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Serena Williams at the U.S. Open

Analytics, scouting first-time opponents, additional coaching input, new footwork drills and treating doubles like practice — so far it’s adding up to winning.

Serena Williams is into the third round of singles in her final U.S. Open.Credit...Michelle V. Agins/The New York Times

An underdog with the oddsmakers against the No. 2 seed, Anett Kontaveit, on Wednesday, Serena Williams will be back on familiar ground as the favorite against the unseeded Ajla Tomljanovic on Friday.

The word is out, expedited by the roars in Arthur Ashe Stadium: Williams has worked her way with great speed back into form and into the third round of her final U.