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2758Maximum standard deviations (math help needed)

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  • monepeterson
    Nov 27, 2003
      First of all, please excuse the inarticulate nature with which I'm
      about to explain my problem:

      I'm tracking team performances from year to year in the NBA and NHL.

      The methods I'm using are simple but have some problems. The first is
      winning percentage minus the mean (.500) divided by the standard
      deviation for winning percentages that year. The second is point (or
      goal) differential divided by the standard deviation for point
      differential that year. Rob Neyer and Eddie Epstein did this for their
      "Baseball Dynasties" book, although they made the mistake of doing
      seperate deviations for runs scored and runs allowed and then adding
      them together.

      I know that the maximum standard deviations for any team in any given
      year is square root (n-1) where n = the number of teams in the league
      that year, and I've factored that in.

      But there's another factor, and I don't know how to resolve it.
      There's also a maximum SD possible for a team depending on how high or
      low the league standard deviation is. Um, right?

      For winning percentage, I think it's one divided by the league SD. Is
      that right?

      But for linear numbers like point and goal differential, I have no
      clue where to start. In 1976, the standard deviation for point
      differential in the league was historically low, making the Golden
      State Warriors of that year look like one of the best teams of all
      time. While the Warriors were really good, they have no control over
      how even the rest of the league is, so I'm trying to account for that.
      Is there a way to account for that? Preferably in the form of a
      formula I can toss into Excel?

      Hope the question is clear.

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