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Catch rate

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Each species of Pokémon has a catch rate that applies to all its members. Higher catch rates mean that the Pokémon is easier to catch, up to a maximum of 255. 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. The formula also takes into account the following factors:

The rarity of the Pokémon (i.e. how often it appears in the wild) is independent of 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, who has a catch rate of 255.

Poké Balls that guarantee capture (the Master Ball and Park Ball, and any ball used in the Entree Forest) bypass the catching formula entirely.

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.
  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 value 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 = (HPmax * 255 * 4) / (HPcurrent * Ball), where all divisions are rounded down to the nearest integer. The minimum value of f is 1 and its maximum value is 255. The value of Ball is 8 if a Great Ball is used or 12 otherwise.
  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 = Catch rate × 100 / Ball, where the value of Ball is 255 for the Poké Ball, 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, where s is 10 if the Pokémon is asleep or frozen or 5 if it is paralyzed, poisoned, or burned.
  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 curious properties that do not apply in later generations:

  • The amount of times a Poké Ball shakes before it breaks free (or not at all if it misses the 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 situations, a Great Ball is more effective than an Ultra Ball. In particular, Pokémon with high catch rates, no status, 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 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: 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—ten times as many.

Approximated probability

Using a simulation of the capture algorithm, a general formula for the probability of catching a Pokémon was found.

Probability of Capture = p0 + p1

where

p0 = statusAilment / (ballMod+1)
  • statusAilment = 12 if poisoned, burned, or paralyzed, 25 if frozen or asleep, 0 otherwise.
  • ballMod = 255 if using a Poké Ball, 200 if using a Great Ball, and 150 otherwise.

and

p1 = ( (catchRate+1)/(ballMod+1) ) * ( (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.

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 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, 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 = max((3 × HPmax - 2 × HPcurrent) × ratemodified / (3 × HPmax), 1) + bonusstatus

with the final value rounded down to the nearest integer, 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.

Shake probability

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

a 0-1 2 3 4 5 6-7 8-10 11-15 16-20 21-30 31-40 41-50 51-60 61-80 81-100 101-120 121-140 141-160 161-180 181-200 201-220 221-240 241-254 255
b 63 75 84 90 95 103 113 126 134 149 160 169 177 191 201 211 220 227 234 240 246 251 253 255

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.

Capture method (Generation III-IV)

Modified catch rate

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

Catch formula 1.png

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 for sleep and freeze, 1.5 for paralyze, poison, or burn, and 1 otherwise).

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 HeartGold and SoulSilver. The modifiers for these balls are applied directly to the Pokémon's catch rate, rather than in the formula as bonusball is always 1, and the catch rate can not 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 anymore likely than a regular Poké Ball.

Shake probability

The shake probability is calculated as follows:

b = 1048560 / sqrt(sqrt(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 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, approximates a/255. However, due to rounding errors produced when calculating b, this approximation can be significantly inaccurate: all a values greater than 200, for instance, yield the same b value, 65535 (which results in a 99.994% chance of a successful capture).

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

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:

Catch formula 5.png

Capture method (Generation V)

Modified catch rate

Generation V follows the formula in Generation III-IV, with all divisions above rounded down to the nearest multiple of 1/4096. However, there are three alterations:

  • bonusstatus is now 2.5 for sleep and freeze (instead of 2).
  • Capture Power factor: if a Capture Power is active, the catch rate is multiplied by a factor and rounded down to the nearest multiple of 1/4096.
    • Capture Power ↑: ×1.1
    • Capture Power ↑↑: ×1.2
    • Capture Power ↑↑↑, S, or MAX: ×1.3
  • Dark grass factor: This factor is multiplied into the HP factor (3 × HPmax - 2 × HPcurrent above) and then rounded to the nearest multiple of 1/4096. This factor is applied if the battle occurs in dark grass, and depends on the number of Pokémon that have been caught in the Pokédex, as shown in the table below, usually making it harder to catch a Pokémon.
Number Caught Multiplier
> 600 1
451-600 3686/4096 (90%)
301-450 3277/4096 (80%)
151-300 2867/4096 (70%)
30-150 2048/4096 (50%)
< 30 1229/4096 (30%)

If the modified catch rate is greater than 255, the Pokémon is guaranteed to be caught (but a critical capture check will be performed anyway).

Shake probability

The formula for b is

b = 65536 / sqrt(sqrt(255/a))

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

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)

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×.

Shake probability

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

b = 65536 / (255/a)^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.

Critical capture

Since Generation V, 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.

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

Poké Ball effectiveness rates

Ball Rate Notes
Poké Ball Poké Ball
Great Ball Great Ball 1.5×
Ultra Ball Ultra Ball
Master Ball Master Ball N/A Never fails, except against unidentified ghosts, the ghost Marowak, and Kyurem when under Ghetsis's control
Safari Ball Safari Ball 1.5× only usable in Safari Zones
Level Ball 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 Lure Ball 1× or 3× 3× only if fishing
Moon Ball Moon Ball 1× or 4× Always 1× due to a glitchGSC
4× only if used on a Pokémon in the Nidoran♂, Nidoran♀, Clefairy, Jigglypuff or Skitty families HGSS
Friend Ball Friend Ball
Love Ball Love Ball 1× or 8× 8× only if used on a Pokémon of the same species and gender as the player's PokémonGSC

8× only if used on a Pokémon of the same species as, but opposite gender of, the player's PokémonHGSS

Heavy Ball Heavy Ball -20, 0, +20, +30 or +40 -20 if used on Pokémon weighing less than 225.8 lbs. (102.4 kg)GSC/451.5 lbs. (204.8 kg)HGSS

No modifier if used on Pokémon weighing between 225.8 lbs. (102.4 kg) and 451.5 lbs.(204.8 kg)GSC
+20 if used on Pokémon weighing between 451.5 lbs. (204.8 kg) and 677.3 lbs. (307.2 kg)
+30 if used on Pokémon weighing between 677.3 lbs. (307.2 kg) and 903.0 lbs. (409.6 kg)
+40 if used on Pokémon weighing more than 903.0 lbs. (409.6 kg)

Fast Ball Fast Ball 1× or 4× 4× only if used on Magnemite, Grimer, or TangelaGSC

4× only if used on a Pokémon with a base Speed of at least 100HGSS

Sport Ball Sport Ball 1.5× only usable in the Bug-Catching Contest
Net Ball Net Ball 1× or 3× 3× only if the target is a Bug- or Water-type Pokémon
Nest Ball Nest Ball 1× to 4× ((40 - Pokémon's level) / 10)×, minimum 1× (reached at level 30)RSEFRLGDPPtHGSS
((41 - Pokémon's level) / 10)×, minimum 1× (reached at level 31)BWB2W2XY
Repeat Ball Repeat Ball 1× or 3× 3× only if target has been caught previously
Timer Ball Timer Ball 1× to 4× ((number of turns passed in battle + 10) / 10)×, maximum 4× (reached at 30 turns)RSEFRLGDPPtHGSS
(1 + number of turns passed in battle * 1229/4096)×, maximum 4× (reached at 10 turns)BWB2W2XY
Premier Ball Premier Ball
Luxury Ball Luxury Ball
Dive Ball Dive Ball 1× or 3.5× 3.5× only if divingRSE or surfing/fishingFRLGDPPtHGSSBWB2W2XY
Dusk Ball Dusk Ball 1× or 3.5× 3.5× only if inside a cave or night
Quick Ball Quick Ball 1×, 4×, or 5× 4× only on the first turn of the battleDPPtHGSS
5× only on the first turn of the battleBWB2W2XY
Heal Ball Heal Ball
Cherish Ball Cherish Ball
Park Ball Park Ball N/A Never fails, only usable in Pal Park
Dream Ball Dream Ball N/A (when used in Entree Forest) Never fails due to only being usable in Entree Forest

Examples

Most legendary Pokémon have a catch rate of 3. 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 in Generation IV 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.

Alternatively, if a Timer Ball were used after the tenth turn in Generation V or after the thirtieth turn prior to Generation V, the chance of capture is 3 * 4 * 1.5 / 255 = 18/255 ~ 7.1%, or about 14 or 15 Timer Balls required on average.

Quotes

Shakes Generation I Generation II Generation III Generation IV Generation V Generation VI
0 You missed the Pokémon! Oh no! The Pokémon broke free! Oh, no! The Pokémon broke free! Oh, no! The Pokémon broke free! Oh no! The Pokémon broke free!
1 Darn! The Pokémon broke free! Aww! It appeared to be caught!
2 Aww! It appeared to be caught! Aargh! Almost had it! Aargh! Almost had it!
3 Shoot! It was so close too! Shoot! It was so close, too! Aargh! Almost had it! Gah! It was so close, too!
Caught All right! <Pokémon> was caught! Gotcha! <Pokémon> was caught!

Trivia

  • Some people claim to have discovered button combinations that increase a Pokémon's catch rate. This was partly true in Generation I, as button input could slightly influence random number generation. This required frame-perfect timing; thus it is only used by tool-assisted speedruns.
  • If used outside of the Entree Forest (which is not possible in regular gameplay), the Dream Ball has a catch rate of 1×.

See also

References

External links

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