Badges increasing stats? What happened to that?

[Lindz]

Ya back in Gen 1 & 2 after you got certain badges you'd also be told one of then 4/5 non-HP stats would be increased. What was up with that? I never noticed no stat changes! They also dropped it from Gen 3 on. Did your POKéMONs Attack stats really go up from beating Brock way back when? Did that apply to the ones in your party or all of 'em in total? I never understood this at all!

[S_M]

Gen3 did it too I seem to remember, at least in RS. I remember asking this way back on Serebii and the best answer I got was that it globally increased your attack/etc by a small percentage in all of your battles.

[Jerichi]

I thought it threw some EVs into those stats for the Pokemon that were in your party.

[Lindz]

I dun remember being told in any Gen3 game of the stat up thing but it was there and for reals? Crazy!

[empoleon dynamite]

I've looked this up before, it's weird how we know so much about the hidden mechanics in Pokemon game, but I've yet to see a concrete answer on this. What gives?

Anyways, from what I've gathered,

Gen I/II apparently had some percentage cap on stats or something which was lifted by obtaining certain badges. Gen III removed this cap but kept the text as the Gym Leader's Pokemon gave off the EVs pertaining to each stat. They removed it in Gen IV (except for against Pryce for some reason), probably because it was misleading or pointless.