The video has all of baseball buzzing, especially fans in Kansas City unaccustomed to having one of their players identified by a national magazine as "the best pitcher in baseball."
Whether Greinke has reached that level is open to debate, but he certainly has climbed the charts with a 6-0 start and two earned runs allowed in 45 innings for a stunning 0.40 ERA. He has yielded 30 hits (for a .189 average against) and eight walks while striking out 54 hitters.
"I like to take a look at a guy, his last start or two," Abreu said. "It will let me know his philosophy, how he pitches against lefties, his command, his best out-pitch.
"Who's hitting, it doesn't really matter as long as it's a lefty. There aren't a lot of guys who hit the way I do. But I can pick up things, like how he's pitching guys inside, the break on his curveball, his changeup. I'll look at all of his pitches so I can have an idea when I go up there, a game plan."
During his 2 1/2 seasons with the Yankees, Abreu had some experience with Greinke. In 14 at-bats, Abreu has collected four hits (.286) and has gone deep once, with four RBIs. He walked one time and struck out twice.
"He has a pretty good fastball," Abreu said. "In curveball situations, it's a matter of whether he can throw it for a strike. He also has a changeup."
After a scalding start, Abreu has seen his average tumble from .363 to .318 with a 1-for-16 slide. He has no walks and three strikeouts during the stretch.
Lower-back tightness that surfaced last Friday night in New York while Abreu was stealing a base is no issue, he maintained.
"The back is fine," Abreu said. "I feel good."
When you're a .300 career hitter with 6,597 at-bats, you don't sweat the small stuff. Abreu, as cool as they come, was content to be in the designated-hitter role against Greinke. He'll be back in the outfield in the series finale on Sunday when the Royals send right-hander Kyle Davies out against Shane Loux.
"It's good to refresh, get a few DH at-bats," Abreu said. "I'll see what I can do."
Abreu has fit right into the Angels -- on the field, with his aggressive style on the bases and discipline at the plate, and in the clubhouse, where he has emerged as a popular figure with teammates frequently seeking his advice and counsel.
With 12 steals -- he has not been caught -- Abreu is tied with teammate Chone Figgins for third in the Majors, behind Carl Crawford and Jacoby Ellsbury.
"I love it here," Abreu said. "This team is aggressive. We all run here. It's a way to start a rally, put pressure on the pitcher. If he worries about you, it can take away his concentration on the hitter, and the hitter can do some damage.
"Running the bases aggressively is a way to change the game, give your team some energy."
Lyle Spencer is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.