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They write there are Pidgey and Rattata with 2-5 levels in Viridian Forest but I didn't come across a Pidgey above Level 3 and only one Level 4 Rattata. Is it a lie or is there some special subarea where you can get Level 5 Pidgey?
I'm assuming you meant the area outside Viridian Forest. I can confirm from experience there are level 5 Pidgey in the early game, but they're very rare to come by. They're on Route 1 (just north of Pallet Town where you get your starter from Professor Oak). I'm not sure about a level 5 Rattata that early. You can catch a level 10ish Rattata on Route 4 after Brock and Mt. Moon but before Misty (and the rival fight to the north of Cerulean City). I hope this helps.
Distributes the levels unevenly. Probably works like this for most older games, more or less. (Saw similar distributions for original Red/Blue/Yellow.) Possibly extends to current games too. (Knows about SoS calls in Sun/Moon definitely having different rates for different allies, such as 1% Politoeds.) Lacks the technical knowledge to verify, though.