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Re: [Speed cubing group] Method for Handicap Competitions

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  • Dan
    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 As you say, if you were using an out of date statistic, it
    Message 1 of 13 , Jul 1, 2005
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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 As you say, if you were using an out of date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
      > >
      > >
      > >
      > >
      > >
      > >
      > >
    • Sachin Shirwalkar
      No Dan but there is a way to beat this. If you are considering only the best improvement done by a person then I ll do my worst times in the first 30 solves
      Message 2 of 13 , Jul 1, 2005
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        No Dan but there is a way to beat this. If you are
        considering only the best improvement done by a person
        then I'll do my worst times in the first 30 solves and
        then in the real solves i'll solve normally. So my
        scores come out far better than the 30 previous ones.

        Though this looks like a good idea. Keep working on
        this.

        Sachin


        --- Dan <dan_j_harris@...> wrote:


        ---------------------------------
        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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      • Dan
        Yeah but that s the problem with anything involving people. What s to stop me from posting an average of 15.00 on UWR list, even thought I ve never been under
        Message 3 of 13 , Jul 1, 2005
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          Yeah but that's the problem with anything involving people.

          What's to stop me from posting an average of 15.00 on UWR list, even
          thought I've never been under 16? And it's not that unbelievable
          really. But it might be a bit odd, statistically, I might post a
          fake average where all the hundredths of a second were under .50 for
          example, which is statistically very unlikely. It's also unlikely,
          given enough cubes, that you would beat your long term average by
          more than 3 SD's.

          But yeah, I agree with you, but if people want to cheat, then
          they're only really cheating themselves.

          Dan :)

          --- In speedsolvingrubikscube@yahoogroups.com, Sachin Shirwalkar
          <sachin_civilian@y...> wrote:
          > No Dan but there is a way to beat this. If you are
          > considering only the best improvement done by a person
          > then I'll do my worst times in the first 30 solves and
          > then in the real solves i'll solve normally. So my
          > scores come out far better than the 30 previous ones.
          >
          > Though this looks like a good idea. Keep working on
          > this.
          >
          > Sachin
          >
          >
          > --- Dan <dan_j_harris@n...> wrote:
          >
          >
          > ---------------------------------
          > 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
          > > >
          > > >
          > > >
          > > >
          > > >
          > > >
          > > >
          >
          >
          >
          >
          > ---------------------------------
          > YAHOO! GROUPS LINKS
          >
          >
          > Visit your group "speedsolvingrubikscube" on the
          > web.
          >
          > To unsubscribe from this group, send an email to:
          > speedsolvingrubikscube-unsubscribe@yahoogroups.com
          >
          > Your use of Yahoo! Groups is subject to the Yahoo!
          > Terms of Service.
          >
          >
          > ---------------------------------
          >
          >
          >
          >
          >
          >
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        • Tyson Mao
          Hey... there are three Sundays between now and, the 16th are there? Fine, maybe two, but you can have people all do the Sunday contests? And just have them
          Message 4 of 13 , Jul 1, 2005
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            Hey... there are three Sundays between now and, the 16th are there?
            Fine, maybe two, but you can have people all do the Sunday contests?
            And just have them submit their results to both you and Jon, and for
            the last one, they just have to submit before the 16th.

            Tyson Mao
            MSC #631
            California Institute of Technology

            On Jul 1, 2005, at 3:02 AM, Dan wrote:

            > 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
            >>>
            >>>
            >>>
            >>>
            >>>
            >>>
            >>>
            >
            >
            >
            >
            >
            > Yahoo! Groups Links
            >
            >
            >
            >
            >
            >
            >
          • Tyson Mao
            Is there some prize that s really worth it? That s why we can t do handicap competitions as an official event because there s no sure way to ensure honesty.
            Message 5 of 13 , Jul 1, 2005
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              Is there some prize that's really worth it? That's why we can't do
              handicap competitions as an official event because there's no sure way
              to ensure honesty. For non-official events, and all that other sort,
              such as Sunday contests, or speedcubing.com averages, so far, we've
              been relying on the honesty of the cubers, and it's been working in my
              opinion. There really aren't that many doubtful records, and if
              someone lies, I personally don't care, because your sub-14 average on
              speedcubing.com means nothing to me if I beat you in a tournament.

              If you end up posting a fake average, then you waste the rest of your
              life trying to protect this lie, and trying to prevent people from
              finding out the truth. You're reduced to nothing more than a person
              who makes up excuses on why his times are so slow. It's just not worth
              it :-P

              Tyson Mao
              MSC #631
              California Institute of Technology

              On Jul 1, 2005, at 9:17 AM, Dan wrote:

              > Yeah but that's the problem with anything involving people.
              >
              > What's to stop me from posting an average of 15.00 on UWR list, even
              > thought I've never been under 16? And it's not that unbelievable
              > really. But it might be a bit odd, statistically, I might post a
              > fake average where all the hundredths of a second were under .50 for
              > example, which is statistically very unlikely. It's also unlikely,
              > given enough cubes, that you would beat your long term average by
              > more than 3 SD's.
              >
              > But yeah, I agree with you, but if people want to cheat, then
              > they're only really cheating themselves.
              >
              > Dan :)
              >
              > --- In speedsolvingrubikscube@yahoogroups.com, Sachin Shirwalkar
              > <sachin_civilian@y...> wrote:
              >> No Dan but there is a way to beat this. If you are
              >> considering only the best improvement done by a person
              >> then I'll do my worst times in the first 30 solves and
              >> then in the real solves i'll solve normally. So my
              >> scores come out far better than the 30 previous ones.
              >>
              >> Though this looks like a good idea. Keep working on
              >> this.
              >>
              >> Sachin
              >>
              >>
              >> --- Dan <dan_j_harris@n...> wrote:
              >>
              >>
              >> ---------------------------------
              >> 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
              >>>>
              >>>>
              >>>>
              >>>>
              >>>>
              >>>>
              >>>>
              >>
              >>
              >>
              >>
              >> ---------------------------------
              >> YAHOO! GROUPS LINKS
              >>
              >>
              >> Visit your group "speedsolvingrubikscube" on the
              >> web.
              >>
              >> To unsubscribe from this group, send an email to:
              >> speedsolvingrubikscube-unsubscribe@yahoogroups.com
              >>
              >> Your use of Yahoo! Groups is subject to the Yahoo!
              >> Terms of Service.
              >>
              >>
              >> ---------------------------------
              >>
              >>
              >>
              >>
              >>
              >>
              >> _______________________________________________________
              >> Too much spam in your inbox? Yahoo! Mail gives you the best spam
              > protection for FREE! http://in.mail.yahoo.com
              >
              >
              >
              >
              >
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              >
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              >
              >
              >
              >
            • Dan
              No, of course not. Maybe you re missing the point. There s no need for a handicap in speedcubing tournaments, because there are a lot of sub 20 cubers, and
              Message 6 of 13 , Jul 1, 2005
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                No, of course not. Maybe you're missing the point.

                There's no need for a handicap in speedcubing tournaments, because
                there are a lot of sub 20 cubers, and those cubers who aren't sub20
                will have lots to aspire to, and to be honest, if they want to win,
                they'll have to improve.

                But for a small competition, where there maybe be on or two sub
                20ers, a 30, 40, and a minuter, for example, and the averages are
                spread wide, then it makes it a lot more fun for everyone involved,
                rather than just going through the motions to make the eventual,
                predictable winner.

                Dan :)

                --- In speedsolvingrubikscube@yahoogroups.com, Tyson Mao <tmao@i...>
                wrote:
                > Is there some prize that's really worth it? That's why we can't
                do
                > handicap competitions as an official event because there's no sure
                way
                > to ensure honesty. For non-official events, and all that other
                sort,
                > such as Sunday contests, or speedcubing.com averages, so far,
                we've
                > been relying on the honesty of the cubers, and it's been working
                in my
                > opinion. There really aren't that many doubtful records, and if
                > someone lies, I personally don't care, because your sub-14 average
                on
                > speedcubing.com means nothing to me if I beat you in a tournament.
                >
                > If you end up posting a fake average, then you waste the rest of
                your
                > life trying to protect this lie, and trying to prevent people from
                > finding out the truth. You're reduced to nothing more than a
                person
                > who makes up excuses on why his times are so slow. It's just not
                worth
                > it :-P
                >
                > Tyson Mao
                > MSC #631
                > California Institute of Technology
                >
                > On Jul 1, 2005, at 9:17 AM, Dan wrote:
                >
                > > Yeah but that's the problem with anything involving people.
                > >
                > > What's to stop me from posting an average of 15.00 on UWR list,
                even
                > > thought I've never been under 16? And it's not that unbelievable
                > > really. But it might be a bit odd, statistically, I might post a
                > > fake average where all the hundredths of a second were under .50
                for
                > > example, which is statistically very unlikely. It's also
                unlikely,
                > > given enough cubes, that you would beat your long term average by
                > > more than 3 SD's.
                > >
                > > But yeah, I agree with you, but if people want to cheat, then
                > > they're only really cheating themselves.
                > >
                > > Dan :)
                > >
                > > --- In speedsolvingrubikscube@yahoogroups.com, Sachin Shirwalkar
                > > <sachin_civilian@y...> wrote:
                > >> No Dan but there is a way to beat this. If you are
                > >> considering only the best improvement done by a person
                > >> then I'll do my worst times in the first 30 solves and
                > >> then in the real solves i'll solve normally. So my
                > >> scores come out far better than the 30 previous ones.
                > >>
                > >> Though this looks like a good idea. Keep working on
                > >> this.
                > >>
                > >> Sachin
                > >>
                > >>
                > >> --- Dan <dan_j_harris@n...> wrote:
                > >>
                > >>
                > >> ---------------------------------
                > >> 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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