XIMP Scoring with Fouled Boards
Section 4.2.4 of the White Book describes the method of XIMP Scoring of Boards with fewer results than other boards.
Can someone please explain to me why, when calculating the datum, quote "we ignore 1.0 top and bottom scores".
If this a general process when calculating all such scores?
Comments
When we are Cross-IMP-ing, we do not calculate a datum. We only have a datum if we are using Butler IMPs and the example in WB 4.2.4 relates to Butler IMPs and not Cross-IMPs.
I have not encountered Cross-IMP-ing in a small sub-field and it is not immediately clear what WB 4.2.4 suggests, so perhaps an example might be helpful.
Barrie Partridge - CTD for Bridge Club Live
The example in 4.2.4 is for Butler scoring abd is mainly of historical interest
The calculation for XIMP scoring is made much simpler because the scoring is 0-based. (Neuberg looks complicated because you have to shift the average score as well as rescale the result.) The only complication for XIMP is what we divide the sum of comparisons by: 1, number-of-comparisons, and root(2rc) are popular choices.
The calculation is to scale the raw sum by the number of actual to expected results, and then divide.
Say the scoring method is XIMP/c where c is the number of comparisons, and boards are played 10 times, so the normal score for a board played 10 times is sum_j(imp(x_i - x_j)) / 9
If there are only 8 results in a group of comparable results on a board, the score is (sum_j(imp(x'_i - x'_j))*10/8)/9
Just to check that I have understood your last 2 paragraphs, Robin, I will paraphrase them as follows:-
(a) one Sums the Differences between the IMPs scored on the board in question and all the other boards in the Result Set
(b) the result of (a) is multiplied by the (Ratio of the Complete Set to the Result Set)
(c) the result of (b) is divided by the (Complete Set number minus 1)
However I do not understand the second paragraph in your answer, eg what is root(2rc) and what do we do with it?
There are three or four ways of doing XIMP scoring:
1. Use the sum of the imps of the score difference, and do not factor the sum: 'raw XIMP', denoted XIMP
2. XIMP/c, where c is the number of comparisons, c = r-1, where r = number of results); 'XIMP by comparisons', renoted XIMPc in EBUScore
3. XIMP/r, which is rarely used (but is the neatest for factoring); renoted XIMPr in EBUScore
4. XIMP/q, where q = √(2rc), which is used for a subsequent conversion to victory points; 'root(2rc)', denoted by XIMPq in EBUScpre ('q' for quadratic?)
'root(2rc)' is just ascii for √(2rc)
Thanks for the above explanation Robin.
When Googling Cross-IMPs most of the sites I have found discuss what you refer to as 'XIMP/c', with occasional fairly dismissive references in such descriptions to 'raw XIMP' and 'XIMP/r'. Is there a site or document that is the definitive official specification of Cross-IMP scoring?
I suspect our White Book has as many references to XImps as you will find anywhere, but the scoring method is usually described in the conditions of contest and may vary from event to event.
One last point, if the sub-field contains just 1 result, ie the fouled board was played just once, there will no other scores with which to compare the result; in which case do both pairs playing the fouled board get awarded +3 IMPs, or some other other amount?
2 IMPs is the standard amount for IMP-scored pairs as opposed to teams.