Mrstickball said:

"One should remember that, in America, the average price for a X360 in January (as per NPD) was $263 USD. So Arcade penetration is something fierce now"

A increase is always better then a decrease is the way I see it. Especially in this bad economy.

average cost = [(a%*360T)(200)+(p%*360T)(300)+(e%*360T)(400)]/(360T)

where: 360T= total 360 sales, a% = percent of total sales by arcade, p%=percent of total sale from pro, e%=percent of total sales from elite

1 equation - 3 unknowns means this isn't enough information to prove your claim.  so do you have facts to support your claims or not?  so far you don't.

Well first of all, you don't know the price elasticity on video console. You may know the theory of it but in that case you should know that lower price is not equal to the same rise in sales. To meassure the elasticity between 2 different products like 360 vs PS3 is not the same as within the same product. The elasticity is much higher between Pro and Elite then between Pro and Arcade and thus we can belive that the change in price doesn't effect the ratio between Pro and Arcade that great.

I know that Arcade did top around 50% but that was when it took over after Core. The good price with wireless controller and memorycard created a great rise. But with the new 60gb model and the low difference in price I belive that the Pro model is on top again and that it offers most 360 for the bucks and that most consumers find that this model has most value.

I suppose it's also diffrent from region to region. Is the difference still 199 vs 299 in the US? In Sweden it's 1800 vs 2500 which is about 80 dollars in difference.

 You are silly.

How can a 63% YoY increase with a 25% price drop be anything but extremely impressive? Going by history of console price drops the X360 should have reached the mass market price earlier. At this point in time the PS2 had dropped to $179 already and was about to be dropped to $149 (in May 2004 - it's 4th year) - while the X360 still has a very popular $300 SKU beside the Arcade $200 one.

And yet the X360 is selling close to PS2 levels now. It's a huge success.

I think one of the factors at play is how people can rank the consoles in their minds if all three cost the same amount.

You can be:

You can get an Xbox 360 for $200-$400, Wii for $250, or PS3 for $400 essentially. But I think its fair to say that alot of people only have a slight preference one way in favor of PS3 or 360. Given that the Xbox 360 is selling for $268 (per Gamasutra) in the USA, scenarios 1-4 are likely the most common, probably to 70-80% of the market. Price drops when PS3 is immediately beneath Xbox 360 will change some minds to PS3 but, when Xbox 360 is beneath PS3 in preference, and gets a price drop it probably changes more minds since it is cheaper already and offers comparable experiences. Wii outsells Xbox 360 2:1 or more in most markets even when 360 is within 10% by average price or cheaper so Xbox 360 price cuts would only switch some people in scenarions 1 and 6 toward Wii because it is sufficiently differentiated.

So...in terms of weighting and how purchasing patterns in the six groups could go:

Thats very rough, but it would be 45m Wiis, 33.5m 360s, and 26.5m PS3s based on preferences of the six groups. I'd wager Wii will finish a bit higher and the others a bit lower but its not a bad guess off the top of my head.

If you have total sales numbers for the 360 over that time you should have a pretty dang good piece of a priori information.  If the total sales numbers are the same ones MS used you can also assume your variables are all integers which will probably reduce this to just a single solution, you might be out of luck and get more than one but probably not.  

It was not only up 63% on itself, but had an 80% change over the PS3 which is pretty big. Granted it was supply constrained, yadda yadda yadda, but MS has to be pretty pleased with those numbers to their most direct competitor.

Just because you have 3 unknowns doesn't mean that you can't have baseline numbers for the minimum number of arcade units sold per month.

If you used the assumption that 0% of the ultra-expensive Elites were sold (which any sold would drive the Arcade ratio up), and that all units sold were either Arcades or Pros, you'd end up with Arcades selling 37% of all Xbox 360's sold in January. That's the worst case scenario for Arcades.

Now, the next assumption would be reasonable: that 10% of all units sold are Elites...Which has been the average from my understanding. If value e was assumed at 10%, then the Arcade marketshare would be closer to 47.5%/42.5%/10.0%.

So worst case scenario would be 37% for Arcade sales, and best case (assuming the Elite didn't sell more than 10% of all consoles, which is doubtful it'd be higher), at 47.5%

So pick a number between 37-47.5%.