Max Stats are the highest possible levels of statness a Pokémon can have. For the purposes of demonstration, I will be referring to Porygon2's stats to help explain the concept of Max Stats.
Porygon2's highest possible stats are: HP 373 / AT 258 / DF 278 / SA 308 / SD 288 / SP 218 This is as high as they can get. However, not every Porygon2 is going to wind up with stats like this. In fact, very few Pokémon will ever wind up with their stats maxed out like this. It is due to the Determining Values, or DV's, of a Pokémon that makes their stat setups different.
There are four DV's, Attack, Defence, Speed and Special. Both Special Attack and Special Defence run off the same DV, and Health is calculated from the four. There are 16 DV's, 0 ~ 15, each one representing 2 stat points. A DV of 15 is Max. If my Porygon2's Attack stat is Max (which it is) the stat will be 258. On the other hand, my Porygon2's Defence is 14. 278-2=276. One DV point equals two stat points. In total, a stat can be off the Max by as many as 30 points. There is no possible way to raise the stats any higher than what the Pokémon's DV's determine.
DV's are determined randomly when you catch or recieve a Pokémon. To obtain my Porygon2, I saved right next to counter and kept checking my Porygon until I got one with stats I liked. This works with all Pokémon except for the GS Legendaries. Once you release Raikou, Entei and Suicune from the tower, their stats are set.
The Health stat is determined by the other four stats. HP starts at 0. If the Attack stat is odd, +8. Defence, +4. Speed, +2. Special, +1. Simple enough.
My Porygon2's DV's are as follows: Attack 15 / Defence 14 / Speed 1 / Special 14 What does this mean? It means my Porygon2 has a Health stat of 10. It gets +8 for having an odd Attack DV and +2 for having an odd Speed DV. (In the Pokémon world, 1 is odd and 0 is even.) Thus, its stats are actually: HP 363 (-10) / AT 258 (Max) / DF 276 (-2) / SA 306 (-2) / SD 286 (-2) / Speed 190 (-28) This is a very good Porygon2, if I do say so myself. The low Speed is not a concern because it has Agility.
At Lv. 100, if your Pokémon has not gained all 63 points, it can still scrape them together by using the Box Trick. Usually, leveling up is what sets off the Stat EXP to bolster your stats. Putting your Pokémon in the box has the same effect. So, if your Lv. 100 Porygon2 uses up all of its PP several times fainting things and you place it in the box, its stats will rise by 3 or 4 points. This will ONLY increase its stats to the Pokémon's personal Max stats! My Porygon2 has raised its stats to 363/258/276/306/286/190. They will NOT rise any more, because that is my Porygon2's personal Max Stats.
And that's all there is to it. Simple, ne? ^_^ If you have any questions, please EMail me at uiru@cephiro.com.