Two veteran managers, facing a sudden-death game, decided to give the ball to Marcus Stroman because they had determined he had the right stuff — diabolical sink to his pitches and unsinkable faith in himself.

In a decisive Division Series Game 5 against the Rangers in 2015, Blue Jays manager John Gibbons turned to Stroman, as did Jim Leyland for the World Baseball Classic final in 2017. Both times Stroman excelled, which is part of his credentials as contenders mull acquiring the small righty over the next week.

The Yankees, in particular, try to determine whether a pitcher can handle not only stressful games, but their specific pressurized situation. Another diminutive righty, Sonny Gray, had pitched well in his only playoff appearance for Oakland, giving the Yankees a level of comfort that he would not buckle in New York. Yet Gray was overwhelmed by the environment.

“I know this (New York) is a different place and I know 100 percent (of players) don’t work out,” said Leyland, who won pennants in both leagues and the World Series with the 1997 Marlins. “But if anyone can do it, I think it is (Stroman). I think he would thrive in (New York).”

Gibbons, who was Stroman’s only manager in Toronto until this year, said, “I love the kid. He is a great competitor. He’s volatile and emotional, anyone can see that. He wants the spotlight. If there is a big game to pitch, he wants it. Some guys shy away from it. He has a chip on his shoulder big time. He’s very sharp, intelligent, went to Duke. Yes, most definitely (he can handle New York).”

Stroman, an All-Star for the first time, is generally viewed within the industry as the most likely top starter to be traded before Wednesday’s deadline. The 28-year-old does not become a free agent until after the 2020 season. But the Blue Jays recognize his value may never be higher: He is having his best season (2.96 ERA) at a time when the field of high-end available starters is small and many contenders are searching for rotation help — hence, it is a seller’s market.

The Yankees, Astros, Braves, Phillies and several other contenders hunger to upgrade their rotation. Offers for Stroman were tepid after he left a June 29 start with what was termed a cramp in his non-pitching shoulder and didn’t pitch again for two weeks. But in three starts since, including holding Cleveland to one run in seven innings Wednesday, Stroman has a 1.80 ERA and .549 OPS.

The number of suitors and quality of offers have both increased with recent success and the Blue Jays internally believe they now have a floor with which they are comfortable and that bidding can further increase the potential return in the coming days, making it more and more likely Stroman is dealt before his next scheduled start on Tuesday. The Yankees are not currently perceived as a front-runner. They have not pursued him with the same ardor as J.A. Happ last year and the Blue Jays like other contenders’ farm systems better.

“I would think (he’d) fit in any contending team,” Leyland said. “There is no fear. I think the world of him. Like a lot of guys now, he shows his emotion. Some are OK with it, some it rubs the wrong way. That’s just him. He wants the ball, that’s the big thing.”

Leyland had Stroman pitch the WBC final against Puerto Rico. There was some possibility of Chris Archer pitching the final, but there was discomfort that Archer did not stay with the team the whole time while Stroman was committed to the club. Stroman no-hit Puerto Rico for six innings before faltering to open the seventh of what would be an 8-0 title-clinching US win.

“It was Dodger Stadium, it was 50,000 people and I couldn’t have picked someone better to start that game,” Leyland said. “The guy was exactly what we needed. He was proud to be there. He was determined to win that game. He’s a jewel, in my opinion, a great addition for anyone, not just the New York Yankees.”

Stroman tore his ACL in spring training 2015 and there were questions if he could even return. He did in time to make four September starts as Toronto clinched its first playoff berth since winning consecutive titles in 1992-93. The Blue Jays came back from 0-2 down vs. Texas to tie the series. Gibbons insists his use of David Price in relief in Game 4 was not to avoid starting the lefty, who to that point had struggled in the postseason, in Game 5.

But Gibbons did not flinch because Stroman was the choice to start the decisive game, in which he yielded two runs in six innings. Gibbons said he was confident in Stroman in part because of what is often viewed as a negative with the Long Island native.

“He is going to speak his mind and rub some people wrong,” Gibbons said. “One thing about the kid, he lays it out, you know what he’s thinking, where he stands. He is determined to maximize his career. One way to do that is to be in the spotlight and he believes that. But he is absolutely unafraid of that spotlight.”