BOSTON -- Though the math didn't look pretty for the Red Sox as they got set to open a four-game series with the rival Yankees on Friday night at Fenway Park, manager Alex Cora made it clear that he's not ready to make a concession speech, or anything close to it.

Cora's genuine optimism and belief that his team is still capable of an epic late-season run is admirable, considering the team's baffling inconsistency all season long, not to mention the fact Chris Sale is out for the season and David Price has pitched two innings since Aug. 4.

"I know we haven't played well, but we're still talented. We're still good," said Cora. "We've still got two weeks. We can get on a run. Although you guys don't believe me, but I feel that way. I told the guys today, 'Let's do what we have to do this weekend. We've got to win the series. And we know we have to keep winning series, but if we make it and we play that game, I don't think too many people would like to match up with us in a playoff series.'

"And that's a fact, because we're that talented. [The Yankees] are good, Houston is good, Minnesota is good, Cleveland is good, the A's are good. We're good, too. We haven't been consistent, obviously. But as far as talent, we're still one of the best teams in the big leagues. The thing is, we haven't proved it. That's the difference."

Cora spread that message to his players that there is still time to prove it in an informal setting -- not a team meeting.

With 22 games left in the season, the Sox entered Friday's game trailing the Rays by seven games (six in the loss column) for the first American League Wild Card spot and the Athletics by 6 1/2 for the second spot. Not only that, but they also trailed the Indians by 5 1/2 games.

To play in the AL Wild Card Game on Oct. 2, the Sox would have to vault ahead of two of those three teams.

Even Cora would admit that winning the division is basically a fantasy at this point, given the 16 1/2-game deficit to the team they are hosting this weekend.

"Like I told the guys today, I know where we're at, I know the odds are against us, but whatever percent chances we have, we still have a chance to play them in October -- as of now," said Cora. "So let's not get ahead of ourselves. We're still hungry."

Cora continues to feel the respect that other teams have for the defending World Series champs.

"We know where we're at and for everything I heard around the league and whoever we play, [Twins manager] Rocco Baldelli told me, 'I'll see you in a month.' I don't think he's planning on going on vacation to see me," said Cora.

But if Cora wants to avoid starting his vacation at the beginning of October, his team will need an historic finish.

Health updates

Price would have started Friday night's game if not for the recurring discomfort he felt in his left wrist in a bullpen session on Wednesday. But the lefty was able to play catch prior to the game.

Cora had an encouraging update on reliever Heath Hembree. The righty, who has been out since Aug. 2, was at last able to throw a side session, meaning there's still a chance he can pitch again this season.

"We'll see how he reacts the next few days. At least that's a positive," said Cora.

What about first baseman Steve Pearce, who last played for the Red Sox on May 31?

"Not much. He hasn't been able to run, so I don't want to say we're going to shut it down, but obviously as you guys know, there's no games down there [in the Minors]," Cora said. "It's going to be hard to get him back."

Cora visited with Papi

With Instagram photos surfacing on Thursday of Yankees players Edwin Encarnacion and Gary Sanchez visiting Red Sox legend David Ortiz, Cora was asked if he's had a chance to see his former teammate, who suffered a gunshot wound in the Dominican Republic on June 9.

"I visited David before the road trip," Cora said. "He's in a good place. He looks good. He's watching every game. He's paying attention. I'm glad the boys were able to go over there. A lot of the guys have stopped by throughout. A lot of energy. Obviously he lost some weight. He's back to eating mangu and salami and all of that good stuff. He's in a good place."