The Yankees are going to have a tough time getting into the playoffs this year, and it’s not because the Red Sox acquired reliever Mike Remlinger from the Cubs yesterday. The math is simply all wrong. Don’t roll your eyes – this isn’t a statistics thing. It’s a simple matter of mortality. The season only has so many games left before it expires. The Yankees face an uphill battle to pass the Sox before they simply run out of opportunities.

The Yankees are only four and a half games out (four in the loss column), with six games remaining between the two teams. Certainly if the Yankees take four of the six, their chances will get a serious boost. Still, Boston will have so many other opportunities to restore or even increase the gap between the two teams in other games. If the Sox just maintain their current winning percentage of .577, they will go 29-22 for the rest of the season. That means the Yanks will have to win 34 of their remaining 52 games to finish with at .580 and pass their rivals to the north. That’s 34 wins in 52 games, a clip of .654 – the equivalent of 106 wins over a full season.

Given the number of runs scored and allowed by the Yankees, they should have won 59 games by this point in the season. That is to say, with the team’s current offensive and defensive abilities, they are roughly where they should be. How does a team with .545 stuff boost its game up to .654? There are a couple of ways to look at it:

1. Bolster the offense. The way Yankees starting pitchers are dropping – Carl Pavano, Kevin Brown, Chien-Ming Wang, and Jaret Wright are all out of action, and the team announced yesterday that Randy Johnson will miss his next start – it may not be safe to assume that the pitching will maintain its current level of 5.05 runs allowed per game, but let us dream. Allowing runs at that rate, Yankees’ pitchers will give up another 263 runs this year. The Yankees offense averages 5.45 runs per game. If this, too, remains the same, the Yankees will score another 284 runs by the end of the season. Bill James’s Pythagorean Theorem has shown that won-lost records have a predictable relationship to runs scored and allowed. The Pythagorean Theorem allows us to ask this question: if the pitching remains the way it is, how many more runs do the Yankees need to add to expect to win 94 games?

The answer: 25 runs. Scoring just 25 more runs (and not all in one game) would greatly increase New York’s chance of winning 94 games on the season. It’s not obvious where those runs will come from. The Yankees offense is very good already, with the third-most runs scored in the majors, trailing the park-inflated Rangers and the Red Sox. The suspects for replacement are obvious – the mix and match center fielders, the part-time first basemen – but it’s not clear that replacing one of them will be enough. Alex Rodriguez may not create 25 more runs through the rest of the season (he probably will, but it’s not a sure thing).The Yankees would have to acquire a real hitter, or more likely a combination of real hitters, to upgrade the two weak positions if they’re going to have a chance to upgrade their scoring.

The most obvious scenario is an outfielder – any outfielder – who can put Bernie Williams, Tony Womack, and pals on the bench for good. Any upgrade to the position will give the Yankees a serious push. All season long, the Yankees have let this position fester and cost them games both offensively and defensively. Here’s a very simple formulation: If the Yankees do not somehow improve center field, and immediately, they will not go to the postseason this year.

Parenthetically, as disappointing as Carlos Beltran has been for the Mets, he by himself would likely have erased the scoring gap. Thus, another Yankees season will go down in memory as a campaign in which they punted on Beltran and paid for it.

2. Improve the pitching/defense. Assuming, again, that the number of runs stays constant and the Yankees score another 284 runs before the year is out, the team would need to improve the pitching by 24 runs. That would cut the number of runs allowed per game from the current 5.05 to 4.60.Unless the Astros decide to divest themselves of Roger Clemens – and that’s not going to happen – it is, again, spectacularly unlikely that the Yankees will be able to pull off a reduction of almost a half a run per game.

Should the Yanks acquire better relief pitching August 31, the postseason roster deadline, it will have neither the ability nor the time to make enough of an impact. As for improving the defense, if Willie Mays himself came back to play center field for the Yankees, he couldn’t close the gap on his own.

In summary, then, it’s likely all over for New York; the Yankees are not going to pass the Red Sox, and the surging Athletics will probably deny them the wild card. Call it a case of death by neglect. The Yankees knew what they had to do – knew since last season, in fact – but they couldn’t quite accomplish it. The injuries to the pitchers tell a great part of the story, but the Yankees also built a rotation peculiarly inclined to get hurt. It’s time for desperate measures.

None of these scenarios consider the possibility that the Red Sox will improve their pace before the end of the season, winning more than 58% of their games. If that happens, the Yankees won’t have any chance, even if they acquire Mark Prior and Junior Griffey at the deadline. It’s only August, but for the Yankees, it’s the bottom of the ninth.

Mr. Goldman is the author of “Forging Genius,” a biography of Casey Stengel, released this year.