By Marc Normandin

The first half of the baseball season is over, and the second half has begun. Sure, baseball and its fans like to consider the games after the All-Star break to be the start of the second half, but a little math never hurt the sport no matter what some of television's talking heads might say, and everyone has played at least 81 games to this point. So, we're at the stage where it's time to see what the game has in store for us for a second act.

Specifically, it's time to see which teams can put a charge on in the season's second half, helping erase the problems from the first that have kept them from being in a playoff spot already or made it questionable whether they can hang on to the one they currently have. Today, we'll look at five teams to watch out for in the second half, the ones who just might make enough noise in their remaining games to reach October baseball.

Pittsburgh Pirates

The Pirates didn't start the season strong, posting a 25-30 record while being outscored by the opposition by 34 runs through the season's first two months. Based on that, they were lucky to be that close to .500. Since then, though, they've gone 19-10 while scoring 28 more runs than they've allowed, not only helping to close the gap on their overall run differential but also pushing them to two games behind the Dodgers and Nationals for a NL wild-card spot. While the damage of the first half can't be erased entirely, they managed to keep things close enough with their strong June that a solid second half could mean they'd make the playoffs for the second year in a row. Not bad for a team who, until last year, hadn't even finished with a winning record in over 20 years.

There's reason to believe they can keep this performance up. Top prospect Gregory Polanco didn't join the roster until almost mid-June, and has managed a .306/.392/.435 line after hitting a homer to help the Pirates beat the Diamondbacks on Wednesday. Clearly, he's been an improvement over Jose Tabata, Travis Snider and friends in right field, and the Pirates have won 14 of 21 since he arrived. Similarly, the Ike Davis/Gaby Sanchez platoon at first base didn't exist until a few weeks into the season, and while neither is setting the world on fire, they're competent, and keep the Pirates from having another hole in the lineup. Shortstop Jordy Mercer has also helped over the last 44 games: In his first 32, he hit just .161/.204/.195, essentially giving the Pirates two pitchers in their lineup each night. He's posted a .710 OPS since, though, which when you consider the position and park, isn't all bad. He could use some additional OBP, but given what he was doing before, the Bucs will take this.

The rotation could use help, as Edinson Volquez is exactly what everyone except the Pirates knew he was, and Francisco Liriano has been both ineffective and injured (another non-surprise for anyone who has seen his Baseball-Reference page before). Jeff Locke has stepped up his performance, however, and the Pirates are reportedly on the market for a pitching upgrade this month: They can still fix this thing, and become the threat they hoped to be during the second half.

Boston Red Sox

The Red Sox are well under .500, haven't put together much of a sustainable positive track record at any point in the season, own the 12th-worst record in the American League and can't seem to get anyone to hit. With all that in mind, why would we ever consider them as a team to watch in the second half? They've still got the talent and time for a minor miracle to occur.

It's admittedly a long shot, but if Dustin Pedroia can return to form, rookie Xander Bogaerts ends his first-ever struggle as a professional, Daniel Nava and Brock Holt continue to provide offense in the outfield corners, Stephen Drew stops looking like someone who missed all of spring training and two months of the season, Jackie Bradley's bat comes around to resemble his minor-league one, and Mookie Betts provides the spark the Red Sox have desperately needed in their lineup in Shane Victorino's extended absence, then all of a sudden this team has the lineup that they were expected to from day one. That's not too much to ask, right?

The rotation already seems to be mostly fixed, so there's that, as the Red Sox demoted Felix Doubront to the bullpen for the sake of Brandon Workman, who has been strong in his first wave of major-league starts dating back to last year. (Wednesday's tough outing aside.) If they can find a taker for Jake Peavy, then they can upgrade the rotation once more by placing Rubby De La Rosa in it. Clay Buchholz, their best pitcher when he was on the mound during their championship 2013 campaign, seems to be working his way back to effectiveness after a DL stint, and both Jon Lester and John Lackey have been dependable throughout an otherwise disappointing season for Boston. If most of the above can just go right in support of these starters, they could start winning a whole lot of games.

The clock is ticking for them, though: The AL might be mediocre now, keeping alive their playoff chances, but it might not be mediocre forever.

Seattle Mariners

The Mariners have played some pretty bad baseball at times in 2014. They were outscored in March/April and went 11-14 thanks to it, but they had some built-in excuses, as injuries kept them from being at full strength. They've managed to go 36-24 since while outscoring their opponents by 75 runs, though, and it's helped them into a wild card spot. Why are they here in the teams to watch out for if they're already technically in playoff position? They're just now approaching full strength.

For the first time this season, the rotation now features all of Felix Hernandez, Hisashi Iwakuma and Taijuan Walker. As both Erasmo Ramirez and Brandon Maurer have failed spectacularly in the meantime, getting back Walker, one of the better rookie arms in the game who had success in his brief 2013 time, is huge. With Chris Young also in the mix, looking healthy and effective and in a park that can benefit him, the Mariners suddenly have a legitimate rotation to lean on for the first time in too long.

The lineup could still use some love, but if the rotation keeps at what they've been doing -- only better now that Walker is around -- it might not matter. They already are in possession of a wild card spot, and while they might never catch the Athletics, they've got the roster to give the AL West three of the five playoff spots this October.

Greg Holland leads one of the most dominating bullpens in baseball in Kansas City. (Getty Images)

Kansas City Royals

The Royals' lineup was an absolute joke for the first month-plus of the 2014 season. They hit 24 homers as a team through the season's first two months, with the entirety of May's offensive output coming in at 20 percent below the league average. As happened last summer, though, their bats heated up with the weather, and the Royals were an effective offensive machine in June, batting .279/.328/.421, good for a 114 OPS+.

The pitching has been even better, and for longer. James Shields has struggled of late, but he's not known for doing so, and has still managed to give the Royals plenty of innings to lessen the load on the bullpen. Danny Duffy (157 ERA+) and rookie Yordano Ventura (125 ERA+) have stepped in for Shields as staff leaders, while both Jeremy Guthrie and Jason Vargas have done what they have made a career out of by beating out their adjusted ERA while providing innings. The bullpen has been lights out, and the combination of the two has the Royals ranked third in the AL in ERA+. They remain dead last in OPS+ on the offensive side, but that could change with some of their bats -- such as Salvador Perez, Alex Gordon and Billy Butler -- waking up before it's too late to matter.

The lineup will never be among the AL greats as constructed, but if they can continue to hit something even close to what they did in June, with their pitching, they might even end up back in first place in the AL Central. As is, they're only a couple of games out of a wild card spot, and might be better equipped for one than either of the teams currently in possession of them.

Cincinnati Reds

The Reds shouldn't be where they are right now. They've dealt with injuries to their only viable hitters (Jay Bruce and Joey Votto), watched Mat Latos hit the disabled list and Homer Bailey struggle, and even saw elite closer Aroldis Chapman miss some time. They managed to survive all of that, though, and while they sit 7.5 games out in the NL Central, they're just three games behind the crowded NL wild card picture. And, as mentioned, they're healthy now.

It also helps that rookie center fielder Billy Hamilton has not only seen his defense improving -- he's not all that far removed from being a shortstop -- he's also put together a more useful line at the plate. Hamilton hit .330/.350/.504 in June, and while you can't expect that from him forever, if he can even produce around where he is on the season (.283/.314/.406 with 35 steals in 47 attempts) he'll be more useful than he was prior to his surprising June. The Reds needed Hamilton to be decent and for Todd Frazier to rebound if they were to get away with losing Shin-Soo Choo to free agency, and both of those things are happening. If they can just stay healthy from here on out -- and both Bailey and Bruce show a little more of their past selves -- then a wild card berth is not out of the question.

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Marc Normandin writes and edits for Over the Monster, a Boston Red Sox blog, as well as SB Nation's baseball hub. He's one of many behind the e-book "The Hall of Nearly Great," and has written for BaseballProspectus, ESPN, and others. You can follow him on Twitter at @Marc_Normandin