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This is my first question across the StackExchange network, and it seems a lot easier than other questions I've seen on here (so I hope it doesn't bore you!), but I can't seem to come up with the answer myself.

I'm re-writing an old browser game. Each player has 8 separate measures of their power (for simplicity, they can be A-H). Each of these is currently ranked highest to lowest.

What I need to do, is devise a formula to enable a global ranking list.

What I've thought of so far:

  • For each player, sum their A-H values and then sorting each player highest->lowest.
    • Possible problem: As each of A-H is calculated differently, resulting in some being harder to increase than others, this would bias the global ranking towards the stats that are easiest to increase.
  • Something to do with what I believe is 'normalisation' (please correct me if I'm wrong) - to combat the above bias towards any one particular stat by putting them all on the same scale. Not too sure how I'd go about this though, or if it's even an accurate way to do what I'm after.

Thanks!

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You need a way to add "weight" to each rank that justifies the ranking. One possible way:

$$A - 1$$ $$B - 2$$ $$C - 4$$ $$D - 8$$ $$E - 16$$ $$F - 32$$ $$G - 64$$ $$H - 128$$

Now when you add the rank values, individual weight matters. This example may be extreme for your game, because rank 'H' is so much more powerful than the rest combined. You'll need to decide how much each of these ranks should weigh.

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