As inevitably happens to the manager of a onetime champion sports team who has presided over a long series of recent losses, the executive producers of American Idol were dismissed Saturday as part of an overhaul that will also see at least three of the show's four judges depart. Rumors that Nigel Lythgoe and Ken Warwick would be removed from the show, whose ratings fell by more than 25 percent in the past season, had been circulating for weeks. Lythgoe confirmed them when he tweeted on Saturday, Just had 10 days in the Bahamas, rain everyday. I get back to the States and get fired. Sad! Later he added, Yes, don't worry. I'm on #SYTYCD [So You Think You Can Dance]. Fox still loves me. It's not a personal thing. They just feel Idol needs new leadership after 12 Seasons.