13x500=6,500
3800 from main quests (4226 * 0.9)
22 * 35 = 770 (dailies)
22 * 24 = 528 (collections assuming missing a few but also getting some 2s&3s ?)
------
5,098
That's 3 grand prizes short of a full set.
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Let's try it in reverse:
5,100 currency
13 grand prizes
=392 per GP
=19.61 per staff.
That's not super likely. I think @pauly7 was right about 60% of players coming up short.
I just added everything up for Beta and did the math and my cost per staff was about 22.75, or 301 staffs on about 6850 knowledge. Or 455 knowledge per grand prize. That is 5915 for 13 grand prizes. I opened all the 18 and 45-point beacons I could, but I opened a lot of the wrong 45 and hurt myself on potential currency wins. One extra 80 knowledge win and I would not have bought the 100 knowledge I did.
And don't forget a max evolve Ashen Phoenix still gets you an extra 110 knowledge, even after the drop in rewards, 1 point each for the first 40 quests and 2 each for the last 35. Plus the 100 from the newsletter. That makes about 5300 for Live, so winning a poor amount of just 600-700 extra knowledge will get you to the 5900-6000 needed for for a complete set, if you can keep your average per staff at 23 or less.
So, as usual, this is another "do you want the grand prizes or the daily prizes" decision.