NEW YORK — ABC’s “Wide World of Sports” will be converted from a 90-minute anthology series to the umbrella for most of the network’s weekend sports coverage.The plan, effective Jan. 3, will end the venerable Saturday program that airs at 4:30 p.m. in most markets, known for its Roone Arledge-coined phrase, “the thrill of victory, the agony of defeat.” Instead, “Wide World” will become the moniker for the Alphabet web’s entire sports slate, with the exception of college football and “Monday Night Football,” allowing ABC to have a live studio operation for about four hours on each weekend day with scores, as NBC now has with its “Sports Desk” cut-ins. “It gives us a lot more flexibility to program … without having to squeeze things into a 90-minute show,” said Steve Anderson, senior VP of production. The move also comes as ABC and parent Walt Disney Co. seek to tap the brand equity of the “Wide World” label, and as ratings for the January-to-August anthology, which debuted in 1961, have tapered off in recent years amid competition from Disney’s own ESPN. For the season just ended, “Wide World” earned a 2.6 rating and a 7 share, down 16% from the prior year. Robin Roberts will continue as the main studio host for the program but will segue to hosts for specific events, to include figure skating, PGA golf, CART and NASCAR auto racing and college basketball. A title sponsor will be sought for the update segments.