# Create from multiple local ranks, a global one

I have a players, who have played in multiple games and each player is ranked local. For example:

Player1 = {1,2,2,1,2,3,1}
Player2 = {2,1,3}


Now I want to create a global ranking from the locals. What is the best approach to do that? I tried it with t-Test, but having Players like this:

Player1 = {1,1,1,1,1,1}
Player2 = {2,2,2,2,2,2}


I receive a p value, which is NaN

Edit: The players don't have the same amount of played games.

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I don't understand your notation. What does "ranked local" mean, and what do the numbers mean? –  Qiaochu Yuan Aug 18 '11 at 20:41
It means, that every player has a ranking in couple of challenges. Player1 = {1,2,2,1,2,3,1} are the local rankings for every challenge, he did took a part. –  apzur Aug 18 '11 at 21:14
@Qiaochu: I think the goal is to aggregate tournament rankings where each player participates in some subset of the tournaments. –  zyx Aug 18 '11 at 21:55

• Include in each player's score $n$ "virtual" games, where $n$ is the number of players per local game, each with a mediocre rank (i.e. $(n+1)/2$ if the rankings are from $1$ to $n$). Based on the generalized rule of succession, I think this should approximate the "true" rank of each player, but it does give some players who've been lucky in their past games (and thus ranked higher than they expect to in the future) an incentive not to play any more.