While the allure of the Bruins kept the Yankees from signing Cole out of high school, they have long viewed the drafting of Cole as a long-term, long-shot investment, because they began to forge a bond and parted on good terms. Cashman alluded to this when he spoke to reporters on Friday in Stamford, Conn., before his annual practice run rappelling down the Landmark Building as part of the city’s holiday festival.

“Various members of our franchise — Damon Oppenheimer is our scouting director still; him and a number of our staff members — they got a chance to know Gerrit Cole because we drafted him way back when,” Cashman said. “So some of our people know Gerrit Cole already on a personal level, him and his parents.”

Cashman also said, predictably, that the Yankees enjoyed their meetings with Cole and Stephen Strasburg, another elite free-agent starter represented by Scott Boras.

“You see how they carve lineups up, but you never get a chance to know better the person,” Cashman said. “So in both those cases they’re really good, genuine people, good family people, so despite their competitive nature when they have the ball on the mound every five days, you walk away realizing that they would fit in anybody’s clubhouse in a real positive way.”

Niceties and comfort are necessary factors in free agency, but the highest bid almost always matters most. The Yankees understand that signing Cole will require more than the largest guarantee ever given to a pitcher — David Price’s $217 million deal with the Boston Red Sox before the 2016 season — and possibly more than Zack Greinke’s record $34.4 million average annual salary for a pitcher.

Their primary competition seems to be the teams closest to Cole’s home: the Angels, who play about five miles from Cole’s high school in Orange, Calif., and the Dodgers. Cole has told the Yankees that geography is a factor, but not a deal breaker. The true difference maker most likely will be the desperation of the teams involved.