This section goes further into depth and the game's calculations. This section can be skipped and you can go back to this later, but it helps to understand one move of the game, Hidden Power. IVs, sometimes called Determinant Values (DVs), are hidden values in the game that generates the random stats of your Pokémon. In the Second Generation, IVs range from 0 to 15. In the Third Generation, IVs range from 2 to 31. What do I mean by random stats? For example, a Pokémon with an Attack IV of 8 might have an Attack of 334, while a Pokémon with an Attack IV of 14 might have an Attack of 342. The higher the IV, the higher the stat. For GSC, there are 5 IV stats: HP, Attack, Defense, Special, and Speed, with each one ranging from 0 to 15. Note that both Special Attack and Special Defense from GSC comes from the same IV stat. This means that Special Attack and Special Defense in GSC will always complement each other. For RSE/FRLG, there are 6 IV stats: HP, Attack, Defense, Special Attack, Special Defense, and Speed, with each ranging from 2 to 31. IVs are irrelevant when battling over GameBoys because it is so hard to get ones with the IVs you like. Once again, IVs are hidden values (there are ways to find it if you search for an IV calculator on the internet) and are random. However, if you battle online, where you can set the IVs of your Pokémon, then it will play a huge factor.
1) Shiny Pokémon
In the Second Generation, and only in the Second Generation did IVs have anything to do with Shiny Pokémon. Basically, if all of your IVs are 10 (HP, Attack, Defense, Special, and Speed), then your Pokémon is shiny. Granted that having IVs of 10 will not yield the greatest stats, but if you battle online and want to make your Pokémon shiny, then make all of its IVs 10.
2) Hidden Power
As I stated above, IVs come into calculation with the move Hidden Power. Before I go on, this is a fair warning. The rest of this guide will consists of lots of numbers and calculations. This is a strategic part of Pokémon, and serious battlers know better than just push buttons. While this will be very interesting to some, knowing sections I - IV would already make you a better battler by far. However, the rest of the guide will separate the good from the great.
Back on topic, Hidden Power is a move that does from 68 and 70 damage and can be any type except Normal. While this seems random, it is only to a point. The random part is to get the IVs needed for Hidden Power's type and damage, since IVs determines Hidden Power's type and damage. Note that Hidden Power is usually abbreviated as "HP: Type" since you would want to specify which type your Hidden Power is. For example, I would say that my Gyarados has HP: Flying. Now that we know that IVs contribute to Hidden Power, we will find out how.
a) The Second Generation
Attack and Defense IVs determine Hidden Power's type in GSC. For the purposes of the Pokémon not sucking, I will list what IVs needed to get what type from 8-15 instead of 0-15.
Attack IV-Defense IV-Type of Hidden Power
8-8-Fighting 8-9-Flying 8-10-Poison 8-11-Ground 8-12-Fighting 8-13-Flying 8-14-Poison 8-15-Ground
9-8-Rock 9-9-Bug 9-10-Ghost 9-11-Steel 9-12-Rock 9-13-Bug 9-14-Ghost 9-15-Steel
10-8-Fire 10-9-Water 10-10-Grass 10-11-Electric 10-12-Fire 10-13-Water 10-14-Grass 10-15-Electric
11-8-Psychic 11-9-Ice 11-10-Dragon 11-11-Dark 11-12-Psychic 11-13-Ice 11-14-Dragon 11-15-Dark
12-8-Fighting 12-9-Flying 12-10-Poison 12-11-Ground 12-12-Fighting 12-13-Flying 12-14-Poison 12-15-Ground
13-8-Rock 13-9-Bug 13-10-Ghost 13-11-Steel 13-12-Rock 13-13-Bug 13-14-Ghost 13-15-Steel
14-8-Fire 14-9-Water 14-10-Grass 14-11-Electric 14-12-Fire 14-13-Water 14-14-Grass 14-15-Electric
15-8-Psychic 15-9-Ice 15-10-Dragon 15-11-Dark 15-12-Psychic 15-13-Ice 15-14-Dragon 15-15-Dark
You might be wondering how to use these numbers, and it's all very simple. Once again, if you're battling over GameBoys, then don't even consider getting a specific IV for more than one stat, because it is just too hard. If you are battling online, you can set the IVs so it will yield a certain type of Hidden Power. For example, you want your Celebi to have HP: Electric. You should then set your Attack IV to 14 and your Defense IV to 15. Note that Celebi doesn't use its Physical Attack (or it shouldn't) anyways so lowering its Attack IV won't really make a big difference. Now, how do you know what will be the power of Hidden Power? The Special IVs determine this. Once again, I will provides IVs from 8-15 to not Butcher your Pokémon's Special.
Special IV-Power of Hidden Power
8-68 9-69 10-69 11-70 12-68 13-69 14-69 15-70
b) The Third Generation
The Third Generation is more complicated, since all IVs are considered into Hidden Power's type. It is crucial to consider the best IVs for your Pokémon. For example, to get HP: Rock, you can use 31 Hit Points, 31 Attack, 30 Defense, 30 Speed, 31 Special Attack, and 30 Special Defense IVs, or 30 Hit Points, 30 Attack, 31 Defense, 30 Speed, 31 Special Attack,k or 30 Special Defense IVs. Since both yields HP: Rock, we need to pick the better once. Note that one uses 31 Attack IVs and one uses 30 Attack IVs. It is recommended to use the one with 31 Attack IVs since HP: Rock is a Physical Attack and it's more compatible with a higher Attack stat. This is assuming that the rest of this Pokémon's damaging moves are Physical Attacks, as it should be. Here is a list of all the highest combinations of IVs to get different types of Hidden Power with 70 Power. Since all 6 IVs come into consideration, a complete list would be confusing and not needed. Once again, pick the IVs combination that does not exploit your Pokémon's weakness or downgrade your Pokémon's strengths. A common mistake is HP: Ice on Jolteon. You have to choose the combination that retains Jolteon's high Speed, or else Aerodactyl can beat it.
HP/Attack/Defense/Speed/Special Attack/Special Defense
Fighting: 31/31/30/30/30/30, Attack advantage 30/30/31/30/30/30, Defense advantage
Flying: 31/31/31/30/30/30, Attack and Defense advantage 30/30/30/31/30/30, Speed advantage
Poison: 31/31/30/31/30/30, Attack advantage 30/30/31/31/30/30, Defense advantage
Ground: 31/31/31/31/30/30, best combination
Rock: 31/31/30/30/31/30, Attack advantage 30/30/31/30/31/30, Defense advantage
Bug: 31/31/31/30/31/30, Attack and Defense advantage 31/30/30/31/31/30, Speed advantage
Ghost: 31/31/30/31/31/30, best combination
Steel: 31/31/31/31/31/30, Attack, Defense, and Speed advantage 31/30/30/30/30/31, Special Defense advantage
Fire: 31/31/30/30/30/31, Attack advantage 31/30/31/30/30/31, Defense advantage
Water: 31/31/31/30/30/31, Attack and Defense advantage 31/30/30/31/30/31, Speed advantage
Grass: 31/30/31/31/30/31, HP advantage 30/31/31/31/30/31, Attack advantage
Electric: 31/30/30/30/31/31, Special Attack advantage 31/31/31/31/30/31, Speed and Defense advantage
Psychic: 31/30/31/30/31/31, best combination
Ice: 31/30/30/31/31/31, Speed advantage 31/31/31/30/31/31, Attack and Defense advantage
Dragon: 31/30/31/31/31/31, HP advantage 30/31/31/31/31/31, Attack advantage
Dark: 31/31/31/31/31/31, best combination