"I told him, 'These next six weeks may be the one chance you get in your whole career,'" the old man of the Boston Red Sox said he told the 25-year-old rookie first baseman. "'Make the most of it.'"
Ortiz shared his own experience, of how the Red Sox had given him barely 100 at-bats in the first two months of the 2003 season, projecting him as little more than a backup to Kevin Millar (!) and Jeremy Giambi (!!), before Giambi washed out. Ortiz hit 29 home runs and drove in 82 runs in his last 97 games, the gestation period for Big Papi, the larger-than-life slugger.
"He told me, 'Make the most of the opportunity, you've opened some eyes here with how you've played,'" Shaw said. "He said there was no reason I can't keep going and grinding with this opportunity, and force their hand in the future."
Consider their hand forced. One night after the Sox set in motion plans to make a first baseman out of Hanley Ramirez, woefully miscast as an outfielder, Shaw broke a scoreless tie in the eighth inning with a two-run home run, lifting the Red Sox to a 3-0 win over the White Sox.
Shaw now has seven home runs in his first 93 at-bats in the big leagues. The first 15 of those at-bats came over the course of four separate callups, two of which lasted just a day. But since Mike Napoli was traded to the Texas Rangers at the July 31 trading deadline, Shaw has started 18 of the next 21 games, and this week was promoted to the No. 5 spot in the lineup, batting behind Ortiz.
He is batting .333 (26-for-78) this month with all seven of his home runs and 18 RBIs, and is slugging .667.
"I feel like I've been sort of overlooked at different levels -- doubted, you could say, it seems at each level," Shaw said Wednesday afternoon. "'This is his ceiling, he can't do anymore,' and I feel like so far I've broken through every barrier, and that's something I pride myself on.
"It puts a chip on my shoulder, that I want to prove everybody wrong. I just continue to work hard, trying to work hard to prove people wrong, even at this level."
Shaw, a ninth-round draft choice out of Kent State University in 2011, has never been a name featured on the top prospects lists, especially last year, which he began by going back to Double-A Portland for a third time.
"Part of me was hoping I'd start 2014 in Triple-A," he said. "I was coming off the great Fall League I had [a .361 average and five home runs] and thought that might be enough to push it on through . But I didn't, and went back to Portland. When they sent me back to Double-A, I need to get it going, because you run out of chances. When that happened, from that point on it was all right, I need to push my way back onto the scene."
There has been a benefit, he said, for making it to the big leagues on something other than a fast track.
"Failure is such a huge part of this game," he said. "Going through failure at some point in your development is key. I did it for a whole year in 2013.
"Now I know who I am as a hitter. I know the checkpoints to get back to where I need to be."
His one-on-one session with Ortiz, he said, served to buttress his confidence that his success makes him more than just a flavor of the month.
"I took it as a sign of respect," Shaw said. "You watch how he conducts himself, he's very helpful to young guys, but he doesn't say a whole lot, he doesn't approach a lot of guys.
"When he called me over and we had that 10 or 15 minute conversation, after the fact it meant a lot to me, that he wanted to talk to me and wanted to share that information."
The Red Sox have every reason to want the Ramirez experiment to succeed. They are a superior team defensively when Mookie Betts, Jackie Bradley Jr. and Rusney Castillo comprise the outfield, and the Sox are on the hook for $66 million over the next three years to Ramirez. Shaw, by contrast, is cheap labor.
That's why something else Ortiz said stuck with Shaw.
"I told him to come to camp next year ready," Ortiz said. "Ready to play from the first day. Pitchers don't know him now, but next year they will be studying video, reading the reports, they will be ready for him. He needs to be ready for them."
Shaw has five more weeks this season to show what he can do. How well he plays could impact on how the Red Sox view the Ramirez experiment, and whether they will go into the winter looking at Shaw as a viable option. Having grown up in the game -- his father, Jeff, pitched 12 seasons in the big leagues and was an All-Star with both the Reds and Dodgers -- Shaw has a head start on understanding how the game works. What he's done so far is a great starting point; whether he can sustain it will determine if he sticks.
"Mentally you can't come to camp putting pressure on yourself," he said. "I know what I can do and I've learned to control the things I can control, not look at outside things.
"Obviously, there's the Hanley thing. Now that Hanley is playing first base, I'm not going to look at that. I'm just going to worry about what I need to do. I know if I keep playing the way I've been playing up here, I'll be in a good spot, whether it be here or somewhere else. I know what I need to do. I won't be worried about [Ramirez]."