Zero-max imps (new scoring method)
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A few suppositions:

a) using a datum produced from actual scores is a mistake, what actually counts is the optimum contract given the layout.

b) you can't do better than the optimum contract unless the opps make a mistake.

c) conversion to a percentage score using a fixed imps-% ratio  is incorrect; you need to take into account the 'swinginess' of the session.

optimum score

Double-dummy analysis can calculate an optimum score for each board; this is the best score each pair can achieve with perfect bidding and play (assuming we can see all 4 hands).

e.g. if the last making contract is 3H by N/S then the optimum score is +140 if the opps are vulnerable and +100 if not.

I suggest that this is a better way to calculate the datum for each hand.

zero-max imps

Theoretically you shouldn't be able to do better than the optimum score for the hand unless the opps make a mistake; they should suffer but you should not gain. Therefore the best score you can get on a hand is zero!

% conversion

This is calculated by comparison of your score versus the mean of all scores for the session.

%score = 50 + (score - mean)/2

(note that both score and mean are negative)

Trial run

I re-calculated the results for an imped pairs session which took place at Sheffield Bridge Club recently. The outcome was very different.

The original 1st placed pair (+28.9 imps) ended up joint 10th (last) with -103. Looking at their scores they were gifted +18 on 2 boards through opp error.

The pair who originally came 5th won easily (by 11 imps) when re-scored; they only had 1 gift (of 9 imps) from an impossible 6C bid with a combined 23 count.

The pair who were originally last stayed last with -103.

The calculated percentages range from 36.75 to 60.75.

Data

Link to session results used in trial run: https://app.pianola.net/Results/Session287068

Example

Consider the following hand (from a BridgeClubLive online competition), both vul:

West
42
Q653
853
10962
North
A53
A974
742
QJ5
East
Q6
KJ82
AK9
K874
South
KJ10987
10
QJ106
A3
D

I believe the optimum score is +650 for N/S.

When played for real:

2 played in 3, 4 in 2 all making 11 tricks

1 played in 2NT making 8 tricks

Those playing in 4 gained 6 imps,  those playing in 2/3 lost 5 imps, the one in 2NT lost 7 imps.

Those unfortunate enough to be playing against a pair who bid game (which is just down to pure bad luck) lost 11 imps relative to those fortunate enough not to be. How can this possibly be fair?

Using my method everyone would score 0 except for those who failed to bid game; who would lose 9 imps each (or 11 if in 2NT). Doesn't this seem much fairer?