That means that right-hander Jered Weaver, who allowed just one run on two hits over 7 1/3 innings in Game 2 of the Division Series against the Red Sox on Friday, likely won't start until Game 3 on Monday at home against the Yankees.
"In just about every scenario we're looking at, we'll have a lefty start at Yankee Stadium at some point," Scioscia said. "Most likely in [Game 1 or 2]."
Right-hander John Lackey is still expected to start Game 1 at Yankee Stadium on Friday, but Scioscia will have to decide whether to start Scott Kazmir or Joe Saunders in Game 2 on Saturday.
"There are a lot of things we have to look at," Scioscia said. "There are some templates that make a lot of sense. We'll look at home/road splits, how comfortable a guy is at a ballpark on the mound, and how he's faced the lineup."
Kazmir has the most experience against the Yankees, with 14 career starts and an impressive 2.67 ERA, while Saunders is 2-1 with a 6.28 ERA in five career starts against New York.
But neither left-hander has started at the new Yankee Stadium, while Weaver made two starts there this season, but had a 6.08 ERA, which is why he'll likely start Game 3 at Angel Stadium, where he had a 2.90 ERA this season.
Saunders, though, had success at the old Yankee Stadium in his one start there last season when he allowed two runs over six innings to pick up a win. And Kazmir, for all his success against the Yankees, struggled at the old stadium, with a 5.04 ERA there in five career starts.
Kazmir is coming off allowing five runs over six innings in his start against the Red Sox in Game 3 of the ALDS on Sunday, so the door is certainly open for Saunders to start Game 2 of the ALCS at Yankee Stadium.
So while the front-runners appear to be Lackey starting Game 1, Saunders starting Game 2 and Weaver starting Game 3, Scioscia said he's just not ready to make the announcement quite yet.
"As soon as we know, we'll put it out there," Scioscia said. "We need to worry about our own house and what we need to do. There's no advantage to keeping our cards close to the vest."
Rhett Bollinger is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.