Fairness in Movements Chosen by Directors
I played in a club last night. There were 19 tables in total , split into two sections; one of 10 tables (with single hesitation Mitchell) and the other one of 9 tables (with double hesitation Mitchell) , playing two sets of same 22 boards. Both sections were combined to arrive at a single winner across both sections. There were no prizes involved. My questio : is this deemed to be a fair movement for results purposes or should be two winners, n/s and e/w pairs ? Grateful for your comments.
Comments
It's generally inadvisable to separate a Hesitation Mitchell into moving and stationary subfields, because no matter what you do with arrow switches, the subfield consisting of the moving pairs will have some significant imbalances (some pairs of moving pairs play each other, and others don't, and the movement makes no attempt to compensate for that). The fact that moving pairs sometimes sit in the same direction as stationary pairs (it isn't a simple "N/S" versus "E/W") also means that the subfields aren't independent of each other.
In practice, Hesitation Mitchells are almost always played with an appropriate number of rounds arrow-switched. If you do that, then although the level of competition between two moving pairs is still unbalanced, it is much more balanced between a moving and stationary pair, or between two stationary pairs. So having the larger field helps to dilute the imbalance somewhat (although it still exists). (Some Directors don't arrow-switch the table with two moving pairs; omitting that switch makes the moving-versus-moving competition even more unbalanced, but makes moving-versus-stationary a little more balanced – I don't know whether it's a net gain on average.)
When sections are combined, the results for a pair will depend quite heavily on who their table opponents were (having weak table opponents will improve a pair's results – most movements try to balance that by having weak table opponents screw up your comparisons in the rounds where you don't face them, but when combining sections, results from the other section will dilute that effect), and again this is true regardless of whether you split the subfields or not; so there's no reason to split moving from stationary pairs there either.
I don't think the movement is particularly fair, compared to movements designed for maximum fairness – but splitting the subfields wouldn't help (and it is hard to produce a completely fair movement given the restriction of 19 tables but 11 rounds).
The short answer is that there's no particularly good ways to play 11 rounds with 19 tables in terms of balance. This solution seems OK.
All pairs play all the same boards and if both sections are balanced movements this should give a decent balance overall. As Ais notes, Hesitation Mitchells are nearly always arrow switched quite specifically to optimise the balance and played as single winner movements. They're nearly always good rather than perfect in terms of balance.
I can't see an easy improvement without working out the Web Mitchell, and not every director will be confident with that option.
Thank you Ais ans JamesC for your comprehensive response-much appreciated. When I direct and have 19 tables I would have chosen Web Michell but I need 2 sets boards of 26 boards plus some random (about 6 boards) numbered boards for sharing between two mini sections (one for tables 14/15/16 and the other one for tables 17/18/19) , along with one large section for 1-13 tables., giving two winners n/s and e/w. I would omit the last round to get to 22 boards (11 rounds of 2. boards each). If anyone else has any furher comment I would much appreciate it. Thank you so much.
This is probably going to seem like an obvious solution, but could your club make up a triple set of boards to enable you to cope with odd numbers of tables?
If you have 19 tables this doesn't sound like it was a one off - our club has sets of double and triple boards so you can run any number of Web movements.
You can arrow switch or not as you please.
That table switches one pair's polarity each round. Our club's Hesitation Mitchells exclude that table from the final round "arrow switch at all tables" - this appears to sensibly maintain the balance of every moving pair having one round as N-S.
An arrow switch on that table seems illoigical - it would result in one moving pair never being N-S and another moving pair being N-S twice.
Most moving pairs are NS twice - once at the hesitation table and once in the arrow-switch round
Thanks Robin - of course, how foolish of me. So the arrow switching decision at the pivot table on the final round has the following impact: