To Stewart, it was not much of a surprise. He was also teammates with Thames in 2010, with Class AA New Hampshire in the Toronto Blue Jays’ farm system. Thames was 23 that season, and he batted .288 with 27 home runs and 104 runs batted in, leading the Eastern League.

“It was unbelievable what kind of season he had,” Stewart said. “He was the heart of our team.”

Yet Thames did not make much of an impression as a rookie for the Blue Jays in 2011. He batted .262 with 12 homers in 95 games, constantly dreading the prospect of a trip to the bench or the minors. The Blue Jays traded Thames the next summer to Seattle, where he hit .220. He did not appear in the majors in 2013.

To Karon, the agent, the 2014 contract in South Korea represented more than a chance for Thames to make about $800,000. Karon had never encouraged a client so young to play there, but he made an exception for Thames.

“My view was, ‘Look, you’ve always been successful when you’ve played every day, and you’re not going to get the opportunity here,’” Karon said. “He was the last man on the 40-man roster of the worst team in baseball.”

That team was the Astros, who granted Thames his release after Karon finally persuaded him to try the K.B.O. Stewart compared games there to the last few innings of spring training exhibitions, with a few highly skilled players scattered among those with far less polish. Thames clearly stood out, overpowering pitchers who feared him so much that they ultimately sharpened his hitting eye.

“They tried to just throw junk at him all day,” Stewart said. “As a hitter, that would drive me crazy — ‘Oh, my God, just throw me a fastball!’ — and you can see how guys would want to just go up there and hack. But I think that made him more patient.”

The numbers support that theory. In his rookie season with Toronto, Thames swung at 34.7 percent of pitches outside the strike zone, according to PitchFX data. In his first 21 games this season, the figure had plunged by more than half, to 16.8 percent.