And he doesn't mind admitting he was slightly embarrassed when no team in baseball claimed him off waivers, and every organization passed on him during the Rule 5 Draft.
Truth be told, it was one of the toughest periods of Martinez's life. But he refuses to forget it.
"I think about it all the time," Martinez said. "I went from being released to where I am now. It's unreal."
By now, Martinez has told the story hundreds of times.
While watching his then-teammate Jason Castro take batting practice in Toronto late in the 2013 season, the then-26-year-old Martinez made an abrupt decision to revamp his baseball swing.
It was a radical move for Martinez, a 20th-round Draft pick in 2009, who was built like a baseball-crushing machine, but never quite lived up to his run-producing potential in Houston.
After hitting just 24 home runs and batting .251 in parts of three seasons with the Astros, Martinez took notice of Castro's uppercut swing, and -- with the help of longtime Astros bullpen coach Javier Bracamonte -- slowly applied a similar form to his own swing.
It was a high-risk gamble that would pay off down the road. But the Astros grew impatient.
Despite losing at least 106 games in three straight seasons, Houston's farm system was stocked with high-profile prospects. With playing time at a premium, Astros general manager Jeff Luhnow called Martinez into an office at the team's Spring Training facility in Kissimmee, Fla., before the 2014 season. Martinez was told to pack his bags.
"I couldn't believe it," Martinez said. "I mean, they just didn't have a spot for me."
But the Tigers did.
Within hours of being released, the Tigers -- as well as the White Sox and Mariners -- reached out to Martinez and his agent and inquired about the free-agent outfielder.
Martinez was particularly fond of then-assistant general manager Al Avila, who had known Martinez since his playing days at Nova Southeastern University in Fort Lauderdale, Fla. He also had a special relationship with Tigers third-base coach Dave Clark, who had coached him for three years in Houston.
"Detroit was the perfect fit," Martinez said. "It just seemed right from the start."
Forty-eight hours after being given his unconditional release from Houston, Martinez and the Tigers had inked a Minor League deal. The rest, as they say, was history.
In just three seasons with the Tigers, Martinez has made himself into a household name, thanks largely to a picture-perfect swing that has turned him into one of the best hitters in baseball.
Once viewed as an underachiever in Houston, Martinez belted a team-high 38 homers and knocked in 102 RBIs last season to become the first Tigers outfielder to drive in 100 runs in a season since Magglio Ordonez in 2008.
Only five other players in Tigers history had achieved the feat of 38 homers and 100 RBIs before him. The others include Hank Greenberg (four times), Cabrera (three times), Cecil Fielder (twice), Rocky Colavito and Norm Cash each once.
"I am humbled by it," Martinez said at the time. "From a year ago today, it's been quite a change. It's something I always believed I could do. I just feel blessed."
After hitting a combined 24 homers in parts of three seasons with Houston, Martinez fell just two homers shy of becoming the seventh player in franchise history to reach the 40-homer mark.
In turn, he was named to his first All-Star Game and gifted several awards and honors, including his first career Silver Slugger Award. It was a breakout season for Martinez, who wasn't bent on revenge, but he was certainly motivated to prove critics wrong.