English Chess Forum

This arises from a discussion we had at yesterday evening's Surrey board meeting about the penalties which are applied for "incorrect" board orders in matches. It is generally held (I believe) that a devious (or competitive, depending on your point of view) captain might want to change his board order in order to gain some advantage in the match. One of us pointed out that from the point of view of grading theory board order should have very little effect on the result of the match. (To predict the score of the match you work out the average grade for each each team and apply this to work out a predicted score for the match. This works irrespective of the board order chosen by each team - an adavantage gained on oone board is always exactly balanced by an advantage lost on another.)

I should add here the proviso that if two opposing players have a difference in grade of more than 50, then this does affect the calculation slightly - but in practical cases, not very much.

So the question is: if board order doesn't really affect the result of a match, why do we have all these rules and penalties surrounding this issue? Why don't we just let captains arrange their teams in any order they like? (I remember reading somewhere (not sure where) that some 19th century match was played with the teams arranged in alphabetical order (of surname). Why don't we do that now, or allow a perfectly random order? It would certainly cut out a few disputes/ the application of penalties which completely distort match results in an entirely artificial way?

Sorry Mike - interesting idea but I think it would either lead to even more arguments or some kind of arrangement like that in the House of Commons where people are paired with opponents of their choice. The latter might result in the exchange of teamsheets taking away a good chunk of playing time.

Each captain prepares his own team sheet independently (secretly) and once you exchange team sheets there is no going back ...

Then we may begin to hear of courageous, but foolhardy, captains coming under heavy fire from their own side.

Mike Gunn wrote:This arises from a discussion we had at yesterday evening's Surrey board meeting about the penalties which are applied for "incorrect" board orders in matches. It is generally held (I believe) that a devious (or competitive, depending on your point of view) captain might want to change his board order in order to gain some advantage in the match. One of us pointed out that from the point of view of grading theory board order should have very little effect on the result of the match. (To predict the score of the match you work out the average grade for each each team and apply this to work out a predicted score for the match. This works irrespective of the board order chosen by each team - an adavantage gained on oone board is always exactly balanced by an advantage lost on another.)

I should add here the proviso that if two opposing players have a difference in grade of more than 50, then this does affect the calculation slightly - but in practical cases, not very much.

So the question is: if board order doesn't really affect the result of a match, why do we have all these rules and penalties surrounding this issue? Why don't we just let captains arrange their teams in any order they like? (I remember reading somewhere (not sure where) that some 19th century match was played with the teams arranged in alphabetical order (of surname). Why don't we do that now, or allow a perfectly random order? It would certainly cut out a few disputes/ the application of penalties which completely distort match results in an entirely artificial way?

I recall that when I first came to Hastings years ago and first played bar billiards I was interested to note that the Hastings Bar Billiards League, teams of five playing one frame each, drew the pairings and the order of play entirely at random, so the luck of the draw was an important feature.

PB

The problem with statistics is that you can get them to mean whatever you like. What you say about the expected score is correct, but you can't score fractions of a point (other than half) so the statistics don't quite work as you might expect.

Take 2 teams of 6 players. Both teams are made up of players graded 200; 190; 180; 170; 160; 150. Clearly, played in grading order, we might expect to see a drawn match. However, if one team plays the 150 on board 1 we get

A v B
200 v 150
190 v 200
180 v 190
170 v 180
160 v 170
150 v 160

The expected statistical result is still a draw. But, in practice, team B is likely to have an advantage - perhaps psychologically if nothing else!

Come to think of it, Paul, that might be an idea for the 4NCL - including a randomly-paired Bar Billiards League - since some of the chess pairings seem pretty random, to me anyway.

Also, regarding Sean's good example above, the same match result may be arrived at different ways but the individual players' results will be different. Many different results - from 6-0 to team A to 6-0 to team B could come from random pairings of the players. Could it not?

Although the captain of team B could (possibly) secure an advantage if he knew the opposing team order in advance and arranhed his team as you suggest, this advantage would be nullified if neither caotain knew the other's board order in advance.

Off to see West Ham play Southampton ... I wonder what the staistics say about that.

I remember in inter-school chess that if a team faced a much stronger one, and expected to lose every game, a devious captain would arrange his team in reverse playing strength. His team could then be expected to win some games (instead of none at all) and at best possibly draw the match.

Mike Gunn wrote:I should add here the proviso that if two opposing players have a difference in grade of more than 50, then this does affect the calculation slightly - but in practical cases, not very much.

A small point: I think you mean 40, rather than 50, don't you Mike? (The grading system adjusts any difference in grade of more than 40 to be 40.)... The expected match score is a product of the expected individual board scores.

MSoszynski wrote:I remember in inter-school chess that if a team faced a much stronger one, and expected to lose every game, a devious captain would arrange his team in reverse playing strength. His team could then be expected to win some games (instead of none at all) and at best possibly draw the match.

Useful if, and only if, a handicap is in operation (as it is in the Oxfordshire cup, based on division of team, and as it was in some school chess I remember, based on average age of team).

Sean Hewitt wrote:The problem with statistics is that you can get them to mean whatever you like. What you say about the expected score is correct, but you can't score fractions of a point (other than half) so the statistics don't quite work as you might expect.

Take 2 teams of 6 players. Both teams are made up of players graded 200; 190; 180; 170; 160; 150. Clearly, played in grading order, we might expect to see a drawn match. However, if one team plays the 150 on board 1 we get

A v B
200 v 150
190 v 200
180 v 190
170 v 180
160 v 170
150 v 160

The expected statistical result is still a draw. But, in practice, team B is likely to have an advantage - perhaps psychologically if nothing else!

The problem with statistics is that people who don't really understand it think they can get it to mean whatever they like.

Over a long period two evenly matched teams will tend to score equally, but in a single match it is more likely that one or other will win than that the match will be drawn. If you believe the grading system, the par score for a five board match where one team is outgraded by ten points a board is 3-2. I don't suppose any of us would go into such a match thinking that outcome was inevitable. And in the example, team B's top board would expect one point in every ten games, so team B would have a marginal advantage.

The imponderable is the grading system. Is it true that a 10 point grading advantage equates to a 60% score? Easy enough to check, I would have thought.

I think board order makes very little difference so long as the players are reasonably evenly matched. It shouldn't be possible to play your beginner against their GM. The price of team B's minimal advantage is very likely an evening spoiled for both top boards. So a simple rule that teams should be in order of playing strength, with no penalties specified, is enough. Nothing to stop the organiser imposing a penalty if someone does something really blatant.

I write in a personal capacity. As David says the difference is usually small. I think the main reason for board orders being roughly in order of strength is for players to play well matched opponents.

However changing board order does affect the expected match result. The maths is complex, but I can give a pointer in the direction of the argument.

Consider a game with only wins and losses (i.e no draws) using the ECF grading system and consider a three board match between team A and team B. Denote X# as the grade of player # in team X. Then the probability of A winning board 1 is

A1-B1+.5 call this p1

The probability of team A beating team B is the probability of winning least two games

p1=p2=p3=.6

3- 0: p1.p2.p3
2-1 : p1p2(1-p3)+ p1(1-p2)p3+ (1-p1) p2.p3


Now consider team A with A1=200 A2=190 A3=180 and team B: B1=190, B2=180, B3=170

If the teams play in board order then

Team A wins 3-0 with probability .6*.6*.6 = .216
Team A wins 2-1 probability 3*.6*.6*.4 = .432
Total .648


If team B reverses order
p1= .7, p2=.6, p3=.5

Team A wins 3-0 with probability .8*.6*.4 = .192
Team A wins 2-1 probability .8*.6*.6+ .8*.4*.4+.2*.6*.4 = ..464
Total .656

Team B’s expected match points rise.

Generally the more boards and the bigger points difference the better it is for the weaker team to re-order boards.

Mike Gunn wrote:One of us pointed out that from the point of view of grading theory board order should have very little effect on the result of the match. (To predict the score of the match you work out the average grade for each each team and apply this to work out a predicted score for the match. This works irrespective of the board order chosen by each team - an adavantage gained on oone board is always exactly balanced by an advantage lost on another.)

This part of your post is nonsense. The scoring system used for grades does not indicate inherent probabilities.

If one captain plays it straight it is always possible for the other captain to influence the result. Fortunately most captains lack the skills to do this and often influence the result adversely.

It's also possible to increase your teams chances of winning but at the same time this can reduce the chances of not losing ! In a league based on game points, not match points, another completely different strategy is needed.

Brian, I agree with your conclusion, but there is a small mistake in a bit of your working: when team B reverses the probabilities become p1=0.8, p2=0.6, p3=0.4. However, you then go on to use these correct proabilities in your calculation. I feel your maths suppoerts my basic case: changing the board order has an insignificant effect on the expected result of the match.

E Michael White wrote: This part of your post is nonsense. The scoring system used for grades does not indicate inherent probabilities.

Michael, I'm not sure what you mean by this. Do you mean my statement is incorrect in the limited sense that Brian demonstrated? Or just that a prediction is just a guess (howver, statistically a large number of guesses would converge on average to the actual results)? The ECF changed grades recently because the grades were not predicting results, of course.