BOSTON -- Well, so far Boston Red Sox owner John W. Henry is half right. On June 2, when he came out in support of Red Sox GM Ben Cherington and manager John Farrell, he said the Sox still had a chance to be a "great" offense.

"They'll prove us right or they'll prove us wrong," Henry said.

Since his State of the Team address, a rare foray for the owner into the public discourse over his team, the Sox have undergone a transformation at the plate. They come into Tuesday's game against the Baltimore Orioles hitting .296 in June, the highest average in the majors. They're first in hits (205), first in doubles (47), tied for first in triples (8), third in slugging (.466), fourth in on-base average (.343), seventh in runs (94) and 11th in home runs (19).

On Sunday, in a 13-2 rout of the Kansas City Royals, the Sox had 13 extra-base hits -- a number they have exceeded only twice in their history, and the most ever allowed by the Royals in a game.

They've had 10 or more hits in 11 of 20 games this month, including five such games in their past seven. That stretch includes a season-high 18 hits last Tuesday against the Atlanta Braves, and 16 hits twice against the Royals in wins Friday and Sunday.

And the evidence is accumulating that, once again, David Ortiz is making all the speculation about his imminent demise foolish. And while it may be too simplistic to attribute Boston's offensive revival to the big man in the middle, the correlation between his performance and the rest of the offense is impossible to overlook.

In the first nine games of the month, the Sox scored only 28 runs, or just over three runs a game. Then, on June 11, Ortiz hit a home run off Orioles reliever Chaz Roe, ending a streak of 17 games without a home run. It was Ortiz's second 17-game homerless streak of the season and longest since 2011 -- the last time Ortiz was said to be in decline, when he had home run droughts of 24 and 19 games.

Since June 11, the Sox have scored 66 runs in 11 games, an average of six runs per game. They've posted a slash line of .305/.358/.517/.876 with 50 extra-base hits, and have recorded 10 or more hits in six of 11 games.

Ortiz has homered four times in that span, including his 10th of the year, making it 16 straight seasons of double-digit home runs for the 39-year-old slugger. His slash line is .324/.444/.649/1.093 in that span -- by far his best stretch of the season -- and he leads the club in home runs and RBIs (10) over that time frame.

Ortiz is not alone in getting hot: Five Sox players since that date are hitting .300 or better, led by Mookie Betts, who is batting .556 in that span and on Monday was named the American League's Player of the Week. The others are Pablo Sandoval (.429), Blake Swihart (.360) and Brock Holt (.356), with Betts and Holt forming a dynamic combination at the top of the order now that Betts has been restored to the leadoff spot.

But then there is the other side of the equation, the team's pitching. The Sox enter the Orioles series with a 4.27 ERA in June, which ranks 26th in the majors and is well above the average for the month (3.74). That is not what Henry had in mind when he said, "I probably feel better than our fans do" about the quality of the arms the Sox are running out to the mound.

Here again, there are signs that Henry's outlook was not entirely misguided. Boston's rotation this month has a collective 8-6 record and 4.09 ERA, a number that would be even better if right-hander Rick Porcello was not enduring by far the worst slump of his career, one in which he is 0-6 with a 7.50 ERA. Only two starting pitchers in baseball, Shane Greene (0-4, 9.43) and Jerome Williams (0-4, 8.67), have been worse than Porcello over his past half-dozen starts.

But the addition of left-handed Eduardo Rodriguez, who was electrifying in his first three starts, has represented a significant upgrade, and Clay Buchholz (2.81 in June), Wade Miley (3.42) and Joe Kelly (3.71), who is scheduled to face the Orioles on Tuesday, have all pitched much more in line with the team's expectations going into the season.

The rush to judgment on Porcello has been fierce, exacerbated by consternation that the Sox signed him to a four-year, $82 million contract extension before he ever threw a pitch in a Boston uniform. Typically, when a pitcher goes into such a dramatic dive, there is a physical reason attached, but all parties involved insist Porcello is healthy. They point to an eight-inning outing June 3 against the Minnesota Twins -- in which he allowed just two runs but lost -- and his first inning June 10 against the Orioles, in which he struck out the side on 11 pitches, as evidence there is nothing physical involved.

Porcello has been prone to the big inning, however. Four times in that six-game span, the opposition has scored three runs or more in an inning, including a nine-run inning May 22 against the Los Angeles Angels (he was charged with seven of those runs), and a five-run inning against the Royals last Friday.

Manager John Farrell has expressed no inclination to drop Porcello from the rotation; he will be given every opportunity to work his way out of the slump. Porcello already has allowed five or more earned runs five times in 14 starts this season; he allowed five earned runs or more just six times in 32 starts last season. The Red Sox never attached the appellation of "ace" to Porcello when they signed him, but the contract has placed that kind of pressure on him; coming to terms with that pressure may hold the key to his returning to form.

Yet for all the recent positive developments around the club -- taking the series from the Royals deflected attention from Sandoval's Instagram antics -- the Sox still have not won as many as three games in a row since the first week of the season. At 31-40, they remain nine games under .500, and in order to win 90 games -- the typical benchmark used to gauge a division contender -- the Sox would have to go 59-31 the rest of the way, a .656 percentage.

And there is this glaring one-two barometer of their performance to date: They have the worst record in the American League against teams with a record of .500 or better (22-36), and they are the only team in the AL East with a losing record in intramural play (10-21). The Tampa Bay Rays, New York Yankees, Orioles and Toronto Blue Jays are all bunched within three games of the division lead; the Sox are nine games back. Their next 10 games come against the Orioles (3-7), Rays (2-4) and Jays (3-6); Boston has been outscored by a cumulative 177-123 margin by its division rivals.

The next 10 games should offer some clue as to whether the Red Sox have any shot to be competitive the rest of the way, or will continue to find creative ways to self-destruct.