Every battle pet starts with it's own 3 initial stat values:
Health: 100+(initial health stat x pet lvl)
Power: (initial power stat x pet lvl)
Speed: (initial speed stat x pet lvl)
Initial health stat for poor/common wild pets is ~50.
Initial power/speed stat for poor/common wild pets is ~10.
A rare quality pet generally has better initial stats than a poor one.
A rare quality pet is created with an initial stat of >=~12.05 power.
A rare quality pet is created with an initial health stat of >=~61.
lvl1 -> 12 power (12.05)
lvl5 -> 60 power (12.05x5lvl=60.25=60)
lvl25 -> 301 power (12.05x25lvl=301.25=301)
You don't want to lvl up your poor quality pets!
Also it should be noted that certain pets have higher/lower stats such as a roach having a higher base HP stat.
These numbers definitely aren't 100% accurate, however they have been best help and i have quite a fare amount of rare pets in just over an hour. If the numbers don't exactly fit the formula and are off by just slightly(formula says pet should have 500 hp pet has 498) go ahead and try to catch it. It has a good possibility being rare, small possibility of being uncommon, however if it's uncommon you know to look higher than the uncommons stats for a rare.
Happy rare hunting and if you have any questions you can get a hold of me in game or I will check back on here. Hope this helps!