A full Howell is fairest because every pair plays every other pair. However with 10 pairs that means 9 rounds and likely to be 27 boards. Our club finds that too many. If you curtail the Howell it is less fair. You can play a 3/4 Howell but then not all pairs play each other, or a Hesitation Mitchell (6 rounds) which is similar. Maybe a Mitchell is fairer than an incomplete Howell especially if you only compare the two ranks separately as all pairs in each rank play all other pairs in the other rank, provided you complete all rounds which with 5 tables you will. However you be playing 5 board rounds, probably, which to my mind is less fun than 3 board rounds and more variety of opposition (I know that is not the question you asked). I prefer the Hesitation Mitchell as it is an easy movement for the players and a good compromise.
Surprisingly, according to the Manning equality-of-competition algorithm, where 0 is perfectly balanced, the 5 table 3/4 Howell, eg [M38], is better balanced than the full Howell, eg [ M39], having a factor of 1.59 vs 1.81. The Hesitation Mitchell [M47-5] has a factor of 2.10.
Tim's explanation above should say ... Mitchell is fairer ... only if you compare the two ranks separately... (ie leave out "especially"). Each side has a factor of 0 but the sides are not comparable.
Fairness of a full Howell comes down to which directions each board is played in at each table. (This is why, e.g., BBO's "Howells" are so unbalanced: although every pair plays every other pair, the directions are wrong, meaning that some pairs are nearly always sitting in the same direction as some other pairs and so they have a more negative effect on each others' results than would be expected from a balanced competition.)
Howells designed for use when playing in person generally don't get the directions nearly as wrong as BBO does, but they aren't always perfectly balanced. For example, for a 5-table full Howell to be perfectly balanced, for each pair A and each other pair B, A and B would have to be table opponents on 1 of the 9 boardsets, sitting in the same direction on 4 of the 9 boardsets, and sitting in opposite directions but not table opponents on 4 of the 9 boardsets. Designing movements to obey that restriction for every combination of A and B is nontrivial, and sometimes can't be done without making the movement overly complicated.
Comments
A full Howell is fairest because every pair plays every other pair. However with 10 pairs that means 9 rounds and likely to be 27 boards. Our club finds that too many. If you curtail the Howell it is less fair. You can play a 3/4 Howell but then not all pairs play each other, or a Hesitation Mitchell (6 rounds) which is similar. Maybe a Mitchell is fairer than an incomplete Howell especially if you only compare the two ranks separately as all pairs in each rank play all other pairs in the other rank, provided you complete all rounds which with 5 tables you will. However you be playing 5 board rounds, probably, which to my mind is less fun than 3 board rounds and more variety of opposition (I know that is not the question you asked). I prefer the Hesitation Mitchell as it is an easy movement for the players and a good compromise.
I don't think Tim's response could be bettered.
Surprisingly, according to the Manning equality-of-competition algorithm, where 0 is perfectly balanced, the 5 table 3/4 Howell, eg [M38], is better balanced than the full Howell, eg [ M39], having a factor of 1.59 vs 1.81. The Hesitation Mitchell [M47-5] has a factor of 2.10.
Tim's explanation above should say ... Mitchell is fairer ... only if you compare the two ranks separately... (ie leave out "especially"). Each side has a factor of 0 but the sides are not comparable.
Fairness of a full Howell comes down to which directions each board is played in at each table. (This is why, e.g., BBO's "Howells" are so unbalanced: although every pair plays every other pair, the directions are wrong, meaning that some pairs are nearly always sitting in the same direction as some other pairs and so they have a more negative effect on each others' results than would be expected from a balanced competition.)
Howells designed for use when playing in person generally don't get the directions nearly as wrong as BBO does, but they aren't always perfectly balanced. For example, for a 5-table full Howell to be perfectly balanced, for each pair A and each other pair B, A and B would have to be table opponents on 1 of the 9 boardsets, sitting in the same direction on 4 of the 9 boardsets, and sitting in opposite directions but not table opponents on 4 of the 9 boardsets. Designing movements to obey that restriction for every combination of A and B is nontrivial, and sometimes can't be done without making the movement overly complicated.