Todd Zimnoch asked:
So, how do work things out when playing an odd number of rounds? I suppose that ideally you would seed the three least significant teams by the last round into this round robin, but they'll have to play half matches. If the field is scoring on a 20 VP scale, I suppose that 10 VPs should be available in each half match. Would you use the 20 VP scale, double the imp difference then halve the VP award? Is there a special scale? Or is there a different solution entirely?
First of all, the best solution by far is to have a stand-by team who will play or not as needed. It is often difficult to arrange this, although sometimes a local team will accept a free game on this basis.
Second, there are short threesomes, and long threesomes. I have also heard threesomes called triples or triangles. A short threesome is where team A play team B and team C over the same period of time as a full match is played elsewhere. So if there are 8-board matches, a short threesome is played as two 4-board matches. A long threesome takes the same time as two full matches elsewhere, so if there are 8-board matches, a long threesome is played as two 8-board matches.
The way a threesome is actually played is this: three teams are allocated to three special tables, say Blue 1, Blue 2, Blue 3. The E/W pairs move up one table, 1>>2, 2>>3, 3>>1, deal and play 4 boards [short] or 8 boards [long]. Then, when all three tables have finished, the E/W pairs take the boards to their team-mates table and then go to the third table, and play the boards they find there without redealing. Then they return and score.
Despite reading an opinion that no-one likes threesomes, my experience is that people dislike short threesomes, but do not mind long threesomes. However, there are four problems with long threesomes. First, if you are playing an event with an odd number of matches, there has to be at least one short threesome. Second, it is not acceptable to play a long threesome over a meal break, so sometimes there have to be short threesomes [I saw one solution to play a long threesome over a meal break as two short threesomes, but that seems crazy to me!]. Third, if you permit teams not in contention to withdraw before the last match you want to finish with a short threesome. Fourth, the start of a Swiss teams is fairly random, and a long threesome extends that randomness over a second match.
The EBU's solution is to play the first match as a short threesome, the last match as a short threesome, and then fit in as many long threesome as the meal breaks allow. For example, seven matches, two flights, meal after four matches in the A flight and three matches in the B flight:
One other slight problem with short threesomes: they tend to be played a bit slower than the rest of the room because of the mid-match break. So the director needs to keep the speed up over the 4-board mini- matches. If the main matches are an odd number of boards, say 7, then the mini-matches need to be fewer boards, so two 3-board matches.
As far as scoring is concerned, the long threesome is easy: you use the same Victory Point score as for the other matches. But how do you score the mini-matches in the short threesome?
First, to be clear, it is unacceptable if the average VPs available is anything else but the same as for a full match, ie the average should be the same. So if the average for a full match is 10-10, the mini-matches must total 30.
Suppose the results of the mini-matches are
One idea is to score A as +11, B as +5, C as -16. The problem with this is that because of rounding errors there is no guarantee that this will add up to the correct number of VPs. For example let us consider the EBU's 20-0 7/8/9-board scale.
A would get 15 VPs, B 13 VPs and C 4 VPs, total 32. But since the average score per team is always 10 VPs, that means we have given 2 VPs too many. What we need are scales for mini-matches that result up to 10-0.
One suggestion is to "halve" the current scales, so since 10-12 imps leads to 15-5, 5-6 imps leads to 7.5-2.5. Two problems: First 25-29 translates to 12.5-14.5 imps, but half-imps are meaningless [unlike half VPs]. Second and major: it is more difficult to get 15 imps over 4 boards than 30 imps over 8 boards.
How are VP scales calculated anyway? The EBU idea is to try to make all the VP results equi-probable [roughly]. So 13 VPs should occur just as frequently as 6 VPs or 19 VPs. But if this is so their is only one fair answer: calculate VP scales for mini-matches on this basis. The EBU has done that, and here are the relevant scales:
|3 boards|||||4 boards|
Now in our example the scores were
which translates [4-boards in the example] to
so the scores in VPs for the three teams are
which total 30 VPs, and always will by this method.
While there are no mini-match EBL or WBF scales that I know of I would have thought a statistician would be able to construct them easily enough. One problem there is that the standard scale is 25-0, with average being 15-15. That means that the total VPs for each mini-match should total 15, so a draw is 7.5-7.5. There would be a danger of finishing with only half-VPs, so perhaps the solution is to adopt the Irish method: have a scale with a draw 7.5-7.5, but other results in full figures: 8-7, 9-6, 10-5, 11-4, 12-3, 12.5-2, 12.5-1, 12.5-0. Alternatively 7.5-7.5, 8.5-6.5, 9.5-5.5, 10.5-4.5, 11.5-3.5, 12.5-2.5, 12.5-1.5, 12.5-0.5 would seem fair [and strange!].
One other small point: when giving master-points the EBU gives one- quarter National Master point [a "quarter-Green"] for any match won or drawn. For this purpose they add the two mini-matches together after Victory pointing.
Note that details of all EBU scales for full matches and mini-matches, also WBF/EBL scales, can be obtained in the White book, available for download from the EBU L&EC documents page.