IMPed Pairs: towards a better datum
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Even though my previous straw-man (Zero-max IMPs) got hung, drawn and quartered I'm not giving up; there must be a way of making IMPed pairs playable!

A recent online hand highlighted the issue for me: the problem is the datum.

West
K
107
109642
QJ752
North
J76
AK953
AK964
East
108543
QJ
KJ875
8
South
AQ92
8642
AQ3
103
D

The hand was played 11 times; what do you think the datum was?

West
K
107
109642
QJ752
North
J76
AK953
AK964
East
108543
QJ
KJ875
8
South
AQ92
8642
AQ3
103
D

8 N/S pairs played in 4 making 12 tricks, another pair bid and made the slam

1 E/W pair played in 5x making 8 tricks

1 N/S pair played in 3 making 6 tricks (auction was 1-3-pass with E/W silent). Don't ask me!

The datum was N/S +480, so IMPs only changed hands at 3 tables.

The pair in 5x lost 1 imp.

The pair in 3 lost 12 imps.

The pair in 6 gained 11 imps.

The pair who got very lucky  and were 'defending' against 3 got a massive free gift of 12 imps.

The poor pair who's only crime was sitting in the wrong place at the wrong time lost a punitive 11 imps.

So one E/W pair had a net gain of 23 imps relative to another pair (on this single hand) simply through an accident of seating.

That can't be right!

Looking at the hands it would seem to me that the people who should lose imps should be those not bidding the slam.

I previously suggested using double-dummy analysis to calculate the datum; but people quickly came up with counter-examples.

I'm not convinced that using actual scores is any better.

BUT: there is another way!

We can calculate the datum from number of tricks won in each denomination, ignoring the level of contract., thus ameliorating the impact of the bidding.

First, let's eliminate the outliers; any denomination that has only been played in once. So on this hand we ignore the two diamond contracts (one by N/S, one by E/W) when calculating the datum.

Next for each denomination we look at the number of tricks taken and calculate a weighted average. For this particular hand this is pretty easy as we simply have 9 instances of 12 tricks in a heart contract. This gives us a datum of +980 for N/S.

So we now have 0 imps changing hands at the slam table.

The 3 bidders now lose 15 imps (their opps still get a massive free gift)

The 5x bidders now gain 10 imps which seems justified.

The 4 bidders now lose 11 imps each

The IMPs swing from the 'accident of seating' has reduced to 15 imps; the slam victims are still 11 imps worse off than the majority of their rivals.

The slam bidders still have a net 11 imps gain against their actual opps.

The 5 bidders have gained from their enterprising bidding; their opps have lost imps for failing to bid the slam.

Summary

4 bidders now -11 instead of 0

6 bidders now 0 instead of +11

5x bidder now +10 instead of -1

3 bidder now -15 instead of -12

Obviously this is a simple example; but I will produce a worked example for a more complex hand.

Programming this would be fun!