Cross-IMPs

The last post ended with me just throwing some numbers at you. One question you might ask is this: how relevant are average scores to real-life duplicate bridge?

Instead of just summing up all the scores that a certain strategy achieves and dividing by the total sample size, let's instead cross-IMP them. In other words, on each board we'll IMP each result with every other result, add up the IMPs won or lost and divide by 6 (the number of comparisons). What we're essentially doing is running a tournament with 7 pairs all playing the same hands and all using their own strategy on every hand.

We'll do 25,000 hands this time and produce the following statistics:

                      IMPs      Agg
1. Bid 3NT:          +0.986    321.97
2. Invite 3NT:       +0.048    277.32
3. Minor try/invite: -0.107    271.50
4. Minor try/GF:     +1.000    323.60
5. Heart try/GF:     +1.056    324.11
6. Heart try/invite: +0.324    290.55
7. Pass 1NT:         -3.306    138.21

Notice, though, that you get exactly the same ranking list using each method of scoring. Still, cross-IMPs is more what we're used to. For instance, we could multiply the results by 24 and rank them as follows to scale it up to what you might see on a club night:

1st  Heart try/GF    +25.34
2nd  Minor try/GF    +24.00
3rd  Bid 3NT         +23.66
4th  Heart try/inv    +7.78
5th  Invite 3NT       +1.15
6th  Minor try/inv    -2.57
7th  Pass 1NT        -79.34

From now on we'll be cross-IMPing things instead of just using the average. Sometimes we might delve into Match Points, too.