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If I have 3 different metrics and I wanted to find an "average" (not necessarily arithmetic mean) of the 3 metrics so that observations can be ranked, what would be the most "statistically sound" method of doing so?

Here's an example with baseball:

I have 3 metrics:

  • Batting Average (ranges from 0.000 to 0.350)
  • Home Runs (ranges from 0 to 50)
  • RBI (ranges from 0 to 120)

And I want to equally weight each metric and take some sort of average so that I can rank different players, with the best players being great in all 3 metrics.

If I wanted to "average" the metrics so that each metric has equal weight, I could:

  • Standardize each metric so they're all on the same scale and calculate the arithmetic mean
  • Calculate the geometric mean
  • Calculate the harmonic mean

Is 1 of these methods more/less "statistically sound" than the others, in terms of not violating any assumptions or anything of the like?

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  • $\begingroup$ "Statistical soundness" doesn't apply. The right way to combine multiple metrics depends on subjective factors that statistics (alone) cannot determine. $\endgroup$
    – whuber
    Jan 27, 2019 at 23:06
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    $\begingroup$ @whuber thanks for marking this as a duplicate -- I didn't come across that question in my search. Much appreciated. $\endgroup$
    – Evan O.
    Jan 27, 2019 at 23:25
  • $\begingroup$ No need to apologize--it is hard to search for something when there is no evident set of keywords to look for! I am glad that you appreciate the value of finding a relevant pre-existing post--not all new contributors understand that. $\endgroup$
    – whuber
    Jan 28, 2019 at 13:48

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