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.