Mid is the best role to carry
[slayer-jinx-catface]
Just my opinion:
TOP: this used to be the lane where the "better" players came to snowball and carry games. Now, it feels like 50/50. You may find a difficult opponent or an easy opponent. But you most likely have to play a tank. You don't have ignite to help you get kills, which means it's harder to land kills. You have to somewhat rely on your teammates to use teleport. A bad skirmish with junglers just may net your carry potential to 0.
JUNGLE: this used to be the easiest role to carry with by impacting all lanes or getting fed as a carry jungler. You can carry if your laners are actually half decent, which is not a reliable factor. Otherwise, teammates will just hand over free kills, putting you back at square 1.
SUPPORT: good impact in the game but... if your adc is bad, you have to roam or you have no chance in carrying. Your teammates tend to not like roaming supports.
ADC: If you have a terrible support then your chance of carrying the game is almost 0 unless you get to farm for a long time. You are not very relevant early to mid stages of the game.
finally,
MID: Relevant from early to end, and good opportunities to snowball. Having a crappy jungler can make the game a bit difficult, but enemies will gank you left and right center so if you don't get ganked, you can slow down snowballs.
[slayer-pantheon-thumbs]