Howell Scoring

Howell Scoring

For Duplicate Bridge sessions most players regard the Mitchell movement as being the most equitable. With few exceptions, each pair remains N/S or E/W and hence plays the same boards in the same orientation. It has its problems, however. Sometimes there is not time to play all the boards; sometimes, with half a table, some pairs sit out for too long, others not at all; sometimes, in a championship for example, only one winner has to be determined somehow. To alleviate these problems a Howell movement can be used. In a 4 ½ table 25-board Mitchell, say, each pair only meets 4 or 5 other pairs, and 5 pairs sit out for 5 boards, hardly very sociable. In a 4 ½ table Howell [based on a full 5- table 27-board movement, see EBU p35] each pair meets all other pairs, and pairs sit out for only 3 boards.

By no means, however, does this imply that Howell movements are more equitable. Remember that in a Mitchell, as E/W say, you are playing against the N/S pairs, but you are competing against only the other E/W pairs. Nevertheless, you are invariably competing against each of them for an equal number of boards. Using total Match points to determine final rankings is therefore “fair”. In a Howell, even a full Howell, that is not so. Consider a full 5-table Howell. As pair 1 (of 10), you will play one set of boards against each other pair, (that’s fair!?), but you will compete against pairs 2 & 9 only once, against pairs 3, 5, 6 & 8 twice, against pair 10 three times, and against pairs 4 & 7 four times (not so fair!!). If you happen to have a bad night, you will have made virtually certain that pairs 4 & 7 finish in the top three.

Although simple match point scoring of a Howell does give the correct rankings for each set of boards, to then use the overall total match points may bias the apparent result considerably. For a “friendly” club game (are there such things?) that may not be important, but for any one-winner championship, with Master Points issued down to a third of the field, that is a horse of a different colour.

The situation is easily rectified, in principle. From the match-pointed travelling slips, for this particular movement, one simply creates a 10 x 10 table. The entries show the accumulated arithmetical difference in the Match Points earned by each pair compared with each other pair over only those boards for which they were actually competing (by playing in the same orientation over the same boards), together with the corresponding number of boards involved.

From which data one deduces a second 10 x 10 table showing for each pair the average margin of match points (plus/minus) per board when competing against each other pair. To obtain the overall rankings, total these averages (some will be positive, others negative) and divide by the number of pairs against whom they actually competed (there may have been a half table or rover). It is this mean margin per board averaged over all competing pairs that should rightly determine the final results.

But what a pain! So open too, to human error. No wonder it is rarely done, if ever. In this present-day computer world, however, one can score an event at the click of a mouse, given that some noble soul has implemented the underlying algorithm. In practice I expect every traveller would be converted by the computer to percentages before the calculations began. This would produce a more familiar final result after multiplying what would then be the mean percentage gain/loss per board, by the number of boards played, plus 50%.

By using the above method, Howells could be scored just as fairly as Mitchells. Howell about that?