Interesting question, so I looked up the last 10 NBA drafts.
Team with the worst record / Where they drafted and who they drafted / Team that got the no. overall pick and their record / Who they drafted
1996 Vancouver / 3rd pick Shareef Abdur-Rahim / Philly, second worst record / Iverson
1997 Vancouver / 4th pick Antonio Daniels / San Antonio, third worst record / Duncan
1998 Denver / 3rd pick Raef Lafrentz / Clippers, third worst record / Olowokandi
1999 Vancouver / 2nd pick Steve Francis / Chcigo, third worst record / Elton Brand
2000 Clippers / 3rd pick Darius Miles / New Jersey, 7th worst record / Kenyon Martin
2001 Chicago / 4th pick Eddy Curry / Washington, 3rd worst record / Kwame Brown
2002 Chicago and Golden State / 2nd, 3rd picks, Jason Williams, Mike Dunleavy / Houston, 5th worst record / Yao Ming
2003 Cleveland, Denver / 1st, 3rd picks, LeBron, Carmelo
2004 Orlando / 1st pick, Dwight Howard
2005 Atlanta / 2nd pick, Marvin Williams / Milwaukee, 6th worst record / Andrew Bogut
2006 Portland / 2nd pick, LaMarcus Aldridge / Toronto, 5th worst record / Andrea Bargnani
So, over the last 10 years, only Cleveland and Orlando were able to get the no. 1 overall pick with the worst record in the league. Seems like having the third worst record has been a little lucky. And, looks like Vancouver got screwed out of Allen Iverson, Tim Duncan, and Elton Brand ... sucks for them.

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