I don't think we're mathematically ignorant at all.
I called Disney when the package first came out, it wasn't explained to me the way you are trying to explain it. They explained that I would pay 5 nights at rack, plus 6 days of UPH at reg price, and they would give me 2 nights free at BWI and 3 days of UPH free. After going on my plans with tickets etc...they determined that I would be getting off cheaper using the room only code. They were right. Believe me if it were cheaper the other way, I would have switched to the package, and if it were all that great, it would be sold out by now and people wouldn't be hoping and praying for room-only codes. Remember, some people don't need passes, they may have PHP's left from a previous time and only need the room. If I didn't need passes, a room only would give me 7 nights for 1589.00.
You can look at it this way too, and then it makes airforcerocks calculations right. I am using value season to do this:
5 nights at BC at rack rate is $1611.15 (tax included)
On the WDW site, if you price the package for 7 nights, it comes to 2233.36. Take 2233.36-1611.15 and you have 622.21 left, which covers your UPH's for 6 days (this is for 2 adults). Take 1611.15 and divide by 7 and you get $230.00 night. Add on the two free nights of the resort and 3 free days of UPH. Remember when they price the package on the website, the 2 nights and 3 days of UPH are free, so that price you are getting is really for 5 nights of the resort and 6 days of the UPH. YOU BUY 5 and get 7. The price on the package is for 5 nights, they are just throwing in the 2 free nights and 3 UPH days. If you take the package total of 2233.36 and divide that by 7, it comes to about 407.xx per night including the UPH's.
It doesn't matter, I am getting the best deal for myself and that is all that matters. You are getting the best deal for yourself.
Another reason I am saving money is that I would rather have the 30 day FITS pass than the UPH, mostly because I get a free character breakfast for each ticket, unlimited usage of Disney Quest, free admission to the Kennedy Space Center and a few other nice perks including unlimited use of the water parks and the other 4 theme parks.
What it boils down to is that really the package kind of correlates with the rates for the AP and room only codes. You save bigger money if you don't need the UPH's. When I spoke with Disney, this is pretty much what they told me.
