[jallerton]

Vampyr, on 2014-December-22, 07:09, said:

What about using cross-IMP scores from a teams tournament?

This would only really be useful if you had teams of 4 in an all-play-all event with a compulsory swap of opponents half way through each match AND an even split of the comparisons over the event as a whole (each pair sits in the same direction as every other pair about 50% of the time). In practice none of this happens in teams events.

[jogs]

Cthulhu D, on 2014-December-22, 18:26, said:

While watching you make an idiot of yourself *IS* funny, you know she literally has a PhD for her work in this area? Right?

Just shows how worthless a PhD is. Most of the best bridge players are college drop-outs.

[Vampyr]

jogs, on 2014-December-28, 18:54, said:

Just shows how worthless a PhD is. Most of the best bridge players are college drop-outs.

Miaow

[MrAce]

jogs, on 2014-December-28, 18:54, said:

Just shows how worthless a PhD is. Most of the best bridge players are college drop-outs.

[Mbodell]

helene_t, on 2014-December-23, 08:12, said:

Obviously the two scenaria - noise proportional to skill factor, and noise independent of skill factor - are two extremes, and a mor realistic scenario would be somewhere between the two. The again, we really need some real data.

I admit I don't totally follow the various math and models you are doing. I generally think of two different sources of random/luck/changes for people. One is a skilled player choosing a 80% line where an unskilled player settles for a 60% line (here there is still luck with the 80/20 or 60/40 and which lines work). Another is two players with a 2 way guess and no clues that is 50/50 and literally totally luck/random which side is 50/50. At a high level, is your "skill" equivalent to the choice of line and your "noise" equivalent to the 50/50 coin flips and/or does the 80% line come down on the 80 side or the 20 side?

[helene_t]

Mbodell, on 2014-December-30, 03:27, said:

I admit I don't totally follow the various math and models you are doing. I generally think of two different sources of random/luck/changes for people. One is a skilled player choosing a 80% line where an unskilled player settles for a 60% line (here there is still luck with the 80/20 or 60/40 and which lines work). Another is two players with a 2 way guess and no clues that is 50/50 and literally totally luck/random which side is 50/50. At a high level, is your "skill" equivalent to the choice of line and your "noise" equivalent to the 50/50 coin flips and/or does the 80% line come down on the 80 side or the 20 side?

Let's say that there are only two plausible lines for declarer (South), and let's say that all the EW pairs (Mitchell) are robots so we are only interested in comparing the NS pairs. Let's say that it is clear to all all declarers that one line will give 400 and the other 430. Half of the declarers have no clue which is better so they just flip a coin. The other half know that one line is 80% and the other 20% so they take the 80% line.

So for every 100 declarers, we get (on average) these results:
40 skilled declarers get 430
10 skilled declarers get 400 (OK this is not true since either the 80% plan works or it doesn't, but imagine we repeat the scenario on many boards)
25 unskilled ones get 430
25 unskilled ones get 400

The average score is 424 for the skilled ones and 415 for the unskilled ones. So everyone has a skilled-based deviation from the global average of (424-415)/2 = 4.5 so the skill variance is 4.5^2 = 20.25. The luck variance is 15^2 = 225 for the unskilled ones and 0.8*6^2 + 0.2*24^2 = 144, i.e. 184.5 globally.

Something like this (now someone will embarrass me by pointing out that I made a mistake somewhere but you hopefully get the idea ).

In this case, since both the luck and skill factor are about an overtrick, both variances are quite low. If it had been about the 9th trick rather than the 10th, both would be larger, so in such cases the skill and the luck variance will be perfectly correlated. This will obviously not always be the case, but in general the perfect correlation is probably closer to the truth than independence is.

[Mbodell]

helene_t, on 2014-December-30, 06:10, said:

Something like this (now someone will embarrass me by pointing out that I made a mistake somewhere but you hopefully get the idea ).

Thanks, that is roughly what I thought you were meaning but it was much clearer for me to understand from your last post.