }

, the ring is yellow.
* For

128
≤

a
¯

{\displaystyle 128 \leq \overline{a} }

, the ring is green.

If there are two players who have selected different balls, then

a
¯

{\displaystyle \overline{a}}

 will be calculated from the best ball selected.

## Capture method (Generation VIII)

### Pokémon Sword, Shield, Brilliant Diamond, and Shining Pearl

The catch rate formula includes two new multipliers, both of which are level-related. The modified catch rate formula in Generation VIII is:

# a

⌊

3
×
H

P

m
a
x

−
2
×
H

P

c
u
r
r
e
n
t

3
×
H

P

m
a
x

×
4096
×
d
a
r
k
G
r
a
s
s
×
r
a
t

e

m
o
d
i
f
i
e
d

×
b
o
n
u

s

b
a
l
l

⌋

×
b
o
n
u

s

l
e
v
e
l

×
b
o
n
u

s

s
t
a
t
u
s

×
d
i
f

f
i
c
u
l
t
y

{\displaystyle a = \Biggl \lfloor \dfrac {3 \times HP\_{max} - 2 \times HP\_{current}}{3 \times HP\_{max}} \times 4096 \times darkGrass \times rate\_{modified} \times bonus\_{ball} \Biggr \rfloor \times bonus\_{level} \times bonus\_{status} \times dif\!ficulty}

Where all the previous factors from Generation VII are unchanged, and the two new ones are:

* b
o
n
u

s

l
e
v
e
l

{\displaystyle bonus\_{level}}

 is a multiplier based on the level of the wild Pokémon:

b
o
n
u

s

l
e
v
e
l

=
max

(

30
−
l
e
v
e
l

10

,
1

)

{\displaystyle bonus\_{level} = \max\left(\frac{30 - level}{10},1\right)}

.
* d
i
f

f
i
c
u
l
t
y

{\displaystyle dif\!ficulty}

, the difficulty factor, has two different functions, depending on if it is a normal wild battle or a Max Raid Battle:
	+ During normal wild battles, if the player has not obtained the Dragon Badge**SwSh**/Beacon Badge**BDSP** and the wild Pokémon's level exceeds the level of the player's Pokémon currently in battle, the difficulty becomes 410/4096 (~0.1×). After attaining the badge, it is permanently set at 1.
	+ During Max Raid Battles, this is a value that scales based on whether the player is the host or a guest, and on the difficulty of the raid. Namely:
		- For non-event raids, for host players, capture is guaranteed.
		- For non-event, non-Gigantamax raids, for non-host players, the difficulty factor is 2.
		- For non-event Gigantamax raids, for non-host players, the difficulty depends on the Pokémon.

 All other Gigantamax Pokémon not listed
 Meowth | 53/4096

* For event raids, the difficulty factor corresponds to the set "difficulty level" of the raid, namely:

 6 | Cannot be caught

1. ↑ 1.0 1.1 1.2 1.3 1.4 Does not appear in non-event raids, so this value is unused.
2. ↑ Only used for special raids, such as Mewtwo and Zeraora.

Captures during Max Raids take place with the Pokémon at 0 HP and no status conditions. In addition, an additional turn is added to the turn count—this means that it is impossible to get the Quick Ball's bonus, and a Timer Ball always gets at least a 1.3× multiplier.

Although the

d
a
r
k
G
r
a
s
s

{\displaystyle darkGrass}

 multiplier exists within the code, no area is designated as dark grass.

At Newmoon Island or anywhere in Galar during the Darkest Day will give the Dusk Ball a 3× multiplier.

The Great Marsh works the same as in Generation IV.

### Pokémon Legends: Arceus

Pokémon Legends: Arceus}} overhauled many aspects of how to capture Pokémon. Most notably is that the player can throw Pokéballs outside of battles, leading to an entirely new out of battle capture system, and many Pokémon were given heightened catch rates to make out-of-battle capture much easier. The catch rate formula in Legends: Arceus is:

# a
(
0.75
×
r
a
t
e
o
u
t
b
r
e
a
k
)
30
×

(

r
a
n
k

(

3
×
H

P

m
a
x

−
2
×
H

P

c
u
r
r
e
n
t

3
×
H

P

m
a
x

×
s
t
a
t
u
s
×
b
a
l
l
×
b
e
h
a
v
i
o
r
×
b
a
c
k
s
t
r
i
k
e
×
b
e
r
r
y

)

)

{\displaystyle a = (0.75 \times rate + outbreak) + 30 \times \left(rank + \left(\frac{3\times HP\_{max} - 2 \times HP\_{current}}{3 \times HP\_{max}} \times status \times ball \times behavior \times backstrike \times berry\right)\right) }

* *outbreak* is set to 10 if the Pokémon is part of a Mass Outbreak or Massive Mass Outbreak.
* *rank* is a combination of the player's Galaxy Team Rank and the Pokémon's rank and is set to

r
a
n
# k
r
a
n

k

p
l
a
y
e
r

−
r
a
n

k

p
o
k
e

1

{\displaystyle rank = rank\_{player} - rank\_{poke} + 1}

, and is limited to between -5 and 0:
	+ *rankpoke* is set to

	⌊

	l
	e
	v
	e
	l
	−
	1

	10

	1

	⌋

	{\displaystyle \left\lfloor{\frac{level-1}{10}+1}\right\rfloor}

	; it is further increased by 4 if the Pokémon is an alpha, but is never more than 10.
* The *ball* multiplier may be boosted in certain circumstances:
	+ If the Pokémon is flying, then the Feather, Wing, and Jet balls are boosted;
	+ If the Pokémon has not noticed the player, then the Heavy, Leaden, and Gigaton balls are boosted.
	+ If the Pokémon is afflicted by a status condition, then the *status* multiplier is set to 2. A wild Pokémon will be cured of its status condition if the battle is fled.
	+ *behavior* corresponds to the Pokémon's overworld behavior.
	+ If the Pokémon is hit from behind, then the *backstrike* multiplier is set to 1.75. The multiplier persists throughout a battle initiated through a backstrike.
	+ If the Pokémon is eating a Razz Berry, then the *berry* multiplier is set to 1.3.

Pokéballs

Overworld behavior

#### Shake chance

Pokémon Legends: Arceus makes two shake checks. *a* is capped to 255 and the shake chance is then calculated:

# b
65535
×

(

1
−

1
−

a
255

)

{\displaystyle b = 65535 \times \left(1 - \sqrt{1-\frac{a}{255}} \right)}

The game makes two shake checks, checking *b* against a random number between 0 and 65535. If the first check is passed, then the ball will make a low bounce and capture the Pokémon. If the second check is passed, then the ball will make a high bounce and capture the Pokémon. If both checks fail, then the ball will make a high bounce but the Pokémon will escape. If *a* is less than zero, then capture is impossible and the Pokémon will escape without a bounce. The third starter Pokémon is coded to always fail capture on the first attempt.

The game also provides a visual indicator of a player's chance to capture a Pokémon if in the overworld:

* The indicator is orange by default;
* If capture is impossible for any reason then the indicator will show a red cross;
* If the Pokémon is stunned, resting, or eating something that is not a cake, the indicator will be yellow;
* If the Pokémon is sleeping or eating a cake, the indicator will be green.

Due to a bug in versions prior to 1.0.2, Sunshine Form Cherrim is treated as aggressively targeting the player and thus cannot be caught.

## Capture method (Generation IX)

### Pokémon Scarlet and Violet

The catch rate formula is mostly unchanged from Generation VIII, but introduces a new penalty, which is again level-related. The modified catch rate formula in Generation IX is:

# a

⌊

3
×
H

P

m
a
x

−
2
×
H

P

c
u
r
r
e
n
t

3
×
H

P

m
a
x

×
4096
×
d
a
r
k
G
r
a
s
s
×
r
a
t

e

m
o
d
i
f
i
e
d

×
b
o
n
u

s

b
a
l
l

×
b
a
d
g
e
P
e
n
a
l
t
y

⌋

×
b
o
n
u

s

l
e
v
e
l

×
b
o
n
u

s

s
t
a
t
u
s

×
b
o
n
u

s

m
i
s
c

{\displaystyle a = \Biggl \lfloor \dfrac {3 \times HP\_{max} - 2 \times HP\_{current}}{3 \times HP\_{max}} \times 4096 \times darkGrass \times rate\_{modified} \times bonus\_{ball} \times badgePenalty \Biggr \rfloor \times bonus\_{level} \times bonus\_{status} \times bonus\_{misc}}

* b
a
d
g
e
P
e
n
a
l
t
y

{\displaystyle badgePenalty}

 is applied if the wild Pokémon is more than 5 levels above the player's current obedience level, and is equal to

0.8

n

{\displaystyle 0.8^{n}}

, where

n

{\displaystyle n}

 is the number of Gym Badges that would be needed for it to obey.
* b
o
n
u

s

l
e
v
e
l

{\displaystyle bonus\_{level}}

's formula has changed, namely it is now

max

(

36
−
2
×
l
e
v
e
l

10

,
1

)

{\displaystyle \max\left(\frac{36 - 2 \times level}{10},1\right)}

, applied if the wild Pokémon is below level 13, rather than level 20 as in Generation VIII.
* b
o
n
u

s

m
i
s
c

{\displaystyle bonus\_{misc}}

 can be 1.1, 1.25, or 2, for Capture Power Level 1, 2, and 3, respectively, or 1 if it is not in effect. If the battle was initiated with a back strike,

b
o
n
u

s

m
i
s
c

{\displaystyle bonus\_{misc}}

 is multiplied by 2. Against static encounters,

b
o
n
u

s

m
i
s
c

{\displaystyle bonus\_{misc}}

 is always 1.

## Critical capture

Since Generation V, when a Pokéball is thrown, a special type of capture that is much more likely to catch a Pokémon, called a **critical capture** (Japanese: **捕獲クリティカル** *critical capture*), may occur. When a critical capture occurs, the Pokéball 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

Next, multiply *a* by 2 if the Catching Charm is in the player's bag. 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. In Generation V, the success chance for a critical capture is the cube root of the success chance for a regular capture; thus, for example, if the regular success chance is 5%, the chance of success with a critical capture will be about 37%, while if the regular success chance is 50%, the chance of success with a critical capture will be just over 79%. In Generation VI, meanwhile, the success chance for a critical capture is instead 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.

Pokémon Scarlet and Violet have a quirk with the animations of critical captures, namely that a successful capture on a Pokémon that is registered in the player's Pokédex will always appear to be a critical capture, even if it is not, and a failed critical capture animates as a normal capture, but with the Pokémon breaking out after no shakes.

## Examples

From Generation III onward, if a Pokémon's HP is almost depleted, the chance of a single ball catching it can be approximated as

C
a
t
c
h
C
h
a
n
c
e
≈

r
a
t
e
×
b
o
n
u

s

b
a
l
l

×
b
o
n
u

s

s
t
a
t
u
s

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 HP is almost depleted 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 30th turn (Generation III to IV) or 10th turn (Generation V+), 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. ↑ In Generation I, the Pokéball misses Pokémon, instead of the Pokémon breaking out immediately
2. ↑ In Generation V, a Pokémon never breaks free after exactly two shakes

A failed attempt to capture a Pokémon after defeating it in a Max Raid Battle will always yield the message "*Oh no! The Pokémon broke free!*" as the player has only one attempt to catch it.

## Trivia

* If used outside of the Entree Forest prior to Generation VIII (which was not possible in regular gameplay), the Dream Ball has a catch rate of 1×.
* The line if a Pokémon escapes at three shakes in Generation III and IV, "Shoot! It was so close, too!", remains in the internal data of the Generation V games despite not being used.
* In Pokémon Sun and Moon}}, a Heavy Ball will always fail to catch a Pokémon whose weight is less than 220.46 lbs (100.0 kg) and whose catch rate is less than or equal to 20. This is because the game will set the catch rate to 0 when the catch rate becomes negative due to the -20 modifier that is applied. The only catchable Pokémon that this affects are Beldum and the guardian deities. This error was corrected in Pokémon Ultra Sun and Ultra Moon}}.
* The numbers 255, 4096, and 65536 result from the data types used. 255 is the highest number a single unsigned byte can encode. 4096 is the amount of space an unsigned 12-bit integer can encode. 65536 is the amount of space two unsigned bytes can encode.

1. ↑ https://twitter.com/Sibuna\_Switch/status/1610341810655608833