League of Legends - True Tier List and Logical Banning

When playing solo queue ranked games in League, if you are the first player of your team, you get to ban characters from the game, based on yours and your teammates perception of those characters value.

I, on the other hand, am not in favor of banning characters by perception. The logical action would be to ban characters with the highest win ratio, such as Rumble or Singed.

On the other hand, those characters aren't often picked, and a ban on them might prove useless. So what you really want is to ban characters that have the highest probability of being picked AND winning.

First you figure out how likely that character is to be picked, based on the games that it isn't banned.

    P(beingPicked) = %games / (100 - %bans)  

And then:

    P(being picked and winning) = P(beingPicked) * P(winning)

And you get this ban-worthy Tier list:

data retrieved from LolKing on  2013-02-05

• Popularity: % of games played;
• Win Rate: % of games played won;
• Ban Rate: % of games banned;
• AdjGames: % of games played when not banned;
• PickedAndWin: probability of being picked and winning
• PerceivedTier: tier based on banned games;
• Tier: tier based on PickedAndWin probability;
• TierDiff: difference between Perceived Tier and tier.

As you can see there is quite a difference between what actually wins games and what people ban. On the other hand, judging by values in TierDiff, you can see that not many champions are overestimated, and when so, not by much. But, when talking about underestimating champions, you can look at Taric, the number one Tier character right now, Graves, Leona, Sona and Lux and clearly see that these champions' worth is underestimated. So, if you want to be a trickster you should play these.

If you just want to ban the strong ones, you should go for the top tier ones, that are not banned often: Taric, Ezreal, Miss Fortune, Caitlyn, Nunu, etc. All of these are strong game-winning choices that should be banned more.

This is just something to base decisions on. It doesn't account for synergies, or counters. It is also a bit flawed because it is supposedly sampling all ranked games, not just the good ones, like the ones in Silver+ leagues. On a math level I believe this view is pretty strong, tho.