Here are all the champions:
Alistar, Amumu, Anivia, Annie, Ashe, Cho'Gath, Evelyn, Fiddlesticks, Jax, Judicator, Karthus, Kassadin, Master Yi, Morgana, Nunu, Rammus, Ryze, Singed, Sion, Sivir, Soraka, Teemo, Tristana, Tryndamere, Twisted Fate, Twitch, Veigar, Warwick, Zilean.

Present your list of champions that deserve a solo, in order, starting with the most deserving.

My criteria are threefold: Lane dominance (ability to threaten the enemy through leveling faster than them), lane durability (ability to hold your own 1v2), and lategame dominance (the boost provided by soloing is worth it to your team lategame, when you provide some significant benefit due to your increased levels and farm).

Based on that:

1: Karthus. A+ C A. He can easily get first blood, but the only defense he has is his wall of pain. Lategame fed Karthus is a monster.

2: Anivia. A B+ B+. With stellar harassment and great durability, makes a fine solo choice.

3: Fiddlesticks. B A A-. While not generally a first blooder, it is difficult to kill a solo Fiddlesticks earlygame. An early crowstorm is where he really shines.

4: Zilean. B B- A+. Zilean, as one of the best harassers, is best paired vs the enemy carries to keep them in line earlygame. IMO he is the best support in the game, and very level dependent. The boost from the early solo will not be amiss lategame as he supports your team to high heaven.

5: Twitch. A A- B-. A good Twitch is fantastic at shutting a lane down, but lategame his potential is limited vs a good team.


Note that I didn't include typical carry-solos like Ashe or Tristana because I feel that they simply farm the earlygame while not impacting the enemy lane very much. I feel there are better uses for a solo. However, if through a jungler you grab 2 solos, giving them a solo as well is a fine choice.

Other picks that are decent at soloing might be Jax, Singed, Yi, Sion, Sivir, Tryndamere, Twisted Fate, Veigar. They just aren't as high on my list.

I think Karthus goes better with something like chronokeeper or someone who can mess up someone's movement for some lay waste awesome.

1. Tristana A A+ A. Her exploding shot lets her farm real good and hold back the other lane and she's got a sick escape mechanism and she's kind of scary as a late game character

2. Ashe A A A. She's got volley and stuff, carries pretty cool later game and can make people sorry if they try to gank her and it goes bad.

4. Anivia A A A-. She kills stuff pretty good but you need to be good at aiming flash frost for it to be beast. Not really a late game carry but hard to gank and can get first blood and stuff and with guardian angel pretty tough to take out of action (not really worthwhile to focus fire on first with all this!)

4. Twisted Fate A A- B. This guy soloes pretty good and even though he's not a sick carry lategame if he gets some feed and gets ahead he can gate all over the place pushing lanes and ganking kids. He also shoots cards or something and makes people sad because his harassing is so mad

5. Kassadin A B B+. This guy is very strong early game. He can hit caster creeps to keep his mana up and his nuke is very powerful. The faster he gets to 6 the faster he can kill people and if he gets ahead of the curve he becomes a big threat and a strong chaser all game because almost nobody can get away from him

Zilean would be a decent solo but imo his duo capability is far better because when paired with a tank or someone else that can protect him, his harassment is ridiculous.

This is true, but is that enough justification to deny the solo to a possibly better choice?

That being said I hadn't included that. Rushing someone to level 6 can be a gamechanger. But in the same vein, I'd say karthus ult is more important to reach fast, as it ensures a lot of kills.

Morgana can be an excellent solo.

Pit is great for pushing, and pit+root makes her a great candidate for FB.

Warwick should never solo. If he's solo-ing, why not jungle and give your team two solos?