Around the world there are growing numbers of Law 12C3 decisions where weighted scores are applied to do equity. Appeals Committees are able to give such decisions unless their Zone says otherwise [so they may not be given in North America]. Now, with the WBF Code of Practice, Directors around the world are also being given the right to give such rulings. However, not everyone seems certain how these decisions should actually be applied.

Let us look at an example case. Declarer goes off in 3NT but has been misinformed. If he had been informed correctly he would have made either nine or ten tricks in 3NT so the Appeals Committee decide to give him 60% of 3NT+1 plus 40% of 3NT=. In fact, 4 is the obvious contract, making ten tricks.

Some people have been known to work out 0.6x430+0.4x400=418. When compared to the rest of the field, all of whom get 420, that means this pair got a bottom, which is hardly what the Committee intended! Of course, if the Committee had given 70% of 3NT+1 plus 30% of 3NT= then that would be a top, since 0.7x430+0.3x400=421!

Could you not round to the nearest score? Of course, and then this pair get as an average both times, but this is not what the Committee intended. The actual score given by the Committee was 60% of an excellent pairs score plus 40% of an awful pairs score, and any means of calculation that does not reflect this is not correct.

The correct way to calculate a weighted score is to apply the final form of scoring for the board and then apply the weighting. In the example given suppose a top is 50 MPs. If 430 gets 50 MPs and 400 gets 0 MPs then the calculation of the weighting is 0.6x50+0.4x0=30 [but see what John Probst has written]. 30 MPs is a much closer approximation to what the Appeals Committee intended. Note that this calculation is not one that the Committee should be doing: it is for the Directors. The Committee establish the weighting as part of their decision and the Directors apply it in this fashion.

What about teams, with imps and VPs? The method is still the same, with the Committee establishing the weighting. The Directors then calculate the results in imps for the various scores, then apply the weighting to the imp scores. Note that it is not correct to go further and apply the weighting to the VP score: Appeals Committee decisions apply to the results on a single board, not to the whole match. Let us look at a complex example taken from an Appeals decision in the Olympiad at Maastricht.

In Appeal #5, Norway v Latvia, the score for both sides was adjusted to

- 50% of 2= by North (NS +110) plus
- 20% of 2+2 by West (NS -170) plus
- 30% of 4= by West (NS -620)

- 50% of +730, ie 12 imps plus
- 20% of +450, ie 10 imps plus
- 30% of 0, ie 0 imps

This works out to an 8 imp swing which seems an accurate reflection of what the Committee intended.

This method is fine but not best.

If I award 60% of 430 and 40% of 400 then I must add .6 to the 430 frequency and .4 to the 400 frequency and then matchpoint with a frequency table containing these fractions. eg

9 results (English scoring; 2 for a win)

How David does it:

Apply Neuberg to 8 results

score | frq | mps | . |

460 | 1 | 15.875 | The weighted score gets |

430 | 3 | 11.375 | 60% of 11.375 = 6.825 plus |

420 | 3 | 4.625 | 40% of 0.125 = 0.05 |

400 | 1 | 0.125 | Award = 6.875 |

How it should be done:

score | frq | mps | . |

460 | 1 | 16 | The weighted score gets |

430 | 3.6 | 11.4 | 60% of 11.4 = 6.84 plus |

420 | 3 | 4.8 | 40% of 0.4 = 0.16 |

400 | 1.4 | 0.4 | Award = 7.00 |

Why should it be done this way?

Because the assigned scores have meaning within the context of the results found elsewhere on the hand and should carry their weight in the computation of the frequencies and matchpoints. This method does that.

My design for the new EBU scoring system **will** do it this way and the scorer will enter all the weights for weighted and split scores as part of the input. It also involves having separate frequency tables for NS and EW, so it is possible that on a top of 16 the total of NS and EW for any one result may not equal 16. This is not a problem as the frequencies relate either to the NS field (with its split scores) or to the EW field (with its scores). NB
Herman De Wael's
programs seem to do this.

*Editor's note:*

- This article was written during the World Championships in Maastricht, the Netherlands in 2000 and first appeared in rec.games.bridge and Bridge-laws mailing list
- If you want to comment on this article, why not write direct to David Stevenson?
- Or why not write direct to John Probst ?
- We shall be pleased to hear from you!

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