A season after the Boston Red Sox won the World Series, there’s no getting around how lousy the team has been. With a record of 43 wins and 52 losses, the Red Sox entered the All-Star break in last place in the American League East — nine-and-a-half games behind the division-leading Baltimore Orioles and eight games out of the league’s final wild-card spot. Naive estimates of playoff probability, which treat every future game on the schedule as a coin flip, peg Boston’s chances of qualifying for the postseason at just 3.7 percent.For a team in such a predicament, the media’s attention usually turns to which players it should sell off at the July 31 trade deadline. Sure enough, Red Sox General Manager Ben Cherington was asked Thursday about deadline plans, to which he responded:“We’re going to do whatever we feel gives the Red Sox the best chance to be as good as possible as quickly as possible. And we are not conceding 2014 with that statement. … We’ve put ourselves in this position, so the math is working against us a little bit. But stranger things have happened. We don’t see why we can’t win more games than most of the teams ahead of us.”That’s pretty standard fare; Boston wasn’t the only team in such straits to deny the obvious about its deadline-day status. But in Cherington’s case, such a statement might not merely be a case of brazen self-deception. Beneath the Red Sox’s terrible record, there might lurk a good baseball team.The baseball statistics website FanGraphs.com has a mechanism by which it projects — based on the talent of players — the number of wins above replacement (WAR) each team is likely to accrue over the remainder of the season. This process incorporates updated forecasts for each player (using the ZiPS and Steamer projection systems) and playing-time estimates from the site’s depth charts (which take injuries into account).By this measure, the four teams projected to produce the most WAR from the All-Star break onward are the Washington Nationals, Detroit Tigers, Oakland Athletics and … Boston Red Sox.The first three teams on that list have won 58.4 percent of their games this season; Boston has won 45.3 percent. But, as Cherington alluded to, the Red Sox do have the talent to play better. Compared to their preseason (per-plate appearance) ZiPS and Steamer projections, Boston’s batters have produced 4.7 fewer WAR than would have been expected before the season, and that doesn’t even take into account injuries suffered by Will Middlebrooks, Shane Victorino and Mike Napoli during the season. (Interestingly, all of the Red Sox’s WAR shortfall has come on the position-player side; the team’s pitchers have exceeded expectations by 1.8 WAR.)A study by sabermetrician Phil Birnbaum showed that teams frequently see their players’ performances vary wildly around projections due to chance alone. In Birnbaum’s data, there were 1.5 teams per season from 1960 to 2001 who, through simple bad luck, undershot their “true” talent by the equivalent of 11 wins per 162 games — a hypothesis the FanGraphs numbers are asking us to believe about this Red Sox team. (Note as well that Major League Baseball had 17 percent fewer teams per season over the span of Birnbaum’s data than it has today, so the number of teams falling short because of luck in a 30-team league is even larger than the study’s seasonal average.)Birnbaum’s “luck-adjusted” wins from the previous season track much more closely with a team’s wins in the following season than its actual wins from the previous season, which attests to the value of projections that attempt to filter out random variance. That’s a big reason why FanGraphs’ projections expect Boston to post the seventh-best record in the major leagues from today onward, despite its poor record to date. It’s also why, after adjusting for the Red Sox’s projected talent level (instead of treating future games like coin flips), FanGraphs’ playoff-odds report bumps their postseason probability up to 6.6 percent.It’s always possible that in the roller-coaster world of the Red Sox, last year’s World Series winning squad might be the outlier sandwiched between two terrible seasons. But the best public sabermetric projections available agree with Cherington — this team is much better than its record would have us believe (even if it’s still unlikely to make the playoffs).