Catch rate
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 health of the Pokémon (relative to its full health)
- The type of Poké Ball
- Any status condition of the wild Pokémon
- Any active Pass Powers (in Generation V) or O-Power (in Generation VI)
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.
- If a Master Ball is used, the Pokémon is caught.
- Generate a random number, N, depending on the type of ball used.
- For a Poké Ball: 0 to 255.
- For a Great Ball: 0 to 200.
- Otherwise (Ultra Ball or Safari Ball): 0 to 150.
- 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.
- Otherwise, if N minus the status threshold (above) is greater than the Pokémon's catch rate, the Pokémon breaks free.
- If not, generate a random value, M, between 0 and 255.
- Calculate f:
- f = (HP_{max} * 255 * 4) / (HP_{current} * 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.
- 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 Poké Ball, 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.
- 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.
- If d is greater than or equal to 256, the ball shakes three times before the Pokémon breaks free.
- 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.
- 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 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: 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.
Approximated probability
Using a simulation of the capture algorithm, a general formula for the probability of catching a Pokémon was found.
Probability of Capture = p_{0} + p_{1}
where
p_{0} = 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
p_{1} = ( (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 × HP_{max} - 2 × HP_{current}) × rate_{modified} / (3 × HP_{max}), 1) + bonus_{status}
with the final value rounded down to the nearest integer, 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_{modified} is the catch rate of the Pokémon modified by the ball used, but no less than 1 and no more than 255,
- bonus_{status} is the modifier for any status condition the Pokémon has (10 for sleep or freeze, 0 otherwise).
- bonus_{status} was intended to equal 5 for paralyze, poison, or burn, but due to a glitch, the game skips this check.
If 3 × HP_{max} > 255, then both 3 × HP_{max} and 2 × HP_{current} 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 × HP_{max} 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:
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 be modified due to use of apricorn balls or actions in the Safari Zone),
- bonus_{ball} is the multiplier for the Poké Ball used, and
- bonus_{status} 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 × bonus_{ball} × bonus_{status}. 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. In this case, bonus_{ball} 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 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:
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:
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:
- bonus_{status} 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 × HP_{max} - 2 × HP_{current} 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)
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 Poké Ball 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×.
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 (Japanese: 捕獲クリティカル 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 | 1× | |
Great Ball | 1.5× | |
Ultra Ball | 2× | |
Master Ball | N/A | Never fails, except against unidentified ghosts, the ghost Marowak, and Kyurem when under Ghetsis's control |
Safari Ball | 1.5× | |
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 |
Lure Ball | 1× or 3× | 3× only if fishing |
Moon Ball | 1× or 4× | Always 1× due to a glitch^{GSC} 4× only if used on a Pokémon in the Nidoran♂, Nidoran♀, Clefairy, Jigglypuff or Skitty families ^{HGSS} |
Friend Ball | 1× | |
Love Ball | 1× or 8× | 8× only if used on a Pokémon of the same species and gender as the player's Pokémon^{GSC} 8× only if used on a Pokémon of the same species as, but opposite gender of, the player's Pokémon^{HGSS} |
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} |
Fast Ball | 1× or 4× | 4× only if used on Magnemite, Grimer, or Tangela^{GSC} 4× only if used on a Pokémon with a base Speed of at least 100^{HGSS} |
Sport Ball | 1.5× | |
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× (reached at level 30)^{RSEFRLG}^{DPPtHGSS} ((41 - Pokémon's level) / 10)×, minimum 1× (reached at level 31)^{BWB2W2}^{XYORAS} |
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× (reached at 30 turns)^{RSEFRLG}^{DPPtHGSS} (1 + number of turns passed in battle * 1229/4096)×, maximum 4× (reached at 10 turns)^{BWB2W2}^{XYORAS} |
Premier Ball | 1× | |
Luxury Ball | 1× | |
Dive Ball | 1× or 3.5× | 3.5× only if diving^{RSE}^{ORAS} or surfing/fishing^{FRLG}^{DPPtHGSS}^{BWB2W2}^{XY} |
Dusk Ball | 1× or 3.5× | 3.5× only if inside a cave or night |
Quick Ball | 1×, 4×, or 5× | 4× only on the first turn of the battle^{DPPtHGSS} 5× only on the first turn of the battle^{BWB2W2}^{XYORAS} |
Heal Ball | 1× | |
Cherish Ball | 1× | |
Park Ball | N/A | Never fails |
Dream Ball | N/A (when used in Entree Forest) | Never fails |
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 | Generation VII |
---|---|---|---|---|---|---|---|
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. Aside from manipulation of the game's pseudorandom number generator (which, in Generation I, could have been done this way to some minor extent), none of these are true; the game's calculated probability for catching a Pokémon depends only on the above factors and nothing else.
- If used outside of the Entree Forest (which is 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.
See also
References
External links
This game mechanic article is part of Project Games, a Bulbapedia project that aims to write comprehensive articles on the Pokémon games. |