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Article 8U41 by Richard Pavlicek

Did you ever wonder how instant matchpoints are obtained? Well, let me rest your anxiety. They come from the Dart Room at ACBL Headquarters. Prior to every instant matchpoint game, an employee throws hundreds of darts at a wall chart, thereby determining the matchpoints for each possible result.

OK, just kidding. Instant matchpoints are determined by the frequencies of actual results when the deals were played in a previous tournament. Of course, the tournament must be foreign (and preferably not recent) so the chance of anyone having played and recognizing the deals is remote.

For the last seven years I have done the analyses and prepared the matchpoint tables for the ACBL Instant Matchpoint Pairs (usually sponsored by Royal Viking Line). I receive a list of frequencies for the results on each board. To illustrate the process, say Board 1 was played 16 times with the result frequencies below. Matchpointing on a 15 top produces:

N-S Score | Frequency | Matchpoints |
---|---|---|

+450 | 2 | 14.5 |

+420 | 4 | 11.5 |

+400 | 3 | 8 |

+170 | 6 | 3.5 |

-50 | 1 | 0 |

This is easy so far, but what about scores not listed? For instance, what should a score of plus 430 receive? Obviously it should be between 11.5 and 14.5, but what exactly? Or, worse yet, how about a score of minus 100! Since minus 50 gets zero, is there anything worse?

There are various ways to do this. Simplest and most elegant is to imagine a mystery result added to the data, increasing the top by one. Each actual result is matchpointed as if it had *tied* the mystery result, effectively increasing its matchpoints by a half. Each gap (between actual results or at either end) is matchpointed as if *were* the mystery result. The next table shows this adjustment from a 15 to 16 top with all gaps properly matchpointed.

N-S Score | Frequency | Matchpoints | Percent |
---|---|---|---|

… | … | 16 | 100 |

+450 | 2 | 15 | 94 |

… | … | 14 | 88 |

+420 | 4 | 12 | 75 |

+400 | 3 | 8.5 | 53 |

… | … | 7 | 44 |

+170 | 6 | 4 | 25 |

… | … | 1 | 6 |

-50 | 1 | 0.5 | 3 |

… | … | 0 | 0 |

Note that the gap between +420 and +400 is omitted. In theory it would receive 10 matchpoints, but there’s no need to include it because a score of +410 is impossible.

The final column shows the matchpoints scaled to a 100 top or percentage. All percents are rounded to the nearest whole number.

To illustrate the methods, I have greatly reduced the amount of data. Typically, each board has hundreds of results, so the adjustment to a 100 top is actually a reduction from some huge actual top. I wrote a short computer program to perform all the calculations, else I would definitely prefer the Dart Room.

Do I edit the matchpoints in any way? Yes. When two (or more) results yield the same matchpoint score, I either combine them into a single gap or adjust one (plus or minus 1) so the scores are unique. I also remove ridiculous fluke results, like the guy who went for 1400 against a partscore.

Lastly, when analyzing the deals, I occasionally make minor adjustments if I feel the matchpoints wrongly reflect what would happen in an American tournament. For example, suppose bidding a cold slam would receive 95 matchpoints, yet I feel it should be reached by normal, sound bidding. Clearly, this is an injustice to the other side, so I would make an adjustment (including neighboring scores) reducing it to, say, 87 matchpoints.

Sometimes I would like to make *drastic* changes, such as lowering the preceding to 65 matchpoints, but I resist that temptation. One must not forget that the frequencies are based on real-life occurrences, or to put it another way: It’s not nice to fool with Mother Nature.

© 1993 Richard Pavlicek