Max MPs and Hence Percentage Scores in aTruncated Session
I have a question about how to calculate the Percentage Scores for Pairs playing in a truncated session.
My example is a 13 Round Mitchell movement with 13 Tables with a Missing Pair (NS at T13) which has been truncated so that only 11 Rounds are played.
Due to the truncation of the Movement this may mean that one Boardset, lets call it Boardset X, will have been played one more time (12) than any of the other boards. See attached speadsheet.
As not all NS and EW pairs will have played Boardset X, this will lead to the situation in which the NS Pairs, who have played 11 Rounds, will have a MaxMPs of 484 or 480, depending on whether they have played Boardset X or not. Similarly the EW Pairs, who have only played 10 Rounds, will have a MaxMPs of 444 or 440. See attached spreadsheet again.
As Boardset X has been played 1 more time than any other Boardset, we need to apply the Neuberg correction to all the other Boardsets.
My question is what do I take as the MaxMPs for the NS and EW Pairs when calculating Percentage Scores after applying the Neuberg correction?
Do I assume all Boards have been played 12 times and that therefore the NS Pairs' MaxMPs is 528 ((12-1)224) and the EW Pairs' MaxMPs is 484 ((12-1)222), or do I use some other values?
Comments
All boards are scored (neuberged) to a common top, based on the boards played the most times.
A pairs score is based on their match point total for the boards they played, as a proportion of the maximum available to them (boards played x common top).
Thanks, Robin, but, unless I have misunderstood your answer, the above does not answer the question I asked.
Let me try to explain the problem with a specific example:-
In the situation I described above there are 12 NS Pairs whose Max MPs are 484 and 1 Pair whose Max MPs are 480 because they are the only Pair not to have played Boardset X that has been played 12 times (1 more than all the others).
The 'top' is based on Boardset X, played 12 times, so I apply the correction
((M x E) + (E – A))/A, where E=11 & A=10
to the M's for all the other results.
Now consider the unlikely case where the Pair that did not play Boardset X has scored a top on all the hands they have played, ie they have accrued 20MPs on all 24 hands they have played: after applying the Neuberg correction to their 24 scores they will have scored 22.1 MPs on each of the 24 boards giving them a total MPs of 530.6.
530.6 is 109.6% of 484, their Max MPs. This is plainly incorrect, more than 100% is impossible.
**So, my point is that, after applying after the Neuberg correction to the actual MPs scored, the Max MPs used to calculate Average Percentage Scores must also be 'corrected' in some way.
**
However I have not found any discussion or guidance on this issue. Please let me know the EBU's stance on this.
The maximum for the pair is the common/neuberg top x the number of boards played.
If boards have been neuberged then the pairs cannot score 100% on the board, and pairs who played a neuberged board cannot score 100% overall.
This assumes the board has 10 scores, and the neuberg top is based on 11 scores, which does not match the example.
If some boards are played 12 times and a pair score 20/20 on a board played 11 times, the common top is 22 and the 20/20 is ((20 x 12)+(12-11))/11 = 22 -(1/11) = 21.91 out of 22.
Thanks once again for your speedy response, Robin.
I'm sorry, but I still need some further clarification from you. May I stress that it is not the common/neuberg top on an "individual" board that I am having difficulty with, but the sum/accumulation of these tops to give the "Maximum MPs" that could be awarded to Pairs over the whole session. It is this figure which is then used to calculate the "Percentage Scores" for the session.
In the case we are discussing before the MPs are Neuberged 12 NS Pairs could have achieved a maximum of 484 MPs, 1 NS Pair a Max of 480 MPs and 12 EW Pairs a Max of 444 MPs.
The common top, as you say, is 22 MPs per Board as 1 Board has been played 12 times. On this basis after the Neuberg correction has been applied to all Board the Maximum MPs that could be gained by NS Pairs rises to 528 (2224) and for EW Pairs it rises to 484 (2222).
My question is: are these figures, 528 and 484, the correct ones to use in the calculation of each Pairs' Percentage Score?
A subsidiary question is whether there exists a Reference Document that fully describes the Neuberg Correction and its effect not only on individual board MPs but also on the Maximum MPs against which Percentage Scores for the Session are calculated.
Btw this discussion has helped me clarify my thoughts on this matter, for which I thank you.
Wrt the above, every time I type a "star" character to signal multiplication, when It gets posted this is removed and characters appear in italics between the 2 star characters.
Only one NS pair has a maximum of 528 matchpoints. The others all have a maximum of 484.
Only one EW pair has a maximum of 484 matchpoints. The others all have a maximum of 440.
I may have missed something, but I can't help thinking that none of this can arise with the setup you proposed. Something similar could certainly happen though in any movement with a relay table.
Thanks for your reply Gordon.
All the NS players played 24 boards, because the movement was terminated early at Round 12 of a 13 round movement. Since all NS Players played 24 boards each of which had a Max MPs of 22 (after Neuberg) I don't under stand why 1 Pair should have a Max MPs of 484. Could you explain this to me please?
This is part of markdown, two starts for bold, one star as a list bullet, but a star (with spaces) does work: 42 = 6 * 9,
13 tables, 13 EW pairs, 12 NS pairs (no NS 2), 13 board sets, boards 1-26. 12 rounds.
Boards 1+2 are played 12 times (because they were due to be not played at table 2 in round 13).
The common top is 22.
(Sorry if I have still made mistakes.)
Sorry, I didn't follow it through fully. Robin's answer seems correct.
Thank you gentlemen, I am clear now and it makes sense !
May I say that in any discussion of the Neuberg Correction that I have read in the White Book and other documents, whilst the application of the Neuberg Correction to Pairs' Scores is well explained, the corollary that the Maximum MPs for a every board must be increased to match the Max MPs for the most played board is not mentioned (I believe).
Whilst this may be obvious to the bridge 'cogniscenti' like yourselves, it is by no means obvious to mere mortals, like me, until, that is, such a discussion as this has occurred. It is now obvious to me too!
May I recommend that the next time the White Book is edited a discussion of this point is added.
Thanks once again for clearing this up for me.
You could always use the x character for multiply: 42=6x7
I hope people realise that '6 * 9' was deliberate.