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17226Re: [Speed cubing group] Method for Handicap Competitions

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  • Dan
    Jul 1 2:02 AM
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      Hi Leyan, Tyson,

      The 30 - 40 solves would have to be fairly near the time of the
      competition, yes. As you say, if you were using an out of date
      statistic, it wouldn't work, because people's long term averages
      would slowly increase as they improved.

      This, in my opinion, is the main stumbling block of this method, how
      would you get all the competitors to bother to time 30 or 40 solves,
      before the day of the tournament? Perhaps everyone should time as
      many cubes as they possibly can, in a practice session before the
      competition or so.

      Well, I guess we will just have to see what happens on July 16th!

      Dan :)

      --- In speedsolvingrubikscube@yahoogroups.com, Leyan Lo
      <leyanlo@g...> wrote:
      > Where would you get the 30 solves?
      >
      > If you're using solves that span a large time frame, this is not a
      good
      > idea because most people get faster the more they cube. It would
      > probably be more fair to fit their solve times to an exponential
      decay
      > curve up to a constant as a function of time, and then calculate
      their
      > expected average and standard deviation for the day of the
      tournament
      > from the fit.
      >
      > Leyan
      >
      > PS. From the statistics class I took, I remember the number 40
      (Law of
      > large numbers).
      >
      >
      > Dan wrote:
      > > Hi Everyone,
      > >
      > > I would like some input on the following method for judging a
      > > handicap competition, especially whether it is actually feasible
      to
      > > use in a competition!
      > >
      > > 1. From each competitor, have a long term Mean and Standard
      > > Deviation Statistic. From my Statistics course a long tim ago,
      the
      > > number 30 seems to ring a bell in my head, ie you have to make
      30+
      > > solves before the statistics becomes valid.
      > >
      > > 2. After the competition, calculate each competitors average.
      Then
      > > calculate a Normal Probability, with competition average as
      the "x"
      > > statistic, and using the long term Mean and SD. This will
      calculate
      > > the probability of the competitor achieving this competition
      > > average, if they were to make many thousands of averages.
      > >
      > > 3. The competitor who has achieved the lowest average
      probability
      > > would win, and competitors are ranked in order of ascending
      > > probabilities.
      > >
      > > So, all fine in theory?
      > >
      > > I have tried plugging some numbers into a spreadsheet, and the
      > > results are quite promising. But one observation I have made, is
      > > that in real life, results don't seem to "quite fit" the normal
      > > distribution. It is perfectly likely for someone who is quite
      > > consistent in practice, to have a wildly varying average in
      > > competition, and the probabilities end up being almost 0, or
      almost
      > > 1. Is there someway of "stretching" the margins of the normal
      > > probability, so it can cover a wider range of results? One way
      would
      > > be to multiply the competitors standard deviations by a factor,
      but
      > > is this mathematically valid?
      > >
      > > Any help is greatly needed :)
      > >
      > > Dan Harris - www.cubestation.co.uk :)
      > >
      > > P.S. I hated Statistics in college ;)
      > >
      > >
      > >
      > >
      > >
      > > Yahoo! Groups Links
      > >
      > >
      > >
      > >
      > >
      > >
      > >
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