Instead of worrying about trades that may or may not happen, what about the players that are sticking around? Looking at the 10 teams with the best shot at reaching the postseason—that's the current playoff percentage next to the team—based on our Playoff Odds Report heading into Sunday, here are some names you might see down the stretch, or at least when rosters expand to 40 just six weeks from now:

1. New York Yankees (85.9%)
The Yankees are one of the more set teams in the game, but this conversation is impossible to have without the mention of Jesus Montero. While his name came up in the Cliff Lee deal that didn't happen, Montero is likely off the market unless an unknown blockbuster ends up on the table, so it's time to figure out his future in New York. Montero has heated up in a big way of late, batting .317/.442/.512 in July, and could be worth a late-season shot to shore up the revolving DH situation at Yankee Stadium. Also worth a look might be veteran Jonathan Albaladejo, who has gotten plenty of chances, and has been one of the International League's most dominating closers this year, limiting hitters to a .153 batting average while striking out 61 in 46 2/3 innings.
2. Texas Rangers (79.6%)
As written in this spot in the past, it's time to abandon the thought of Tanner Scheppers as a starting pitcher. The Rangers are working him right now in order to get him innings and to get his changeup right, but after getting ripped for 11 hits in less than five innings last time out, his ERA as a starter is 5.84 and it might be time to give up on that notion. The Rangers already have one of the more terrifying bullpens around, but Scheppers has big-league ability right now if he can focus on his fastball/curve combination in short stints. A longshot could be outfielder Mitch Moreland, who has been on fire at Triple-A Oklahoma, and could provide an extra bat off the bench.

3. Atlanta Braves (76.1%)
We've already seen Craig Kimbrell in the big leagues for a brief stretch, and while his monster stuff led to 15 strikeouts in just 8 1/3 innings, his equally monstrous command problems led to 10 walks. Still, big-league stuff is hard to keep down in the minors. Next to Kimbrell, fellow Triple-A righty Stephen Marek could show up in September to pick up some extra innings. The only hitter of note is Freddie Freeman, and while the Triple-A first baseman is the top hitting prospect in the system, he's not getting to the big leagues unless Troy Glaus suffers an injury.

4. Tampa Bay Rays (72.4%)
Jeremy Hellickson has provided a season-long conundrum for the Rays, as he's big-league ready and has been for months, but there's no place to put him. To call up Hellickson would require a dramatic move, like a trade or a move of Wade Davis to the bullpen, and the fear of fixing something that isn't broke could prevent it. The same goes for outfielder Desmond Jennings, who has nowhere to go without an opening in the Rays' outfield. One interesting option: 33-year-old journeyman Winston Abreu has been an unhittable closer at Triple-A Durham, striking out 52 in 35 1/3 innings while giving up just 18 hits, and could provide the bullpen with some extra rest down the stretch.

5. San Diego Padres (70.3%)
The last thing the Padres need is bullpen help, but that might be all they have in a system with precious little at the upper levels. The Padres already added their best relief prospect last week by calling up righty Ernesto Frieri, and there might be more coming in left-hander Aaron Poreda. Acquired from the White Sox in the Jake Peavy deal, the former first-round pick has plus-plus velocity for a lefty, but also carries big command issues. The bad news is that one of baseball's worst offenses has no help coming from within.

The Cardinals have an upper-level system filled with has-beens and never-weres, but if you want to reach a bit, maybe Fernando Salas could help a bit out of the bullpen. If you want to think a bit more radically, however, let's talk about second base, where Skip Schumaker provides grit, effort, and nothing in the way of power or on-base skills. Triple-A second baseman Daniel Descalso is hardly a future star, but he should be able to eclipse Schumaker's .257/.318/.327 line while returning Skip to a more apt utility role.
7. Cincinnati Reds (58.5%)
While the Reds continue to hope Aroldis Chapman can be a power lefty out of the pen by the end of the year, they also have a potential move in the middle of the infield that would take considerable guts. Orlando Cabrera is there for a reason, as he doesn't make mistakes defensively while making consistent contact, but at the same time his sub-.300 on-base percentage is another hole in a roller coaster of a Reds offense. Could Zach Cozart be the answer? He's likely no more of an on-base player than Cabrera, but he offers plus defense and surprising power for the position, with 13 home runs in 94 games at Triple-A Louisville.
8. Chicago White Sox (47.3%)
With righty Dan Hudson and third baseman Dayan Viciedo both in the big leagues, the White Sox have already made their move, but there's a possible surprise in the works with a player who joined the organization less than a month ago. First-round pick Chris Sale was one of, if not the best college pitchers in the draft, and the White Sox have been aggressive with his development, beginning his career in the bullpen and already moving him up to Triple-A Charlotte. He's whiffed four of the six batters he's faced so far in the International League, and could shore up the bullpen by September, if not earlier.
9. Colorado Rockies (46.9%)
If the Rockies are going to reach the playoffs this year, they'll be doing it with the hand they've been dealt, as their top prospects are nearly all at the lower levels and not in a position to help this year. Already up briefly this year, Chris Nelson could return to provide some flexibility off the bench, while a longshot is six-foot-six lefty Scott Rice, an absolute ground-ball machine who might work as a situational reliever.
10. Boston Red Sox (36.2%)
It's funny. The Red Sox are constantly praised as having one of the top systems in baseball, yet it's hard to find somebody who can help them this year. One surprise name that has cropped up in right-hander Michael Bowden, who had seen his prospect star dim by flattening out at Triple-A. Then came a move two weeks ago to a relief role, where he's been nothing short of dominant, allowing just one hit over six innings while striking out five.

A version of this story originally appeared on ESPN Insider Insider.

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No chance of Alex Torres as another lefty in the pen for Tampa? He's on the 40 man, yes?
Isn't Mike Dunn, just called up, likely to help the Braves' pen?
How about Ryan Kalish coming up from Pawtucket to help with a beleagured Red Sox OF? No better than Hermida at this point perhaps.?
He's not on the 40-man and isn't going to get called up unless it is to play every day. He is probably an upgrade, but he also has very little time at AAA and could stand to finish the season there.

Theo is very conservative about wasting option years, so while a September call up is a real possibility if there is space on the 40-man by then, it seems unlikely to happen before late August/early September when he wouldn't need to be optioned to AAA once players got healthy.
Note also with Sale that the Sox have really been dying for a lefty in the pen who isn't Thornton (they don't use Thornton as a lefty specialist). Randy Williams was terrible, and while Erick Threets hasn't given up anything yet charged to him, he has zero strikeouts and Ozzie doesn't seem to trust him.
When Freese comes back the Cards will likely just move Lopez to second if they are looking to upgrade on Skip.
The Padres don't have one of the worst offenses in baseball - it's actually one of the best. They have an OPS+ of 100, tied with the Braves and Cardinals for the 4th best offense in the National League.
There are better stats for that than OPS+. The Padres team TAv is .257 and 21st in MLB (12th in the NL), tied with the White Sox and just behind KC, Oakland, and Arizona.
You can't win as many games as the Padres have, and score as many runs as they have in the home park they play in, with "one of the worst offenses in baseball". That's just stupidity. The Padres have scored 402 runs to date; the Braves have scored 425 playing one more game; the Mets have scored 406 playing in two more games. Now adjust for home park. Do the Braves have one of the worst offense in baseball? Do the Mets?
Please note that TAv is adjusted for park and league. The Braves and Mets are 9th and 12th, respectively, in TAv in MLB, so it's not like they're great, either. In fact, the Mets seem pretty mediocre and play in a pretty tough park, too. Just saying "they've scored more than you would expect from their park" isn't really analysis. Maybe they've outperformed their underlying stats, maybe they've made up some runs going to Arizona and Colorado so many times. Besides, it's not like I'm saying they're on a Houston/Pittsburgh/Baltimore-level on offense.
They rank 22nd in the majors in runs, 23rd in HR, 14th in BB, 26th in OPS, and 27th in TB. They're below average in every standard offensive category except GDP and SB. Beyond the standard ones, they're 26th in wOBA (.312) and, as Patrick said, 21st in TAv.

I don't see how you can claim this is one of the best offenses in baseball, it is by almost every measure one of the worst. Even if you wanna cry Petco Field you're talking about a team that walks and runs the bases and does little else.
Nolan Ryan must have been reading BP today . . .

"The Rangers have moved prospect right-hander Tanner Scheppers back to the bullpen at Triple-A Oklahoma City."
Before the season, Theo was pretty open that there wasn't a lot in the minors to help the major league team this year, which is why they went out and got Bill Hall and made sure to keep 6 starters.

The guys they have brought up haven't been too bad at all - McDonald, Nava, Doubront and now Bowden.
Seems a bit unfair not to mention Allen Craig and Jon Jay when talking about the Cardinals, both of those guys have contributed since returning to the team recently.