Talk:ARAM/@comment-12183650-20130713235913/@comment-18521310-20131002064829

I think your statistics skills are off here. Just look at the way "random" works.

There are 115 champions available currently and 10 players in each game. Let's assume for the moment that in a low-to-medium ELO game, each player owns, on average, 1/3rd of the champions.

Even if that third is evenly distributed accross all champions (which it's not. Because, seriously, who owns Karma? :-p), that means that each champion is owned, on average, by only 3 of the ten players. Free list champions, however, are owned by 10. That alone means that any given free-list champion is three times more likely to be in the game than a given non-free list champion.

That only amplifies when you take into account the fact that not every champion is owned the same amount. Again for sake of argument, let's say that half of all players on Nidalee because of her strength in ARAM games. But only a quarter of the players own Karma. With these numbers, Nid is twice as likely to appear in the game as Karma is. And still only half as likely as any given free-list champion.

Of course, the more champions each player owns, the less "advantage" free list champions have. But also the lower the odds for any one champion. If every player in the game owns every champion, the free list has no effect. But each champion only has a 1:11.5 chance of being in a given game.

tl;dr: Random means that the champions owned by more people are more likely to be selected. Simply because they have more opportunity to be selected. And since free-list champions are "owned" by everyone in every game, they are significantly more likely to be selected.

This would occur even if the random selection process was "roll random champion available to player 1. Roll player two, reroll if already picked. ... repeat for players 3 through 10."