I felt like looking at the rankings even more
If you sort by damage dealt, you have to go down to rank 17 to find a manaless champion, and its Kennen
Zed is #34 on damage dealt and Yasuo is #45, 4 from the bottom
If you sort by damage taken, you have Vladimir at #3 and Akali at #5. Yasuo is #15 and Zed is #22.
If you sort by minions killed, Yasuo is #4, Vladimir is #10 and Zed is #24
If you sort by gold earned, Yasuo is #8 and Zed is #16.
If you sort by kills, Akali and Kat are #1 and #2, Zed is #6, and Yasuo is #21.
Picking a mana champ in mid is simply gimping yourself.
This statement is factually incorrect. There is no evidence in any of these statistics that mana using champions are suffering to perform as well as manaless champions. The only category manaless champions seem to shine in is number of kills, but ironically enough they struggle to actually output large amounts of damage in a game.
If anything, this evidence shows that if you pick a manaless champion and aren't superbly good with them, you're gimping yourself.
If you want kills, pick Fizz or Talon instead of Zed
If you want high damage numbers, pick Karthus or Velkoz, not Yasuo
If you want a lot of farm, pick Karthus, Ziggs, or Veigar, not Zed or Yasuo
If you want to take damage for your team, pick Swain.
http://champion.gg/champion/Zed/Middle
Take a look at the champion matrix, the funny pentagon graphic. Notice how Zed earns more gold and gets more kills than the average midlaner, only to win less and have less damage output.
http://champion.gg/champion/Yasuo
Look at the one for Yasuo. He kills more minions on average just to do less damage and win less.
http://champion.gg/champion/Katarina
This is Katarina's. All she stands out in is kills. All the gold she gets goes towards killstealing, not damage output.
http://champion.gg/champion/Velkoz
Now look at Vel'Koz. He kills the same minions as an average midlaner, but has tons more kills, assists, damage, and a much higher winrate.
Picking a mana champ in mid is simply gimping yourself.
This is simply wrong.