Probably not. According to simulations, the Sox have just a 6 percent chance of getting into the playoffs. But this is baseball, after all, and it ain’t over until it’s over. Getting to the playoffs may be unlikely, but it’s not impossible. Other teams have come back from worse odds.

They may have lost Tuesday night, but in recent weeks the Red Sox have been hot. They’ve won eight of their last 10 games and even escaped last place for a few days. After months of underperforming, this streak has begun to rekindle the hopes of Red Sox fans. But can the team still make the playoffs?


Are they really playing better, or is it just luck?

The Red Sox really do seem to be playing better, particularly on offense. Before the current streak began, they had been averaging 3.7 runs per game with a dismal .367 slugging percentage. During this latest streak, though, they’re scoring six runs per game and benefitting from a slugging percentage of .490.

How do we know the Sox have just a 6 percent shot?

The Red Sox are last in their division, 8½ games behind the Orioles. They’re also six games back in the wild card race, behind six other contenders.

Calculating exactly how likely they are to make the playoffs from this position in the standings is terrifyingly complex. You need to estimate not only how well the Sox are going to play, but how well everyone else is going to play. And then you need to think about what happens when particular teams play each other. When the Sox beat the Orioles, for instance, it doesn’t just improve the Red Sox record, it also knocks the division leaders down a peg. In the days ahead, the Sox still have six games against the Orioles, and nine against the Yankees.

One way to account for all of these different variables is to run computer simulations. You give a computer enough information to estimate the outcome of each single game, and then let it run through the rest of the season – thousands of times. Baseball Prospectus does just this, and what they find is that the Red Sox make the playoffs in about 6 of every 100 simulations.


How many games would they have to win?

There’s a scene in the classic baseball movie “Major League” where the coach announces that his team needs to win 32 more games to make the playoffs. In the real world, it’s a lot harder to figure out how many games will suffice, because it depends on how your rivals do.

Let’s assume, though, that everyone else in the league keeps playing exactly as well as they’ve played so far this year. How good would the Red Sox have to be to win a playoff berth?

In this scenario, the the Orioles would finish with a record of 90-72. So, to win the division, the Red Sox, who are now 47-53, would have to win 44 of the remaining games while losing just 18.

Getting one of the wild card spots is slightly easier. Currently, the Mariners have the inside track on the second spot, and at the current pace they’d finish the season 86-76, meaning the Red Sox would have to close out with a record of 40-22.

Either way, for the Red Sox to make the playoffs, they’re going to have to get red hot, and fast. Even playing as well as last year’s team won’t be enough. If the 2014 Sox win as many games down the stretch as the 2013 team did, they’ll still end up just 84-78.


Does this mean the Red Sox should give up?

Not necessarily. It’s true that they’re unlikely to make the playoffs, but then unlikely things happen all the time. Some people are audited by the IRS (0.6 percent). Others are dealt royal flushes (0.00015 percent). If you’re looking for inspiration, here are a few touchstones.

■ In 1914, the Boston Braves opened the season 10-24. At the end of July, they were 44-45. In August and September, however, these “miracle” Braves went 45-11 and ended up winning the World Series.

■ The 1973 Mets started out 48-60. That put them in last place in the division, 11½ games back. Their odds of getting into the playoffs at the point were way below one percent. But down the stretch, they got hot while everyone else turned cold. And they ended up turning Tug McGraw’s catch phrase into an anthem, ““You Gotta Believe!”

■ At this point in 2007, the Colorado Rockies were 50-49, 5½ games behind the division leader. As late as mid-September, they were 77-72, with just a 2 percent chance of getting to the post-season. Thanks to a 14-1 finish, though, they found their way into a wild card spot and, ultimately, to the World Series.

The chart below shows just how dramatic some of these turnarounds were. At the same time, it suggests that if the Red Sox are going to make the playoffs, it will require them to pull off one of the greatest comebacks in baseball history.


Should I really be optimistic?

Optimistic, no. But it doesn’t hurt to be hopeful, and all hope is not yet lost. A week ago, the odds against the Red Sox looked much worse than they do today. If the team keeps slugging and scoring runs, their odds will look better and better. And if everything goes right, perhaps someday people will talk about the 2014 “miracle” Red Sox right alongside those “miracle” Braves.

In baseball, every day brings new stats and new numbers. The calculations used here reflect games played through July 22.

More from Evan Horowitz:

Evan Horowitz digs through data to find information that illuminates the policy issues facing Massachusetts and the United States. He can be reached at evan.horowitz@globe.com. Follow him on Twitter @GlobeHorowitz