HAVANA — If there was a breakout star of the Rays’ visit to Cuba, it was a guy who did not even play.

Chris Archer said he took some guff for not playing from Cubans, even as he tried to explain the Rays were just staying on schedule and it was Matt Moore’s turn to pitch Tuesday, when Tampa Bay beat the Cuban National Team 4-1.

Not playing did not temper the Rays’ ace, however. He already had a reputation as gregarious, curious and friendly, but that might not have been recognized nationally because he plays in small-market Tampa. But in Cuba, Archer served as a spokesman for the team at several events, was front and center at a clinic for Cuban kids and generally was seen having a great time in this environment.

Then just before the game, the Rays lined up to meet the First Family and, well, Archer stood out. He kidded both President Obama and his wife, Michelle, that they did not respond to his tweets to get together in Cuba. He presented the President with a glove, not his own, but rather Moore’s because he knew Obama was a lefty.

Archer called it “the highest compliment” of his life that the President had praised him for how he conducted himself in interviews.

Archer said he thanked the First Lady for all the work she does in the community and told her, “Anytime I can help, I am on board.”

This was Joe Torre’s second visit to Cuba, including a setup meeting in December. Still, the idea that President Obama and Cuban leader Raul Castro would sit together was difficult to process.

“You have to understand I was in basic training in 1962 during the Cuban Missile Crisis,” said Torre, who is MLB’s chief operating officer. “So I have some feel for the history, and so I was not surprised we didn’t have relations all those years. But now to be here and see all this enthusiasm, it really is something.”

Was this just nothing or a strategic decision by whomever was playing the music at Estadio Latinoamericana in the hours before the game and before the U.S. and Cuban presidents entered? At least a dozen songs played that were all in Spanish. Then, the first song in English was not a current hit. It was a Billy Joel song, but not among his most famous. It was “Honesty,” which includes the lyrics, “Honesty, it’s hardly ever heard, but mostly what I need from you.”