WHIRLWIND EXPLANATION: Pokémon have a fixed, permanent score from 0 to 31 for each stat that affects how good that stat can ever get.

This calculator will figure out that score (called a "gene" or, more obtusely, an "IV") for you, so you can discard the unworthy. It's more accurate for higher-level Pokémon, so it's helpful to go into a level 100 wifi battle with someone and check your Pokémon's stats from there.

Stat calculator

Gyarados
Gyarados 		Base
stats		 Stats Effort Possible genes (IVs)
Level
HP 95
297–327
31
Attack 125
252–283
31
Defense 79
161–192
31
Special Attack 60
123–154
31
Special Defense 100
203–233
31
Speed 81
165–196
31

Congratulations, you've narrowed your Pokémon's stats down exactly!

This Gyarados's Hidden Power inflicts Dark damage, with 70 power.

And for your copy/pasting pleasure:

31 HP; 31/31 Physical; 31/31 Special; 31 Speed

or start over