Red Sox first baseman Triston Casas told The Boston Globe’s Julian McWilliams pregame that he’s begun taking practice swings and is up to about 30 at a time.

That was news to manager Alex Cora when asked about it in his pregame presser, who simply said “good” and “if that’s the case that’s a good sign.”

Casas is eligible to come off the 60-day IL on June 21 but according to Cora he is targeting the start of the club’s road series in Miami (July 2-4) for a potential return. Casas is from South Florida and grew up about a half hour from Marlins Park in the city of Plantation.

UConn honored

Prior to Saturday’s game the Red Sox honored UConn men’s basketball, the two-time defending NCAA Division 1 champions who claimed their sixth national championship in program history this past April.

Alex Karaban, a Southborough resident and a likely preseason All-American, threw out the ceremonial first pitch.

“It’s super exciting and super cool being in here,” said Karaban, who played for Algonquin Regional High School as a freshman and who has started on each of UConn’s last two championship teams. “This is my first time walking on the field.”

Also present was head coach Dan Hurley, who last week found himself at the center of one of basketball’s biggest stories when news broke he was being courted by the Los Angeles Lakers to be their next head coach. Hurley wound up deciding to remain at UConn, and Karaban said the last few days have finally brought some certainty as the Huskies look ahead to trying to win a third straight title.

“This is really the first time we’ve been able to be connected as a team and have no distractions,” Karaban said. “Really just moving forward now and it’s been awesome so far.”

Extra innings

Right-hander Chris Martin (anxiety) will begin his rehab assignment with the WooSox on Sunday. Infielder Romy Gonzalez (left hamstring strain) had Saturday off but will play first base for Worcester on Sunday as well. … Outfielder Wilyer Abreu (sprained right ankle) ran the bases at full speed pregame Saturday and is on track to potentially return in time for next weekend’s road trip to Cincinnati. … Yankees ace Gerrit Cole, who has yet to make his season debut due to elbow inflammation, was at Fenway Park and told reporters that he’ll be back soon. He and the club are still discussing an exact target date but after missing the first two and a half months his return appears imminent.