MP vs IMPs

[akwoo]

Q.F.T. I don't think there is anyone on this planet with a complete understanding of algebra.

 

I didn't attempt to read Arend's thesis so I can't say that you are wrong. I suspect that you don't know what algebraic geometry is, though. (Hint: it doesn't have much to do with geometry except in a very abstract sense).

 

As half an algebraic geometer, I'd like to dispute this! If you don't think algebraic geometry has much to do with geometry, you learned it from the wrong perspective.

 

(Okay - maybe the Bridgebase forums are the wrong place for mathematicians to be fighting over mathematics. :) )

[jogs]

Q.F.T. I don't think there is anyone on this planet with a complete understanding of algebra.

You're right, only need partial understanding of algebra. The terms never shift from the right side

of the '= sign' to the left. It helps to understand Excel. The functions are in Excel.

Enter your set of data into column A. Click the function you want.

 

fx

 

For mean click average.

For variable click var.

For standard deviation click SQRT for square root of variance.

[Cthulhu D]

You're right, only need partial understanding of algebra. The terms never shift from the right side

of the '= sign' to the left. It helps to understand Excel. The functions are in Excel.

Enter your set of data into column A. Click the function you want.

 

fx

 

For mean click average.

For variable click var.

For standard deviation click SQRT for square root of variance.

 

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

[Zelandakh]

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

You mean knowledge of Excel functions doesn't give me a complete understanding of maths?!!? :o

 

You will be telling me next that I cannot get a complete understanding of bridge by using a pseudo-mathematical equation and some big words... ;)

[helene_t]

FWIW I ran the simulations again but with the per-board skillfactor proportional to the noise level. As discussed earlier, I would expect this to favour matchpoints. I simply multiplied the skill factor with the noise - some rescaling of the parameters in order to give similar correlations as before may be appropriate, as you can see the correlations are much weaker now:

 

The average Spearman correlations between strength and IMP scoring was (as a function of shape parameter of the skill factor distribution and number of tables):

 .1;3  .1;9   .1;27  1;3    1;9    1;27   10;3   10;9   10;27 
 0.316 0.376  0.394 0.503 0.584   0.617   0.562 0.640   0.675

 

For MPs:

 .1;3  .1;9   .1;27  1;3    1;9    1;27   10;3   10;9   10;27 
0.348 0.423   0.452 0.506 0.610   0.651   0.543 0.645   0.690

 

As before, maatchpoints are favored by large fields and imps by small fields when the board population is homogenous. This is what you would expect since when the board population is homogenous it doesn't matter much whether the noise and skill factor are correlated or not since both are roughly constant. But for heterogenous sets of boards (shape parameter for the skill factor equal to 0.1 or 1), matchpoints are generally favoured. Again, this is what one would expect.

 

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.

[jallerton]

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]

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]

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

 

Miaow

[MrAce]

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

 

http://www.bridgebase.com/forums/public/style_emoticons/default/dry.gif

[Mbodell]

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]

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]

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.