BOSTON—In the season’s first 16 games, perhaps the Orioles can take some satisfaction in having the same record as the defending World Series champion Boston Red Sox.

Both teams are 6-10. However, the Red Sox have a much larger payroll and a panoply of stars.

One is left-hander David Price.

Price ran his record against the Orioles to 15-6 with seven scoreless innings on Sunday. He allowed just three hits in the Orioles’ 4-0 loss to Boston.

The Orioles didn’t get a runner to third base until Price left the game in the eighth. They had runners on first and third in the eighth and ninth, but couldn’t score.

Orioles starter John Means did his part to keep the Orioles close, giving up one run on four hits in five innings. Xander Bogaerts hit a three-run home run against Josh Lucas in the eighth to break open a tight game.

“The changeup today really saved me,” Means said. “Everything else I wasn’t really locating very well. I wasn’t locating in. I wasn’t locating up.”

Means gave up a run in the fourth on a single by Steve Pearce, a double by J.D. Martinez and a sacrifice fly by Bogaerts.

A surprise addition to the club, Means has pitched well and has a 1.98 ERA.

“I just want that role of being able to do whatever they ask me to do, and I come to the field ready to go at all times,” he said. “And I do like starting. It’s what I’ve always done. So yeah, I’m just very comfortable.”

Manager Brandon Hyde has liked what he’s seen from his left-hander.

“Means was really good,” Hyde said. “He gave us a chance to win. We just couldn’t — runner on second base and nobody outs three times, and you don’t advance him once. It’s tough to win that way.

“I like his aggressiveness. I like today he dumped a few curveballs or breaking balls in for strikes, too, which he hadn’t done and that’s something that he’s going to continue to improve on and be another weapon for him to have that third pitch. And he did that a few times today just to kind of lock up guys, maybe dump a breaking ball in to get ahead in the count. And, again, he had a really good changeup.

“I like the way he moves around his fastball, a couple punchouts on elevated fastballs. Pitched with a really, really good tempo and keeps you in the game.”

Cedric Mullins, who struck out twice and flied to deep center in the eighth, cited the inefficient offense.

“Honestly, it was us not taking advantage of opportunities that we had early offensively,” he said. “We had guys on second base with no outs, and we just couldn’t execute plays, including myself. I had an opportunity to move the guy over and botched it. That’s kind of what cost us today.”

The Orioles tied a major league record by allowing a home run in each of their first 16 games. The 2009 Philadelphia Phillies, who won the National League pennant that year, were the last team to do it.

It was the first time this season the Orioles were shut out, and they’ve lost nine of 11.

Brocail ejected: Pitching coach Doug Brocail was ejected by first base umpire Stu Scheurwater in the sixth inning. It was Brocail’s ninth career ejection, six as a pitcher and third as a coach.

Scheurwater was also responsible for former manager Buck Showalter’s final two ejections as a manager on balks against Darren O’Day.

“There were a few questionable check swings that didn’t go our way,” Hyde said. “All three didn’t go our way, and I think Broke [Brocail] had enough. There was a lot of yelling from the dugout and Broke got singled out.”

After Chris Davis was called out on strikes to end the game, Hyde was yelling at home plate umpire Ben May as he walked past the Orioles’ dugout.

“That ball might have been up. I thought it might have been up,” Hyde said.

“I haven’t seen the replay on it. It looked up from where I was. But that didn’t cost us the game. What cost us the game was not being able to move runners and score runners off David Price, who was really good today and you’ve got to be able to execute with him on the mound. And not being able to keep the ball in the ballpark in the eighth inning after we put together a nice rally in the top half.”

Cobb update: Starting pitcher Alex Cobb is eligible to come off the 10-day injured list on Tuesday. Cobb, who has been hampered by back spasms, will not pitch for several days.

“Probably going to push him back a couple of days as of right now,” Hyde said. “It’s a little bit unclear.”

Cobb threw on Saturday and is likely to pitch against Minnesota next weekend if he doesn’t have any more pain.