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6/17/2014 7:58 P.M. ET

Gwynn remains Strasburg's favorite player

WASHINGTON -- Stephen Strasburg was 4 years old when he first watched the Padres play. It took him just one game to pinpoint his favorite player: the team's hard-nosed, uncompromising right fielder wearing No. 19, Tony Gwynn.

More than a decade later, Strasburg earned a scholarship to play for his hometown university, San Diego State, where Gwynn -- who died Monday at age 54 -- was the head coach. The Nationals right-hander then lived out the dream of every young athlete across the world, gaining wisdom from his lifelong hero and one of the greatest baseball minds to ever play the game.

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"I was a fan first," Strasburg said while addressing the media for the first time since Gwynn's death. "It just so happens that our lives seemed to intertwine."

Strasburg arrived at San Diego State in 2007, and the first time he met with his new teammates and Gwynn -- who had just been voted into the Hall of Fame in his first year of eligibility with more than 97 percent of the vote -- the baseball legend had a unique message.

"One of the first things he said was, 'Yeah, I'm going to the Hall of Fame this year, but I'm just your coach,'" Strasburg said. "There's so many things that I'm never going to forget."

Strasburg absorbed much in the art of baseball from Gwynn during his time at San Diego State, and he developed into a No. 1 Draft pick for the Nationals in 2009. But when asked to reminisce about the things he learned from Gwynn, Strasburg did not mention any skills particular to the game. The lessons Gwynn instilled in him were much larger than that.

"It started with just how to be a man, how to handle the ups and downs, and not everything goes your way in life. … I struggled with that," Strasburg said. "He really helped me understand that it's not necessarily the results; it's the work you put in every single day. That's what matters at the end of the day: that you give it everything you've got."

Gwynn became family to Strasburg over the years: a mentor, a best friend and a brother. When Strasburg made his Major League debut in June 2010, Gwynn was in the stands sitting next to the pitcher's great uncle, making sure to describe in detail everything that was happening on the mound.

"He wasn't going to miss that," Strasburg said. "And I thought it was just such a special experience for my family, specifically, to be there watching it, my debut, with this legend back in San Diego."

Strasburg said seeing Gwynn became tough over the past few years, largely because of the Hall of Famer's ongoing battle with salivary gland cancer. Last offseason, Strasburg said he saw Gwynn the least out of any year in which he had been in the Majors.

Nonetheless, Strasburg was able to smile Tuesday while recalling his time with Gwynn: once a coach but forever his favorite player.

"He's impacted so many players," Strasburg said. "And I'm just so blessed to be one of them."

Harper takes step toward full batting practice

WASHINGTON -- Nationals left fielder Bryce Harper hit with two hands on Tuesday for the first time since tearing a ligament in his left thumb, manager Matt Williams said. Harper sustained the injury while sliding into third base against the Padres on April 25.

Williams said Harper took soft toss in the cage as part of his continuing rehab program, and he hoped to get the slugger on the field in the next few days to evaluate the progress.

Harper, who had been doing one-handed work with a bat in the cage in recent weeks, reported no thumb pain to Williams after his two-handed batting session Tuesday. When the two sat down to talk, Harper said he felt ready to take the next step.

"It's not full go, and it's not real, full batting practice yet, and you need that," Williams said. "But he's excited about the progression of it moving forward. It won't be long."

Williams said the team targeted a return date after July 1 if Harper's rehab continued to go well. But it depends on how the injured ligament reacts when Harper takes real batting practice.

General manager Mike Rizzo said he did not anticipate making any trades or dramatic roster moves upon Harper's return.

"These things usually have a way of taking care of themselves," Rizzo said.

Worth noting

• Nationals left-hander Gio Gonzalez (shoulder inflammation) on Wednesday against the Astros will make his first start since May 17. Williams said Gonzalez threw a bullpen session on Monday without any discomfort.

• Pitcher Bryan Harper, Bryce's brother, has been promoted to Double-A Harrisburg from Class A Advanced Potomac, where he went 1-0 with a 2.59 ERA over 31 1/3 innings this season.

Daniel Popper is an associate reporter for MLB.com. He also can be found on Twitter @danielrpopper. This story was not subject to the approval of Major League Baseball or its clubs.