Magikarp in depth
The carp that climbs the Dragon Gate
The jumping is not a whim on the designers' part. Carp really do swim upstream, and that behavior gave rise to a Chinese legend: any fish that manages to get over the Dragon Gate waterfall, on the Yellow River, will transform into a dragon. In China, the story was used for centuries as an image of social advancement, especially in connection with the imperial examinations, where a candidate from a humble background could become a civil servant through sheer persistence. The whole design is right there: a ridiculous fish that keeps jumping until one day it becomes a furious sea serpent. The final irony is that Gyarados ended up Water- and Flying-type, never Dragon-type, which still irritates part of the audience. The legend's echo survived somewhere else — in the Dragon Egg Group that Magikarp drags around without earning it.
The names point to the same joke in two languages. The Japanese, コイキング (Koiking), combines 鯉 (koi, carp) with “king”, a royal title attached to the most common animal in the pond. English crosses magic with carp: magic that does not appear anywhere until level 20.
Two moves and a salesman
In Red and Blue, its complete level-up movepool consisted of Splash at 1 and Tackle at 15, with 35 power at the time, and not a single compatible TM. Flail did not exist yet. The second generation gave it Flail at level 30, and the eighth moved it up to 25, where it remains. There was also an old distribution of specimens that knew Dragon Rage, the only time this fish has dealt real damage on its own.
Kanto's other legacy is commercial. In the Pokémon Center on Route 4, a man sells a Magikarp for 500, and the price is the whole point of the character: he asks for money for something you can catch for free in any puddle. The scene comes from the anime and has returned in several later games.
Feebas, Wishiwashi, and the school of useless fish
The idea of a deliberately useless creature hiding a second form has had descendants. Feebas repeats the formula in Hoenn with a much more convoluted evolution condition, and Wishiwashi takes it to the opposite extreme: instead of growing, it joins up with a thousand others. Neither has achieved the original's status, perhaps because they arrived after the joke had already been told.
In 2017, Nintendo released Pokémon: Magikarp Jump, a whole mobile game devoted to training carp to jump high, with more than thirty different scale patterns to collect. A Pokémon whose only acknowledged ability is jumping ended up starring in its own title, and the game is exactly about that.