"He was the guy that would challenge [you], even when you were doing well," Miller said. "Even if I had a no-hitter -- which I threw about three of them in high school -- he was always, 'Great game, but what about the walk in the second inning? What happened there?' He always made a good point: Strive for perfection. You are never going to obtain it, but you have to strive for it."
Even when Miller stands on the mound today, he often recalls specific lessons from his father.
As a veteran reliever, Trever has learned to thrive in highly pressurized situations. But he hasn't always been willing to tackle arduous situations.
When he was around eight years old, Miller's baseball team was on the verge of upsetting an opponent that hadn't lost in two years. With two outs and facing a pitcher who had just walked the bases loaded, young Trever stepped to the plate in what he deems the "perfect situation to be a hero."
Except it never came to be. Looking for a walk, the youngster watched two pitches go down the middle of the plate before swinging -- and missing -- on strike three.
It wasn't until Trever began to quibble on the car ride home, blurting out that he had been hoping to "just walk" like the rest of his teammates, that he saw his father's quiet rage.
"That just set him off," Miller recalled. "He just bent the steering wheel in half right to him. You could have heard a pin drop in the truck after that. I think you heard somebody breathing. My sister was like "What did you just do?"
After he calmed down, Terry had a talk with his son, sharing a lesson that Trever will never forget.
"He said, 'You don't walk at this level. You swing the bat,'" Miller recalled. "That's the only way you are going to get better, swing the bat, take the chance."
Over the years Miller has learned to call those chances his "rocking chair" moments.
"Never be afraid of the rocking chair moment," he said. "Which is bases loaded, [Boston's] Manny Ramirez at the plate, the game on the line. Don't be afraid to go out there and succeed, because if you are successful, you'll have that rocking chair moment. Just sitting around with your grandkids, saying, 'Let me tell you something about your grandpa'.
"So I'm not afraid of that moment. If I fail, I fail, but I want to be out there in that situation. And I think that started from that moment on."
Even today, Trever still finds himself in awe of his nearly 60-year-old father.
Terry has had a multitude of knee problems, including two knee surgeries and an extensive procedure involving flipping the arteries to allow smoother blood flow.
"His legs look like a road map and he never complains," Miller said.
The left-hander likens his father's fighting spirit and "never be satisfied" mantra to himself, and that of his daughter, Grace Elizabeth, who has a rare genetic disorder.
"I can say that, honestly, he was my hero when I was a little boy, and he still is today," he said.