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A glimpse at the standings on Fenway Park’s left field scoreboard certainly suggests the Red Sox have positioned themselves to make a run.

On the surface, a 5 ½ game deficit in the American League East — which will become either a 4 ½ game or 6 ½ game hole depending on the outcome of Sunday’s first-half finale — doesn’t seem insurmountable.

That said, the cold splash of reality is that, while wiping out such a deficit isn’t uncommon, it is rare, particularly in the AL East. No AL East team in the last 25 years has overcome a first-half deficit of more than three games to win the division. The last teams to do so were the 1989 Blue Jays, down seven at the break, and the 1988 Morgan Magic Red Sox, down nine at the break.

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The Red Sox have a .477 winning percentage. Of the 380 teams to make the playoffs from 1914 through 2014, just six had a winning percentage of .477 or worse in the first half, and two of those instances, the 1995 Yankees and 1981 Royals, came in strike seasons.

Excluding the strike-shortened years of 1981 and 1995, only seven teams have ever made the playoffs after posting a losing record in the first half. Three of those instances have come since the playoff format expanded to include a wild card round, though it’s been 12 years since the 2003 Twins became the last case of a team to reach the postseason after a sub-.500 first half.

Since the postseason expanded to include the LCS format in 1969, just 19 of 270 playoff teams (7 percent) have had a negative first-half run differential — including 14 of the 166 teams (8.5 percent) to make the playoffs in the wild card era.

However, only one of those playoff teams — the 1981 Royals, who were outscored by 49 runs before the strike but who made the playoffs by winning their division in the second half of the year — had a worse run differential than the Sox in the first half. No other team in a non-strike year has made the playoffs after getting outscored by more than 36 runs in the first half.

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In other words, there’s plenty of reason for skepticism about the Red Sox’ chances. History suggests that they’re a statistical longshot.

That said, the Sox have, at a minimum, put themselves in a position where — particularly if Clay Buchholz appears likely to return — their chances of a rise in the standings can’t be dismissed completely, particularly given the flawed division. Teams go on hot streaks, sometimes unexpected ones, that can reconfigure divisions completely in the second half.

The 2012 A’s, for instance, were nine games behind the Rangers at the All-Star break, in possession of a flat .500 record. They hit the gas while the Rangers hit the wall, resulting in Oakland winning the AL West on the last day of the regular season.

Meanwhile, it’s hard to ignore the evidence of the last three weeks. Remember, this is what the standings looked like at the end of Saturday, June 20:

TeamWLGB
Tampa Bay4030
New York38301
Toronto37333
Baltimore35334
Boston304010

And here they are from June 21 through Saturday:

TeamWLGB
Boston126
Baltimore9103.5
New York9103.5
Toronto8125
Tampa Bay5158

In the span of just under three weeks, the Sox have highlighted a division of instability, one in which a team can gain at least 3 ½ games on every one of its competitors. While Buchholz will miss some time, Dustin Pedroia will soon return to a lineup that has started to assert itself as one of the deeper offenses in baseball.

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In that universe, it’s difficult for even a flawed team to dismiss the notion that it possesses a puncher’s chance of sprinting to make up a considerable amount of ground in a relatively short period of time — regardless of what history says about the unlikelihood of doing so.

More by Alex Speier


Alex Speier can be reached at alex.speier@globe.com. Follow him on Twitter@alexspeier.

Correction: An earlier version of this story stated that the Red Sox were 4½ games back in AL East as of Sunday morning. They were 5½ games back.