INDIANAPOLIS — Matt Birk has some fond memories of his experiences at the 1998 NFL Scouting Combine following a stellar career at Harvard.

But his first one is his biggest. Huge, actually.

“I was in a van [coming from the airport] and it was just me and Flozell Adams, who was one of the top prospects at the time. Flozell was around 6-7, 330, which is obviously big, but back then in ’98 that was really, really big. I’m thinking to myself, ‘If everybody’s like this guy’s size, I got no shot,’ ’’ Birk said as he laughed at the recollection. “But luckily not everybody was his size.’’

For the record, Adams (nicknamed “The Hotel’’ for his massive size) was drafted in the second round and the offensive tackle went on to earn five Pro Bowl nods in a 13-year career. And that Birk guy? The sturdy center fell to the sixth round and all he did over his 14-year run was earn two All-Pro selections, six invites to the Pro Bowl, and a Super Bowl championship.

Not bad for a guy who arrived in Cambridge with his sights set on an economics degree and no fantasies about playing in the National Football League.

Even through his first two seasons with the Crimson, Birk wasn’t on any NFL radar screens. But he had a breakout junior year — he credits the guidance of coach Tim Murphy and then-offensive line coach Joe Philbin as big reasons for his improvement. Then in his senior year, Birk received “a late invite to the now-defunct Blue-Gray All-Star Game and I think my performance there — I played well enough to earn an invitation to the combine.’’

He arrived at the league’s annual cattle call feeling no pressure to prove anything. After all, he wasn’t living out a dream, because his dreams never involved the NFL. His attitude was to give his best shot and see where it takes him.

“It was just kind of a whirlwind,’’ Birk said. “Back then it was rare for someone from Harvard to be there, so I was little bit of a sideshow. People, were like, ‘Harvard? Really?’ ’’

Now, however, it’s not so rare for Harvard guys to participate in the combine, or the NFL, for that matter.

In recent years, Jamil Soriano, Ryan Fitzpatrick, and Zack Hodges have received the call. The program hit a milestone this year when Harvard became the first Ivy League school with two players invited in the same year. That’s the same number of prospects here from the University of Michigan — and double the amount of kids from the University of Texas.

In talking to some of the Harvard players who have made the trip in recent years, they all pointed to one reason for the uptick in invitations: Murphy, whom Fitzpatrick called, “the driver of the program’s success.’’

Hard to argue there. Since his arrival in 1994, Murphy has led the Crimson to a 156-63 record and has either won outright or shared the Ivy League title nine times. The Crimson are on a run of 15 straight winning seasons.

Fitzpatrick said Murphy’s commitment to recruiting nationally — and internationally — has been one of the biggest reasons for the growth of the program. Fitzpatrick, who has played for six NFL teams, acknowledged he “embarrassingly’’ didn’t realize Harvard even had a football team until he received a recruiting letter in high school.

Now, with Harvard Yard having been the setting for ESPN’s wildly popular “College GameDay,’’ twice, it’s a safe bet every recruit knows about Murphy’s program.

“Coach Murphy has really legitimized the program by providing players with the resources to become successful,’’ said Fitzpatrick, who said the school didn’t have a strength coach when he arrived in 2001. They do now.

Murphy gets the credit from his players, but he deflects it back to the guys who suit up every day.

“We’ve obviously had a lot more really outstanding players in the last 15 years than maybe we did in the [previous] 10 years,’’ said Murphy. “I think there’s a lot more interest in Ivy League schools these days for student-athletes who realize that you can sort of have your cake and eat it too. You can have a world-class education, have a great collegiate experience, and at the same time play a great level of football, and if you’re good enough [the NFL is] going to find you. Whether that means Alabama, Ohio State, Stanford, or Harvard, they’re going to find you.’’

That’s certainly been the case on Murphy’s watch. The coach said the school’s had “30-plus kids sign NFL contracts over the last 15 years and we expect three or four more this year.’’ Some of those players have been invited to the combine, some haven’t.

Currently there are seven Crimson alums in the NFL — Fitzpatrick, Cameron Brate, Desmond Bryant, Nick Easton, Kyle Juszczyk, Tyler Ott, and Zack Hodges. That number is likely to increase by at least two, as current combine participants Cole Toner, an offensive lineman, and tight end Ben Braunecker are legitimate prospects.

“I also think it is a case of success breeds success,’’ said Fitzpatrick, who has thrown for 154 career touchdowns. “Playing football at Harvard is no longer seen as a consolation prize for high schoolers that aren’t good enough to play at the FBS level. Kids are making the decision to go to Harvard knowing that playing at the next level is still possible.’’

And now Toner and Braunecker are the latest Crimson set to take their game to the next level — both are projected to be middle-round selections. Like Birk, and every other Crimson recruit, neither came to Harvard with aspirations of an NFL career.

“Not at all,’’ said Toner, a government major with a 3.6 GPA. “Though it did become a goal by after my sophomore year.’’

Braunecker is a molecular biology major who hopes to one day go to medical school and cure infectious diseases.

“I didn’t go to Harvard expecting to be an NFL player,’’ he said. “I just got good, and then decided, well, I should probably give this a shot. It’s something I love, I’m pretty good at it, so why not?’’

While Harvard kids might be at a disadvantage in some areas when it comes to combine preparation — “A lot of these kids, not the Harvard kids, will actually drop out of school and just train 24/7 and not have to balance the academics,’’ said Murphy — they are used to the combination of the physical and mental grind.

“Part of the point here in Indy is to physically and mentally tax you and see how you perform under those conditions,’’ said Birk. “And I think, certainly, having a pretty robust school schedule combined with football and those demands [helps].’’

As Braunecker said, “You learn a lot about yourself when you’re crushed or pulled apart both ways on the football field, and with a pretty hefty academic load. One of those things I developed from all that pressure was how to dedicate yourself to a task.’’

The task of succeeding in the NFL is something Murphy is confident his charges can accomplish.

“I am a little bit biased, but I think the common denominator with all our players that signed [with NFL teams] — they’ve obviously been great athletes, you can’t get to that level unless you’re a great athlete — but they’re even greater kids and I think that character aspect is one of the things a lot of NFL teams are really trying to identify,’’ said Murphy.

Birk, now the NFL’s director of football development, echoed the sentiments of his old coach when he said, “You know, in football, character always wins.’’

Jim McBride can be reached at james.mcbride@globe.com. Follow him on Twitter @globejimmcbride.