The good news on Brandon Woodruff is that the Mississippi State alum threw a 25-pitch bullpen session on Tuesday following a similar session on Saturday. What remains uncertain is when the 30-year-old right-hander might come off the injured list and rejoin the Milwaukee rotation. “I have to get to a certain point where I get the pitch count up,” the ex-Wheeler High star told mlb.com. “Once I get to live BPs, that determines the speed of how this thing will go.” So, maybe late July? Woodruff has been out since April 11 with a shoulder injury. He had a 0.79 ERA in his two starts of 2023. The Brewers are second in the soft National League Central, a half-game back of Cincinnati, but almost certainly need a healthy Woodruff to stay in playoff contention. He is a two-time All-Star who is 42-25 with a 3.14 ERA since he arrived in the majors in 2017. He has a 3.18 ERA in eight postseason appearances from 2018-21. … Madison Central alum Spencer Turnbull (neck injury) has begun throwing sessions but no timetable has been reported for his potential return to Detroit. After missing all of 2022 following Tommy John surgery, he was 1-4, 7.26, this season before being shut down on May 13. P.S. Ole Miss product James McArthur, called up by Kansas City on June 24, has yet to make his MLB debut. The 6-foot-7 righty had a 4.87 ERA at Triple-A Omaha after being acquired in a trade with Philadelphia. … Former Biloxi High star Colt Keith is expected to make his Triple-A debut today for Toledo (Detroit system) at Columbus. … Ex-Ole Miss standout Tim Elko is expected to make his High-Class A debut today for Winston-Salem (Chicago White Sox) at Aberdeen.