David Ortiz had a double, but the Sox offense was otherwise hardly worthy of the term. (AP)

A steady drumbeat of offense proved a hallmark of the Red Sox’ march to the best record in the American League. Through the team’s first 65 games, the Sox led the American League with 5.3 runs per game, with regular yields of six or more runs.

But of late, the supply of runs has diminished. That trend continued on Wednesday, as the Sox were subdued by Jeremy Hellickson and the Rays in a 6-2 loss. The Sox have now scored five or fewer runs in each of their last nine games — their longest such streak of the year — while averaging exactly 3.0 runs per contest, 12th in the AL in that stretch.

The result? A sideways 4-5 stagger through games against AL East foes.

WHAT WENT WRONG FOR THE RED SOX

– Although he turned in a solid outing, Ryan Dempster labored through his first inning. He allowed two runs (both earned) coming on three consecutive hits. Desmond Jennings, the second batter of the game belted a ball over the Green Monster. Ben Zobrist and Evan Longoria then strung back-to-back singles together, with the second run coming on a James Loney sacrifice fly.

Dempster continued to be home run prone this season, now having given up 16 on the year, which is tied for third most in the big leagues. In addition, Dempster has had his struggles with the first inning long ball, as Jennings’ blast was the fifth home run Dempster has surrendered in the first inning.

Still, although Dempster was saddled with the loss, dropping to 4-8, his yield of three runs in six innings gave the veteran his ninth quality start in 15 outings this year, a 60 percent rate that is third best on the team behind Clay Buchholz (83 percent) and John Lackey (63 percent).

– Jose Iglesias had a tough night all-around, going 0-for-2 (with a walk) to snap his 18-game hitting streak and making his first error on the season. The error came when a Jonny Gomes throw from left field skipped by the usually sure-handed Iglesias, allowing Longoria to advance to second base following his single in the first inning.

– Mike Napoli’s struggles in June continued as he went 0-for-4. In his last 11 games (since June 4th), Napoli is hitting just .167 with a .311 OBP, .194 slugging percentage and has struck out 16 times in 44 total plate appearances.

WHAT WENT RIGHT FOR THE RED SOX

– Jonny Gomes delivered a pair of RBI infield singles, both in the direction of Rays third baseman Evan Longoria. In his last eight games (six starts), he’s now hitting .379/.379/.655.

– Jacoby Ellsbury continued his outstanding June, delivering a pair of hard singles to improve to .333 with an .848 OPS in June.

– Jarrod Saltalamacchia, who entered the game mired in a 2-for-22 slump, blasted a double off the wall in center, his first extra-base hit in seven games. He did, however, strike out in his other three at-bats, giving him 12 punchouts in his last 28 plate appearances. More impressive than the hit was the catcher’s line was the fact that Saltalamacchia was playing at all, given that one day earlier, he became the first Red Sox catcher to start both games of a doubleheader since John Marzano in 1992.

Griffin Tewksbury contributed to this report.

Left-hander Trey Ball was taken by the Red Sox with the No. 7 overall pick (New Castle High School)

Red Sox first-round selection Trey Ball made his first of what he hopes are many visits to Fenway Park on Wednesday afternoon prior to the Red Sox game against the Tampa Bay Rays.

The Red Sox selected Ball with the seventh overall pick in the 2013 Major League Baseball draft earlier this month. Ball, a high school pitcher from Indiana, will be sent to Fort Myers, where he will pitch in the Rookie Level Gulf Coast Red Sox.  But first, after signing on Wednesday for a $2.75 million bonus, Ball spent a day at Fenway Park with his family.

“It’s been amazing,” Ball said of his first trip to Fenway. “It’s been a great experience. I love the city.”

During his first trip to Fenway, Ball walked through the clubhouse, played catch with Clay Buchholz and took in batting practice in right field alongside John Lackey. Ball, a 6-foot-6 left-hander, was easy to distinguish on the field. The New Castle (Ind.) High School alum stood out both for his knee-high socks and wore his socks and the fact that, relative to the big leaguers with whom he one day hopes to play, he is rail thin.

Ball took a few minutes after batting practice to address the media. But first, the 18-year-old received an introductory “greeting” from some of the players.

Ball named second baseman Dustin Pedroia as the leader of the verbal abuse, but added, “They were just giving me a hard time. It was a good time.”

Red Sox manager John Farrell spoke of Ball’s presence among a clubhouse of major league players.

“I think he got a taste of some of the guys in our clubhouse too. And to his credit, he handled it great. You’ve got an 18-year-old kid who walks in with a jacket and a tie, who obviously comes from a good family. You can see that. And he did his family proud,” Farrell said with a grin, “given what he heard.”

General manager Ben Cherrington also spoke of Ball’s makeup prior to the game and cited it as one of the main reasons for selecting him with the teams first pick.

“When you go through the checklist of things you need to see in a high school pitcher to invest a first round pick in, he just checks all the boxes,” said Cherington. “He’s big. He’s athletic. We got to know him really well. This is a good kid, great work ethic, highly competitive. He’s got the makings of three pitches. Obviously, it’s a high school pitcher so it’s not going to be a particularly quick path, but we think he has a chance to be really good one day and we’re excited about watching him.”

The sentiment was reciprocated. Ball, who wore No. 24, was asked about what it felt like to wear a Red Sox jersey for the first time.

“It feels amazing,” he said. “It’s a dream come true.”

After belting a two run-walk off home run in the ninth on Tuesday, Jonny Gomes gets the start in left field as the Red Sox look to sweep the series from the rival Rays.

Jose Iglesias, who went 1-for-3 in game two of Tuesday’s double header, remains in the lineup and enters the series finale with a .435 batting average on the year.

According to multiple industry sources, the Red Sox’ deal with first-round pick Trey Ball is in the last stages before becoming official. The No. 7 overall pick in the 2013 draft is expected to sign today, with a media introduction to follow.

UPDATE, 4:12 p.m.: The deal is now official. Ball signed for a bonus of $2.75 million, nearly $400,000 less than his $3.246 million slot recommendation at the No. 7 pick.