A former RotoWire columnist, Mark Edelman, wrote about this strategy about five years ago, and I won a couple leagues doing a version of it.
The premise is that assists mostly come from point guards, and that makes them expensive. But if you take all shooting guards (which are usually cheaper), you'll usually get more threes, more points and as good or better percentages. Point guards are typically better at steals, but that's not a hard and fast rule as Larry Hughes (when healthy), Allen Iverson (when he was a SG), and even small forwards like Ron Artest, Caron Butler and Shawn Marion are often among the league leaders in that category.
Ignoring point guards in the early and middle rounds, I was able to get solid big men, small forwards and scoring guards, and then fill in with Rajon Rondo or Jose Calderon types. It also helps to get good passing big men - like Lamar Odom or Andrew Bogut, just to hang around in the assists category and not be so far back that you can't make a pickup or trade and get back into the mix later.
It's a lot harder to tank a category like blocks (having bad centers usually costs you in rebounds and points), or FT percentage - once you tank it by drafting Shaq and Ben Wallace, there's no going back. At least with assists, I was able to make some moves and finish in the middle of the pack in that category.
In a competitive league, you're rarely going to be strong everywhere, but by letting go of a category almost completely, you can consolidate your strengths and get the most out of your players' contributions.