Butler scoring is one method of scoring a pairs’ event as if it were a teams’ event. For Butler scoring a ‘datum’ score is first calculated, which is the average score on each board. In order to avoid extremes the best and worst score(s) is usually omitted from the datum calculation. The datum score is rounded to the nearest 10 points. The score that you actually obtain is then compared with this datum score, to give you an ‘average team score. So if the average is + 478, the datum score is +480 (North/South). If you as North/South actually scored +200, you have performed worse than average, and your Butler imps score would be -280 (480-200) converted to imps. North/South -8 imps; East/West +8 imps.
Cross-Imp Scoring (Imp Pairs)
Cross-imping is also a (better) method of scoring pairs’ as if it were a teams’ competition. It has largely superseded Butler Scoring. It is extensively used on online platforms, and in ‘Trials’ where entry is on a teams’ basis, but to assess the performance of each pair in the team, cross-imp scoring is necessary. In cross-imping, if say you are North/South, at every other table that the board is played, the East/West at that table are considered to be your team-mates, and an imp score can be calculated for the play of that board. The total of each of these plays is added together, and simplistically then divided by the total number of other plays, to give an average imp score – the cross-imp score So for example if as North/South you score +420, and the board is played a total of six times (including your own play), and the five other East/West scores are -450, +100, +200, -400, -590, then your score of +420 is compared with each of the other plays to give imps. of -1, +11, +12, +1, -5: total +18. So your cross-imp score would be 18/5 = +3.6 x-imps (and you opponents would score -3.6 ximps) (there are modifications to the above method, involving more complex mathematics, but the above is commonly used)
The advantages of cross-imping (as against Butler) include:
- Cross-imping is considered fairer and more like teams’ scoring, since imps are calculated using actual bridge results, not artificial averages. The imp scale was determined using bridge results, so to bring non-bridge scores into the equation in un-sound.
Butler scoring has a built in bias, in that the imps available to NS and EW can differ. With cross-imping, the NS and EW scores always balance.
with Butler scoring, you average first then calculate later, which is mathematically un-sound. With cross-imping you calculate first then average later.
it should be that small differences in scores separate players in an expert field, yet with Butler, making that extra trick can mean nothing. Different scores can score the same imps.
with Butler, the extremes are discarded before computing the average. This is un-sound, as it suggests that the extremes are always irrelevant which is not always true. With cross-imps, the scores at all other tables are used. The only real disadvantage is that players cannot calculate the match result themselves, which they can in teams events, or in Butler events once the datum has been announced. But this should not be a concern