The Formula
The following variables are involved in the catch rate:
Catch Rate (C): Set for the species of Pokemon attempted to capture. Varies from 3 to 255.
Ball Rate (B): Depends on type of ball used.
HP Factor (H): Let M = Max HP, and C = Current HP. H = (3M-2C)/(3M) = 1 - 2/3(C/M)). For the sake of this guide, we will use the HP Ratio, R, as defined as C/M = R, so H = 1 - 2R/3. Thus, the smaller R is, the larger H is and the better the capture rate.
For the purposes of this guide, we will only use 3 different R levels, and as such 3 different H values. At Full HP, R = 1, and as such H = 1/3. At half HP, R = 0.5, and H = 2/3. At 1 HP, R will be close to 0, and as such H will be close to 1 (and will be calculated as H = 1 for the guide).
Status Factor (S): S = 1 for normal, S = 1.5 for paralysis or poison/burn, and S = 2 for sleep or freeze. Obviously, Poison and Burn should only be used on Pokemon immune to their effects (which pretty much means only Clefairy), and freezing is unreliable, so sleep and paralysis will be the main factors.
The success rate, X, is approximately calculated as such:
X = C*B*H*S/255
This is not an exact number, but it is a good approximation for our purposes.
The Ball Rates
Poke Ball: 1 - The bread-and-butter Poke Ball. It's good to always have a lot of these handy, as even with their low catch rate, they can be used with perfect or near-perfect results under the right conditions. Note that the Premier Ball is equivalent to the Poke Ball in all but looks.
Great Ball: 1.5
Ultra Ball: 2
Two other commonly-used balls. The Ultra Ball, though, shouldn't ever really see much use as the specialized balls are cheaper and have greater catch rates under the right conditions.
Heal Ball: 1 - This ball is used early-game, where caught Pokemon go straight to the party.
Dusk Ball: 4 if nighttime or in cave - Probably one of the more useful specialized balls, the Dusk Ball can practically guarantee captures at night, and are probably the most useful balls to use against Legendaries. Just make sure to do all your capturing at night with these.
Nest Ball: 3 if Pokemon is level 19 or lower, 2 if Pokemon is between levels 20 and 29 - Might be useful if going hunting for low-level Pokemon and you want to save Dusk Balls or Love Balls.
Net Ball: 3 if Pokemon is Water or Bug type - Good for Water and Bug types.
Quick Ball: 4 if used in first 5 turns, rate decreases by 1 every turn afterwards - Another very useful ball, particularly if all you need to do to capture the Pokemon is paralyze it, or even if it's possible to just catch it at full health (or just one False Swipe is needed).
Repeat Ball: 3 if you already have that species of Pokemon - might as well use it if the condition applies.
Timer Ball: increases by 1 every 10 turns, to a max of 4 at 31 turns - If you can drag out a battle that long, use it, but otherwise it's not that effective.
Safari Ball, Sport Ball: 1.5 - These are used in specific areas. Notable in that, in the Safari Zone, all Pokemon must be caught at full health, while in the Bug Catching Contest, your chances of winning greatly improve if the Pokemon is caught at full health. So in these cases, you will likely be dealing with H = 1/3.
Fast Ball: 4 if Pokemon can flee from battle - The first of Kurt's special balls, this is the ball to be used on Roaming Pokemon. There's a fair amount of them, so stock up and have fun.
Friend Ball, Luxury Ball: 1 - The reason to use these balls is as such: a Pokemon caught with a Friend Ball will start out with a base happiness of 200, while a Pokemon caught with a Luxury Ball will grow in happiness twice as fast. In both cases, it makes any kind of friendship-based evolution, as well as getting max Happiness for Return purposes, much easier.
Heavy Ball: Unique - This Ball has a special modifier, in that, instead of a multiplier, it adds a value to (C*B*H*S) before being divided by 256. Don't ever use it on a Pokemon under 220 lbs, as that actually makes the capture rate worse. Otherwise, it's +20 if the Pokemon is between 440 and 660 lbs, and +30 if the Pokemon is more than 660 lbs. Because of how the math works out, it turns out this ball probably won't see much use over the multiplier balls except against the legendary Pokemon that are over 44o lbs. and have a really low catch rate. More on that later.
Level Ball: 2 if your Pokemon is higher level than the opponent, 4 if your Pokemon is over twice the level of the opponent, and a whopping 8 if your Pokemon is over four times the level of the opponent - As you can see, this ball can reach ridiculously high catch rates... though never against a level 25 Pokemon. Still, if trying to catch a low-level but low-catch-rate Pokemon, this ball could be really useful.
Love Ball: A massive 8 if your Pokemon is of the opposite gender - Quite possibly the most useful ball for everyday catching. As long as you have at least one Pokemon of each gender, you can guarantee yourself that huge catch rate. However, it won't work on genderless Pokemon, including... most legendaries. As it turns out, this is the single best ball to use against Latias and Latios...
Lure Ball: 3 if the Pokemon was fished up - Pretty much the same as the Net Ball, except it only works on fished-up Pokemon.
Moon Ball: 4 if the Pokemon evolves via Moon Stone - In other words, used to capture Nidorina, Nidorino, Clefairy, Jigglypuff, and Skitty.
And finally...
Master Ball: 255 - A.K.A. insta-catch.
Poke Balls by Catch Rate
255: Master Ball
8: Level Ball (>4x opponent's level), Love Ball (opposite gender)
4: Dusk Ball (night/caves), Quick Ball (within first 5 turns), Timer Ball (after 30 turns), Fast Ball (fleeing Pokemon), Level Ball (>2x opponent's level), Moon Ball (evolves w/Moon Stone)
3: Quick Ball (6-10 turns), Nest Ball (under level 20), Net Ball (Bug or Water-type), Repeat Ball (already have target species), Timer Ball (after 20 turns), Lure Ball (fished-up)
2: Ultra Ball, Quick Ball (11-15 turns), Nest Ball (level 20-29), Timer Ball (after 10 turns), Level Ball (> opponent's level)
1.5: Great Ball, Safari Ball, Sport Ball
1: Poke Ball, Heal Ball, Friend Ball, Luxury Ball
Capture Formula Recap
X = C*B*H*S/255, where:
C = capture rate of Pokemon
B = ball's capture rate
H = 1/3 if Pokemon is at full health, 2/3 if Pokemon is at half health, and 1 if Pokemon is at 1 HP
S = 1.5 if Pokemon is paralyzed, 2 if Pokemon is asleep, and 1 if Pokemon has no status
Capture Plans
Checkpoint 1: C = 255
The easiest Pokemon to catch. Here are the ways to guarantee or near-guarantee a capture:
Rate-3+: Throw at max HP
Rate-2: Status, and throw at max HP, OR bring to <1/2 HP and throw
Rate-1.5: Sleep, and throw at max HP, OR status and bring to <1/2 HP, OR bring to 1 HP
Rate-1: Status and <1/2 HP, OR 1 HP
As a note, even at full health, a rate-1 ball still has a 1 in 3 chance of catching the Pokemon. If using a Safari Ball at max health, you're looking at a 50% chance of catching the Pokemon.
Checkpoint 2: C = 190
Still not too hard. To guarantee a capture (or get near):
Rate-4+: Throw at max HP
Rate-3: Status OR 1/2 HP
Rate-2: Sleep OR 1/2 HP
Rate-1.5: Status and 1/2 HP OR 1 HP
Rate-1: Sleep and 1/2 HP OR Status and 1 HP
If using a Safari Ball, capture rate is about 37%; Sport Ball + sleep = 75%.
Checkpoint 3: C = 120
Here, it gets a little harder:
Rate-8: Throw at Max HP
Rate-4: Status OR 1/2 HP
Rate-3: Sleep OR 1/2 HP
Rate-2: Status and 1/2 HP OR 1 HP
Rate-1.5: Sleep and 1/2 HP OR 1 HP
Rate-1: Sleep and 1 HP
At max HP, a Safari Ball has about a 23% capture rate, while a Sport Ball with sleep has a 47% capture rate.
Checkpoint 4: C = 75
At this point, options for guaranteeing captures become limited.
Rate-8: Status OR 1/2 HP
Rate-4: Status and 1/2 HP OR 1 HP
Rate-3: Sleep and 1/2 HP OR Status and 1 HP
Rate-2: Sleep and 1 HP
Rate-1.5: Max of 88% with Sleep and 1 HP. Safari Balls have about a 15% chance of working; Sport Balls succeed 29% of the time with Sleep.
Rate-1: Max of 59% with Sleep and 1 HP.
Checkpoint 5: C = 45
A common checkpoint as the generally-hardest tier of Pokemon to catch outside of legendaries and a couple of special cases. It is very difficult, though not impossible, to guarantee a capture here.
Rate-8: Sleep OR 1/2 HP
Rate-4: Sleep and 1/2 HP OR Status and 1 HP
Rate-3: Sleep and 1 HP
Rate-2: Max 71% with Sleep and 1 HP.
Rate-1.5: Max 52.9% with Sleep and 1 HP. Using a Safari Ball, you are looking at about a 6% capture rate. Good luck with that. With a Sport Ball and a Pokemon to put the target to sleep, that rate jumps to 12%.
Rate-1: Max 35% with Sleep and 1 HP.
Checkpoint 6: C = 3
The single hardest checkpoint. Most of these Pokemon are legendaries, though you also have to deal with Beldum/Metang at this catch rate...
It should be noted that ensuring a capture here is nearly impossible. In fact, it's impossible to have a capture rate over 20% with these beasts! The closest you can come is to bring the Pokemon to 1 HP, sleep it, and use a rate-8 ball, all of which will result in a decent 19% catch rate. However, that is only practical with Latias and Latios, on whom a Love Ball can be used.
Here are various catch rates using a rate-4 ball:
9.4%: Sleep and 1 HP
7.1%: Paralyze and 1 HP
6.3%: Sleep and 1/2 HP
4.7%: Paralyze and 1/2 HP OR 1 HP
3.1%: Sleep OR 1/2 HP
2.4%: Paralyze
1.6%: Throw at Max HP
Oh, and if you're trying to catch a Beldum in the Safari Zone, you'll be working with a 0.6% capture rate... good luck with that. >_>
Heavy Ball evaluation
How does the Heavy Ball fit into all this? It adds up to 30 to the value of C*B*H*S. Now, B will automatically be set to 1, so the question when comparing this ball's worth to a rate-4 ball is: does a x4 multiplier "add more" than 20 or 30 to this value?
Let's take a look at four examples with a mathematical analysis.
Snorlax:
Catch rate: 25. Gendered, so the comparison is to the even-greater Love Ball. At 1 HP while asleep (extremely difficult if Snorlax has Leftovers), the Love Ball clearly wins out, being able to guarantee the capture, while a Heavy Ball only has a 31% chance of capture. What about at lower HP levels, or without a status? After all, that Snorlax sure loves to Rest... Well, a sleeping Snorlax at full health is caught 52% of the time by a Love Ball... whereas the Heavy Ball only has an 18% chance of capturing. Even at full health without a status, the Love Ball clearly wins out, with 26% success vs. 15% with the Heavy Ball. So no use here.
Groudon/Kyogre:
With a catch rate of 5, it turns out that, with Sleep and 1 HP, a rate-4 ball and a Heavy Ball both have the same capture rate: 16%. It should then also be noted that, if the Groudon/Kyogre is any bit healthier than that level, the Heavy Ball will win out. For example, a rate-4 ball will catch a 1/2-HP sleeping Groudon with a 10% success rate; a Heavy Ball will catch it with a 14% capture rate. So here, a Heavy Ball has the advantage.
Take a look at some other Heavy Ball markers:
Paralyze and 1 HP: 15%
Paralyze and 1/2 HP OR 1 HP: 14%
Sleep OR 1/2 HP: 13%
Paralyze: 13%
Throw at Max HP: 12%
One thing to notice about the Heavy Ball is that, because of the additive nature of its bonus, there really is little difference in throwing one at full HP and throwing one at 1 HP and Sleep, so it is essentially an "effortless" ball.
Lugia/Rayquaza:
Catch rate of 3, but the Heavy Ball only adds 20 to the catch value. How does that work out?
Turns out, even with only a 20 increase, the Heavy Ball performs better than a rate-4 ball at Sleep and 1 HP, giving a 10% chance of capture as opposed to the 9.4% chance for a rate-4 ball. Of course, this difference only gets greater the less the target has been weakened...
As before, there isn't a huge amount of difference between a Heavy Ball thrown at full health. A full-health, no status Lugia or Rayquaza will have a catch rate of 7.8%. That catch rate will increase somewhat linearly depending on how much the target is weakened.
Arceus:
In the off-chance that Arceus can be captured in HG/SS, it is looking at similar catch rates to Groudon and Kyogre against the Heavy Ball. In particular, thrown at max HP, a Heavy Ball has a 12% chance of capturing Arceus.
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