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PR, Error Rate and mEMG
Posted By: Michael Petch In Response To: PR, Error Rate and mEMG (Turz)
Date: Friday, 19 August 2011, at 2:19 p.m.
Shamelessly reprinted from the XG manual:
Performance How is the rating computed:
1. General The Rating of a player is determined by how many Normalized equity the player lose per decision in average.
The overall rating after a match is calculated by dividing the sum of the equities lost by the number of decision the player made.
for instance if a player made one blunder of -0.105 equity and one error of -0.035 after playing 13 moves his performance is 0.140/13=0.0108
2. Equivalence between performance and Elo There is, roughly, a linear relation between Elo (GammonSite equivalent) and performance:
Elo=2240-performance*16500
Actually the Elo formula is more complex in order to take into account very bad performance and also performance when you outplay the computer. The actual formula is result := 1/(1+exp(-performance*40-1.12))*2000+732
in the previous case the player played at a 2240-0.0108*16500=2062 Elo
3. Performance Rating (PR) Performance rating express your performance using a easy to manipulate number.
PR= -performance*500
It is independent of the elo setting you are using.
4. Categories Performance are categorize as follow:
Performance Category Name Color Code Elo Equivalent Performance Rating
P>+0.0000 Wow! Underline Black 2240 and more Less than 0.0 +0.0000>P>-0.0050 World Champ Underline Black 2162-2240 0.0-2.5 -0.0050>P>-0.0100 World Class Black 2077-2162 2.5-5.0 -0.0100>P>-0.0150 Expert Black 1986-2077 5.0-7.5 -0.0150>P>-0.0250 Advanced Green 1792-1986 7.5-12.5 -0.0250>P>-0.0350 Intermediate Green 1593-1792 12.5-17.5 -0.0350>P>-0.0450 Casual Player Red 1405-1593 17.5-22.5 -0.0450>P>-0.0600 Beginner Red 1167-1405 22.5-30.0 -0.0600>P Distracted Red 1167 and less 30.0 and more
5. Decisions A decision is a checker move a cube double that is considered non obvious by the computer. Are consider as obvious the following:
A force moved A move for witch the Best choice and the worse choice have an equity that are less than 0.001 different A double Action where the Equity before doubling and after doubling is the same (optional double) A double Action where the Equity before doubling is 0.200 bigger than the equity after double (obvious non double) A double action where the Equity before doubling is 0.200 bigger than the equity after drop (obvious Too good to double) A double action where the Equity before and after double is very negative (This correspond to lost position when trailing a lot in the match)
Are never consider as a obvious:
A double decision resulting in a double A take decision
6. Particular cases a) One pointer One point match performance is calculated slightly differently: a factor 1.5 is applied to any error. This mean that a move is considered a blunder if it is 0.080/1.5=0.053 different than the best move.
In the example given in paragraph 1 if the match was a one point match the performance would have been 0.0108*1.5=0.0162 and the Elo equivalent would have been: 1989.
This factor has been computer empirically from simulation and real games played on GammonSite
b) NackGammon Nackgammon games are typically longer (about 28% longer than regular games). They are also more complex. A ratio of 0.952 is apply to the equity.
This mean that a blunder threshold is 0.084 (rather than 0.080). Again using the example of paragraph 1, if the game would been a NackGammon one the performance would have been 0.0108*0.952=0.0102 for a elo equivalent of 2081
c) NackGammon in one pointer Both ratio are apply giving a total ratio of 1.428
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