[1eyedjack]

What conclusions can you draw if, over a very large population of hands, you find that your average IMP result measured against double-dummy par varies significantly from your average IMP result actually achieved?

By "very large population", you can assume that factors cause discrepancies between "double-dummy par" and "good bridge" (such as singleton kings dropping offside when a finesse would be normal play) would in the long term benefit each side equally.

[hotShot]

If it is significantly higher, this would suggest that your opponents play significantly worse than the DD-Solver.
An analysis of card play I did a few years ago showed that the average beginner loses more than 1 trick per board to the DD-solver while it takes GIB and WC player 4-5 boards to lose 1 trick to the DD solver.
Combined with bad bidding this means a lot of IMPs.

Can't imagine that your average could be lower ....

[1eyedjack]

If my opponents play significantly worse than the DD solver, then I would expect that effect also to be reflected in my actual results, so that the comparison of Actual v Par would remain unaltered. All that would happen is that both scores would be skewed to the positive, but each to the same extent. What am I missing?

[Radrag]

Your teammates are better, or worse, than you.

[billw55]

hotShot, on 2011-September-27, 02:00, said:

If it is significantly higher, this would suggest that your opponents play significantly worse than the DD-Solver.
An analysis of card play I did a few years ago showed that the average beginner loses more than 1 trick per board to the DD-solver while it takes GIB and WC player 4-5 boards to lose 1 trick to the DD solver.
Combined with bad bidding this means a lot of IMPs.

Can't imagine that your average could be lower ....

There were stats posted to these fora not long ago, compiled from vugraph records and therefore generally world class players, and certainly national class. I don't remember the exact figures, but roughly the result was that declarer beat deep finesse by about a quarter trick per board before opening lead, but lost to it by a similar margin after the lead (meaning the table lead was included in the double dummy conditions). The net result was that world class defenders were giving away almost half a trick per board on opening lead. I found that fascinating.

[hotShot]

Looking at your actual results (assuming they are from BBO XIMP play)

Playing in a heterogeneous environment has a systemic bias.
Lets assume 2 pairs of beginner play a partscore. Each beginner will miss a trick he could take, but since there are 2 defenders and one declarer, the result is +1.
Lets assume 2 expert pairs play the same board, Nobody misses a trick., the result is =.
So you lose playing the par score.

If you play a lot of "swiss" tourneys where good player soon meet good opponents and the same applies to weak players this effect is significant.

[hotShot]

billw55, on 2011-September-27, 06:18, said:

There were stats posted to these fora not long ago, compiled from vugraph records and therefore generally world class players, and certainly national class. I don't remember the exact figures, but roughly the result was that declarer beat deep finesse by about a quarter trick per board before opening lead, but lost to it by a similar margin after the lead (meaning the table lead was included in the double dummy conditions). The net result was that world class defenders were giving away almost half a trick per board on opening lead. I found that fascinating.

If each side plays half of the boards, 1/2 a trick at the lead is about 1 trick in 4 boards.

[Wackojack]

A friend of mine as a young man invented a variable forcing pass system and then gave up playing for about 20 years because he could not legally play his brainchild. A couple of years ago we agreed to try out his system on BBO. I managed to persuade a few known opponents to play against us ranging from half decent to expert. I recorded our results on XL including a par comparison. We played 376 hands and the results are a below

The forcing pass record to 30 March 2010
Hands played 376
Imps per hand from start Total 0.33 As Declarer 0.41 As Defenders 0.23

Contested auctions we played 32%
Contested auctions opponents played 32%
Uncontested auctions we played 22%
Uncontested auctions opponents played 14%
Par comparison 0.44

A chart showed that our imps average and par comparison after 100 hands were both exactly zero. After that time the average of both increased progressively except that the par comparison had a greater variance than the actual imp average.

My initial thought was that the par comparison variance is higher because of the nature of the imp scoring so that would explain par comparison being about 25% higher. But I have yet to think that through in detail.

Lets take a theoretical situation where both we and our opponents will in an uncontested auction bid to par (more or less). Also let us say that the field over the long run will be equally below par in both directions. Then any difference between the par and actual imps would be in the effectiveness or otherwise of the destructive bidding of each partnership. Thus if the imp average of the partnership was significantly higher than the par average, it could indicate that their destructice bidding was outbidding par. I could get evidence of this (or otherwise)from the results if motivated.

[nigel_k]

Radrag, on 2011-September-27, 03:31, said:

Your teammates are better, or worse, than you.

What matters most is whether your teammates are better or worse than their opponents. If they are better, you will be comparing against scores that on average are better than par. And vice versa.

When you keep records, you want to separate out the results against people who are significantly worse than you are so they don't skew the result.

[FrancesHinden]

billw55, on 2011-September-27, 06:18, said:

There were stats posted to these fora not long ago, compiled from vugraph records and therefore generally world class players, and certainly national class. I don't remember the exact figures, but roughly the result was that declarer beat deep finesse by about a quarter trick per board before opening lead, but lost to it by a similar margin after the lead (meaning the table lead was included in the double dummy conditions). The net result was that world class defenders were giving away almost half a trick per board on opening lead. I found that fascinating.

There are plenty of vugraph presentations that are neither world class nor national class. The average standard is higher than an average club, but don't pretend that it is only, or even mainly, expert players.

[FrancesHinden]

1eyedjack, on 2011-September-27, 01:41, said:

What conclusions can you draw if, over a very large population of hands, you find that your average IMP result measured against double-dummy par varies significantly from your average IMP result actually achieved?

By "very large population", you can assume that factors cause discrepancies between "double-dummy par" and "good bridge" (such as singleton kings dropping offside when a finesse would be normal play) would in the long term benefit each side equally.

I would conclude that my assumption is incorrect (I don't agree with the assumption in the first place, so perhaps that is an unsurprising conclusion for me).

I think the other main point has already been mentioned - if you are looking at teams-of-four results, then the relative standard of your teammates (who are likely to be fairly constant in your comparisons) is relevant. If my teammates are very strong then they will generally be beating double-dummy par, so when I score up with them I will on average have more imps/board than I should do against DD.

I realise that perhaps I misunderstood the question. Do you mean that your {result against DD par} is consistent at 2 imps/board, and {actual result} is consistently different at 3 imps/board - so they vary significantly from each other; or do you mean that the difference between the two averages varies a lot over time?

[1eyedjack]

FrancesHinden, on 2011-September-27, 13:29, said:

I would conclude that my assumption is incorrect (I don't agree with the assumption in the first place, so perhaps that is an unsurprising conclusion for me).

Can you be more specific about the assumption that you say that I make which is incorrect? Perhaps my assumption that the population of hands is sufficiently large for any statistical conclusion to be reliable? There will be a correlation between the population size and the minimum discrepancy that would be significant. It is some decades since I did this sort of thing at school and it has never been reinforced in my job. What population size do you think that you would need, in order to draw a conclusion that a diffference of x IMPs is "significant"?
Or perhaps my assumption that both orientations at the table in the long term benefit equally in the discrepancy between DD and "good bridge"? Why would you disagree with that? Are the hands not random?
As far as I can tell those are the only two assumptions that I have made. Oh, I suppose also that I am putting trust in the software that calculates it.

FrancesHinden, on 2011-September-27, 13:29, said:

I think the other main point has already been mentioned - if you are looking at teams-of-four results, then the relative standard of your teammates (who are likely to be fairly constant in your comparisons) is relevant. If my teammates are very strong then they will generally be beating double-dummy par, so when I score up with them I will on average have more imps/board than I should do against DD.

Actually I meant to ask in the context of playing XIMPed pairs, playing with a variety of pickup partners, each hand played 16 times on BBO.

FrancesHinden, on 2011-September-27, 13:29, said:

I realise that perhaps I misunderstood the question. Do you mean that your {result against DD par} is consistent at 2 imps/board, and {actual result} is consistently different at 3 imps/board - so they vary significantly from each other; or do you mean that the difference between the two averages varies a lot over time?

The former.

[hotShot]

I would suggest the following check:

Pick from all the boards where declarer did not go down those where the DD-par is of the same denomination and level ( partscore, game or slam zone).
Since the effects of game or slam bonuses are eliminated, the result only depends on the number of tricks taken.

   0 -   10 =  0        	
  20 -   40 =  1      	+1 M,NT / +1,+2 m
  50 -   80 =  2      	+2 M,NT / +3,+4 m
  90 -  120 =  3 		+3 M, NT

You can calculate how many IMPs you should have won.
If your set is large enough and if distortions are averaged out, these IMPs and the actual XIMPs won should be the same.
The IMP scale is not linear so I doubt that distortions average out. It also indicates that the actual extra IMPs for an overtrick would be smaller than based on over (under) tricks.
But any significant deviation would indicate some sort of bias.