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I'm working with baseball statistics and I have a list of the players' batting percentages. I want a formula that will tell me what percentage of the data is represented from a player's score compared against the others as a percentage.

For example, I have PlayerA, he has the highest batting average in the sample, so he is represented as 100%. PlayerB has the second highest batting average, he is represented as 98%. The percentage is NOT dependent on the size of the population (i.e., if the total population were 50 and I wanted to measure the value from the population directly then it would go by twos down to zero). The measurement is a percentage of the range of values. So if five players all had close batting averages their percentages would all be nearly the same.

Another way to phrase this would be, e.g., I am 6'2" and I know the height of each member of the population. After I plug in this formula I am able to discern that I am taller than 72% of the population. It seems like it would be related to a Z-score but I'm not positive.

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    $\begingroup$ What do you intend to do with this "normalized percentage" once you have it? Your answer to this matters: for some purposes it will be fine, but for other purposes it's a lousy number to use, because it depends on the two most extreme players--the best and the worst--and in general it's a bad idea to base one's analyses and decisions on such exceptional quantities. $\endgroup$
    – whuber ♦
    Aug 30, 2012 at 21:10
  • $\begingroup$ First of all, you are not 72% of the total height of the population. You might mean that you are 72% as tall as the tallest person; or you might mean that you are taller than 72% of the people. Either one would be easy to calculate, given the data. The second is called a percentile. Also, a player's score does not represent any percentage of the data. Why not give a list of scores and tell us what numbers you want? $\endgroup$
    – Peter Flom
    Aug 30, 2012 at 21:11
  • $\begingroup$ @Peter I believe the OP may have a third interpretation in mind, which is to convert each observation $x$ into $(x - x[1])/(x[n] - x[1])$ for a population $x[1] \le x[2] \le \cdots \le x[n]$: a "percentage of the range of values." $\endgroup$
    – whuber ♦
    Aug 30, 2012 at 21:13
  • $\begingroup$ That's certainly possible @whuber. I hope he can explain what he means. $\endgroup$
    – Peter Flom
    Aug 30, 2012 at 21:17
  • $\begingroup$ @whuber By normalized percentage I mean that the top score will be 100 and the lowest will be zero. For example a batting average of .280 means nothing without the comparison to other scores. so I am trying to see what one score's value represents among the whole population. $\endgroup$
    – Zombian
    Aug 30, 2012 at 21:28

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After the discussion in comments, it turns out that what @Zombian wants is a percentile.

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