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197 - 11pt matches needed for statsig with 50 Elo difference

Posted By: Rich Munitz
Date: Monday, 27 July 2009, at 3:08 p.m.

In Response To: $$$ 11 - 11 point matches - what is statsig? (Philippe Michel)

So if there is a 50 Elo difference, the probability of the weaker player winning a single 11 pt match is 44.14%.

Then the question is how many such matches are required so that the probability of the underdog winning less than half the matches is greater than 95%?

An odd number of matches will reach this threshold sooner since "less than half" is N/2-0.5 whereas for even numbers it is N/2-1

At 197 matches, the chance that the underdog will win no more than 98 matches is 95.08%

For even trials, it is not until 212 matches that the probability gets to 95.01%

We can determine this ahead of time because the skill difference between the two players is a given and the probability distribution can be calculated in advance - we just don't know which player is the stronger one. However, if we don't know the skill difference ahead of time, then no confidence level can be determined without actually running the trials and factoring in the outcomes.

Messages In This Thread

• $$$ 11 - 11 point matches
  Rod -- Sunday, 26 July 2009, at 11:10 p.m.
  • $$$ 11 - 11 point matches
    Bill Riles -- Sunday, 26 July 2009, at 11:12 p.m.
  • $$$ 11 - 11 point matches
    Rod -- Sunday, 26 July 2009, at 11:22 p.m.
    • $$$ 11 - 11 point matches
      debra -- Sunday, 26 July 2009, at 11:32 p.m.
    • $$$ 11 - 11 point matches
      adambulldog -- Sunday, 26 July 2009, at 11:33 p.m.
      • Already made and accepted *NM*
        Rod -- Monday, 27 July 2009, at 1:40 a.m.
    • $$$ 11 - 11 point matches
      Seth -- Monday, 27 July 2009, at 2:12 a.m.
    • $$$ 11 - 11 point matches
      Bill Riles -- Monday, 27 July 2009, at 2:28 a.m.
      • $$$ 11 - 11 point matches - what is statsig?
        Rich Munitz -- Monday, 27 July 2009, at 3:43 a.m.
        • $$$ 11 - 11 point matches - what is statsig?
          Keene -- Monday, 27 July 2009, at 4:37 a.m.
        • $$$ 11 - 11 point matches - what is statsig?
          Philippe Michel -- Monday, 27 July 2009, at 11:32 a.m.
          • 197 - 11pt matches needed for statsig with 50 Elo difference
            Rich Munitz -- Monday, 27 July 2009, at 3:08 p.m.
            • 197 - 11pt matches needed for statsig with 50 Elo difference
              playBunny -- Tuesday, 28 July 2009, at 2:39 a.m.
              • 197 - 11pt matches needed for statsig with 50 Elo difference
                Jason Lee -- Tuesday, 28 July 2009, at 2:59 a.m.
  • $$$ 11 - 11 point matches
    Chuck Bower -- Monday, 27 July 2009, at 4:52 p.m.
  • $$$ 11 - 11 point matches
    Coolrey -- Monday, 27 July 2009, at 4:57 p.m.
    • $$$ 11 - 11 point matches
      Rich Munitz -- Monday, 27 July 2009, at 7:33 p.m.
      • $$$ 11 - 11 point matches
        Seth -- Monday, 27 July 2009, at 11:38 p.m.