[Trinidad]

Trinidad, on 2012-February-22, 23:40, said:

Anyhow, you did it wrong. For the calculation of the datum, you forgot to include our own score (which, of course, is an absurd requirement for Butler scoring, since who would want to IMP against his own score?*).

barmar, on 2012-February-23, 10:56, said:

If you had to omit your own score, you'd have to calculate a different datum for each pair, which would be as much work as Cross-IMPs.

So while it may be mathematically absurd, it's required for practicality.

I tried to make it clear that this was a requirement for Butler while at the same time showing how this is mathematically absurd (and thereby giving yet another reason why Butler should be abandoned). Maybe I should have phrased something a little clearer.

Rik

[barmar]

It seems like that's only a problem if you know the distribution of scores when you're playing the board, and I'm not aware of any game format where players would be privy to that information.

But it's not really correct to say that the result doesn't affect your score. It's true that you'll get 0 for the board either way. But what matters is your score compared to other pairs. If you bid the slam you get a better score than half the field, raising your final rank; if you don't, you get a worse score and your rank will be lower. In IMP-against-the-median it would be possible to win the event with a total of 0 IMPs -- if every board were split between two results, with the higher one being the majority and you're the only pair always in that group (you'll have all 0 scores, everyone else will have a mix of 0 and negative scores).

The fact that your result doesn't affect your score in some cases is hardly unique. Consider a BAM hand where an accident happens at one table, producing a huge number. Meanwhile at the other table a normal contract is bid. But because they're comparing with a huge number, it doesn't matter if they make the contract or not. We can see that they're wasting their time when watching it on Vugraph, but it doesn't affect their play because they don't know what happened at the other table.

[pran]

barmar, on 2012-February-23, 15:41, said:

[...]The fact that your result doesn't affect your score in some cases is hardly unique. Consider a BAM hand where an accident happens at one table, producing a huge number. Meanwhile at the other table a normal contract is bid. But because they're comparing with a huge number, it doesn't matter if they make the contract or not. We can see that they're wasting their time when watching it on Vugraph, but it doesn't affect their play because they don't know what happened at the other table.

Now this is an example which has no relevance with neither Butler nor Cross-IMPs (contrary to the similar assertion on weighted IMP-scores).

BAM is essentially using matchpoint scoring where the amount of a victory is irrelevant.

[barmar]

pran, on 2012-February-24, 02:49, said:

Now this is an example which has no relevance with neither Butler nor Cross-IMPs (contrary to the similar assertion on weighted IMP-scores).

BAM is essentially using matchpoint scoring where the amount of a victory is irrelevant.

So? I was just giving another example of situations where the actual result at your table has no effect on your score for the board. The post I was replying to implied that consequences of your actions should be a criteria in deciding how good the scoring method is. So if BAM is reasonable, so would be IMP-against-median.

[Trinidad]

barmar, on 2012-February-26, 20:21, said:

So? I was just giving another example of situations where the actual result at your table has no effect on your score for the board. The post I was replying to implied that consequences of your actions should be a criteria in deciding how good the scoring method is. So if BAM is reasonable, so would be IMP-against-median.

It is implied in a matchpoint form of scoring (whether BAM or MP pairs) that the actual value of your score is irrelevant. The only thing that counts is the number of pairs you beat.

The key of IMP scoring is that the actual value of your score is relevant. Of course, IMP-against-median is a way to calculate an IMP pairs, and if people want to play it by all means do, but the fact that it is possible that a large variation in your result doesn't affect your IMP score means that it has little to do with IMP scoring.

Rik

[barmar]

Trinidad, on 2012-February-27, 17:08, said:

The key of IMP scoring is that the actual value of your score is relevant. Of course, IMP-against-median is a way to calculate an IMP pairs, and if people want to play it by all means do, but the fact that it is possible that a large variation in your result doesn't affect your IMP score means that it has little to do with IMP scoring.

But as I pointed out, what matters isn't the actual value of your score, it's the relative value.

However, I just did a quick check, and realized that IMP-against-median has a significant difference from cross-IMP: the latter cares about the number of pairs you beat or lost to. With median IMPing, the sizes of the groups of scores can influence which score becomes the median, but then when you compare everyone against it, size no longer matters. With cross-IMP, there's a significant bonus to being the ONLY pair that bids (and makes) the game or slam -- the bonus is multiplied by the number of other pairs (much like getting a top versus just Ave+ in MP). Butler also achieves this, because the size of the other group drags the datum closer to their score. With a median, you get the same number of IMPs no matter how many other pairs there are.

The two methods actually produce pretty similar results when the field is evenly split among results. The difference is mostly apparent to outliers.

[Trinidad]

barmar, on 2012-February-27, 19:53, said:

The two methods actually produce pretty similar results when the field is evenly split among results. The difference is mostly apparent to outliers.

Of course, the methods give approximately the same results when the field is evenly split among the results. There is also nothing wrong in using medians to estimate things (life time of a light bulb, amount of food and drinks to be bought before a party, amount of tax you need to pay, ..., or an IMP pair score). Many people do this all the time, but the smart ones are aware that they make an error. Often you don't need to have exact figures. (Does it matter that people drink 2.342643 bottles of wine at my party if I estimated that they will drink between 2 and 3? Either way I will end up buying three bottles.)

- Calculating with medians (or modes) is usually easiest, but it will come with the largest error. If this error is perfectly acceptable, by all means ( ) use medians.
- Calculating with averages (more precisely: means), such as Butler, is a little more difficult and will be more accurate. If the calculation that you are performing is linear (IMP scoring is not) you will even get the correct answer: If I know the mean amount of wine that people drink on average, I will be able to tell the total wine consumption by multiplying the mean by the amount of people. However, knowing the mean won't tell me how many people will not be allowed to drive anymore and, therefore, will be sleeping over.
- Calculating with the whole set of results (Cross-IMP) requires more work, but it will give you the correct answer.

Rik