How Stats Are Transferred Through Breeding:

you know that they say, 'two pokemon of the same level and species aren't the same'? their stats are different because of DVs (diversification/determinant values, though the 'D' stands for a different thing on different websites), which are a lot like the IVs of the newer versions of pokemon (go here for zapper's IV guide: http://www.cheat-database.info/display/singlecheat.phtml?id=36954), except that DVs are a number from 0 to 15 instead of 0 to 31. at the same time, though, in the stat calculation formula, the DVs are counted for twice so the max stats of a pokemon in the old versions are the same as the max stats of a pokemon in the advanced generation (as long as its a neutral nature, BTW).

each pokemon has a random 4-bit number from 0-15 (the DV) assigned to each of its stats, and once you catch a pokemon those numbers are set in stone. the HP DV is a little different; to save space it uses the last bit of each of the other four DVs (eg. if you had DVs of 0101, 1001, 0110, and 1101, the HP DV would be 1101, and i'd tell you what that string of 1's and 0's is as soon as i learn to count in binary). the DV for special attack and special defense is shared in GSC (gold/silver/crystal), so that it would be possible to trade with RBY (red/blue/yellow).

DVs can influence an individual stat only by a maximum of 32 (when you're at level 100, of course), but can effect your overall stats by up to 160!

in the old days of red, blue and yellow, the only way to find perfect (15 in each stat) DVs was to catch a whole bucketload of pokemon and hope one of them has perfect DVs. there is only a 1/65536 chance of finding a pokemon with perfect DVs this way. but since you can now breed, there are much greater odds of such things.

to breed, simply leave two compatible pokemon, male and female, in the day care center. check their compatibility by pressing A on them while they're in the daycare center. if it says anything other than 'its brimming with energy!' or 'it shows no interest in xxx', then they're compatible (and they can be incompatible with eachother even when they're the same species sometimes - if their special and defense DVs are the same, the game thinks they are directly related prevents them from breeding with eachother, so you get that moral message saying, 'dont breed parents with their babies!'). walk (or bike) a lot of steps (which can sometimes be a LOT) and voilá! check back on the old man and you get an egg. to hatch it, walk (prefferably bike) a whole lot more steps. the egg will be the species of the female (or non-ditto parent, if ditto is used), with the TM moves of the male, plus some moves called 'egg moves' that can only be found on such-and-such when you breed it with a male so-and-so that knows the egg move. any move possessed by both parents (as long as the parents aren't eevee evolutions) get passed down too.

The egg's attack DV is chosen at random, and is used to determine the egg's gender:

If the DV is lower than the Species Gender Number, the Pokemon will be female.
Otherwise, it's male. -1 is the neutered group.

Table of numbers:

0: Tyrogue, NidoranM, Tauros

2: Bulbasaur, Charmander, Squirtle, Eevee, Snorlax, Chikorita, Cyndaquil, Totodile, Togepi, Omastar, Kabutops, Aerodactyl

4: Growlithe, Machop, Elekid, Magby, Abra

8: anything not listed

12: Cleffa, Vulpix, Igglybuff, Corsola, Snubbull

16: NidoranF, Miltank, Chansey, Kangaskhan, Smoochum (nup; 16 is not a misprint. it makes sure that every one of these pokemon are female)

1-: Magnemite, Voltorb, Staryu, Porygon

(so male pokemon ARE stronger if they were bred! though this is no real concern if the pokemon is a special sweeper and/or an all-female pokemon)

the speed DV is also determined at random.

the Defense DV is passed down from the parent with the opposite gender of the egg (from the mother if its a boy; from teh father it its a girl), or from the ditto parent if you use ditto.

the special DV is also passed down from the parent with the opposite gender of the egg, or from the ditto parent if you use ditto, BUT it has a 50% chance of being offset by exactly 8 (plus or minus, whichever one).

the HP is determined by the last bit of the other DVs.

now lesee those odds on getting a pokemon with max DVs... ok, if i use a ditto with max DVs in Def and Special, hmm...

1/16 (for the attack DV) x 1/16 (the speed DV) x 1 (the defense DV) x 1/2 (the special DV) = 1/512 (and the HP is automatically maxed if all your other DVs are too).

notice its a lot less random than 1/65536. and for special sweepers (that need no attack, only special), its even easier:

1 (the attack DV can be anything you like) x 1/16 (the speed DV) x 1 (defense) x 1/2 (special) x 1/2 (HP, which, when all other DVs are maxed, has a 50% chance that the unused attack DV will end in a '1') = 1/64

lastly, 512 eggs is a LOT of eggs (as is 64, though its not that bad with special sweepers), so as long as you find you've got about 90%-or-so (depending on how patient you are) of the maximum stats (an average of roughly 13.5 DVs for each stat you care about), you can just about jump for joy and get on to the more interesting parts of training your pokes. oh, and dont bother about this if the only battling you'll ever do will be against the dimwitted computer; this breeding is meant to give whoever bothers an edge in link battling (computer battles are too easy; you dont need all this help).

...whats that? how do you get a ditto with 15 DV in both special and defense? well, theres two ways to do it:

1. catch 256 dittos

...or:

2. get a pokemon which already has 15 DV in both special and defense, then trade it to Red/blue/yellow (if its not already in there; i find it easiest to find out a pokemon's DVs if i have the unlimited rare candy trick: raise the newly caught pokemon to level 50 without training it at all, then look at the stats. the way you figure it out is by going: 'the stat you see on the status screen' minus base stat = IV. for a list of pokemon's base stats, go here: http://dynamic.gamespy.com/~psypoke/dex/pokedex.php?id=001&view=stats), then teach it the mimic TM. (give a pokedoll bought at celedon dept store to copycat in saffron)

then, fight a wild ditto with this pokemon in front. first thing you do (before it uses transform), you use mimic. mimic its transform before it overwrites transform with your moves. the ditto should get transform again, even after it has transformed into you. once it transforms into you a second time, catch it! the ditto has had its IVs transferred over from the mimicer, and you can use it for breeding any time once you trade it back into gold/silver/crystal! (PS: if the mimicer was a shiny eg. the red gyarados from pokemon gold/silver/crystal, then the ditto also becomes a shiny. its blue!)