There's a lot of things that influence what stats you get when you finally overcome the odds and receive a Pokemon at level 100. Say you have a Salamence, and you decide to battle someone else's level 100 Salamence. Your Salamence uses Dragon Claw and takes half of the opponents HP away. In return, the other Salamence uses Dragon Claw as well and takes all of your Salamence's HP away. "What gives? Shouldn't the attacks do the same amount of damage?" Well, no. More than likely, the Salamence that got knocked out probably had lower HP and Special Defense than usual, along with Special Attack. This is influenced by a lot of values, but in particular, Individual Values.
Individual Values have the most influence on any stat of any Pokemon. It's what makes every single Pokemon unique and have different stats. Say we have the mega-defensive bug type, Shuckle, and it's EV trained in both defense and special defense and it's at level 100, and a neutral nature. If we look at the base stats for this Pokemon's defense and special defense, they both say 230, so you'd figure there wouldn't be much of a difference, right? Well, in reality, there can be a pretty wide difference. At level 100, this Shuckle has a defense stat that is 466, and a Special Defense stat equaling 542. Quite a wide difference there, about 80 points separated. A person using this Shuckle had better watch out for attack based moves if they are relying on defense.
As for technical information pertaining to Individual Values, the equation for it will –usually- give a number between 0 and 31. Keep in mind that the equation's we have to the IV's are not the same as in the game, but they are extremely close. With these equations, it's best to calculate it closest to level 50 as possible for accurate results. If you're looking to calculate a Pokemon's IVs that you have trained, then hopefully you know the Effort Points it gained. If you don't then the math will be completely inaccurate if you just stick the stats in the equation. If you don't already know, Hidden Power is calculated completely on IV's.
As you can see there's a lot of things you need in order to do these equations to get the Individual Value that this returns to you. The most important thing you need is the stat, apparently. The second thing you need is the Stat, which is basically what effect the personality has towards your stats. Now because we know that Natures can give a +10% increase towards a stat, or a -10% decrease towards a stat, we need to convert that to an actual number so that it can work in the equation.
If the Nature gives a +10% increase to a stat, then the Stat = 1.1
If the Nature doesn't have an effect towards the stat, then the Stat = 1
If the Nature gives a -10% decrease to a stat, then the Stat = 0.9
The last thing you need are the Effort Points gained from battle, which are explained in another guide. Effort Points are equal to zero if you never battled with it yet, or used rare candies to level up, or even used the daycare to level up. Anyway, suppose I went through Colosseum twice and caught two Forretress. Let's find all we can about the information we need about them so we can determine the IVs.
Hope I helped