DETROIT—The Detroit Pistons worked the phones last summer, trying to trade for a superstar to shake up their roster.

They ended up standing pat because a deal didn’t make sense.

Two games into the season, Allen Iverson was the answer to their hopes in a blockbuster that generated rare buzz for the NBA in November.

Detroit acquired the former NBA MVP on Monday for All-Star point guard and former finals MVP Chauncey Billups, top reserve Antonio McDyess and project Cheikh Samb.

“We just felt it was the right time to change our team,” Pistons preside...

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