@ dobwal - My initial calculations set the "# of months" value of the latest hardware sales as zero. Yours set it as 1. The former implies all hardware sales took place on the last day of the month and the latter implies that they all took place on the first day of the month. That's why there is a discrepancy between our calculations. Your numbers would put the ATO at 13.3 months, which naturally, if you took more time to reach the same attach rate would result in a lower purchase rate. Neither value makes sense, actually. paawl made the reasonable suggestion to use 0.5 months as a starting value, instead, so latest month would be 0.5 next would be 1.5, etc.
New numbers based on this change (and I also did less rounding this time, only rounding the final figure) come up as:
ATO:
360 - 12.8
PS3 - 7.5
Wii - 7.5
Purchase Rate:
360 - 0.59 games per month, 7.1 games per year
PS3 - 0.61 gpm, 7.4 gpy
Wii - 0.70 gpm, 8.5 gpy
This is the point. All of my initial posts were a response to the OP, which was attempting to show that MS's claims didn't hold up. My initial problem was with the OP trying to normalize the attach rates of the 3 consoles by time since launch. So I came up with the Attach Rate/ATO calculation as a better alternative. Next, I wanted to see if there was some statistical backup for points made by other posters that new console buyers show higher purchase rates and by extension as the console owner poulation increases you would see a decline in purchase rate.
Hence the initial buy rate calculation and the subsequent attempts to make what I thought was a more valid comparison by attempting to show what the 360's purchase rate was when it was in a similar position to where the other 2 consoles are now in ATO. I even showed what the purchase rate of the other 2 consoles would be if they followed a similar trend when they got to the point where the 360 is now. This satisfies me, at least, that MS's claims do hold up and the conventional wisdom that the 360 is selling software at an unusually high rate is not just based on succesful PR.
LOL my bad.