It is distinctly possible that after this week, the Boston Red Sox will never have to play in this Yankee Stadium again.

Then again, after the spring of 1865, Ulysses S. Grant never had to visit Virginia again, either. This is known as going out on top, or at least going out while you're well ahead.

For the vast majority of an eight-decade run, the New York Yankees largely defeated the Red Sox whenever it mattered most, particularly in New York. The record is going to show that all-time at the Stadium, the Yankees lead the series, 483-283. From 1950 to this moment, the Yankees are 283-203 against the Sox in the Bronx. Clearly, a something more than subtle trend had emerged.

But now, as the days of this historic baseball edifice dwindle down to a precious few, the situation has changed in a way that once seemed impossible. To prolong the life of Yankee Stadium, the Yankees would have to reach the postseason. They have been in the postseason for 13 straight seasons. This season, they are in trouble.

As the Red Sox and Yankees begin their three-game series at the Stadium on Tuesday night, the Yankees are a truly distant third in the American League East and they are five games behind the second-place Red Sox. The ironic part of this particular three-game set is that these teams are no longer playing for the primacy of the baseball world. In this case, they may well be playing for the right to finish second to the Tampa Bay Rays in the AL East, and thus have a shot at the Al Wild Card berth.

This late-August series in the Bronx will feature the fundamentally changed circumstances of the two teams -- the Yankees chasing, the Red Sox being pursued.

The Yankees have not won a World Series since 2000. The Red Sox have won two since then, making them the only team with two championships in the that seven-year period. The Yankees have won the last three season series between the two teams, and six of the last seven, but let's make this clear: If New York wins the season series and Boston wins the World Series, the Red Sox have the better season.

The Yankees probably need to sweep this series to keep their postseason hopes intact. The Red Sox can't afford to let that happen, not only because they would lose even more ground to the amazing Rays, but because they are also locked in a tight battle for the Wild Card with whichever AL Central team finishes second, the Twins or the White Sox.

So, as always, there is something serious at stake here. That is the constant in the rivalry. The variable, which never used to be a variable, is which team is on top. At Yankee Stadium, the Yankees held the lead for what appeared to be 80 years. The Red Sox have been baseball's best twice in a four-season period. But those would be the most recent four years.

To even attempt a comprehensive listing of the memorable moments that have occurred between these two teams at this ballpark would test cyberspace's infinity. For most people, the favorite moments are a reflection of rooting interest.

In recent history, for instance, if you're a Yankee fan, Aaron Boone's dramatic home run off Tim Wakefield in the 11th inning of Game 7 of the 2003 AL Championship Series, capping a comeback victory, would be a suitably thrilling Stadium moment.

If you're a Red Sox fan Game 7 of the ALCS in 2004, the 10-3 triumph finishing a historic-making, precedent-shattering comeback, would be a moment for the ages, made even better by the fact that the celebration was held on enemy turf.

Here's a favorite moment that, in a way, worked out for both clubs, although it was temporarily all Yankees. It epitomized the intensity of the rivalry and the quality of the competition.

It was July 1, 2004, the 12th inning of the usual nail-biter between these two clubs, with the Red Sox threatening to score, with runners on second and third, two outs. Trot Nixon hit a pop up behind third, and Derek Jeter made a full-out sprint for the ball.

Jeter had one thing on his mind and one only, and that was making the catch. He made the play, which was remarkable enough, but then, the direction and the speed of his attempt conspired to put him on a crash course for the stands. Jeter went into the stands, headfirst. For his troubles he emerged with a bloodied chin, a badly swollen, reddened face and a bruised shoulder. But he also made what turned out to be the game-saving catch. The Yankees went on to win, 5-4, in the 13th.

How could this possibly work out for the Red Sox? The benches were emptied in this extra-inning game. But one member of the Boston club was not quite available to play. That was shortstop Nomar Garciaparra.

The contrast was striking. One shortstop, Jeter, sacrificing himself for the good of his team; the other shortstop, Garciaparra, being rested from a previous injury. Garciaparra was once a franchise icon for the Red Sox, but after an episode like this, you have to wonder how much he suffered in the shortstop comparison. Less than one month later, the Red Sox were to trade Garciaparra in a deal that made them a better defensive club and helped them win the World Series for the first time in 86 years.

That kind of play, and that kind of ramification, set this rivalry apart from any other.

As these clubs meet for what might be the last time on this historic ground, we contemplate the past as well as the present. Since Yankee Stadium has been open, the Yankees have won 26 World Series and the Red Sox have won two. But over the past four years, it's Red Sox 2, Yankees 0. And in this season, the Red Sox will leave Yankee Stadium in what was once an improbable position, but now seems to be the order of the day-they'll be ahead of the Yankees.