This gave me the info I needed.  You performed a correlation analysis based on the percentage market share for each month, instead of the raw numbers.  That does not tell us who is in competition.  Take July to August 08 for instance.  The Wii actually sold more in August, but lost market share because the 360 and PS3 were both up.  Doing the analysis by percentage like you did makes the Wii look like it lost sales to the 360 and PS3, but in actuality, this is not the case.

Doing the analysis with just the raw numbers gives a much different picture:

Wii vs 360 = 0.954
Wii vs PS3 = 0.880
360 vs PS3 = 0.862

What this tells me is that the sales numbers of these consoles are highly dependent on what time of the year it is.  They all rise in the holidays, and they all fall during the summer.  That is why the correlations are so close to 1.

On initial examination, we can also say that those consoles with the lowest correlations are in the most competition.  That would be the 360 vs PS3, and Wii vs PS3.  For whatever reason, the Wii vs 360 does not seem to be as in as much competition.

Given that these numbers are so close, a closer examination is probably in order.  Possibly going week by week.

EDIT:  I gave this a little more thought, and here is what I came up with.  The big problem is that the holidays skew the correlation towards time, instead of the competition.  One way to make this more relevant would be to just eliminate the holidays from the analysis.  Another way to do this would be to take smaller chunks of data.  An example could be using the weekly data over a three month period of interest (like around the time of a price cut, although you have to be careful the cut is not around the holidays).

Actually its the raw numbers which are misleading due to very many reasons.

Your console might see a continous increase over the years but this doesn't mean much as long as its market share is not improving.

And I dont understand you can't see the fact that 360 is quite stable recently with similar numbers, so not so affected by the debut of the ps3 slim although wii plummeted in sales, delivering one of the worst performances in its history! I dont have time to cite, but you can find various stuff even on this website hinting to that. Clearly Ps3 stole much more from wii, rather than 360.

theRepublic said:

...

The raw data can be used as random variables, but market share percentage cannot.  The reason for that is because market share percentage is directly dependent on the sales of the other consoles.

(Broke up your reply to make responding to it easier.  Each paragraph is responded in order.)

Correlation was never meant to be used with percentages.  Correlation indicates the strength and direction of a linear relationship between two random variables.  The raw data can be used as random variables, but market share percentage cannot.  The reason for that is because market share percentage is directly dependent on the sales of the other consoles.

Let's do a simple example.  Imagine there are only two consoles.  Console A's sales are increasing over time.  Console B's sales are increasing over time at an even faster rate.  In this scenario, Console B's market share is growing and Console A's market share is shrinking.  The correct correlation (based on the raw data) would give a positive result because both numbers are increasing over time.  The incorrect use of correlation (based on market share percentage) will give a negative number because one number is increasing and one number is decreasing. (EDIT: With only two consoles, the correlation by market share percentage will always be -1.  It is obvious that is wrong.)

Look at this graph http://vgchartz.com/hwcomps.php.  The bump at 8/2/09 is from the release of Monster Hunter 3 in Japan.  Look before and after that bump.  The sales of the Wii are flat.  The Wii did NOT 'plummet' in sales.  The 360 is NOT 'stable' either.  It has actually increased in sales because one model of the 360 had its own smaller price cut.  In other words, the PS3 sales were NOT stolen from either the Wii or the 360 in this case.

You have given the perfect example why the market share percentages need to be used, instead of sheer numbers. As you have suggested, two rows of numbers, both increasing might be negatively correlated in terms of market shares, this is exactly what we are looking for.

First of all, regression is not merely meant to measure the raw numbers, in my lifetime both as a student and a teacher, I applied and was told to apply a lot of regression analysis like this, based on ratios.

Secondly, Using the raw sales numbers here will yield completely disastrous results since a lot of external factors will comprimise the net affect. For example, during an economic recession, all variables might shrink leading us to believe they are all positively related. Or in an economic expansionary period, or in holiday seasons, sales will go up, all in the same direction, leading us to believe they are positively related. Likewise if you try to apply the correlation analysis with regards to raw numbers in pairs, you will get all positive numbers, meaning they are complemtary goods, and one increases the sales of the other, and there is no competition between them, which is NONESENSE, and completely misleading. Of course we know that, because none of them are actually "complementary goods", so they've got to have zero or negative correlation, if not, there is something wrong with your data or assumptions.

Finally, suppose that wii has a market share at around 50% before, and 360 has 28%, with PS3 at 22% (Just made up numbers). If a PS3 price drop has caused the wii share to decrease to 35%, with PS3 at 40% and 360 at 25%, you can easily argue that PS3 has a much greater effect on wii, rather 360, as showed very recently.

For those who want to check the data and the procedure, here is the excel : http://rapidshare.com/files/288962580/console_correlation.xls

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.

You have given the perfect example why the market share percentages need to be used, instead of sheer numbers. As you have suggested, two rows of numbers, both increasing might be negatively correlated in terms of market shares, this is exactly what we are looking for.

First of all, regression is not merely meant to measure the raw numbers, in my lifetime both as a student and a teacher, I applied and was told to apply a lot of regression analysis like this, based on ratios.

Secondly, Using the raw sales numbers here will yield completely disastrous results since a lot of external factors will comprimise the net affect. For example, during an economic recession, all variables might shrink leading us to believe they are all positively related. Or in an economic expansionary period, or in holiday seasons, sales will go up, all in the same direction, leading us to believe they are positively related. Likewise if you try to apply the correlation analysis with regards to raw numbers in pairs, you will get all positive numbers, meaning they are complemtary goods, and one increases the sales of the other, and there is no competition between them, which is NONESENSE, and completely misleading. Of course we know that, because none of them are actually "complementary goods", so they've got to have zero or negative correlation, if not, there is something wrong with your data or assumptions.

Finally, suppose that wii has a market share at around 50% before, and 360 has 28%, with PS3 at 22% (Just made up numbers). If a PS3 price drop has caused the wii share to decrease to 35%, with PS3 at 40% and 360 at 25%, you can easily argue that PS3 has a much greater effect on wii, rather 360, as showed very recently.

For those who want to check the data and the procedure, here is the excel : http://rapidshare.com/files/288962580/console_correlation.xls