Breeding for IVs
This guide explains how to breed Pokémon with very high IVs. If you're new to breeding, at this point you will want to know just what the heck an IV is. IV stands for Individual Value, and are part of what determines how strong a specific Pokémon can become in a certain stat (HP, Attack, Defense, Sp.Atk., Sp.Def., Speed). There are three other things that affect Pokémons' stats: Base Stats (BSs), Effort Values (EVs), and some thing called the Pokémon's Nature. I will briefly explain each one, but the bulk of this guide deals exclusively with IVs.
Base Stats
The Base Stats are the most fundamental characteristic of every Pokémon species. As with IVs, there is one for each stat, and they range from 1 - 255. The BSs of every member of a specific species of Pokémon are the same. They are completely unalterable by legitimate means.
Effort Values
Effort Values are the only permanent stat modifier that can be readily changed on a specific Pokémon (IVs and Nature can be controlled via breeding, but once they're determined they cannot be altered). EVs can have values between 0 – 252 for any stat, and every Pokémon starts with 0 at birth/capture and can accumulate a total of 510 across all stats. At level 100, 4 EVs translate to 1 actual stat point. For a more in depth look at EVs, see
http://bulbapedia.bulbagarden.net/wiki/EV
.
Nature
If you've been paying attention to your Pokémon, you'll probably have noticed a field called “Nature” among their stats. It can have values such as Hardy, Lonely, Brave, Adamand, Naughty, etc. What you may not have realized is that this isn't just flavor, but has an actual effect on your Pokémon's stats. Every Nature increases one stat by 10%, while decreasing another by the same amount. A Nature that increases and decreases the same stat has no net effect, and is therefore said to be neutral. For a complete list of Natures including which stats they alter, see
http://bulbapedia.bulbagarden.net/wiki/Nature
.
A Pokémon's Nature is typically assigned at random when it is encountered/born, but it can be controlled via breeding. If one of the parents hold an Everstone, that parent's Nature will be inherited by its offspring.
Individual Values
Individual Values can have values between 0 – 31 for each stat, and at level 100 one IV point equals one actual stat point. Unlike EVs, there is no cap for the IV total; it is theoretically possible to have a Pokémon with 31 in every IV. Statistically, the best you can hope to achieve is 31 in three of the six stats, with the remaining three being left up to chance.
Like Nature, IVs are typically assigned at random when a Pokémon is encountered. Unlike Nature, IVs are always at least partly deterministic when a Pokémon is bred, however. Specifically, a child will always inherit exactly three of its parents' twelve stats, with the remaining three being random. Each of the three inherited stats can come from either parent. For example, a child could inherit its mother's Attack and Sp.Def. and its father's Speed, or it could inherit its father's HP, Attack and Sp.Atk.
Additional control over which IVs are inherited can be exerted via the EV-enhancing items, or the Power-items as they are also known. By equipping one parent with a Power Weight/Bracer/Belt/Lens/Band/Anklet, the IV of the stat affected by that item will always be passed down to the offspring. Two more stats are inherited at random from the parents, and the remaining three are as always completely random. This may not seem very significant, but as you will soon see, this lowers the odds of breeding a 31/31/31 IV Pokémon from astronomical to totally manageable.
You need to be able to check what IVs your Pokémon have. Otherwise it would be rather tricky to breed selectively for them. The game does not directly expose the IVs anywhere, but there are plenty of hints. For the complete theory behind how IVs are calculated, see
http://bulbapedia.bulbagarden.net/wiki/IV
. For the purposes of this guide, it is enough that some very clever people have written IV calculators that are available online. There are several different once to choose from and none of them seem better than the others, so just pick whichever you like the most.
Breeding
In order to actually breed that 31/31/31, you will need a couple of things. First and foremost, you need the EV-enhancing items, as detailed above. Without them, the probability for breeding a 31/31/31 is about the same as the probability for breeding a shiny under ideal conditions. Furthermore, you will need one Pokémon with an IV of 31 for each of the IVs you want to breed for. You have a few options for which exact Pokémon to get:
- Lots of Pokémon from the same species
This can work if the Pokémon you want to breed is relatively common, and you are only interested in breeding that one species and no others. I wouldn't recommend it though, because it means that if want to breed a Pokémon with a 31 Attack IV and your initial Attack IV contributor is male, the previous generation must produce a female offspring with the desirable traits. This will normally decrease the viable egg frequency by 50%, although it can be considerably more or less than that if you're breeding something with a skewed gender ratio.
- Lots of Pokémon from the same Egg Group
This is even worse than the previous option. When you breed two Pokémon of different species in the same Egg Group, the mother's species determines the species of the offspring. This means that all of your IV contributors must be male, and it also decreases the viable egg frequency by at least 50%.
- Lots of Dittos
This is normally what you want to do. Ditto is genderless, but it can breed with almost any Pokémon, regardless of its Egg Group. The non-Ditto parent always determines the offspring's species, so you can even breed your male starters this way. If you intend to breed more than one species, Dittos is definitely the way to go. Breeding with Dittos is a lot more predictable than breeding within a specific species, so for the remainder of this guide I will assume you are using Dittos.
Regardless, actually catching these Pokémon is probably the most time consuming part of breeding a 31/31/31. Every wild Pokémon has a 1/32 chance of any given stat having an IV of 31. Since there are six stats, wild Pokémon have a 1 - (31/32)6 chance of having at least one IV of 31. Once you have caught a Pokémon with 31 in one of the IVs, that probability decreases to 1 - (31/32)5, and then to 1 - (31/32)4, and so on. Therefore, you will on average have to catch 1/(1-(31/32)6 )+1/(1-(31/32)5 )+1/(1-(31/32)4 )+1/(1-(31/32)3 )+1/(1-(31/32)2)+1/(1-(31/32)1 ) ≈ 81 Dittos on average. With luck, you could get away with less than that. Without luck... Well, you get the idea. Thanks to
/u/MissKelly087 for correcting my math here.
Once you have the Pokémon you need, it's time to start breeding. Make sure the original non-Ditto parent has the Nature you want. If there is a particular IV you are more interested in than the others, you should breed that IV into your line last. Let's say you want to breed a Modest Gastly with 31 Sp.Atk., 31 Sp.Def., and 31 Speed, and you're most interested in Sp.Atk.., followed by Sp.Def. You should then start by breeding Speed into the line.
Generation 0: Modest Gastly (Everstone) + 31 Speed Ditto (Power Anklet)
This will produce a Modest Gastly with 31 Speed 100% of the time.
Generation 1: Modest 31 Speed Gastly (Everstone) + 31 Sp.Def. Ditto (Power Band)
This is were it gets a bit tricky. After Sp.Def. has been forcefully passed down, there are two more stats to be inherited, and 10 stats to choose from (five from either parent). You need one of those stats to be the Gastly's speed. The first stat has a 9/10 chance of not being Gastly's speed. The second stat has a 7/8 chance of not being Gastly's speed if the first one wasn't. Thus, the chance of either of the two remaining inherited stats being Gastly's speed is 1 – 9/10 * 7/8 = 21.25 %.
Generation 2: Modest 31 Speed 31 Sp.Def. Gastly (Everstone) + 31 Sp.Atk Ditto (Power Lens)
This is the most time-consuming breeding step, but it will almost certainly be quicker than catching those 81 Dittos. After Sp.Atk. has been forcefully passed down, you need both the remaining inherited stats to be Gastly's Speed and Sp.Def. The first stat has a 2/10 chance of being either Gastly's Speed or Gastly's Sp.Def. If either Speed or Sp.Def. is chosen the first time, the last stat has a 1/8 chance of being the other one. The probability of both stats being the ones you need is 2/10 * 1/8 = 2.5 %.
/u/wowfan85 pointed out that there is a way to significantly speed up this step. See comment (ctrl+f wowfan85), not enough space here.
All in all, in order to breed a single 31/31/31 Pokémon, you will need to catch some 60-80 Dittos (on average), and then go through three generations of breeding and about 46 eggs (again, on average).
Optionally, you can now start mass producing 31/31/31 Gastlys (or whatever Pokémon you've been breeding). Once you get that first 31/31/31, breeding more of the same species (or even the same Egg Group) becomes significantly easier.
Generation 3+: Modest 31 Speed 31 Sp.Def. Gastly (Everstone) + Modest 31 Speed 31 Sp.Def. 31 Sp.Atk. Gastly (Power Lens)
Sp.Atk. is forcefully bred into the offspring. The first of the two remaining inherited stats have a 4/10 chance of being either parent's Sp.Def. or Speed. The second remaining inherited stat has a 2/8 chance of being either parent's Sp.Def. or Speed, depending on which one was chosen first. Combined probability is then 4/10 * 2/8 = 10%.
Illustration of the above:
http://imgur.com/zJ7tzWD
Why not make a couple dozen or a few hundred of these and send them all into Wonder Trade? 100% of the offspring will be Modest and have 31 Sp.Atk., and 70% will also have either 31 Sp.Def., 31 Speed, or both!
