Might simply be that demand dropped quickly like a rock, which is very often the case with warriors titles. Just compare first week sales and any subsequent weeks of those games on famitsu: There's generally a 80%+ falloff for the second week, and it continues downwards from there.

50 %+ isn't really a steep drop though, it's pretty common I think. Some games (especially JRPGs) drop 80 % in week 2.

And one thing to consider is that sales and shipments are the same for digital copies, so if the game only shipped 500k between November 24 and the end of the year, the majority of that can probably be contributed to its digital sales in that timeframe.

That was a typo, it was supposed to be 80%+

In other words, demand drops very quickly for these games, physical or otherwise. Being a Nintendo title possibly give it some legs, but still just minimal progression

Bad game, bad word of mouth, low public interest. The fact this was the only Nintendo exclusive title for christmas season still beyond me

So a game that has probably sold 3-4 million copies by now is a game with bad word of mouth? Have you seen how many reaction videos there are on the reveal of that game? And each of those channels has a bunch of followers.

The game has sold tremendously, and those who wish BOTW had more story components are probably very satisfied by the story building AoC does. There clearly is public interest if it's the best selling he in the series or on the way to be.

It's definitely not a bad game.  I'm enjoying myself a lot with it.

I think a fair amount of people wanted it to be BotW2 instead of a Warriors game, so there is an element of disappointment there from the people who wanted it to be something else.

All Warriors games have always had even way worse legs than this game. Appart from that the game got great critics and user reviews and is generally considered one of the best, if not the best Warriors game ever.

It did not have bad word of mouth. In Japan it was the first Warriors game to not completely drop of like a rock but instead still charts relatively high.

Fair enough, makes more sense with 80 %+. Still think it had to have been overshipped though, at least in the sense that I don't think sales were nearly at 3 mil when they reported 3 mil shipped, it's just not realistic otherwise considering that it's the holiday quarter and using the games sales trajectory on Famitsu as a guideline. But I suppose you could just see it as stocking up for the whole holiday right away, in which case you wouldn't really call it "overshipping".

I highly doubt that during those 4 days they actually sold all those 3 million units they shipped but, like the user above said, maybe they were stocking up for the whole Holiday. 

Depends on how much they actually sold in the first 2-3 weeks vs how much they sold in total 

3 million copies in few days is an outstanding even for most of Nintendo IPs, but a half million increase 2 months later its launch is not