Arriving at San Diego State in 2007 out of West Hills High School in nearby Santee, Calif., an unheralded Strasburg was nothing close to what he would become down the road. He moved from setup man to closer as a freshman, finishing 1-3 with a 2.43 ERA and seven saves.
Shedding pounds and a soft label by adding muscle and endurance with a demanding conditioning program, Strasburg busted into the rotation in 2008 and was on his way to stardom, going 8-3 with a 1.57 ERA.
"He didn't understand what he had to do when he came here," Gwynn said. "He didn't understand that to be one of the best, you have to roll up your sleeves and work. He got to work, and his fastball went from 90 to 97 miles an hour [as a sophomore]. That's when the light bulb came on. He said, 'I think I can do this.'
"He went from the eighth inning to closing as a freshman, and we told him his sophomore year that he'd be starting once a week. He kept making progress, and by his junior year, everyone saw how dominant he was."
Strasburg was 13-1 with a 1.32 ERA for the Aztecs as a junior, gaining national attention virtually unprecedented at the time. Bryce Harper, his Nationals teammate, took it to a new level, but as the No. 1 pick by Washington in the 2009 First-Year Player Draft, Strasburg came as heavily hyped as any prospect in history.
"Our pitching coach, Rusty Filter, gets credit for what Stras did on the mound," Gwynn said. "I didn't do much to make him what he became. The athlete puts the work in. To see him now, what he's doing, it's a great feeling."
It was on road trips that Gwynn evidenced Strasburg's emerging fame during his junior year.
"In the past, people would congregate in front of the bus because I was there," Gwynn said. "Now they were coming to see this pitcher they'd heard and read about. We talked to Stephen about the responsibility that came with all this. He has handled things extremely well."
Having just arrived for the festivities, Gwynn had not had a chance to see Strasburg and wasn't sure he'd be able to do so, given the hectic nature of things.
"He sent me a text recently," Gwynn said. "We stay in touch."
Strasburg is one of four former Aztecs in the Major Leagues who were coached by Gwynn. Indians starter Justin Masterson, White Sox closer Addison Reed and Dodgers outfielder Tony Gwynn Jr. all benefited from the master's teachings. His son, of course, is a source of immeasurable pride to Tony Sr.
His trip to Kansas City was Gwynn's first excursion outside San Diego since undergoing surgery on Feb. 14 for the removal of a new cancerous tumor inside his right cheek.
"I'm coming along, doing all right," he said. "My energy's coming back."
He had a malignant growth removed from the same spot in August 2010.
Gwynn regaled an overflow crowd inside the museum with tales from his remarkable career, drawing animated reactions as he recalled memories of his relationship with Ted Williams.
"The 1999 Fenway game has to be my favorite [All-Star Game]," Gwynn said. "Being there with Mr. Williams, after all he'd done for me, had to be the best. My best game actually was in 1994, when I scored the winning run."
He had two hits and two RBIs for the National League that night in Pittsburgh.
Williams, San Diego's eternal gift to the game, convinced Gwynn that with a few alterations, he could turn on inside pitches and unleash some power. Sure enough, Gwynn put the Splendid Splinter's advice to work and became a more dangerous hitter, starting with that 1994 strike season. When it ended in August, Gwynn was smoking hot at .394, convinced .400 was in range.
"Sure, I was going to hit .400 that year," Gwynn said, drawing a response from the museum gathering. "I used to think it would be a contact guy like Ichiro [Suzuki], but Barry Bonds changed my mind, because he walked so many times."
Gwynn had a career-high 17 homers in 1997, batting .372 with 220 hits -- at age 37.
Dodgers superstar Matt Kemp, who happened to be at the museum with agent and former star Dave Stewart, was getting ready to depart.
"Matt, leaving the room, is a guy who's entirely capable of hitting .400," said Gwynn, a .338 career hitter. "A guy like [Albert] Pujols could do it. I think it will happen."