Suggestion for score when playing at a table

[mrdct]

An issue germane to this discussion is the merits of cross-imping as compared to scoring-up against an average (with or without the exclusion of outliers). I'm still yet to hear a convincing argument as to why cross-imping is superior.

 

Interestingly, I was informed by the scorer of Australia's Youth Butler Trials (which changed from scoring-up against an average to cross-imping a few years ago) that after rescoring the event using both methods, the final ranking was exactly the same for the three years that he recomputed everything; so I expect there isn't much difference. Youth Butler Trials might not be a great example as it's quite a small field (5 or 6 tables) with fairly significant variation in the standard of the players, so I'd be keen to hear of any similar analysis that might have been done in events such as the Cavendish. Of course there are hundreds of thousands of hands that have been played 16 times in the MBC of BBO that could be similarly analysed.

 

As I stated previously, my gut feel is that there probably isn't much in it so I prefer to score-up against an average but exclude some outliers to reduce the volatility. Scoring-up against an average, I think 12 results (16 scores less 4 outliers) is quite sufficient and has the advantage on BBO that the scoring is very timely.

[barmar]

Cross-imp scores are much easier to relate to team game scores. Suppose you make your contract, while every other pair bids the same contract and goes down 1. Your cross-imp score will be the same as if you were in a team game and made your contract while the other table went down. As the number of other pairs that duplicate your result goes up, this score is then prorated based on the fraction of pairs that duplicated your result; e.g. if the results are half making, half going down, everyone gets half the team game IMP score (if it's a vul game, they get half the 10 IMPs for making game, or +/- 5).

 

Butler, on the other hand, calculates IMPs against a meaningless number, because scoring is non-linear. Suppose half make a non-vul game and half go down 1, the datum is 235, and everyone gets +/- 6 IMPs. It's even worse for vul game: +/- 6 IMPs with cross-imps, +/- 8 with Butler. What's happening is that the IMP scale normally flattens out large score differences, and Butler stretches them out again.

[helene_t]

Barmar's argument is the main reason for prefering XIMP to butler. There are a few other arguments:

- Less effect of the discreteness of the IMP scale. Suppose you chose 3NT over 4M for the same number of tricks so you get 10 points more than you might have. At butler this will usually yield an IMP difference of 0 but may yield an IMP difference of 1, depending on what the datum score. At XIMPs it will give you some fractional IMP because the 10 points will matter relative to some tables but not relative to others.

- How many IMPs do you get for being 16.754 points ahead of the datum? 0 or 1? Of course a decision has been made for the Butler score but that is somewhat arbitrary. At XIMPs you don't have the issue.

- You don't have to remove outliers at XIMP because the method is inherently robust. Removing outliers is probably necessary at Butler but there are problems with it. In a very small field you cannot really remove outliers. Suppose there are 3 tables and you remove one outlier at either end. If two tables have 6♥= and the 3rd table has 4♥+2, then datum would become 6♥= for 0 IMPs to the slam bidders, which feels wrong.

 

But of course Dave is right. It matters very little, especially in large fields. In a field of two tables it makes a lot of difference: If you score 20 points more than the other table, you win 1 IMP at XIMP and 0 IMP at Butler. Of course nobody would use butler for a two-table event but it illustrates the difference between the two scorings in small fields: The spread of the comparison is reduced at butler because you are comparing to an average to which you contribute yourself. Unless you become an outlier and get removed. So Butler scoring in small fields favors strategies with right-skewed distributions of the points scored.

 

Also, because of the nonlinearity of the IMP scale, the shrinkage of the difference relative to datum is more severe for small differences than for large differences. So in small fields, Butler makes the high-stake boards (slam decisions) relatively important, more so than XIMP does. (This is not related to outlier removal).