What is the maximum Elo rating that Magnus Carlsen could have if he loses the World Chess Championship 2014 to Anand? Would this result from a 6.5-5.5 result or would the relative rating change mean that if he lost more quickly that would be better? Also, are the players playing 12 rounds regardless of the current score?
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The match ends when a player reaches 6.5. If Anand won the next four games in a row, the match would end.– ClevelandNov 14, 2014 at 18:23
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2The least bad Elo result for Carlsen in a match-losing scenario would happen if he lost 6.5-5.5, yes. Imagine he lost the match 6.5-3.5; that is like the 6.5-5.5 result but without the benefit of winning two more games, which would have increased his rating.– dfanNov 14, 2014 at 18:30
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1 Answer
In a hypothetical situation where Carlsen knew that he was going to lose the match and his number one priority was to preserve his rating points, then his best option would be to lose as quickly as possible. As pointed out in this question (EDIT: Values updated as per JiK's comment below), Carlsen will lose 1 rating points for each game he draws with Anand. The only way that he could extend the match and not lose points in the process would be to win as many games as possible before losing.
Assuming Anand wins with the minimum possible score of 6.5/12, Carlsen will lose a minimum of 17 points (11 draws x 1, 1 loss x 6). This does not change if draws are replaced by a win for either side.
However, if Anand was going to win with a draw and 6 wins, then Carlsen stands to lose 37 points. If Carlsen somehow knew this would be how Anand would win, then he could attempt to interpose as many of his own wins (up to 5) as possible, ameliorating the loss somewhat. Even in this situation, Carlsen's best result remains a net loss of 17 points.
EDIT: And to answer the question as it is worded in the title: Carlsen's rating (assuming no results outside the WCC match are counted) would be no more than 2863.0 - 17 = 2846.0
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1The question you link to is for last year's match. With current ratings (2863 vs 2792), Carlsen's expected result against Anand is 0.60, which means his rating change is +4.0, -1.0, or -6.0 if he wins, draws, or loses, respectively.– JiKNov 16, 2014 at 11:10
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@JiK Thanks for that. I'm changing the values in the question but leaving the link there because it provides a decent explanation if someone wants to do some further reading.– DTRNov 16, 2014 at 17:53
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I think the claim in the first sentence is wrong. Carlsen would have lost more Elo points if he lost a short match. Nov 16, 2014 at 18:05
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@DagOskarMadsen Yes, on further inspection the values JiK gave me can't be correct. Elo rating performance works out such that the final score is all that matters, so the result of a 6.5-5.5 win would be the same regardless of whether it is +6=1-5 or +1=11-0. I'm reverting to the previous version until I can fix this.– DTRNov 16, 2014 at 18:23
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Nevermind, found what I thought the problem was. JiK's values are correct. Reverting the revert to the unreverted vert.– DTRNov 16, 2014 at 18:50