OK, Japan rates:

Wii - 0.331

PS3 - 0.234

360 - 0.306

Wii clearly comes out on top, PS3 struggling in 3rd and 360 not too far behind Wii in 2nd though it has sold so few consoles that it's not really all that relevant.

Wii adjusted for Wii Play - 0.289, still ahead of PS3!

EDIT, origionally had adjusted Wii rate at 0.259, corrected to show 0.289. 

I don't really understand where you're coming from. Surely it favours no system as it's taking install base and  average time of ownership out of the equation. If what you say is true regarding better selling consoles benefitting from this approach then how come PS3 comes out on top when it has been selling significantly less that 360 and Wii of recent??

If I'm missing something please explain further. 

& finally the finale, NA + Japan rates-

Wii - 0.543

PS3 - 0.491

360 - 0.585

Not surprisingly adding the territories benefits the 360 due to it's tiny Japan install base not dragging down it's attach rate significantly. One thing of interest though is that Japanese gamers buy waaaaay less games than their NA counterparts, about half in fact!

Oh and Wii adjusted for Wii Sports and Wii Play - 0.458. Again, this shouldn't be all that surprising since Wii has a bigger portion of it's install base in Japan than PS3 & 360.

 If a system is selling well, it tends to sell more software than it otherwise would. When people buy systems, they tend to buy a lot of games to start with.

So for example, the 360 started its life with an attach rate of nearly 4. Four! That's the highest in history, in fact. If we were to do this analysis in the first month of the 360's lifespan, the tallies would look something lke this:

Average time of system ownership: 1 month
Games purchased per month: 4

It would look absurd, but that's because the system had 100 percent new owners who were all buying new games to go with their system. As time goes on, they tend to buy less games/month, so the average is weighted down. 

 I'm stripping down attach rates to a monthly basis, how does that favour any 1 system?

I do see what you're saying now, though think the difference it makes is negligible when compared to the other methods of tracking attach rates. The console which would lose out due to this process is 360 due to it being an older system but then it also benefits from this position as a lot of it's games have had time to be discounted and re-released as platinum(or whatever the 360 equivalent is) which obviously gives it's software sales a boost over the Wii and PS3 which are too young to have a budget range(or if they do already, not one of significance). So all in all I think this comparison is as accurate as we're going to get in the 'who's console sells more games per console' argument.

It would be interesting to do this again next holiday season as as the systems age this discrepency will cease to be of any real significance.

Thanks for your input! 

 The only way newer sales matter more is due to the fact that most people buy software with their hardware. However, this effect should be negligible after launch since new hardware sales are only a tiny fraction of the total userbase each week.

What would be interesting is taking into account the PS3 and 360 attach rates stripping out their bundles such as motorstorm/resistance (Europe/US) and other like the 360 xmen/etc. Its a bit harder I realize but its only fair.