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Error rate differences

Posted By: Maik Stiebler
Date: Friday, 12 November 2010, at 6:05 a.m.

In Response To: Error rate differences (Timothy Chow)

If, when you play matches against me, I blunder away 15% MWC per match compared to perfect play on average, and you blunder away 5% MWC per match compared to perfect play on average, you win 60% of the matches. One way to see that is via the unbiasedness of luck adjusted results. I'm in a hurry so I will just give a sketch of the argument: You can derive a perfect measure of luck from perfect evals in the same way that it is done with the imperfect evals of real bots. Convince yourself by induction that if you use that perfect measure of luck, your current theoretical mwc at any point in the match is 50% + cumulative luck so far (cl) + difference in cumulative errors (dce) so far. Thus, when you win, cl is 100% - (50% + dce) and the luck adjusted result (lar) is 50%+dce. When you lose, cl is 0% - (50% + dce) and the lar is also 50%+dce. As lar is always 50%+dce, average lar in the example is 60%. As lar is unbiased, the average real result is also 60%.

Messages In This Thread

• Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
  happyjuggler0 -- Thursday, 11 November 2010, at 5:53 a.m.
  • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
    Michael Petch -- Thursday, 11 November 2010, at 6:19 a.m.
    • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
      higonefive -- Thursday, 11 November 2010, at 6:37 a.m.
      • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
        Michael Petch -- Thursday, 11 November 2010, at 6:45 a.m.
        • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
          higonefive -- Thursday, 11 November 2010, at 7:13 a.m.
          • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
            Michael Petch -- Thursday, 11 November 2010, at 7:49 a.m.
            • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
              higonefive -- Thursday, 11 November 2010, at 9:19 a.m.
              • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
                Michael Petch -- Thursday, 11 November 2010, at 9:49 a.m.
      • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
        Rich Munitz -- Thursday, 11 November 2010, at 6:47 p.m.
        • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
          Fabrice Liardet -- Friday, 12 November 2010, at 10:56 a.m.
    • American football analogy?
      Chuck Bower -- Thursday, 11 November 2010, at 6:42 p.m.
      • American football analogy?
        Rich Munitz -- Thursday, 11 November 2010, at 7:05 p.m.
      • American football analogy?
        Michael Petch -- Thursday, 11 November 2010, at 9:01 p.m.
  • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
    mtuhtan -- Thursday, 11 November 2010, at 6:24 a.m.
  • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
    Maik Stiebler -- Thursday, 11 November 2010, at 6:51 a.m.
  • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
    Christian Munk-Christensen -- Thursday, 11 November 2010, at 8:21 a.m.
    • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
      Michael Petch -- Thursday, 11 November 2010, at 9:04 a.m.
    • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
      rew -- Thursday, 11 November 2010, at 1:55 p.m.
    • the old
      garyo -- Friday, 12 November 2010, at 6:32 p.m.
  • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
    phil simborg -- Thursday, 11 November 2010, at 1:53 p.m.
  • Error rate differences
    Timothy Chow -- Thursday, 11 November 2010, at 3:25 p.m.
    • Error rate differences
      Maik Stiebler -- Thursday, 11 November 2010, at 8:37 p.m.
      • Error rate differences
        Timothy Chow -- Friday, 12 November 2010, at 1:06 a.m.
        • Error rate differences
          Chuck Bower -- Friday, 12 November 2010, at 2:51 a.m.
        • Error rate differences
          Maik Stiebler -- Friday, 12 November 2010, at 6:05 a.m.
          • Error rate differences
            Fabrice Liardet -- Friday, 12 November 2010, at 10:48 a.m.
            • Error rate differences
              Timothy Chow -- Friday, 12 November 2010, at 6:15 p.m.
              • Error rate differences
                Maik Stiebler -- Friday, 12 November 2010, at 10:32 p.m.
                • Error rate differences
                  Timothy Chow -- Friday, 12 November 2010, at 11:44 p.m.
                  • Error rate differences
                    Maik Stiebler -- Saturday, 13 November 2010, at 8:49 a.m.
            • Error rate differences
              Maik Stiebler -- Friday, 12 November 2010, at 10:42 p.m.
              • Error rate differences
                Fabrice Liardet -- Sunday, 14 November 2010, at 7:35 p.m.
                • Error rate differences
                  Maik Stiebler -- Sunday, 14 November 2010, at 7:46 p.m.
  • Who is the better BG player: the one who has the lowest error rate, or the one who somehow maximizes the difference between his errror rate and that of his opponent?
    Steve Mellen -- Thursday, 11 November 2010, at 10:00 p.m.