Roles in order of ability to potentially carry games.
Before we get into this, here's my definition of carrying.
Carrying is the act of making plays outside of the normal realm of your responsibilities in order to win the game. In other words, taking initiative. Making stuff happen around the map. Going above and beyond what gets you carried.
And I've seen a lot of crazy shit from team carries, so here's, in order, the roles best suited for carrying.
1 - Jungle
Let's be honest, nobody is surprised by this one. Jungle has the easiest access to all lanes and he has Smite. You also don't see him on the map most of the time before he shows up in a lane delivering damage, CC, or a combination of both of them. This allows for unparalleled objective control as the jungler can surprise you, force you back, and then take a tower, dragon, or Rift Herald. Junglers have the ability to get their own lanes ahead as well and, after a few tank items, can dominate teamfights too with a well played catch (like Zac, Gragas, or Jarvan). Their entire kits are often loaded with playmaking tools and junglers are either Fiddlesticks/Yi or the first characters in the fight.
2/3 - Support/Mid
This one should be surprising. A lot of it is dependent on the champions played, but support and mid are, IMO, vying for second place.
Supports have a high potential to carry because, like junglers, they have a high ability to make plays. With champions like Leona, Nami, and Thresh, bot laner are dependent on these champions to force fights and get kills. I rate them not nearly as high as junglers because supports are more tied to a lane than junglers. They also often come with a level disadvantage and their need to usually stay by their carries in 5v5 teamfights. However, in the midgame there is nobody I see rack up a higher body count than a competent Leona pushing for objectives in every lane. And again, while they're more tied to a lane than junglers they are less tied to laning than anyone else, meaning it's ok for supports to roam far more frequently than anyone else. The best and worst example of carrying from experience is Bard, because while his entire kit is one big play, its so open ended people fail at playing him because there were 3 other possible actions he could've taken with his ultimate that would've had better results.
Unless your support is Soraka and your midlaner is Twisted Fate, I personally rate mid just under support. Mid is full of champions that have fantastic abilities and kits. The problem? You're a squishy champion with (usually) awkward/delayed self-peel aside from "well just kill them faster". This means you have to play carefully and mind the rules of engagement. Sit behind your tanks and poke until the teamfight begins, and once the huge spells are burned then you're able to go in and deal consistent damage. Sure, as Ziggs you can get that game-winning ultimate on both their carries and win the teamfights, and there is far more open ended gameplay than the two other roles, but it's not as consistent with safer champions. The real carry potential comes from you having the 2nd most lane access behind the jungler. This allows for picking up easy kills on botlane through a well timed roam or taking a dragon with your jungler while their team is none the wiser.
And before anyone asks, I think the champion that has the most carry potential for mid is LeBlanc. So then why does she fall off? Because late-game her only option in teamfights is to carry. If she cannot do that, any teamfighting mage even with a gold deficit of 50-100 less cs will likely be more useful than her.
4 - Top
A majority of top's gameplay comes from one thing - teleport. Teleport is a fantastic summoner spell that allows them to deliver basically jungler presence from anywhere on the map. The catch? It's slow to activate and it comes with a hefty cooldown. Of course, top laners have other tools to win fights, but none is nearly as prevalent as TP. However, even recently I've seen some fantastic playmaking come from top, in the form of ballsy Lissandra players, Kennens, and Malphites. Top lane as a whole though is wrought with champions who don't make plays but follow up on them. Champions like Renekton or Irelia, staple toplaners, don't have much carry potential outside of zoning in lane and in teamfights and splitpushing.
5 - ADC
I know what you're thinking. How could a champion with so much raw damage be rated so low on their ability to carry? Refer to the top section. It's their job deal tons of damage and win teamfights. An AD that is dishing out damage is simply doing what they're designed to do. They're constrained by the same laws that say squishies need to sit back and wait for all the mobility/CC to blown, and then they can go in and rack up a body count. So what makes me so sure of this?
Corki. As soon as Corki got some serious playmaking tools he was moved to midlane.
But for the most part, ADCs are just doing their job. Cait is supposed to drop traps under your tower and then auto you when you step on them. Ezreal is supposed to Q you incessantly. There are a few exceptions, namely the utility champions and Lucian. The utility champions, such as Ashe, have spells like ECA that allow for picks on unsuspecting midlaners or caught out supports. And in Lucian's case, he simply picks them out by overwhelming them with damage and mobility.
Keep in mind, this is only carry potential. This doesn't mean your role is the easiest to get carried on nor the hardest. This is just the roles I've seen have the easiest time carrying games.
