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With nearly one-fourth of last week’s list moving on, let’s jump right in to another busy edition of The Stash List

The Graduates: (1) Matt Moore, (2) Steven Matz, (9) Jon Singleton, (13) Roberto Osuna, (18) Manny Banuelos, (22) Miguel Sano

No doubt due to the power of being no. 1 on last week’s Stash List, Moore plowed past the eligibility threshold for inclusion on this list as he wraps up his rehab. Moore threw a 35-pitch bullpen session at Tropicana Field on Monday and will jump into the Rays rotation on Thursday afternoon against the Indians. The lefty makes for a strong waiver wire target, as there won’t be many pitchers returning from injury over the rest of the season who are widely available and carry the upside that Moore does.

Matz’s debut as a part of the Mets six-man rotation couldn’t have gone much better, as he went 3-for-3 at the plate with four RBI and pitched 7 â…” innings with six strikeouts, allowing only one earned run after giving up a leadoff home run to Brandon Phillips. Somewhat curiously, Terry Collins allowed Matz to pitch into the eighth with a four-run lead—when he was already over 100 pitches on the day—which is certainly interesting handling of a pitcher making his major -debut and reportedly on an innings limit this season. After walking over three hitters per nine innings at Triple-A Las Vegas, Matz walked three in his debut and will need to limit the free passes at the big-league level to avoid being a drag to the WHIP category.

Singleton was summoned back to the majors last Friday and after sitting out in his first game back, he started two of Houston’s next four games (both times as the Astros designated hitter). Since he was held out of the lineup against RHP Michael Pineda and LHP Danny Duffy, it’s hard to say what exactly the Astros plans are for him. With Chris Carter hitting six home runs in each of the last two months (with a .318 OBP in May and .348 OBP in June), it looks doubtful that Singleton will displace him at first base, even on a platoon basis. With El Oso Blanco, Preston Tucker, and Carter ahead of him for at-bats between 1B/LF/DH, it will likely be hard for Singleton to make much of an impact with the leftover plate appearances. Singleton’s best chance for at-bats would be a move of Evan Gattis to the outfield, but as the Braves found out, that’s not a pretty sight.

Since Brett Cecil’s demotion from the closer role, Osuna has picked up his first two saves of the season and is no longer eligible for the list, as his ownership has also crossed the 25 percent line. Steve Delabar has picked up the only other save since the change was made, but it was an extra-inning affair where Osuna had already pitched in the ninth of a scoreless game. It remains a committee situation, but it looks as though John Gibbons is most comfortable giving the ball to Osuna in high-leverage situations at this point.

Banuelos received the call to fill Atlanta’s fifth-starter role with Williams Perez needing a D stint for his injured foot. Banuelos posted a 1.59 ERA over his last 11 Triple-A starts, although he owns a scary walk rate of over four per nine innings this season. Banuelos is on an innings limit in his first full season back from Tommy John (after pitching 76 1/3 innings last year in the Yankees organization) and could find himself in the Braves bullpen once Perez returns.

Sano has shaken off the rust he understandably showed earlier in the season after missing all of last year and has caught fire over the last two months at Double-A Chattanooga. Sano’s monster June output of .329/.432/.658 brought his OPS on the season to .918, and his six home runs brought his total to 15 on the year. Between his half-season in 2013 at the Double-A level and this season, the 22-year-old Sano owns a .255/.359/.557 line in 133 games with 34 home runs and 103 RBI. Sano should assume most of the designated-hitter at-bats for the Twins now that Kennys Vargas (who was demoted to Double-A as the other half of the transaction) is out of the way.

The Dropouts: None

1) Patrick Corbin, LHP, Arizona Diamondbacks (Last week: 3)

Corbin made 79 pitches (50 for strikes) Friday at Double-A Mobile in his most recent rehab start, going six innings, and giving up four hits and two earned runs. Chip Hale said Corbin is slated to make one more start in the minors before joining the D’backs rotation against Texas during their July 7-8 series. He will likely take Allen Webster’s spot.

2) Hector Olivera, 2B/3B, Los Angeles Dodgers (Last week: 4)

Olivera has been sidelined since June 20th due to a strained hamstring. In the meantime, Justin Turner just concluded a monster June with the Dodgers, clubbing his way to a .330/.385/.614 line with six home runs for the month. Turner, who now has 11 home runs on the season, was obviously on the roster when the Dodgers gave Olivera $62.5 million this offseason, but he’s hitting so well that it’s getting tougher to imagine the Dodgers moving him to the bench, making it likely that Olivera sees some time in left field in the minors when he returns from injury in an effort to enhance his versatility.

3) Kyle Schwarber, C/LF, Chicago Cubs (Last week: 5)

Schwarber hit a home run in his fifth game in the Pacific Coast League, but has struggled a bit overall with the bat in his first eight games. It’s nothing to be concerned about as it’s only been 30plate appearances, but what bears watching with Schwarber while he’s in Iowa is how much action he sees in left field, which to this point is zero—just as it was at the Double-A level this season.

4) Rusney Castillo, OF, Boston Red Sox (Last week: 6)

5) Kevin Gausman, RHP, Baltimore Orioles (Last week: 8)

Gausman is reportedly set to start today and then be sent to the minors afterwards. I’ve seen this movie before, and I don’t like it. With Bud Norris’ ERA approaching 7.00, one would think the Orioles would see Gausman as a solution, but it appears "The Human Yo-Yo" will continue to be spun.

6) Corey Seager, SS, Los Angeles Dodgers (Last week: 11)

Jimmy Rollins continues to play a respectable shortstop defensively in Los Angeles, but has shown virtually no improvement with the bat this season, seeing his OPS tumble for the third consecutive month—all the way down to a paltry .552 mark in June. After struggling initially after his promotion, Seager has a .290 average with a .798 OPS (with six home runs) in 52 games at Triple-A Oklahoma City. The first-place Dodgers are understandably hesitant to dispatch the highly respected Rollins, but a team with hopes for a deep October run can’t continue to roll out a shortstop with a sub-.600 OPS for very much longer, can tit?

7) Joey Gallo, 3B/OF, Texas Rangers (Last week: NR)

Gallo was sent to Triple-A Round Rock on Tuesday, as Josh Hamilton made his way back from the DL. Gallo started eight games in left field and one game in center after Adrian Beltre returned to the lineup, and should see quite a bit of action in the outfield in his first taste of the Triple-A level. Gallo’s month of extremes in the majors was largely expected as he showed the monster power (five home runs in 98 plate appearances) that is so enticing, but also struck out 43.9 percent of the time, up from his 33.6 percent strikeout rate earlier in the year in Double-A. It’s doubtful that Gallo’s time in the Pacific Coast League is going to quell those concerns, so when Gallo does return to the majors, be prepared to deal with the lack of contact in exchange for the power.

8) Arismendy Alcantara, 2B/OF, Chicago Cubs (Last week: 7)

9) Brandon Beachy, RHP, Los Angeles Dodgers (Last week: 16)
10) Martin Perez, LHP, Texas Rangers (Last week: 17)

11) Jose Berrios, P, Minnesota Twins (Last week: 21)

Similar to his former teammate at Double-A Chattanooga, Berrios likely needs to be challenged at a new level. Including his 15 starts this season, in which he’s struck out 92 hitters in 90 1/3 innings with a 3.08 ERA, the Twins top pitching prospect has a 3.22 ERA in 23 starts at the Double-A level, and he’s given up just eight home runs in his 131 1/3 innings of work.

12) Javier Baez, INF, Chicago Cubs (Last week: 12)

Baez will hear his name in plenty of trade rumors this month, and a trade would almost certainly signify his best chance to make a fantasy impact over the rest of the season. He is still rehabbing his thumb injury and hasn’t gotten on the field since June 7th. Unfortunately, his Instagram account did not feature any updates this week of when he will do so. He did appear relaxed during his recent pedicure, though, so there is that. Always remember, #realmengetpedis.

13) Joe Ross, RHP, Washington Nationals (Last week: NR)

14) Daniel Norris, LHP, Toronto Blue Jays (Last week: 10)

The Blue Jays added 24-year-old Matt Boyd to the 40-man roster and called him up from Triple-A on Sunday to fill the rotation slot vacated by the injured Aaron Sanchez. Despite already being on the 40-man and pitching in the same rotation in Buffalo, Norris was bypassed and the Jays will reportedly keep Boyd in the big-league five until Sanchez is able to return, which could happen shortly after the All-Star break.

15) Steve Delabar, RHP, Toronto Blue Jays (Last week: 14)

Delabar picked up his first save of the season on June 24th as Marco Estrada’s perfect game bid spilled over into extra frames. Roberto Osuna has gotten the ninth-inning call in the Jays two traditional save opportunities since Brett Cecil’s demotion, but John Gibbons could turn to Delabar if Osuna struggles.

16) Trevor Story, INF, Colorado Rockies (Last week: NR)

After hitting a robust .281/.373/.523 with 10 home runs and 15 stolen bases with Double-A New Britain, Story was promoted to Triple-A Albuquerque on Tuesday night, which according to Rockies GM Jeff Bridich is a “Story story, not a Tulo story.” The Rockies prospect will see work at second base, shortstop, and third base with the Isotopes, and his usage will likely reflect how the Rockies intent to deploy him should he get the call to the majors. I touched on Story’s long-term fantasy impact earlier in the season, but it’s important to remember in the short term that he has experienced an extended adjustment period at each new level in the minors.

17) Aaron Nola, RHP, Philadelphia Phillies (Last week: 19)

Nola hasn’t found the Triple-A level any more of a challenge that Double-A, and has won his first three starts and struck out 18 in 17 2/3 innings. Philadelphia’s plans for Nola (and generally everything else) remain a mystery, but Nola is certainly a bright spot in an otherwise abysmal year for the Phillies.

18) Stephen Piscotty, OF, St. Louis Cardinals (Last week: 20)

19) Richie Shaffer, 1B/3B Tampa Bay Rays (Last week: 23)

Shaffer smashed another home run on Wednesday, bringing his Triple-A total to 11 in 30 games. With the Rays first basemen continuing to struggle in James Loney’s absence, Shaffer has played five of the last six games at first base in Durham.

20) Rafael Soriano, RHP, Chicago Cubs (Last week: 24)

21) Nomar Mazara, OF, Texas Rangers (Last week: 25)

22) Oswaldo Arcia, OF, Minnesota Twins (Last week: 15)

23) Kris Medlen, RHP, Kansas City Royals (Last week: HM)
Medlen pitched his first rehab start at the Triple-A level on Monday, throwing 72 pitches and giving up two runs on four hits without registering a strikeout. The Royals plans for Medlen when he is done with his 30-day rehab assignment in mid-July remain unclear, but as long as Jeremy Guthrie is pitching as awfully as he is (5.94 DRA), and Medlen continues to be stretched out as a starter, the situation is worth monitoring.

24) Evan Scribner, RHP, Oakland A’s (Last week: NR)
25) J.J. Hoover, RHP, Cincinnati Reds (Last week: NR)

As the calendar turns to July, it’s officially time to speculate about which closers will be dealt and who will be left standing to assume the role of the ever-important closer for a non-contender. Two prime candidates to be dealt in July are Tyler Clippard and Aroldis Chapman, and Scribner and Hoover could be the beneficiaries. Neither of these guys is anything special, but as the saying goes, “paper is paper” and saves are saves. They all look the same in the column no matter the ugliness of their source. Scribner has Edward Mujica and Drew Pomeranz standing in his way for saves should Clippard be dealt, and Hoover’s main competition is Manny Parra. If either of the incumbents goes, these two could be the guys closing out meaningless games in August and September.

Honorable Mention: Jon Gray, Jose De Leon, Sean Nolin, Brandon Morrow, Joe Wieland, Nick Tropeano, Luis Severino, Aaron Blair, Mark Appel