Some posters have mentioned it already, but the Avs team is part really good luck, and part smart acquisitions. When Roy was here, he had his own vision for the team and there were moves made that did not blend well with what they already had. There seemed to be a focus on big and strong, getting guys like Brad Stuart, Jarome Iginla and Francois Beauchemin. Roy wanted more moves and more power, but when he didn’t get his way he rage quit and left the Avs a bit of a mess as they were part his image and part Sakic’s.
This leads directly into the losing year, a historically bad season followed by losing in the lottery draft as well. However, that season turns out to be a gift in disguise. Duchene demands out, meanwhile some of the Avs other pieces re-affirm their desire to turn the Avs around (I think this was huge for team culture), and they end up getting Makar.
Once Sakic was the sole decision maker you can see his vision for the team starting to take shape. They start acquiring mobile defensemen that can move the puck, they acquire forwards with good possession advanced stats. The team has even started to draft with that vision in mind.