Belichick uses the tools at his disposal.
If he has a bunch of draft picks, he picks players in the draft; if he doesn't have any draft picks, he knows he can't draft anybody.
Seems simple.
If he has a bunch of cap money to spend, he spends it; if he doesn't have any cap room money, he knows he can't spend it on anybody. He had such money in 2003 and 2007, he didn't all the other times.
Seems simple.
Belichick and Pioli are not one dimensional. They know that there are five ways to acquire football talent with which to win football games. To succeed, they use them all. They also know that all the Teams have the same resources, so you have to excel in each method as well. These acquisition avenues are:
a) draft picks (everyone get the same amount; get more, use them better)
b) UDFA picks (everyone get them; get more or better ones)
c) veteran FA pickups who have excelled (ex-starters "over the hill" guys; select well)
d) trades for players (everyone can; get the best values)
e) veteran pickups who have not yet excelled (developmental scrubs, chose carefully, coach them up)
In general BB/SP use trades as the final source to fill holes that exist, after all other methods have proven to be insufficient. Bill has recognized that Teams are only as strong as their WEAKEST link; not how strong their STRONGEST players are.