The Real War is between Wii and the HD consoles

[theRepublic]

freedquaker said:

theRepublic said:

(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

(Responded paragraph by paragraph)

No, it is the perfect example as to why market share is flawed.  As shown in the post above, completely independent numbers appear to be negatively correlated when setup in a 'market share' configuration.

Correlation analysis can be applied to ratios, but only so long as those ratios are not directly dependent on each other.  One example would be the unemployment rate and the homeless rate.  The reason this works is because these ratios are calculated with numbers that are not derived from each other ( unemployed/[unemployed + employed] and homeless/[homeless + those with homes] ).  It does not work for market share because market share numbers are by definition dependent on each other ( Wii/[Wii + 360 + PS3] and 360/[Wii + 360 + PS3] and  PS3/[Wii + 360 + PS3] ).  In the first example, the variables from one calculation do not show up in the other calculation.  In the second example, the same three variables show up in each calculation.

In my posts above, I already said that this type of correlation analysis will show that time of year has a bigger impact than direct competition.  That is why I recommended doing the correlation analysis along smaller time frames.  Actually, the Wii very well could be a complementary good with the HD consoles.  Many people have theorized that this could be the case.  At this point, we don't know if it is or isn't.

The only way that a market share analysis would work like that would be if the same total number of consoles were sold week to week, or month to month.  That is not the case, so we must look at the raw numbers.  Let's look at the price drop http://vgchartz.com/hwcomps.php?cons1=Wii&reg1=All&cons2=PS3&reg2=All&cons3=X360&reg3=All&start=40048&end=40083.  The PS3 sales increased without making the sales of the Wii or 360 go down.  This means that those extra consoles that Sony sold were not at the expense of the Wii or 360.  These were people who were not going to buy those consoles anyway.  This means that those consumers were not in direct competition.  The analysis with the raw numbers would show this, while your analysis would incorrectly assume that all those consumers were in direct competition.