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Dropper solution?
Posted By: Tom Keith
Date: Tuesday, 17 September 2013, at 8:04 p.m.
In Response To: Dropper solution? (Bob Koca)
Here are my quick and dirty answers.
Player A 2000 rating against player B 1600 rating. What is ratings change for each player in the following situations?
A 400 point rating difference gives the favorite (A) a 77% chance of winning a 7point match, the underdog (B) a 23% chance. If we can calculate the probability of each player winning and losing the match, we can prorate the awarded points.
Situation 1: Drop after first few moves of 7 point match. Bot says 52% to player B.
You could round this off and say it is like the beginning of the match. Player B has gained 2% MWC, so 23 + 2 = 25% MWC.
Situation 2: Drop at DMP race of 7 point match. Bot says 50%
2. In a race there is presumably little skill difference left so B will win the match 50% of the time.
Situation 3: Drop at DMP (beginning of game). Bot says 50%
3. This is now a 1point match. The Elo formula is not very accurate on 1point matches but if you ignore that B should win the match 39% of the time.
Back to the rating formula. When A wins a 7point match over B, he gets 2.42 ratings points. When A loses the match, he loses 8.17 ratings points. Interpolate between these values according how likely each result is. Here is A's rating change in each situation:
Situation 1: 75% * 2.42  25% * 8.17 = 0.23
Situation 2: 50% * 2.42  50% * 8.17 = 2.88
Situation 3: 61% * 2.42  39% * 8.17 = 1.72

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