The Real War is between Wii and the HD consoles

[theRepublic]

WereKitten said:

Again: take 100 triads of totally random numbers generated by the computer. Calculate the "market shares" from them and calculate the correlations between the share coulmns: the results will be negative.

This does not prove that the raw numbers represent competing goods: the numbers were random, thus independent by definition. And quite obviously if you compute the correlations between the random columns themselves, you'll get somethig very close to zero.

Frankly I would have to dust my statistics books, but you can probably calculate on paper how much correlation you're introducing by using x/(x+y+z) instead of x.

I expect the use of shares to be viable if you had much more than 3 consoles so that the negative correlation each console causes on the other via the normalizing denominator is much less than the "real" correlation between the raw data.

I did it just to see how bad it actually was.  I set up a spreadsheet to calculate correlation between the random numbers and correlation between 'market share'.  I then cycled through a bunch of random numbers.  Here is what I saw.

Worst case scenario:

Raw Number Correlation = 0.02
Market Share Correlation = -0.69
Difference = 0.71

Best case scenario:

Raw Number Correlation = -0.03
Market Share Correlation = -0.34
Difference =  0.31

This shows how it is possible for completely independent numbers to appear related when setup in a 'market share' configuration.