i've only written unfinished drawerfic for pokémon, so you won't find any on my AO3, but it's generally a combination of 1) what i want to ship, 2) which protagonist i personally played the first time i did a run of the game, and 3) whatever weird headcanons i happened to develop as a kid, so:
kanto: red; i make blue and green siblings as a play on their names getting swapped between the english and japanese releases, and because they have the same hair color. johto: kris is "my" canon protagonist, but i actually wrote so much drawerfic of her as a kid that i basically created a whole new storyline where she becomes a legendary hunter and works with lance, lol. so i give the canon-ish storyline to gold, which makes shipping him with silver easier for me, yay. lyra/kotone is gold's cousin. hoenn: may/haruka is my protagonist, with brendan/yuuki as birch's son/assistant. i ship may/haruka with lisia/lutia. sinnoh: dawn/hikari, with lucas/kouki as rowan's assistant. unova: i like to make hilbert/touya and hilda/touko twins who go on the whole journey together! which i think is a somewhat common strategy? so they're both "protagonists," although, yeah, i give the more shippable N interactions to hilbert and then ship hilda with cheren.
i don't have strong feelings past this because B2W2 is when i stopped being very active in the fandom; i played XY and sunmoon but never developed any mental storylines about them. probably by default i would make everyone else girls because i like girls.
i think my preferences are fairly in line with the fandom at large now that i've typed it all out. and i would wager one of the biggest factors is just which gender the writer happened to play when they played the game themself - red and gold/ethan/hibiki being more common than blue/leaf or kris/lyra/kotone makes a lot of sense because for the older generation of fans, red was the only option and kris only existed in a special edition of the game, so most everyone played as red and gold. plus there's some influence from the PokeSpe manga.
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kanto: red; i make blue and green siblings as a play on their names getting swapped between the english and japanese releases, and because they have the same hair color.
johto: kris is "my" canon protagonist, but i actually wrote so much drawerfic of her as a kid that i basically created a whole new storyline where she becomes a legendary hunter and works with lance, lol. so i give the canon-ish storyline to gold, which makes shipping him with silver easier for me, yay. lyra/kotone is gold's cousin.
hoenn: may/haruka is my protagonist, with brendan/yuuki as birch's son/assistant. i ship may/haruka with lisia/lutia.
sinnoh: dawn/hikari, with lucas/kouki as rowan's assistant.
unova: i like to make hilbert/touya and hilda/touko twins who go on the whole journey together! which i think is a somewhat common strategy? so they're both "protagonists," although, yeah, i give the more shippable N interactions to hilbert and then ship hilda with cheren.
i don't have strong feelings past this because B2W2 is when i stopped being very active in the fandom; i played XY and sunmoon but never developed any mental storylines about them. probably by default i would make everyone else girls because i like girls.
i think my preferences are fairly in line with the fandom at large now that i've typed it all out. and i would wager one of the biggest factors is just which gender the writer happened to play when they played the game themself - red and gold/ethan/hibiki being more common than blue/leaf or kris/lyra/kotone makes a lot of sense because for the older generation of fans, red was the only option and kris only existed in a special edition of the game, so most everyone played as red and gold. plus there's some influence from the PokeSpe manga.