David Price dealing with split fingernail on pitching hand

David Price has pitched past the sixth inning in just one of his six starts this season.Barry Chin/Globe staff

Even on a night when David Price put together six strong innings, he walked off the mound with another problem to deal with.

Price threw 103 pitches over six innings in Saturday’s 6-3 loss to the Angels.

When he returned to the dugout after what was his final inning, he pulled pitching coach Carl Willis aside to talk privately in the hallway leading to the Red Sox clubhouse.

As it turned out, Price had an issue with a split nail on the middle finger of his pitching hand. This comes after the lefthander developed a blister on the ring finger of his pitching hand during his June 8 start against the Yankees.

Price has made six starts since coming off the disabled list on May 29, going 2-2 with a 4.76 ERA.

“While I thought he was still very strong [Saturday] night, felt like it was a chance to hopefully stay ahead of something more severe taking place,” manager John Farrell said. “So he’s dealing with a little bit of a cracked nail on that finger — not the same finger in which the blister appeared on.

“Felt like, this was something that he’s dealt with in the past. He knows that it can lead to something that might affect him more. So to take him out of the game at that time rather than risk further cracking of the nail and further severity to the way it feels, he was out of the game.”

Price has pitched past the sixth inning only once since returning from an elbow strain that forced him to miss the first 49 games of the season. After Saturday’s game, he said he wanted to stay on the mound but understood Farrell taking precautions.

“He’s a fierce competitor,” Farrell said. “He’s of the mind-set to complete and finish games. That’s how he’s wired. That’s how he goes about his work in between starts to prepare for that physically and [I] love that about him. And when you don’t achieve what you’d hoped to — or in that case the length of a game, because I thought he threw the ball with a lot of power last night — he wants more. And we love that about it.”

Farrell said Price will be day-to-day but doesn’t expect the fingernail to be an issue when Price is scheduled to take the mound Thursday against the Twins.

Farrell still adamant

With some time to sleep on his heated exchange with crew chief Bill Miller, Farrell’s thoughts on a balk call that led to his ejection Saturday night didn’t change.

He still firmly believed that Kole Calhoun asked for time out before Miller called reliever Fernando Abad for a balk.

“I saw the video, and I still stand with my position, nothing’s changed,” Farrell said.

Miller made the balk call from third base. From the dugout, Farrell said, it was clear that plate umpire Ryan Blakney had raised his arms to give Calhoun time before Miller’s call.

“Could hear it from the dugout,” Farrell said. “Which again, verbally hearing it after the home plate umpire’s arms were raised — it wasn’t the balk call, it was the timing of it. So to me, that was the issue.”

It was the 17th time in his career Farrell was ejected, the 12th with the Sox (he was also ejected twice as pitching coach).

This was the third time he was tossed by Miller. Farrell said he didn’t realize they had history.

“Honestly, I didn’t know,” Farrell said. “Someone brought it to my attention that’s been the third time. I don’t have a toteboard of who’s done what and how many times.”

Miller said Farrell poked him in the heat of the moment. Farrell said it was incidental.

“I knew there was contact made,” he said. “I didn’t bump him, though. The tip of my finger touched his shirt.”

Even though Farrell and Miller were nose to nose, with spit flying, Farrell said, “I don’t think I erupted.”

Asked if he thought the incident was something that could galvanize the Red Sox, Farrell said the way things unfolded could have a positive effect.

“As quickly as everyone convened on the diamond, everyone saw what took place,” he said. “We saw it from the dugout. So to me, if we’re in unison, I think that can be a benefit. That wasn’t the intent in the moment. It was a disagreement. But if it’s felt otherwise, then that’s a benefit.”

Role players

Coming into the season, the set-up role in the bullpen was up for grabs. As the season’s halfway point approaches, it’s still there for the taking.

Farrell mixed and matched Matt Barnes, Joe Kelly, Heath Hembree, and Robby Scott early in the season.

Barnes emerged as a reliable eighth-inning arm until inconsistency crept in. Now Kelly has become a dependable option, stringing together a career-high 21 straight scoreless appearances, including the eighth inning in Sunday’s 4-2 loss to the Angels.

But Barnes has struggled in his last three outings, giving up as many runs as outs recorded (four), with five walks. And Kelly’s usage is monitored to make sure he doesn’t tax a shoulder that’s given him trouble throughout his time with the Sox.

But ideally, Farrell would like to have the role pinned down.

“When Matt Barnes is throwing effectively as he’s shown, he’s got the stuff to attack lefties and righties with equal ability,” Farrell said. “Joe Kelly, who’s in that spot right now, we’ve got some limitations on the frequency of use. So, yeah, you’d love to be able to say you’ve got a guy identified for the final three innings, but we’ve been in a situation to mix and match a little bit.

“The group out there, the body of work has been very good, very strong. We’re not without some hiccups along the way, but getting Matt Barnes back on track, being as consistent would be important for us.”

More picks in fold

The Sox now have 27 of their 40 draft picks signed after reaching agreements with six more players on Sunday.

They signed third-rounder Brett Netzer, seventh-rounder Tyler Esplin, 11th-rounder Andre Colon, 12th-rounder Beau Hanna, 19th-rounder Angel Gonzalez, and 34th-rounder Luis Torres. Netzer was assigned to Single A Lowell. Esplin, Colon, and Hanna will report to the Gulf Coast League. Gonzalez and Torres will report to the Dominican Summer League.

Rehab on tap

Eduardo Rodriguez (knee) responded well a day after throwing a simulated inning on Saturday and will begin a rehab assignment with Double A Portland on Thursday. He’s expected to throw between 75-80 pitches. The hope is that he will only need one rehab start before returning to the Sox rotation . . . Brian Johnson (shoulder) went through a full bullpen session, throwing all fastballs. On the disabled list since June 15, he’ll go through a progression of bullpen work before beginning a rehab assignment.