"The thing my dad's always told me more than anything over all these years is to stay loose, relax and try to have fun," Dellucci said.
So when his dad, Michael, saw him struggling earlier this season, he knew the problem; David, feeling the pressure to impress a new club, wasn't enjoying himself enough.
"When I watched him on TV, he was just so serious," Michael said. "I could tell by his face. He was just very, very serious."
Something had to be done.
"I kept calling him to remind him to have fun," Michael said. "I can tell by his face if he's smiling and having fun. He's doing that now, and that makes me feel good."
It's just the kind of guidance that Michael has lovingly offered his son for years, the kind that's cast David into the player he is today.
"He's been wonderful," David said. "He taught me an awful lot just through watching him and the amount of respect and care he showed everyone. So a lot of those lessons, about being a good person on and off the field, came through baseball."
And they started early.
When David was seven, his first year of organized ball, his dad had to teach him a few things about teamwork. David, you see, may have been having too much fun. Playing center field, he fielded a single up the middle and sprinted home. David was trying to tag the runner scoring from second.
Dad explained to David that baseball was a team game and thought that would be it. But then the same play arose a few innings later, and David again ignored the catcher and dashed to the plate himself.
"He was just thrilled by the excitement," Michael said with a laugh. "But I had to chew him out, I guess."
And from then on, David played along with his friends.
More than a decade later, David points to a similar talk from his father following one of his college games at the University of Mississippi.
Before the game, David was as locked in as ever during batting practice. Every swing seemingly brought an arcing drive over the right-field wall. The pregame power exhibition was so impressive that David could not stop talking about it afterward. Even after an 0-for-4 night, he bragged to his dad.
"Did you see my batting practice? Did you see how far I was hitting the ball?" David recalled telling him.
Dad simply responded: "Son, it doesn't count -- batting practice. It only counts when you do it in the game."
The talk changed everything.
"That kind of refocused my attention at that period of my life in college," David said. "It kind of set me straight a little bit. And pretty much, my college career took off right then. That was a defining moment for me."
Dad's statement wasn't harsh. David knew what he meant. It was the words of a man who only wanted what was best for his son. The words of a man whose work never allowed him to play sports as a child and who wanted every opportunity for his child.
And besides, the two were back to joking around a few minutes later.
"He's just been so wonderful, even now in my career," Dellucci said. "He's the person I'll still call for advice, whether it's in life or in baseball. He's absolutely been great."