Mitchell / Howells and scoring (percentages)
(re: below - please correct me where I am wrong)
The percentage score is calculated from a percentage of potential tops. Each board is scored from as 0, 2, 4, 6 etc., points from the pair getting the worst score (points) and so getting a score of 0 points to the pair getting the best score (top) and getting 10 points. So, for example if there are 6 pairs and they played 24 boards and they came top on every board they would have 24 x 10 points (240 points) and that would be 100% and if they had got 10 tops, 10 seconds and 4 bottoms (10x10)+(10x8)+(4x0)=180 their percentage would be 75% (180/240).
There are lots of different movements but principally we have Mitchell (a 2 x winner movement) and Howell (a 1 x winner movement).
With Mitchell movements E/W pairs compete against all other E/W pairs for the best score playing the same boards against other N/S pairs; it is essentially two competitions i.e. E/W’s against all other E/W’s and N/S’s against all other N/S’s. So what does it mean if the E/W winning pair won with an average of 90% and the N/S winning pair won with an average 80%? That could be because the winning E/W pair competed against a set of weaker E/W pairs and the winning N/S pair competed against a comparable stronger set of N/S pairs. If that is repeated week after week (that strong E/W pair competing against a set of weaker E/W pairs and so getting a higher weakly average number) and at the end of the year we total the averages of that pair and divide that by the number of games they played over the year to produce and average for the year. It is likely to produce a higher annual average that the comparable N/S pair.
With the Howell movement each pair play all boards and all other pairs (not the same boards against other pairs). So, for example if there are 5 pairs and they played 27 boards and they came top on every board they would have 27 x 6 points (162 points) and that would be 100% and if they had got 20 tops, 4 seconds and 3 bottoms (20x6)+(4x4)+(3x0)=136 their percentage would be 84% (136/162).
Comments
Re above . . . one of the things I am trying to understand (increase my understanding of) is just how balanced (fair) Howells are i.e. are every pair always playing every board against every other pair?
It depends on the Howell. But most of the ones in EBUscore are pretty much optimised.
You don't play every board against every other pair, on each board you play against one pair directly and are matchpointed directly against every other pair that plays in the same direction (slightly less than half the field, for 5 tables, the 4 other NS pairs, for example). That does leave 4 EW pairs that you don't really compete against on that board, save in the rather abstract sense that if they get a great result one NS pair gets a correspondingly good one. But usually you will have the same amount of direct machpoint comparisions against each pair. Which is pretty fair.
Thanks James for the helpful reply
One the question of which movemnet is 'fairest' ScoreBridge comments on some as e.g preferred. Does the EBU publish a list of which movemnets are best balanced/fairest?
The EBU Movement Manual does concern itself with balance.
https://www.bridge-warehouse.co.uk/products/movements-manual
This document is referenced by the movement in EBUScore - leading 'M' for Manning.
There is an older book on movements 'Duplicate Bridge Movements' by Farrington. I have seen this in bridge clubs but not read it. It is referenced as 'F' in EBUScore.
There are other books from Sweden and Australia with much more detail.