# Gen V Capture Mechanics

Thanks to poccil of Ultimate Pokémon Center for unearthing the formulas for the first version of this page and magical for independently analyzing the algorithm and giving some corrections.

The fifth generation brings several interesting new things to the table when it comes to capturing Pokémon. If you're wondering how things worked in the first, second or third and fourth generations, go there instead. If you just want the catch rate calculator to find out how likely you are to catch some Pokémon, that's here.

## A Note on Mathematical Functions

(If you don't care about math or ludicrously small margins of error in Pokémon formulas, feel free to skip this bit.)

Perhaps the most interesting change in the inner mechanics of Black and White compared to the previous Pokémon games is that they no longer feature pileups of rounding errors in all the formulas thanks to working with integers from start to finish. Instead, now we're dealing with numbers of a precision to the nearest 1/4096th in all the intermediate stages in the formulas.

What does this mean, exactly? Well, if you do calculations with three digits after the decimal point, that's accuracy to the nearest 1/1000th, while four digits would be to the nearest 1/10000th, so it's somewhere between that. The reason we're working with one four-thousand-ninety-sixths instead of something convenient like one thousandths is that in the DS's memory - as with all computers - the numbers are represented in binary, where the first binary digit ('bit') after the point means halves, the second means quarters, the third means eighths and so on - twelve bits after the "decimal point", in particular, gives us accuracy to the nearest 1/4096th.

It can get a bit confusing to think of things in terms of 1/4096ths, and ultimately the fact is that gives us plenty enough accuracy to make the rounding stop truly mattering in all but the most exceptional of cases. Thus, in most of the discussion on this page I will pretend there is no rounding at all. However, if you want to be completely accurate, the real formula for X for instance looks like this:

`X = down(round(down(round(round((3 * M - 2 * H) * G) * C * B) / (3 * M)) * S) * E / 100)`

where `down(x)` means rounding down to the nearest 1/4096, equivalent to `int(x * 4096) / 4096`, and `round(x)` means normal rounding to the nearest 1/4096, equivalent to `round(x * 4096) / 4096 or int(x * 4096 + 0.5) / 4096`. In the other formulas on this page, the contents of every set of parentheses will in reality be rounded to the nearest 1/4096 (the `round` function described here), but I won't bother to mention it.

## The Catch Rate Formula

So if we take all those weird rounding functions and some extraneous parentheses out of the formula above, we get this:

`X = (((3 * M - 2 * H) * G * C * B) / (3 * M)) * S * E / 100`

Isn't that a nice jumble of letters? Don't worry; I'm about to explain all of them.

### X (Final Capture Rate)

If you compare the full formula to the fourth-generation formula, most of it actually looks pleasantly familiar:

`X (gen IV) = (((3 * M - 2 * H) * (C * B)) / (3 * M)) * S`

The only new additions, then, are the G value, the E value, and that division by 100 at the end - which is compensated for by the fact E is usually 100, as you'll see. This should make it relatively simple to grasp the fifth-generation formula. Indeed, like in the fourth generation, X represents the success rate of this particular capture. However, also like in the fourth generation, the purpose of X is to be plugged into other formulas, and this time those formulas aren't quite as straightforward, so don't count your chickens yet. For now, let's just observe that as before, a higher X means a better chance, and X is maxed out at 255 - specifically, if it's 255 or more at the end, the Pokémon will be automatically caught and the rest of the procedure will be skipped.

### M (Max HP) and H (Current HP)

Again, this is the maximum and current HP of the Pokémon being captured. Like in the fourth generation, the formula is really implementing the fraction of its HP that the Pokémon you're trying to catch has left. Thus, if we take this fraction, H / M, name it F and rearrange the formula a little, we get the following:

`X = G * C * B * (1 - 2 * F / 3) * S * E / 100`

And what this means is that since F is a fraction, ranging from some small value that is not quite zero (since you can't have a Pokémon at 0% HP and still catchable) up to one, a Pokémon starts out with an X number of about G * C * B * S * E / 300 when at full health and becomes something approaching G * C * B * S * E / 100 - three times the full-health value - as you whittle it down. Since a higher max HP means one current HP is a smaller fraction of the max than if the maximum were lower, high-max-HP Pokémon (either by virtue of having a high base HP or just being high-leveled) are actually easier to catch than low-max-HP Pokémon if you liberally apply False Swipe.

This is all stuff that's identical to how it worked in the fourth generation minus the rounding errors, so I won't dwell more on it. If you want more details and observations, see the gen III/IV capture mechanics.

### G (Grass Modifier)

Time for the first new value in the formula! In normal grass, caves or other terrains, this value is a neutral 1. However, if the battle takes place in thick grass (the ultra-tall darker-colored grass where the Pokémon are higher-leveled and wild double battles may occur), this value depends on how many Pokémon you've already caught (!). If more than 600 different species are "Caught" in your Pokédex, this value is 1 like normal; if you've caught 451-600 species it's 3686/4096 or roughly 0.9; if you've caught 301-450 it's 3277/4096 or around 0.8; if you've caught 151-300 it's 2867/4096 or around 0.7; if you've caught 31-150 it's 0.5; and if you've caught thirty Pokémon or less, it's 1229/4096 or around 0.3. Since this is a multiplier in the formula, higher is better - and if you haven't caught more than thirty Pokémon, this cuts your X to 30% of what it would otherwise be. Ouch.

What this basically means is that at the beginning of the game, when you've caught few Pokémon, it is extremely difficult to capture Pokémon in thick grass. Try to put off catching Pokémon there until you're ready. Meanwhile, slightly lower-leveled versions of most of the same Pokémon tend to be found in the normal grass on the same routes anyway, so it's better to go for it there.

### C (Capture Rate)

Like in the fourth generation, this number is generally the most pivotal value in the formula and starts out being the intrinsic capture rate of the Pokémon species whose capture is being attempted, with common early-game Pokémon like Patrat and Lillipup having a capture rate of 255 (meaning easy to catch), most legendaries having a capture rate of 3 (meaning hard to catch), and other Pokémon taking on various values in between. You can find this value in most online Pokédex, such as veekun. The capture rates of old Pokémon have not changed since the fourth generation.

Since there are no Apricorn balls in the fifth-generation games, this value has returned to its pre-HG/SS simplicity and there really is nothing more to it. Whoo!

### B (Ball Bonus)

This is a multiplier that depends on the type of Pokéball you're using and the various conditions that affect the performance of individual Pokéballs, as follows:

Poké Ball, Premier Ball, Luxury Ball, Heal Ball, Cherish Ball
B = 1
Great Ball
B = 1.5
Ultra Ball
B = 2
Master Ball, Dream Ball
The capture is automatically successful, bypassing the formula altogether. If you really want a B value, pretend it's infinity.
Net Ball
B = 3 if one of the Pokémon's types is Water or Bug; B = 1 otherwise
Nest Ball
B = ((41 - Pokémon's level) / 10), minimum 1
Dive Ball
B = 3.5 when on water; B = 1 otherwise
Repeat Ball
B = 3 if the Pokémon's species is already registered as caught in the Pokédex; B = 1 otherwise
Timer Ball
B = 1 + (number of turns passed in battle * 1229/4096), maximum 4. Since 1229/4096 is approximately 0.3, the bonus reaches its cap on the eleventh turn.
Quick Ball
B = 5 on the first turn of a battle; B = 1 otherwise
Dusk Ball
B = 3.5 at night and inside caves; B = 1 otherwise

Note that the only balls that have significantly changed since the fourth generation are the Quick Ball, which now dominates all other balls with a multiplier of 5 on the first turn of battle, and the Timer Ball, which has received a massive buff: instead of taking a mind-numbing thirty turns to start to shine, a Timer Ball will now be better than a Dusk Ball on the tenth turn of battle and max out on the turn after. The Nest Ball also now maxes out at a ball bonus of four like the Timer Ball instead of the 3.9 it was for level 1 Pokémon in the fourth generation.

### S (Status)

The status modifier, which has been slightly changed since the fourth generation: if the Pokémon is asleep or frozen, S = 2.5 (making these better statuses even better than before); if the Pokémon is poisoned, paralyzed or burned, S = 1.5; and otherwise, S = 1.

This is the other new factor in the X formula. During normal gameplay this value is 100. However, by playing Entralink missions with your friends over local wireless, you can receive a Capture Power from another player, which can change this value to 110, 120 or 130 depending on the level of the Capture Power (one, two or three up arrows give 110, 120 or 130 respectively; S and MAX both also give 130). This gives a 10%, 20% or 30% boost to the X value, respectively.

All in all, the fact this happens only when you're playing with friends in the Entralink means that most of the time, the X value will actually be the same as it would have been in the fourth generation, save for the rounding stuff and the couple of values that have changed. So what's the big deal about the new capture formula? Well, that's in what happens after X is calculated.

## Critical Captures

Once the game has determined X, it will implement one of Black and White's interesting new features, "critical captures". Like a critical hit when attacking, this is a (partly) random occurrence where the ball will make a whistling sound while flying, shake a little in mid-air after sucking the Pokémon in, and then shake only once on the ground before either breaking or successfully capturing it. As you might guess, a critical capture is considerably more likely to succeed than a normal capture.

So how does the game determine whether you're going to get a critical capture? Well, first it calculates a value CC:

`CC = int((min(255, X) * P) / 6)`

After the game has determined CC, it is compared against a random number ranging from 0 to 255; if the random number is less than CC, the capture will be a critical capture. In other words, the probability of a critical capture equals CC / 256.

CC, as you can see, is dependent on both the already-calculated X (capped at 255) and a mysterious P value. What is this P value? Well. Remember the grass modifier G and how it depended upon your Pokédex completion?

Yep.

### P (Pokédex Modifier)

If more than 600 species are registered as caught in your Pokédex, this value is 2.5; if you've caught 451-600 this value is 2; if you've caught 301-450 this value is 1.5; if you've caught 151-300 it is 1; if you've caught 31-150 it is 0.5; and if you've caught thirty Pokémon or less, it's 0. In short, critical captures are much more likely the more Pokémon you've already caught, and in fact they're just plain impossible at the beginning of the game.

It seems a little disappointing that the chances of getting a critical capture are only really good when your chances of catching the Pokémon normally would have been great anyway. But any chance of a critical capture at all will boost your overall chances by a little, and once you've caught a lot of Pokémon, critical captures can make things somewhat significantly easier.

## Throwing a Ball

So what happens in Black and White when you throw a ball? Well, first we calculate a variable Y...

`Y = int(65536 / √(√(255 / X)))`

If you read the mathy bit on my gen III/IV capture formula page, you'll know that this is almost exactly what my simplified Y formula for those games looked like (barring that this one has 65536 where that one had 65535) - which makes sense, considering the only reason this wasn't the formula then was that the rounding between the individual operations of the formula was screwing things up; now that we don't have to worry about rounding, this simpler formula is possible. Ultimately, however, this means that this formula, too, is in practice almost identical to the fourth-generation one. So what's the big change?

The big change is that in the third and fourth generations, four random numbers were generated and compared to Y, where any one of the random numbers being greater than or equal to it would result in the Pokémon immediately bursting out of the ball. In the fifth generation, only three such random numbers are generated - and only one for a critical capture. This means that every single Pokémon is considerably easier to catch - they only get three chances to escape now, or sometimes even only one, instead of four. Unless, that is, you're in thick grass and haven't caught that many Pokémon yet (warning: link contains profanity).

"So wait," you say, "what about the shakes? The ball can still break without shaking, and it can still shake three times!" Well, that's true. But in Black and White the ball can no longer shake twice - try it yourself sometime. Curiously, the message they took out was not the previous generation's message for two shakes ("Aargh! Almost had it!"), but instead the classic "Shoot! It was so close, too!" message we used to get when it shook three times - now it says "Aargh! Almost had it!" for three shakes.

Just to make things more confusing, if a critical capture fails, it will shake once before bursting open, but the message will be "Oh no! The Pokémon broke free!", which is otherwise used when the ball doesn't shake at all.

So to summarize: if the first random number is greater than or equal to Y, the Pokémon will burst out immediately (in a normal capture) or after one shake (in a critical capture), with the message "Oh no! The Pokémon broke free!" If the first random number is less than Y but the second is greater than or equal to it, the Pokémon will burst out after one shake with the message "Aww! It appeared to be caught!" If the first two are less than Y but the third check fails, it will burst out after three shakes (again, note there is no such thing as two shakes anymore) with the message "Aargh! Almost had it!" And if all three random numbers are less than Y, or the only random number in the case of a critical capture, the Pokémon is successfully caught. The probability that a single random number will be less than Y is `Y / 65536`; the probability that three random numbers will all be less than Y is `(Y / 65536)3`. This simplifies to `(X / 255)0.75`, and since the square roots in the fifth generation are pretty exact, that's quite a good approximation. (However, don't forget that it's an approximation of your chance of succeeding with a non-critical capture only; with critical captures, the chance is even higher than that.)

Like in the fourth generation, the game skips all this if X is 255 or more, since that results in a guaranteed capture from the Y formula anyway (it leads to Y being at least 65536, and the random numbers only go up to 65535 so they will always be less than Y). Otherwise, the final chance that you will capture the Pokémon then equals the chance of a successful critical capture plus the chance of a successful normal capture, or `(CC / 256) * (Y / 65536) + (1 - CC / 256) * (Y / 65536)3`.

## Catch Rate Calculator

To approximate your chances of catching any Pokémon, enter the appropriate information into this form. The number of balls needed is rounded up from the strict average, but you should of course always bring considerably more balls than that for safety. Also note that these ball numbers naturally become inaccurate if the capture rate for the ball changes during the course of the battle, such as if you're using Timer Balls prior to when the multiplier maxes out at 4, you're using balls that compare the Pokémon to yours and your Pokémon get switched, or you switch to using a different type of ball.

The calculator will do the calculation for each of the thirty-two possible HP IVs. If you check the "Show detailed report?" box, it will show the exact chance for each given IV; otherwise, it will show the overall chance assuming each HP IV is equally likely (which is normally the case). Note, however, that if the Pokémon isn't at full health or False Swiped, the inaccuracy of the estimate of the Pokémon's current HP is generally going to introduce a bigger margin of error than IV-induced variation in the max HP will, making the detailed report not very meaningful.

Approximation of current HP: