[acoales]

Is there a sensible way of scoring a fouled board when aggregate (total-point) scoring is used? I'll supply the hand in case.

Dealer N, All Vul

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This was played 3 times
+660 3NT by north making 11 tricks
+600 3NT by north making 9 tricks
+110 3C by south making 9 tricks
At the next table North and East hands held 12 & 14 cards. The wrong card was transferred back resulting in exchange of D8 and H5.

Dealer N, All Vul

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After this results were
+150 1NT by N, 9 Tricks
+120 1NT by N, 8 Tricks
-100 3H by N, 8 Tricks
-200 (twice) 4H by N, 8 Tricks
-200 3C by S, 7 Tricks
-300 (twice) 4H by N, 7 Tricks
ALSO an average would be required by an east-west pair (N/S vacant at one table).

On the night I ruled that no scores should be awarded for this board. This seems hard on the pairs who scored well both before and after the foul-up. But the changed spot cards make the choice of Hearts as trumps pretty routine (but most unlikely to achieve a game score).

The way I thought it might be scored was to treat it as two separate boards - board 13 before fouling and board 13F after fouling.
Considering the north-south pairs only, for board 13 there were scores of +660, +600 and +110. Pairs who "missed this board by sitting out or by playing 13F" would be awarded an average of +460.
Playing the fouled board 13F resulted in N/S scores of +150, +120, -100, -200 (3 times) and -300 (twice). Pairs who "missed this board" would be awarded an average of -130.
Adjusted scores would be for N/S who played 13
+660(-130)=+530
+600(-130)=+470
+110(-130)=-20
and adjusted scores for N/S who played 13F
+150(+460)=+610
+120(+460)=+580
-100(+460)=+360
-200(+460)=+260 (3 times)
-300(+460)=+160 (twice)
With negated scores for their opponents.

AND the E/W pair who missed the board entirely would be awarded -330. (+330 being the total of the averages for N/S for these two configurations)

[blackshoe]

Quote

Law 87 Fouled Board
A. Definition
A board is considered to be fouled if the Director determines that a card (or more than one) was displaced in the board, or if he determines that the dealer or vulnerability differed between copies of the same board, and the contestants who should have had a score comparison did not play the board in identical form for such reason.
B. Pairs and Individual Scoring
In scoring a fouled board the Director determines as closely as possible which scores were obtained on the board in its correct form and which in the changed form(s). He divides the scores on that basis into groups and rates each group separately as provided in the regulations for the tournament. (In the absence of a relevant regulation the Director selects and announces his method.)

It seems to me that in effect, this fouled board has divided the field into two. The fields are different. In effect, you have two different games. That said, I didn't find anything in the White Book, so the last parenthetical sentence in 87B applies. IAC, the EW who "missed" out because they had a sitout should not get anything at all for this board, since they weren't scheduled to play it in the first place. Unless your Conditions of Contest for aggregate scoring establish something else, like "average of the scores actually obtained".

[acoales]

I think awarding the average score obtained in the "missed" hands should be universal in aggregate scoring. Otherwise pairs will be penalised or given bonuses depending on the hands which they skip. Averages are automatically applied by the ScoreBridge scoring program.

Stirling Union Bridge Club (in Scotland) is the only other Club where I have encountered aggregate scoring. In years BC (before computer) the pairs at Stirling pair kept their own scores and the records in the boards were used only to derive and award the appropriate averages where pairs missed boards.

Aggregate scoring is only appropriate with two-winner Mitchell Movements where the movement is completed. Averages would then be awarded only to pairs who sit out at a half table.

At Camberley Bridge Club we reserve aggregate scoring for only one event. The trophies for this were presented by members who played rubber bridge and it was thought that aggregate scoring was the closest approach to rubber bridge in a duplicate competition.

I agree that the fouled board has divided the field in two. I only query whether there is a fairer way of amalgamating the sections other than by ignoring the board in question.

[blackshoe]

What a scoring program does is not necessarily the best way to do whatever it is, or even necessarily a legal way. However, in this case, it does seem reasonable that a sitout pair should get the average on the board.

Aggregate scoring would seem to be a somewhat archaic method. It would have been so much easier had the scoring been matchpoints. :-)

[gordontd]

Because aggregate scoring is so rarely used (though perhaps not as rarely as acoales suggests) I doubt anyone has bothered to find a solution equivalent to the Neuberg formula as used when scoring for matchpoints. However, if one were to do it, my first thought is that you would find the average scores and the standard deviations for the two groups and then apply an adjustment to the smaller group so as to give them the same average and SD as the larger group. Any mathematicians out there like to comment on this as an idea, or try to implement it in practice?

[gordontd]

A further thought about this is that in this particular instance you might apply the small sub-fields formula from the White Book.

4.2.3.3 Small sub-fields
If the size of the group is at most three and is at most a third of the total number of scores
Neuberg’s formula is not used. Instead a group of two scores is scored with a top as 65% and a
bottom of 55%, and a group of three scores is scored with a top of 70% and a bottom of 50%;
with intermediate and tied scores scored as for ordinary match-pointing.

Since the standard adjustment in aggregate is 100 points, this would mean that your six pairs would each get 0, 100 or 200 on top of the average score from the larger field.

[weejonnie]

Not a mathematician but it seem sensible to take the average of the first three scores (660 600 110) = 460 and give the pairs +200 +140 -350

Then take the average of the last group (+150 +120 -100 -200 -200 -200 -300 -300) = -130

Giving +280 +250 +30 -70 -70 -70 -170 -170

non-playing pair get 0

Alternatively we could work out the par score on each version of the hand and award NS/EW how they did compared to the par contract.

[acoales]

Thank you all for your attention. I like weejonnie's suggestion for scoring. And I'd choose to compare with the average made on the day rather than the par score. It is obviously fair in that neither section of the players is favored by the scoring, each section having an average of zero.

I'll refer committee members to this strand for their opinions.

[RMB1]

 gordontd, on 2019-July-21, 01:41, said:

Because aggregate scoring is so rarely used (though perhaps not as rarely as acoales suggests) I doubt anyone has bothered to find a solution equivalent to the Neuberg formula as used when scoring for matchpoints.

To score at aggregate scoring when there are fouled boards once should work with aggregate-relative-to-average.

All scoring methods are best thought of:
1. compare my score with each other scores, and apply some function to the difference
2. sum over all other scores
3. divide the sum by something

In match points the function is 2,1,0 (1,0.5,0 in US) depending on whether the difference is +ve, equal or -ve.

In cross imps, the function is the IMP scale.

Aggregate scoring works the same if the function (in 1.) is just the difference, and the score is my score - the average of all scores. (There is some fudge to do with dividing by the number of results or the number of comparisons - an issue we also get for cross imps.)

If there are no artificial scores and no fouled boards, then 'the average of all scores' is the same for all pairs sat the same way, and can be ignored.

[RMB1]

I think the neuberg formula for aggregate is just to award: score - average for the subfield. On the fouled board, all pairs are scored relative to average, where as on all other boards they are scored as relative to zero.

You should be scoring relative to average if there is a half-table.

[acoales]

Without mishaps we award the average score for the board(s) they missed to pairs who sit out. Overall this is equivalent to deducting the average score from the pairs who played the cards and will rank pairs in the same order. I would say that scoring relative to average, as weejonnie and RMB1 have suggested, would be a general improvement. The range of totals for N/S and E/W would both range about zero. And, provided it is known where an error occurred, this method extends quite simply to scoring split sections.

Pairs might be more encouraged by seeing more balanced results. On our competition night (whether or not the problematic board is included) N/S held the "better" 23 or 24 hands. Only a couple of N/S total scores fell below zero and the E/W winners held a small negative total.

Inclusion of the problematic board would be likely to affect 2nd and 3rd places in both directions.

[gordontd]

 RMB1, on 2019-July-21, 09:56, said:

I think the neuberg formula for aggregate is just to award: score - average for the subfield. On the fouled board, all pairs are scored relative to average, where as on all other boards they are scored as relative to zero.

It seems to me that the problem is that some boards are flatter than others, which is why I suggested a further adjustment to equalise the std dev.

[lamford]

 gordontd, on 2019-July-21, 13:03, said:

It seems to me that the problem is that some boards are flatter than others, which is why I suggested a further adjustment to equalise the std dev.

The form of scoring, total points, is closer to rubber bridge, so there is a huge element of luck anyway, assuming people do not play all boards, if I understand it correctly. For example, if 23 of the 24 boards were in 1NT and one in 7NT, only the last board really matters, and the pairs scoring +2220 are the only ones who can win the event. I would not make any further adjustment because some people played different versions of the fouled board. If you do that you should adjust for the SD of all boards that people played.

And I thought aggregate scoring went out with the death of whist drives. It is only usable in events like the Hubert Phillips, where at least it is head to head.

[acoales]

gordontd helpfully explained how to follow the guidance in the EBU White Book. This we have adopted by giving artificial scores to the 6 pairs who played the boards as dealt. The EBU committee who adopted that strategy, albeit principally for MP scoring, must have given it considerable thought. If the problem should occur again with a larger group to be split out I'll follow weejohnie's method.

Scaling to equalize the standard deviations at first seems attractive but raises further questions. Which way should scaling occur? - to that of the larger section? - to the higher or to the lower std. dev.? Should sample or population standard deviations be used? How many times must a board be played to give a significant std. dev? All this could provide an article in a mathematical journal but is, I think, only of theoretical relevance.

Even if no board had been fouled, our competition would have been fairer for N/S pairs scheduled to play all 24 boards. The E/W pairs to play just 22 boards and to be compensated by the average scores of the other E/W pairs on the 2 boards to be missed.

[blackshoe]

If you have two fields (NS and EW) it might be fairer to EW who had a sitout to not count those two boards at all for any EW. That's off the top of my head, so I might be... what's that word? Begins with a "w" I think.