"We've got to keep him on schedule," manager Kevin Cash recently noted.
Pitching for Triple-A Durham against the Orioles' Triple-A Norfolk squad, Odorizzi allowed one run on five hits, including a home run, and he struck out five in 6 2/3 innings. Of the 90 pitches he threw, 67 were for strikes.
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"It was kind of like the last time out, great all-around day," Odorizzi said. "Pitches got in, up-and-downs -- actually, got one more up-and-down than I was scheduled to. Making pitches, stuff was good. One bad split in the last inning [on the solo home run] ruined my day -- no, it was a great day."
After Odorizzi retired the first hitter in the third inning, he got paid a mound visit by assistant athletic trainer Mark Vinson. Odorizzi explained that the skin on his right middle finger was dried out after originally being a blood blister.
"Turned into a callus," Odorizzi said. "Just needed a little cut and file, and we were good to go."
At this junction of Spring Training, starting pitchers are fine-tuning for the regular season. For the Rays, that means an Opening Day date at Tropicana Field against the Blue Jays on April 3. Unless something unforeseen occurs, Odorizzi will make his first start of the season on April 5 against the Blue Jays.
Odorizzi will pitch Saturday against the Pirates in Bradenton, and he expects to throw 105 pitches before getting cut back in his final start of the spring in advance of his first start of the regular season.
As for Tuesday, Odorizzi obviously won't be with the team in Havana.
"I'll be in here first off, doing my work," Odorizzi said. "But I'll have [the game] on. See what the guys are doing. Looks like a pretty unique experience they have going on there."