Who will win the 2013 Candidates?

[Christopher Kreuzer]

Thanks for pointing out the problem with the link in my post above, Chris.

Nothing wrong with the link. The Chessbase site just seems to be intermittent recently.

[Christopher Kreuzer]

Carlsen is, quite simply, the positionally most acute player in the world.

I've been looking at some of your comments on the games, and it does seem magical the way Carlsen can draw his opponents into these sorts of positions where he emerges with an edge and then wins. Almost as good as the way he can defend inferior positions.

[Christopher Kreuzer]

Also, Carlsen beat Gelfand, and Grischuk in successive rounds in the first half of the tournament, and then Svidler later. I'd lay good odds that Carlsen will achieve 2-0 against one of those three.

I got this one right, 2-0 chalked up against Gelfand.

So I'd say the odds are more like 80% that Carlsen should be able to close it out from here, unless Aronian or Kramnik go on a run of wins.

Excitingly for the tournament, Aronian and Kramnik both won as well. If they keep that up, it may go right down to the last round as John Nunn predicted. Certainly, the only realistic winner now will be one of Carlsen, Aronian and Kramnik, as the others are now too far behind. I wonder if the chasing pack will lose a smidgen of motivation, and I wonder, now the group of likely winners is narrowing, who Anand would like to see win the tournament?

The key round looks to be the round 12 clash on Easter Friday (I presume none of the players refuse to play on religious holidays) between Aronian (with White) and Kramnik (with Black). Carlsen plays Ivanchuk that day. In some ways, he would hope for a draw in that Aronian-Kramnik game, or a win for Kramnik. It looks likely, depending on what happens tomorrow in round 11, that both Aronian and Kramnik may have to go for a win in that round 12 game.

[MartinCarpenter]

I very much doubt if Anand will care - they're all exceedingly dangerous. Kramnik has all that match experience of course, Aronian would be taking his likely best chance at the title and likely hugely motivated and Carlsen is well Carlsen

[Jonathan Rogers]

I believe that Carlsen will stay ahead, and will very likely win his two remaining Whites. But if Kramnik were to beat Aronian, then I wonder whether he would then have the better tie break to aid his pursuit.

I thought VK's win v Radjabov was one of the tournament's best so far, at least in so far as it teaches us a lot.

[JustinHorton]

Kramnik has played fantastically in my view. How many times has he been in trouble? Once, for one move?

[John McKenna]

As has been pointed out elsewhere, the crunch game on Friday is Aronian-Kramnik. Overall, it's still closer than the - Carlsen 76, Kramnik 21 and Aronian 3 - percentage stats in the latest Sonas/Chessbase article, in my opinion. I'd guess 70/29/1 because although the Russians have already played each other, Aronian has to play black against Grischuk in R13 and Carlsen has white against Svidler in R14. In other words there is scope for Kramnik to overtake Carlsen on the home straight (R13 & 14) if he can negotiate the final bend (R12) without crashimg.

[Christopher Kreuzer]

As has been pointed out elsewhere, the crunch game on Friday is Aronian-Kramnik. Overall, it's still closer than the - Carlsen 76, Kramnik 21 and Aronian 3 - percentage stats in the latest Sonas/Chessbase article, in my opinion. I'd guess 70/29/1 because although the Russians have already played each other, Aronian has to play black against Grischuk in R13 and Carlsen has white against Svidler in R14. In other words there is scope for Kramnik to overtake Carlsen on the home straight (R13 & 14) if he can negotiate the final bend (R12) without crashimg.

If Kramnik does win today (I suspect Carlsen will be following that game closely), then he could well win again in the final two rounds, which would be an amazing run of 5/5, which would match Carlsen if he finishes with two wins and a draw. Someone might want to calculate the tie-break possibilities in that scenario (where both Carlsen and Kramnik finish undefeated on +6), though no point doing that until the results of today's round are in.

Certainly if Kramnik were to finish with 5/5 and 6/7 from the second half, after seven straight draws, that would be amazing enough that I'd not be too disappointed if he finished ahead in the tie-breaks. I suspect he would as well, because any possible win over Aronian may count for more (it depends what score Aronian finishes on).

[Alex Holowczak]

As has been pointed out elsewhere, the crunch game on Friday is Aronian-Kramnik. Overall, it's still closer than the - Carlsen 76, Kramnik 21 and Aronian 3 - percentage stats in the latest Sonas/Chessbase article, in my opinion. I'd guess 70/29/1 because although the Russians have already played each other, Aronian has to play black against Grischuk in R13 and Carlsen has white against Svidler in R14. In other words there is scope for Kramnik to overtake Carlsen on the home straight (R13 & 14) if he can negotiate the final bend (R12) without crashimg.

The Sonas statistics take all this into consideration already. They've used Elo to work out the expected score in each game, and used that information to work out a distribution of expected final scores in the tournament. They've then converted that into a probability of winning the tournament.

It's quite high-level statistics that, in other sports, is worth millions of dollars. In Major League Baseball, the Oakland Athletics won the American League West last season with a payroll of approximately $55m. The Los Angeles Angels had a payroll of about $155m, yet they won five fewer games. Oakland had numbers that showed they'd probably win more games then the Angels, because they used these kind of statistics to work it out. They can work out which players are better than other players, and then put a number on their value for money.

[Christopher Kreuzer]

As has been pointed out elsewhere, the crunch game on Friday is Aronian-Kramnik. Overall, it's still closer than the - Carlsen 76, Kramnik 21 and Aronian 3 - percentage stats in the latest Sonas/Chessbase article, in my opinion. I'd guess 70/29/1 because although the Russians have already played each other, Aronian has to play black against Grischuk in R13 and Carlsen has white against Svidler in R14. In other words there is scope for Kramnik to overtake Carlsen on the home straight (R13 & 14) if he can negotiate the final bend (R12) without crashimg.

The Sonas statistics take all this into consideration already. They've used Elo to work out the expected score in each game, and used that information to work out a distribution of expected final scores in the tournament. They've then converted that into a probability of winning the tournament.

It's quite high-level statistics that, in other sports, is worth millions of dollars. In Major League Baseball, the Oakland Athletics won the American League West last season with a payroll of approximately $55m. The Los Angeles Angels had a payroll of about $155m, yet they won five fewer games. Oakland had numbers that showed they'd probably win more games then the Angels, because they used these kind of statistics to work it out. They can work out which players are better than other players, and then put a number on their value for money.

It's an interesting debate on whether Monte Carlo statistics (I vaguely remember how that works, you simulate many times and merge the results in some way?) work in games such as chess. I would have thought, not knowing the details offhand, that analysing team games where rankings exist is more what this sort of approach is better at analysing. Can it be applied to individual sports such as tennis and golf? Going back to team sports, what about cricket or football?

And there are factors that no statistics are able to take into consideration. The human factors (cracking under nerves or pressure) are more evident in individual sports than in team sports. Also, would it take into consideration what I mentioned earlier, that Carlsen seems to finish tournaments stronger than he starts them? I should have added in that earlier analysis that to be fair you would need to look at whether Kramnik finishes tournaments stronger than he starts them - he is certainly doing that in this tournament!

[Mick Norris]

All the players are tired, but the older ones may be feeling it more, Kramnik certainly seemed to imply this yesterday - he now gets to find out if the fitness training he has done allows him to keep playing good chess in the last 3 rounds - he also said the priority against Aronian is not to lose

I guess they will draw today, and unless Carlsen unexpectedly loses a game he will qualify

I think 14 rounds is probably too many, and that a tournament without the bottom 2 would be better i.e. a 6 player all play all

Ideally, the top 2 playing in a match to meet the champion, but I can't see that happening

[Alex Holowczak]

It's an interesting debate on whether Monte Carlo statistics (I vaguely remember how that works, you simulate many times and merge the results in some way?) work in games such as chess. I would have thought, not knowing the details offhand, that analysing team games where rankings exist is more what this sort of approach is better at analysing. Can it be applied to individual sports such as tennis and golf? Going back to team sports, what about cricket or football?

You need to ask what the aim of the game is. In baseball, to win a game, you need to score more runs than the other team. Because of the way that getting on-base is related to scoring runs, you can draw a link there. You then need to make the equivalent links between pitching and fielding to scoring runs, statistics which exist in baseball. From there, you can draw a link between runs scored and conceded to winning games. Thus it's possible, by comparing the rosters of all the teams at the start of the season, to predict what their final 162-game record would be.[/quote]

In chess, you need to checkmate your opponent to win a game. There's no good way of splitting that task up that you can measure. So the best thing to use is Elo to work out the expected score. They must have a threshold above which an expected score becomes a win. That shouldn't be too hard to work out statistically.

In tennis, the aim of the game is to win a point, but scoring complexities mean that the winner of the most points doesn't necessarily win the match. In golf, the aim of the game is to hit the ball in the hole in as few shots as possible. In both cases, I'm not sure how you subdivide those aims with measurable statistics.

Cricket and football are interesting. In football the aim is to score more goals than the other team, but how do you break that task down into smaller, measurable tasks? In cricket, the aim of the game is to score more runs than the other team, a bit like baseball.

It's an issue of credit and debit, you need to assess performance by some measure you can count.
Batsmen - Credit: Runs scored, leg-byes(?), Debit: Wickets not credited to the bowler (e.g. obstructing the field)
Bowling - Credit: Wickets credited to the bowler(?), Debit: Runs conceded, no-balls, wides
Fielding - Credit: Runs saved in the field, wides(if > 1 conceded, wk only), penalty runs, dropped catches, missing run outs/stumpings

You could work out, for each player, a statistic that takes these kinds of factors into account. There may be others.

You'd need to work out a few things:
(1) Is (say) lbw is credit to the bowler or debit from the batsman. Was it a bad shot or a good ball? You could work that out by turning the pitch into a grid. Each ball then becomes a ball bowled with velocity v, landing at point p, passing the batsman at point q. There ball (v,p,q) would have happened hundreds of times before, so you use what happened on that ball to work out what is expected to happen after that ball, and assign blame to either credit the bowler or debit the batsman.
(2) How do you measure runs saved in the field? Again turn the field to a grid, but this time you might need polar co-ordinates; or at least, have two co-ordinates, a bearing b and a distance s. Then you need to take into account the point the ball was fielded p and the distance the fielder has travelled t. So each shot by a batsman is (b,s,p,t). You look at all previous times that happened, and you can see the expected number of runs scored. So if the expectation is 2 runs, and the batsmen run 3, then you can debit the fielders for bad fielding.

Anyway, after all the crediting and debiting, you can work out which players are better than other players in all areas of the game. At that point, you can work out the value of the team as a whole, and hence work out a probability of who wins the game.

This works in practice in baseball, the Oakland A's can spend $60m and compete on even terms with the New York Yankees, who spend $200m.

And there are factors that no statistics are able to take into consideration. The human factors (cracking under nerves or pressure) are more evident in individual sports than in team sports. Also, would it take into consideration what I mentioned earlier, that Carlsen seems to finish tournaments stronger than he starts them? I should have added in that earlier analysis that to be fair you would need to look at whether Kramnik finishes tournaments stronger than he starts them - he is certainly doing that in this tournament!

There's a natural variance in this for things like injuries, and no statistic exists that can measure the influence on someone's wife dying 2 hours before the game has on performance, for example. This notwithstanding, baseball could demonstrably show that "clutch hitting", i.e. the ability to hit at crucial moments, was just a media phenomenon, and had no statistical merit. I suspect chess would show a similar pattern - except in chess, you can take into account the strength of the opposition by using Elo. All that baseball shows is the most likely outcome, which is used quite often in practice. A good example of this is the weather forecast.

[Clive Blackburn]

In chess, you need to checkmate your opponent to win a game. There's no good way of splitting that task up that you can measure. So the best thing to use is Elo to work out the expected score. They must have a threshold above which an expected score becomes a win. That shouldn't be too hard to work out statistically.

In tennis, the aim of the game is to win a point, but scoring complexities mean that the winner of the most points doesn't necessarily win the match. In golf, the aim of the game is to hit the ball in the hole in as few

And there are factors that no statistics are able to take into consideration. The human factors (cracking under nerves or pressure) are more evident in individual sports than in team sports. Also, would it take into consideration what I mentioned earlier, that Carlsen seems to finish tournaments stronger than he starts them? I should have added in that earlier analysis that to be fair you would need to look at whether Kramnik finishes tournaments stronger than he starts them - he is certainly doing that in this tournament!

There's a natural variance in this for things like injuries, and no statistic exists that can measure the influence on someone's wife dying 2 hours before the game has on performance, for example. This notwithstanding, baseball could demonstrably show that "clutch hitting", i.e. the ability to hit at crucial moments, was just a media phenomenon, and had no statistical merit. I suspect chess would show a similar pattern - except in chess, you can take into account the strength of the opposition by using Elo. All that baseball shows is the most likely outcome, which is used quite often in practice. A good example of this is the weather forecast.

There are other variables too which are peculiar to chess. It would be very difficult for instance make statistical adjustments for playing style, opening repertoire etc. I think that all players, at any level, have certain opponents who they perform better or worse against than you would expect from looking at their respective ratings.

[John McKenna]

Even these days three Russians are not independent individuals - they are Olympiad teammates and will try for the best outcome for their nation. Would not three Englishmen do the same?

[Christopher Kreuzer]

Even these days three Russians are not independent individuals - they are Olympiad teammates and will try for the best outcome for their nation. Would not three Englishmen do the same?

It's an interesting question, but I think we should probably wait until after the event (only a few more days to go) before saying too much on this sort of thing. My view is that they are and should be playing as individuals. Remember that Gelfand said it was difficult for him to beat his friend Aronian, but he did so anyway as they are professionals. Friendships may often count for more than nationalities. And I would expect three Englishmen to try their hardest against each other in such a tournament. It should go without saying. There is also such a thing as internal pecking order and competition and different generations.