Only twice in 20 years has Columbia's football team beaten Harvard, and only once in 25 games away from Cambridge. The Lions last won more than three games in a season in 1971, and they've won a total of 17 games in the nine years since. That's really all you need to know about Columbia football.

Tomorrow, the Crimson opens the 1981 season against a team riding a 12-game Ivy losing streak, a team coach Bob Naso admits "can't help but be better" than last season's 1-9 edition. Perhaps Naso's optimism is founded on the loss of 25 lettermen, including a big chunk of the Ivies' worst defense. Perhaps Naso expects miracles from sophomores like quarterback John Witkowski and running back Jim McHale. Perhaps Naso is just talking like a football coach and really doesn't expect his team to be better at all.

But any team that loses 25 lettermen has to be different, if not better. In fact, Harvard may recognize friendly Baker Field--where it is 10-1 since 1956--more easily than the Columbia team will.

And Harvard will be different, too. An all-new offensive line, where Steve Piurkowsky beat out the only returning starter, John Fancis, at center, will protect newly positioned quarterback Ron Cuccia. New split end Paul Scheper, new flanker Steve Bianucci, and perhaps new halfback Jim Acheson will catch Cuccia's passes.

On defense, four new linemen join Justin Whittington, while new linebacker Marc Mills has to fill the cleats of the departed Bob Woolway. Even the kicker, sophomore Jim Villaneuva, is new, and he will do the punting, too. Definitely not old hat.

With all this novelty, a Crimson rooter looking for a familiar face on which to cast his eyes will probably seek out coach Joe Restic, starting his eleventh season as Czar of the Multiflex. Restic has obviously been a successful Liontamer, with the only blot on his 9-1 career mark the 21-19 defeat in Cambridge two years ago.

Restic also talks like a football coach, and therefore he is taking them one week at a time, and this game is as important as any other. It may be as important, but it won't be as difficult, and the prediction here is while the rest of the Ivy League is standing toe-to-toe slugging it out on Opening Day. Harvard will kayo its featured opponent early, with the sophomores around to mop it up in the fourth quarter. Quarterback Cuccia has never lost a game in his life starting at that position, and the streak won't be in danger this week. HARVARD 35, COLUMBIA 7.

*******

The rest are a bit harder.

CORNELL at PENN: Big Red coach Bob Blackman loves to sing his song of woe, then change his tune every week after a "surprise" win. This year the woe may be real with 33 lettermen gone, including almost every starter. Still, you can't tell me there isn't enough left to beat Penn, a team that topped only Columbia a year ago. Sorry Bob, it just won't work. CORNELL 20, PENN 13.

PRINCETON at DARTMOUTH: Princeton is the sleeper in the Ivies this season, a team that figures to be pretty good, and just might be real good, Dartmouth is the kind of team that gets better as the year goes on (that seems to be true in almost every sport for the Green) and it hasn't beaten Princeton since '78. I go with the Tigers big, PRINCETON 28, DARTMOUTH 3.

BROWN at YALE: Brown never beats Yale these days, but every other year they come close. Four years ago it was 10-9, two years ago 13-12. I'm betting the Bruins can bounce back from last year's 45-17 disaster and give everybody's choice for Ivy champs a ballgame. They won't win, but Hank Landers to Steve Jordan will scare the Elis, and Rich Diana will have to hustle. Call it this close: YALE 17, BROWN 14.

Record to date, 0-0, .000. Ah, perfection.

THE CUBE TOP TEN

1. Oklahoma