Chicago will pick second and Tulsa third. Washington, which had the worst record in the league will pick fourth. The Mystics (5-29) had a 44 percent chance to win the top pick.
The Mercury (7-27) had the second worst record in the league and a 28 percent chance of getting the No. 1 choice.
The 6-foot-8 center Griner, The Associated Press women's college basketball player of the year, guided Baylor to a national championship and 40-0 record.
Griner headlines a talented class. Delaware's Elena Delle Donne led the nation in scoring last season and is a versatile 6-foot-5 guard who can score from almost anywhere on the court. Notre Dame's Skylar Diggins has guided the Irish to the past two national championship games and is one of the most followed female athletes on Twitter.
Phoenix was plagued by injuries most of the season. Star Diana Taurasi only played in eight games and Penny Taylor missed the entire year while recovering from an ACL injury. Candice Dupree also missed 21 games because of a left knee injury.
The Mercury have had the first pick in the draft two other times (2004 and 2007). They selected Taurasi in 2004 and traded the pick in '07.
Washington had the best chance to secure the top pick. Only four times in the 11 previous lotteries has the team with the worst record secured the top pick.
This was the first time that the lottery was shown on television.
"It's great for the league and shows how special this class is," WNBA President Laurel Richie said.
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