Remember that this is largely opinion and it is not based on the best jungle PICKS since that is highly objective and subject to opinion. This list is taking into account the potential of characters to jungle on their own regards to make measuring their capabilities easier. These lists will also be updated even before the new champion is released if they're delayed like they have been for Zyra and Diana.
Tier 3 – Gragas, Evelynn, Singed, Twitch, Galio, Fizz, Pantheon, Renekton, Rumble, Fiora, Twisted Fate, Janna, Blitzcrank, Kennen, Taric, Sion, Ezreal, Soraka, Karthus, Cassiopeia, Lulu, Ziggs, Leona, Heimerdinger, Brand, Yorick, Mordekaiser
For tiers 1 and 2 - the placement is more important towards indicating "who is better" but less so for tier 3. In tier 3, just think of it in brackets as the champions here are more flawed and harder to argue. You can say that the higher tier 3 champions are better than the lower tier 3 though. For Tier 4 and 5 it's pretty much wishy washy.
Tier 1 is based more on general all around high quality junglers. Tier 2 is based on junglers with great aspects and a few flaws but being able to fill a niche that gives them some validity. Tier 3 is taking what Tier 2 is based around and basically pushing the importance on niche a lot more. The other two tiers are just throwaways.
Some people seem to be getting confused with the ranking. It should be obvious by seeing who gets the S scores that S means higher than A.
S scoring is just some video game thing used to say things like “Oh man you are amazing” etc etc. It’s most commonly used in arcade type games.
Btw before I go on I'll just state who it think some of the best PICKS are at the moment. The obvious Mundo and Nocturne (due to tournament player) are there as well as Nautilus (for teams) and Olaf for counter picking-jungle carry status. Lee Sin is always a safe one while Udyr tends to be binary depending on the competency of your team. When all else fails - pick the all purpose Jarvan.
The things that have changed this time around - which aren't much and mostly shifts. Diana is probably what you want anyways and hers are big.
Jax - Moved up even more due to his square jaw and ability to snowball out of control. He likely can never move out of tier 2 because of his weaknesses that can be exploited. However he is still a ticking time bomb even if he gets countered early. Just drag the game out and he should naturally recover ~ of course that is if they let you.
Nasus - Woof Woof
Skarner - Moved above Udyr because of his ability to snowball harder and simple use of his ultimate. Udyr is slightly faster and more versatile than Skarner but Skarner has an easier time ganking and his ultimate can be a game changer.
Master Yi - He's one of those junglers that "can" work once in a full moon and become terrifying but the chances of that require too many conditions to be met. What he can do others can do better without the risk involved. He requires too much gold but has weak ganking and dueling. He's a thief with no escapes that relies on RnG to clear. His ganking is poor except his ambush ganks. Even when it comes to late game terror mode he can still be shut down hard and even easier than those above him that aimed to have done the same thing like Jax.
Diana - Well she's definitely something here. For starters I don't know whether she'll be nerfed or not so don't ask me. Riot has a bad history with assassins because they make bad players feel bad. I'll break it down into pieces.
speed - She's incredibly fast and she maintains that speed throughout the jungle even without offensive items. She gets even faster still and with her speed she can invade quite well to steal camps. Her buff control is fine in that she destroys the camp quickly.
objective control - she is pretty terrible at dragon I won't lie and she won't be buying wriggles in order to slay it. Not much to say here really.
ganking - it is really poor pre 6 and even at level 6 it still suffers from usability issues. For starters she has no disengage and she's pretty smush early even with that shield. If you go in on a bad fight you're asking to die. Once level 6 is achieved her ultimate is a strong gap closer but if used without Q then that's it. What I can observe is that her ultimate lets her gank in two ways. One way is to hop to apply your moonlight and then pounce on them and continue chaining that much like you would with Olaf. The other way is to initiate with your ultimate (thus not refreshing it) and using E for some CC and hoping your teammate is on the ball with you on the game.
Sustain - As long as you get blue then you're set for the rest of the game. The first blue is very vital for her first clearing and after that she should have no real problem as long as she isn't spamming her abilities each camp. Her health sustain is godlike thanks to that shield too. If it wasn't for having to be careful with her abilities then she'd have scored perfectly on this.
Build - This is the real beauty of her. She has so many build paths - including AD/hybrid - that she can work her gold in so many different ways. She hyper snowballs like a god and can certainly dish out heavy amounts of damage with items. One of the most valuable things about her is that she can go triple gp10 into a high cost damage item like rabadon's and then build off of those items well enough. She is very gold efficient even if she does require a steady stream of it.
Her weakness is her lack of real tankiness, crowd control and her weak early dueling. As for whether she's a good pick well she can be you just gotta shift the tanking responsibilities elsewhere and then bring her on board.
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