The 25-year-old is quick to credit the manager with his success.
"It's real good to have a manager who has confidence in you and keeps running you out there," League said. "I'm just happy that I'm getting out there and getting work."
League says that when he arrived with the team in June, Gaston made sure to talk to the young pitcher.
"When I was first called up, I sat [on the bench] a little bit," League said. "But he told me that I'm part of this organization and I'm going to be part of the team. So it's good to have the manager's confidence in you."
Gaston, in turn, has had high praise for the hard-throwing League.
"It's nice to have a power right-hander out there," Gaston said recently. "I've tried to show him that I have confidence in him, and lately he's given me that confidence right back.
"That kid is going to be a big part of this team when we win something."
League will be in the bullpen Sunday backing up Jays starter Scott Richmond, who will be making his third career start. Richmond -- a native of North Vancouver, British Colombia -- will look to earn his first Major League win, as well as salvage a game in Toronto's series with Cleveland.
TOR: RHP Scott Richmond (0-1, 4.91 ERA)
A late rally by the Blue Jays on Tuesday night helped Richmond avoid what would've been a second hard-luck loss in a row. The 28-year-old rookie turned in an effective outing against the A's, allowing three runs on seven hits over 5 2/3 innings in his second career start in the Majors. Richmond struck out four and walked one in the no-decision.
CLE: LHP Cliff Lee (15-2, 2.58 ERA)
Lee rebounded from perhaps his worst start in an otherwise stellar season by going seven innings, allowing just a pair of runs on eight hits with two walks and two strikeouts in a win over the Rays on Monday. In doing so, he became the American League's first 15-game winner. The Rays had Lee on the ropes several times, and he needed 48 pitches just to get through the first two innings, but he never buckled. He pitched a gem against the Jays on May 12, giving up just seven hits in nine scoreless innings but nonetheless walking away with a no-decision.
Jays second baseman Joe Inglett had three hits Saturday, finishing a home run shy of hitting for the cycle. His seven triples lead the Jays and ranks him at third in the AL. ... Third baseman Scott Rolen is batting .571 (4-for-7) in his career against Lee. ... Roy Halladay tossed a season-high 130 pitches in Saturday's start against Cleveland. His previous high was 126, which he accomplished three times, the last coming on Aug. 4, 2007, against Boston. ... Entering Saturday, Jays outfielder Shannon Stewart (high right ankle sprain) had appeared in eight games during his rehab assignment. He was batting .273 (6-for-22) in those games.
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Official game notes
Monday: Blue Jays (Shaun Marcum, 6-5, 3.44) at Tigers (Justin Verlander, 8-12, 4.56), 7:05 p.m. ET
Tuesday: Blue Jays (A.J. Burnett, 14-9, 4.62) at Tigers (Zach Miner, 6-4, 3.57), 7:05 p.m. ET
Wednesday: Blue Jays (David Purcey, 1-3, 7.40) at Tigers (Kenny Rogers, 8-9, 4.92), 7:05 p.m. ET