Osuna still faces a court case in Toronto, stemming from an alleged domestic violence incident earlier this season, and after Monday's appearance hinted that a change of scenery and the game itself offered a respite.
He declined to provide specifics about what led to his May 8 arrest in Toronto, citing an ongoing legal matter.
McCullers left Saturday's 14-0 victory over the Los Angeles Dodgers in the bottom of the fifth inning and will be evaluated later on Sunday.More news: Elon Musk considering taking Tesla private, TSLA stock trading halted
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In a statement, the Astros said their decision to acquire Osuna was based on the information that they gathered during extensive evaluation.
It happened on Monday, with the Houston Astros on the road in San Francisco. We are providing Roberto with the benefit of a great clubhouse and organization as a supportive environment for this fresh start. Time will tell which ones were right and wrong. If there is any type of issue in the future, we will take immediate and decisive action - it will not be tolerated. We understood that it would cause significant debate. The administrative leave subsequently was extended at least four times as Major League Baseball investigated the alleged incident.
He had a 2.93 ERA and nine saves this season before the suspension.