Often, it has simply been a matter of sheer superiority in talent, size and speed. And on more than a few occasions, an uncanny Luck o' the Irish.
But whatever made the difference, for 43 years that difference has always fallen on the side of Notre Dame whenever the Fighting Irish and Navy lined up against each other.
Tomorrow in South Bend, Ind., Navy tries once again to break the longest stretch of domination of one team over another in the Division I Football Bowl Subdivision.
Because Notre Dame is struggling through a 1-7 season, some believe the high-scoring Midshipmen (4-4) have one of their best chances to lift that increasingly burdensome yoke.
Roger Staubach, the quarterback in the Mids' last victory over Notre Dame, on Nov. 2, 1963, doesn't necessarily think Navy needs to beat the Irish to validate its football program. But, he said, "It would be nice to get this monkey off our back so we wouldn't have to talk about it every year and we could talk about the other great things Navy football has done."
Pat Donnelly, a running back who scored two touchdowns for the Mids in the 1963 game, can't believe Navy has been winless in the series since. "You would think that in 43 years you'd get a break one way or another that would allow you to win a game," he said.
Staubach was in the midst of his Heisman Trophy season and Navy was on its way to a No. 2 ranking and an ill-fated showdown with Texas in the Cotton Bowl for the national championship.
Back then, Donnelly said, Navy could look most major football programs in the eye in terms of size and speed.
"It was pre-Vietnam and pre-spiraling salaries in professional football, so Navy could compete in recruiting players," said Donnelly, who worked for Staubach's real estate company after serving more than 23 years in the Navy in civil engineering.
Retired Rear Adm. Tom Lynch, Staubach's center on the 1963 team, recalls the size issue somewhat differently. Players in big-time programs were still bigger than Navy players back then, Lynch said. He was 6 feet 1 and 225 pounds and was among the three or four biggest players on the team.
But Lynch did identify a difference that leveled the playing field somewhat for the Mids - one-platoon football.
"In those days, your best 11 players were the first string, period, on offense and defense, and the next 11 best were the second string," said Lynch, who remains busy as a consultant to the Staubach company, working in private investment and as an executive with a synthetic turf company. Navy's starters could match up with many teams' starters back then, Lynch said, but when depth became a factor, even the esprit de corps that the Midshipmen brought to the competition made it difficult to keep up.
By 1997, when Navy came within a yard of beating Notre Dame again, the differences between the two teams had become significant. Chris McCoy, who quarterbacked the Navy squad that fell a few feet short when receiver Pat McGrew was pushed out of bounds near the 1-yard line on the game's final play, said the Irish outweighed the Midshipmen 30 to 40 pounds a man in that game. Still, Navy dominated statistically and led from the first quarter until just six minutes left to play, when Notre Dame went ahead 21-17.
With the ball at the Irish 29 and time running out, McCoy threw to McGrew, who was just barely beaten to the end zone - and stopped short - by future NFL player Allen Rossum.
"Fortunately or unfortunately, I remember everything about that game," said McCoy, who spent five years in the Navy, lives in Severn and manages the Cross Keys complex in North Baltimore.
"From a player's point of view, it can be a life-changing game, and, hopefully, we'll defeat them this year. If you can win that game, after all these years, it cements your place in Navy history."
McCoy believes that had Navy won that day 10 years ago, it would have propelled the Mids into a bowl game. In turn, that might have been enough to get him a shot at the NFL as a quarterback. Instead, he was signed as a free agent by the Green Bay Packers and switched to running back, where he had little chance of making it as a pro.
"I do believe that one game could have changed my life tremendously," McCoy said, "and it's heartbreaking."
Over the decades, there have been many such heartbreakers. In 2003, a partially blocked Notre Dame field-goal attempt at the gun fluttered through the uprights, giving the Irish a 27-24 win. The year before that, in Baltimore, Navy - a 28-point underdog - had an eight-point fourth-quarter lead but was overtaken in the last 4 1/2 minutes. In 1999, a controversial spot on a fourth-down play that went in favor of the Irish kept Notre Dame's game-winning drive alive. In 1984, Navy lost by a point. In 1976, it was by six.
But as a rule, the scores have been one-sided.
So why play this game year-in and year-out?
In part, Notre Dame does it as a continuing thank you, a gesture of gratitude for the Navy having used the South Bend campus as a training facility for officers during World War II, a move that kept the private Catholic university going at a time when its regular students were off at war.
The Naval Academy does it because of shared values, such as academic excellence, sense of duty and work ethic, Lynch said. And one more thing.
"We are training our Midshipmen for leadership and leadership, many times, in combat," said Lynch, the former center who went on to become the superintendent of the Naval Academy from 1991 to 1994. "And in combat, you're not always going to have as many resources as the people you are engaging - but you still have to engage them.
"So I feel it's valuable to play Notre Dame," he continued, "because in many ways, athletically, they are considered the best. So, you want to play the best, and this is the one opportunity we have to do that."
After 43 years of consecutive losses, Staubach is treating the prospects of a win this year gingerly. "All these Notre Dame guys keep calling me and telling me this is our year, this is our chance, and I think they are trying to psych me out," he said.