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According to team captain Victor Plotkin, the board order was submitted 4-5 months ago and was reasonable at that time. At the Rapid yesterday, Victor pointed out that the final board order would be submitted at the team captains meeting tomorrow.
If Eric Hansen is on second board, Canada has a real chance to make some noise and put in a memorable performance.
The impact of the board order on the overall team result is statitiscally nil. It could be entirely decided by chance and still the team expectations would remain exactly the same.
The impact of the board order on the overall team result is statitiscally nil. It could be entirely decided by chance and still the team expectations would remain exactly the same.
I'd love to see your "statistically nil" mathematical proof, Jean. I strongly suspect the math may be found wanting.
I'd certainly take the opposing view and be happy to make that mathematical argument. To cite but one prime example, I'd argue that the Russian coach likely cost Russia the gold in the 2010 Olympiad. Peter Svidler, who is not on this year's Russian team, should never have been playing the White pieces and that can be manipulated each and every round because of the 5-man team. Svidler himself clearly preferred Black, largely because of his incredible success with his much beloved Grunfeld (check out his World Cup results where he won, if I'm not mistaken, 5 consecutive games with Black and not a single game with White), and was on the record as to how uncomfortable he felt with the White pieces (he was essentially playing to draw with White and win with Black).
Some players score significantly better against 1.e4 than 1.d4 or vice versa. That too, can be manipulated via board order. There are all kind of chess idiosyncrasies that can be micromanaged via board order. More importantly, and more to the point, some players rise to the occasion on a top board while others may perform abysmally. Knowing who that player is more likely to be is a far cry from "statistically nil".
quick test I did - probably missed an important detail(s)
seems to disprove Jean's theory
either way I believe carefully choosing a board order is important
code:
teamA = Object(2600, 2500, 2400, 2300) // rTotal 9800 - seems advantageous on no boards
teamB = Object(2650, 2550, 2450, 2350) // rTotal 10000
totalScore = 0
Print('Example 1 - Expected results for team A per 1 game:\r\n')
for(i = 0; i < teamA.Size(); i++)
{
exp = 1/(1+10.Pow((teamB[i]-teamA[i])/400)) // elo expected result expression at http://en.wikipedia.org/wiki/Elo_rating_system --> Theory
totalScore += exp
x = 'Board ' $ Display(i + 1) $ ': ' $ Display(exp)
Print(x)
}
Print('Total expected score over 4 boards: ' $ Display(totalScore) $ ' out of 4')
Print('\r\n')
teamA = Object(2300, 2600, 2500, 2400) // rTotal 9800 - seems advantageous on boards 2-4
teamB = Object(2650, 2550, 2450, 2350) // rTotal 10000
totalScore = 0
Print('Example 2 - Expected results for team A per 1 game:\r\n')
for(i = 0; i < teamA.Size(); i++)
{
exp = 1/(1+10.Pow((teamB[i]-teamA[i])/400))
totalScore += exp
x = 'Board ' $ Display(i + 1) $ ': ' $ Display(exp)
Print(x)
}
Print('Total expected score over 4 boards: ' $ Display(totalScore) $ ' out of 4')
result:
Example 1 - Expected results for team A per 1 game:
Board 1: .4285368825860409
Board 2: .4285368825860409
Board 3: .4285368825860409
Board 4: .4285368825860409
Total expected score over 4 boards: 1.714147530344 out of 4
Example 2 - Expected results for team A per 1 game:
Board 1: .1176617029524662
Board 2: .5714631174149913
Board 3: .5714631174149913
Board 4: .5714631174149913
Total expected score over 4 boards: 1.832051055197 out of 4
ok
Here's an article on board order that suggests the optimum board order from a mathematical perspective may be 4,1,2,3. A bit simplistic but nonetheless rather interesting.
I came to the same conclusion. In the first case matched the teams by descending ratings. Note that in the second example, I maintained the board order for team B, but simply matched the lower three boards in test 2 to create a seemingly favorable outcome for team A.
Indeed, it is not a mathematical proof, but shows board order matters. The guy in the article could have figured this out in 5 minutes with computer programming :)
I'd love to see your "statistically nil" mathematical proof, Jean. I strongly suspect the math may be found wanting.
I'd certainly take the opposing view and be happy to make that mathematical argument. To cite but one prime example, I'd argue that the Russian coach likely cost Russia the gold in the 2010 Olympiad. Peter Svidler, who is not on this year's Russian team, should never have been playing the White pieces and that can be manipulated each and every round because of the 5-man team. Svidler himself clearly preferred Black, largely because of his incredible success with his much beloved Grunfeld (check out his World Cup results where he won, if I'm not mistaken, 5 consecutive games with Black and not a single game with White), and was on the record as to how uncomfortable he felt with the White pieces (he was essentially playing to draw with White and win with Black).
Some players score significantly better against 1.e4 than 1.d4 or vice versa. That too, can be manipulated via board order. There are all kind of chess idiosyncrasies that can be micromanaged via board order. More importantly, and more to the point, some players rise to the occasion on a top board while others may perform abysmally. Knowing who that player is more likely to be is a far cry from "statistically nil".
Mathematically any board order will give the same mathematical expectations. No complicated proof is necessary : the teams rating averages remain the same! That is all I am saying. What you point out are subjective reasons why this or that board order could give better or worse results. These are unprovable but you can believe in that if you wish. You may be right... about 50% of the time. :)
So basically you guys are diggin up arguments proving(ish) doing "kind of the opposite" of what you would like the board order to look like would improve the expected score of the team..
It doesn't work in every case, actually - if either your team or your opponent's team is pretty balanced, it has no effect. Also it doesn't take into account who is stronger/weaker on which colours - if you have a "colour-specialist" you don't want them on Board 1 or Board 5 because it will kill your flexibility.
The impact of the board order on the overall team result is statitiscally nil. It could be entirely decided by chance and still the team expectations would remain exactly the same.
Last edited by Kevin Me; Monday, 27th August, 2012, 10:43 AM.
Here's an article on board order that suggests the optimum board order from a mathematical perspective may be 4,1,2,3. A bit simplistic but nonetheless rather interesting.
Probably if you look at the makeup of all the teams you'll find examples of "stacking" the board order.
The problem with putting your weakest player on board 1 and sacrificing the board by expecting a loss is that the remaining 3 boards have to score 2 1/2 out of 3 points to win a match. Remember, the format has changed to match points and total points are only used to break ties.
For the player being "sacrificed", it's not much of a way to spend a week. By about round 5 the only thing which comes to mind is, "I want to go home".:)
Using your weakest player on board 1 requires the other team to win that game and simply draw the other 3 games to win the match. So simple is chess. :)
Mathematically any board order will give the same mathematical expectations. No complicated proof is necessary : the teams rating averages remain the same! That is all I am saying. What you point out are subjective reasons why this or that board order could give better or worse results. These are unprovable but you can believe in that if you wish. You may be right... about 50% of the time. :)
Under your specious "rating average remains the same!" argument, Jean, then the 5th board should never play since he/she is lowering said average. Yet Armenia, the perennial overachievers at the Olympiad, sees fit to interject its 5th board whenever they see the need to play for a win - rather than a draw - on board 4. Gabriel Sargissian is higher rated than Tigran Petrosian but is far more likely to draw than to win or lose. A look at their respective opening repertoire will perhaps tell you why. Sargissian plays, for example, the Caro-Kann, while Petrosian plays the Grunfeld and Sicilian, both very much live or die type of openings.
If 4,1,2,3 was the best possible board order everyone would be using it.. thus making 3,4,1,2 the best order.. then everybody would be using it making 2,3,4,1 the best order.. and then back to 1,2,3,4 .. etc.. etc..
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