The problem: He can't really come up with anything that has come close.
He has never pitched in a minor league playoff game or anything remotely reminiscent of one.
He was called up to Double-A for one game in 2014, but by the time he made his first outing for Binghamton, the team was already looking like a lock. Fulmer did not pitch particularly well in his sole appearance -- which came against the Tigers' Double-A club Erie, coincidentally -- and his presence within the clubhouse was short-lived. He was still able to partake in the festivities a few days later when the team clinched, but he never got to pitch in the postseason. He instead underwent season-ending elbow surgery in August of that year.
"I didn't throw well that game, but I got to celebrate with the team because I hadn't gone to the hospital yet. That's the fun part. You've got to do that," Fulmer told ESPN.com. "I haven't pitched in a playoff game or anything close to a last-week-of-season-and-we're-still-in-it type of feel, or we're-only-one-game-out this and that. I haven't done it."
Unlike, say, 33-year-old Justin Verlander -- who has a proven track record of thriving under the spotlight and is known for his propensity to step up when the situation requires it most -- Fulmer is still a bit of an unknown commodity in that respect.
The sensational 2016 campaign Fulmer has put together (10-5, 2.69 ERA), which places him firmly as the front-runner for American League Rookie of the Year, certainly will lend people to believe that he possesses a poise and presence on the mound -- not to mention talent -- well beyond his years. That bodes well for the 23-year-old in the pressure-cooker atmosphere of a pennant race, but success is not a given. No one predicted Fulmer would have this level of success heading into this season. Now, the Tigers will probably have to depend on it to make it to the playoffs. That's an entirely different level of expectation.
The Tigers and their fans stand to learn more about the precocious young pitcher as the stakes are raised with each start.
"If nothing else," Tigers manager Brad Ausmus said, "it will be a good experience for him."
Fulmer himself is looking forward to finding out how he responds to the challenge.
"I'm excited for it," Fulmer said. "I'm not in any way feeling extra pressure. I think once I get on the mound, it will kind of be like my debut, honestly. Once the nerves are gone after that first pitch, you've just got to pitch."
The Oklahoma City native said he plans to pick the brains of his veteran teammates -- particularly Verlander -- for advice rounding into the last stretch of the season. If they have tips to offer, or have any idea of what they would have done differently in retrospect, he will gladly gobble up those kernels of wisdom.
Until then, he's more preoccupied with making improvements on his past two starts, outings which he admitted "weren't my best." He gave up a combined nine runs on 15 hits in 10⅔ innings, with an ERA of 7.59.
Fulmer insists that neither performance was a result of extra pressure, but rather a mechanical issue. After a bullpen session this week, Fulmer is confident that issue has been tweaked with help from pitching coach Rich Dubee.
His next start is Saturday in Kansas City, and he will see if his findings prove productive. Mechanical issues notwithstanding, Fulmer is now contending with another complicating variable -- as are the Tigers.
In the short term, the team needs him to pitch well to make the playoffs. However, the organization also wants to be prudent with his workload -- Fulmer is currently at 130⅔ innings, in addition to 15⅔ in the minors prior to his call-up -- to prevent overuse or potential injury that could jeopardize his long-term future.
The club plans on monitoring his innings moving forward and using off days to provide optimal rest.
Before Fulmer's last start, he had last pitched eight days prior -- his longest layoff between starts this season, besides the All-Star break. He will make his start against the Kansas City Royals on extra rest, as well, which can have an impact on his rhythm and routine -- even if his numbers generally suggest he performs well on extra rest.
"[Whether] numbers say it or not, any time you get out of rhythm, get out of whack a little bit, you don't feel as sharp on your start day," Fulmer said. "Obviously, your fifth day, when you're in a [five-man] rotation, is when you feel the sharpest. When you have a routine and you stick to that when you go to a sixth day, it's OK. You can find something to do for an extra day.
"But when you start getting to seven or eight [days], I've got to find something that works for me. Whether or not I like it or not, I have to find a way to get it done, because I can't make any excuses going out on my start day. After all, I'm healthy and I'm able to pitch, so that means I should be pitching and putting up zeros and getting some wins."
Hopefully, Fulmer said, that happens Saturday.