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All pairs on one line do better at national level than club level? simultaneous pairs scoring, probability

#1 User is offline   pescetom 

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Posted 2018-February-22, 11:17

Each week my club plays a simultaneous duplicate pairs event, in which pairs in different clubs all over the country play the same set of boards at the same time in a single virtual event. At the end of play we get a local classification which ranks NS and EW lines by percentage of matchpoints and then the next day we get a national classification which ranks all pairs by percentage of nationally calculated matchpoints.

Obviously local percentage and national percentage are different: it is one thing to be the only pair in a club to make 7NT and another thing to be the only pair in the country to do the same. Differences rarely exceed 10% and are usually less than 5%.

But I have noticed a curious phenomenon - it often happens that ALL pairs on one of the local lines do better at national level than local level and ALL pairs on the other local line do worse :blink:
The improvement averages up to +5% across the whole line, but is not uniform, so one pair might improve +4%, the next +7%, the next +2% and so on.

Does anyone have an explanation for this? If you play in similar events, does the same thing happen? Certainly it is no coincidence. I imagine it is a statistical curiosity rather than some kind of error, but there still must be some mathematical logic behind it.

It's a small club, we're usually talking about 6-7 pairs per line. One factor that might just have influence is that we don't assign pairs to lines in a truly random way and the stronger pairs tend to concentrate on NS - but this is not always so and in any case EW seems to "benefit" as often as NS. Another is that sometimes we play more boards than most other clubs in the country, and on those few extra boards it is easier to obtain an extreme national score, as relatively few clubs will play them - but this does not happen that often.
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#2 User is offline   barmar 

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Posted 2018-February-22, 12:08

I guess by "line" you mean a specific board?

I suspect in your club most players play similar systems. Sometimes a board is particularly easy or difficult to bid in some systems versus others. If the board is difficult to bid well in your local system, all the pairs in that direction will be at a disadvantage against the more diverse systems played around the country.

But I think this is just a normal statistical anomaly. Suppose there's a relatively even spread from boards that are heavily biased in the plus direction to boards that are heavily biased in the minus direction. Only a few of the boards will be in the middle, where there's not much bias. But psychologically we tend to expect more uniformity, and notice the extremes and think there's something wrong.

Humans have very poor intuition about randomness and statistics. For instance, if shown two patterns of dots, one which is fairly boring and uniform and one that has lots of clusters, and asked which one is more likely to be the result of a random process, they'll usually choose the uniform one, but that's exactly wrong. In the long run things tend to even out, but there will always be short runs that are not even. To illustrate this another way, flipping a coin lots of times should produce about the same number of heads and tails, but it's extremely unlikely to alternate between heads and tails on every flip.

#3 User is offline   pescetom 

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Posted 2018-February-22, 12:37

View Postbarmar, on 2018-February-22, 12:08, said:

I guess by "line" you mean a specific board?

By "line" I mean all pairs playing in NS, or all pairs playing in EW, assuming a Mitchell movement.

View Postbarmar, on 2018-February-22, 12:08, said:

I suspect in your club most players play similar systems. Sometimes a board is particularly easy or difficult to bid in some systems versus others. If the board is difficult to bid well in your local system, all the pairs in that direction will be at a disadvantage against the more diverse systems played around the country.

Actually no, we have a babel of systems. The stronger players mainly play strong-club systems, often with canape' style developments; the weaker players are mainly playing 4-card majors; the intermediates 5-card majors with various degrees of sophistication. But yes, the deals are often tricked to be extreme and this creates more difficulty to the traditional systems than it does to those playing 2/1 or similar.


View Postbarmar, on 2018-February-22, 12:08, said:

But I think this is just a normal statistical anomaly. Suppose there's a relatively even spread from boards that are heavily biased in the plus direction to boards that are heavily biased in the minus direction. Only a few of the boards will be in the middle, where there's not much bias. But psychologically we tend to expect more uniformity, and notice the extremes and think there's something wrong.

Humans have very poor intuition about randomness and statistics. For instance, if shown two patterns of dots, one which is fairly boring and uniform and one that has lots of clusters, and asked which one is more likely to be the result of a random process, they'll usually choose the uniform one, but that's exactly wrong. In the long run things tend to even out, but there will always be short runs that are not even. To illustrate this another way, flipping a coin lots of times should produce about the same number of heads and tails, but it's extremely unlikely to alternate between heads and tails on every flip.

I appreciate your point about poor intuition of randomness and statistics. And as Doris Lessing said, Coincidence is God's way of remaining anonymous :D But here we are talking about all 6 NS pairs improving in overall percentage at national level and all 6 EW pairs doing the opposite, or vice versa. And over the last three years this happened very frequently (12 times in a sample of 23), I would exclude chance.
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#4 User is online   gordontd 

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Posted 2018-February-22, 14:14

It's not uncommon. Many clubs have established practices that ensures one line is stronger than the other. The solution is to insist on drawing for starting positions in simultaneous pairs events. Or play Howells.
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#5 User is offline   pescetom 

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Posted 2018-February-22, 16:13

View Postgordontd, on 2018-February-22, 14:14, said:

It's not uncommon. Many clubs have established practices that ensures one line is stronger than the other. The solution is to insist on drawing for starting positions in simultaneous pairs events. Or play Howells.


That's interesting, because that was my first hypothesis. Ambitious pairs do gravitate towards NS because they like to control the table, also we have some players who have permanent or temporary disabilities that authorise them to sit on NS, and they are usually experienced and motivated. Club rules for the remaining tables are to choose the line by chance, but often the weaker pair will simply accept EW. I did petition for drawing random starting positions (using the computer) but the idea was haughtily dismissed, so little chance there.

I can see that with most strong pairs in NS, another strong pair who sits in EW will gain a significant local advantage: they have weaker indirect opponents with which to confront. And if all the stronger pairs are in NS, then it is intuitive (with the perils mentioned by @barmar) that they all gain at national level and all of EW loses.

But I can't see why all NS should gain when there are clearly some strong pairs in EW, or why EW sometimes all gain and NS all lose. I wouldn't be at all surprised if at national level the tendency for strong pairs to concentrate in NS was more extreme than it is locally, if that could account for it somehow.
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#6 User is offline   blackshoe 

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Posted 2018-February-22, 21:12

Howells. Heh. Anathema around here. We have too many who need to be stationary for one reason or another.
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Posted 2018-February-23, 07:27

View Postblackshoe, on 2018-February-22, 21:12, said:

Howells. Heh. Anathema around here. We have too many who need to be stationary for one reason or another.


We have one who is blind (and needs to be stationary in a separate room so that we can announce all calls and plays) and 2-3 who have problems of ambulation. All strong players.
The good news is that the Federation assigns handicaps to players, so it would still be possible to for the computer to formulate lines of equal strength by distributing the remaining pairs such that each line has an equal total handicap, if this was accepted.
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#8 User is offline   barmar 

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Posted 2018-February-23, 09:45

A particular set of deals will usually be biased towards one direction or the other (again because of the clumpiness of random data), although this will average out over multiple sessions.

If you tend to have most of the same pairs sitting NS and EW every time, then you'll see similar effects of the biases across sessions. So if more of the good pairs sit NS, then when the hands are favorable to NS you'll probably see them mostly doing well compared to the national average.

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Posted 2018-February-23, 10:26

View Postbarmar, on 2018-February-23, 09:45, said:

A particular set of deals will usually be biased towards one direction or the other (again because of the clumpiness of random data), although this will average out over multiple sessions.

If you tend to have most of the same pairs sitting NS and EW every time, then you'll see similar effects of the biases across sessions. So if more of the good pairs sit NS, then when the hands are favorable to NS you'll probably see them mostly doing well compared to the national average.


This is also true, and it might well explain why EW all gained at national level this last week (with an average gain of +4% and one pair that gained +7%) and NS lost equally (except one pair). This time the lines were about equal in strength (which a handicap calculation confirms, average 3.0 vs 3.1), so to cause the swing the anomaly must be to do with the other clubs (maybe widespread NS dominance) or with the set of deals.

Looking at the deals, the question is of course: what is a favourable deal? I guess it is one that plays to our strengths, so if one is strong in all elements of bridge, then a favourable deal is both difficult to bid and difficult to play in the most likely direction. In the case of our club, I would say that overall the defensive play is better than the attacking play which in turn is better than the uncontested bidding. So if the deals are biased such that with real-world bidding one side plays more in defence than in attack, I would expect that side to gain at national level. I was in EW and sure enough I see that 18 times out of 24 (75%) we defended. I don't have the numbers for other pairs underhand but that looks clear enough.
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