By Eno Sarris

Players aren't just numbers on spreadsheets, no. And there are complicated interactions between the players on a roster that we haven't yet figured out. 

But! Each player that a team acquired during this last trade deadline period will replace another player. And both the new player and the original player had projected value. So we can look at what the projections say just happened. 

Which teams improved themselves the most according to the projections? Which teams brought in the best talent with respect to their current talent? Which teams plugged the right holes? 

This won't be easy to figure out completely -- see the caveats above -- but let's try. We're going to focus on the rest of this current season, and major leaguers only. Listed next to each outgoing and incoming player is their rest-of-season projected ZiPS Wins Above Replacement number. 

Yankees (2.0)

Out: Kelly Johnson (0.3), Yangervis Solarte (0.8), Brian Roberts (0.0), Vidal Nuno (0.1), Zoilo Almonte (-0.1)

In: Martin Prado (0.7), Chase Headley (1.6), Stephen Drew (0.3), Chris Capuano (0.1), Brandon McCarthy (0.4)

The Yankees gained two wins by turfing a group of replacement players and Yangervis Solarte. Solarte might hurt in future years -- he was capable of playing all over the diamond with some success -- but in the minor leagues, he never showed a walk rate like the one he's got now, and he's also 27 years old. This is likely his peak year. For that one piece, the Yankees got a strong third baseman finally freed of a pitchers' park, a versatile infielder/outfielder, a shortstop willing to play second base, and two starting pitchers. The ancillary benefits come from pushing the fading Chase Whitley, a converted reliever, back into the bullpen and into spot starting work. 

What clouds this story, though, is the backdrop of losing Masahiro Tanaka. If we put him into the equation, his lost 1.5 wins degrades much of the positive work Brian Cashman did at the trade deadline. But do we know how much Tanaka is left this season? If they get any, the Yankees may make good on the 19.7 percent chance at the playoffs they are showing at FanGraphs right now. 

Mariners (1.3)

Out: James Jones (-0.2), Stefen Romero (-0.2), Corey Hart (-0.1)

In: Chris Denorfia (0.3), Austin Jackson (0.6), Kendrys Morales (-0.1)

The Mariners took the same approach as the Braves, in a way. They went and got three guys that should be scratch or better the rest of the way, and they replaced three guys that were going to be worse than replacement over the final two months. Take your worst position and improve it, even to replacement level, and you've done good work. All for a prospect in Nick Franklin that was out of favor and didn't seem to be part of the team's plans going forward any more. It was a good day for the Mariners, even if they didn't go for the home run swing. Amazing what a real-life center fielder can do for a team.

Cardinals (1.1)

Out: Joe Kelly (0.1), Allen Craig (0.5), Carlos Martinez (0.1)

In: John Lackey (0.9), Justin Masterson (0.9)

At first, the trade for Justin Masterson seemed a little strange. Why pay for a sinker/slider guy with iffy command when you have one on hand already -- especially if the one you have throws much much harder than the veteran you'll trade for? The reason, it seems, is innings. The Cardinals are interested in limiting Carlos Martinez's innings, because he only threw 108 last year, and was already up to 68 this year. Masterson has no such limiting factor. And though Joe Kelly throws in the mid-90s and has some intriguing secondary stuff, he hasn't made the strides yet. John Lackey has been great since he refreshed his elbow ligament, and this analysis shows just how important that switch might be to the team. 

The ancillary benefits here are huge. Top prospect Oscar Taveras now gets more playing time, and by ZiPS, he can be expected to add another fifth of a win himself. But the Steamer projections on FanGraphs are adjusted for depth chart changes, and Taveras is a half-win player by that estimation. That means he can replace Craig's work, and the Cardinals improved themselves even more given how their in-house talent meshes with their new acquisitions. 

Athletics (1.1)

Out: Yoenis Cespedes (1.1), Tommy Milone (0.6), Drew Pomeranz (0.1), Jim Johnson (0.0), Nate Freiman (-0.1)

In: Jon Lester (1.3), Jonny Gomes (0.1), Jeff Samardzija (0.7), Jason Hammel (0.2), Sam Fuld (0.5)

It was the Athletics that gave up the biggest trade piece when it comes to rest-of-season projections. They had an outfielder that was going to give them a win over the rest of the season, and they traded him for a pitcher that was only going to do slightly better in Jon Lester. You might think that was the Athletics trading from a position of need to a position of strength -- when you think of the A's, you think of pitching most years -- but the A's have actually scored more runs per game than any other team in baseball so far this year. And with Jonny Gomes being so good against lefties, and Sam Fuld providing a late-game defensive replacement and solid work against righties, there might be enough here to replace most of Yoenis Cespedes' contributions (without even mentioning the breakout from Stephen Vogt). 

The rest of the replacements are more modest in scope, but upgrades nonetheless. And although moving from Tommy Milone to Jeff Samardzija may not be such a huge thing over the course of a few starts in the rest of the season, it could be huge in the postseason. The A's, maybe more than anyone, were looking forward to their postseason rotation to some extent. If Samardzija is your number four, you're running a great pitcher out there every day. 

Braves (0.5)

Out: Jordan Schafer (-0.1), Chasen Shreve (0.0)

In: Emilio Bonifacio (0.5), James Russell (-0.1)

The Braves didn't do much, but what they did do could have a large impact. Because their backup center fielder was below replacement, and their starting center fielder is also below replacement, getting even a flawed player like Emilio Bonifacio could be huge. As they fall behind the Nationals in the National League East, they'll be very tempted to run Bonifacio out there as a starter and improve their chances even further than this analysis shows. 

Kendrys Morales and Austin Jackson should help bring some needed support to Robinson Cano in Seattle. (Getty Images)

Giants (0.4)

Out: Matt Cain (0.3)

In: Jake Peavy (0.7)

Is this fair? A healthy Matt Cain would have a better number, but a Giants with a healthy Matt Cain may not have traded for Jake Peavy. In any case, it looks like they at least picked up a guy that can approximate Cain for two months, so well done. 

Tigers (0.3)

Out: Drew Smyly (0.7), Austin Jackson (0.6), Ian Krol (0.0)

In: David Price (1.4), Joakim Soria (0.2)

The Tigers got a lot of love for their acquisition of David Price, and in fairness to them, it may be a bigger deal than these numbers show. If the Athletics get some credit for looking forward to the postseason, then the Tigers should also get a gold star for assembling either the best or second-best postseason rotation in baseball. 

But if you're looking just at the ins and outs of what happened the week of the trade deadline, the Tigers gave up two pieces that were expected to contribute significantly over the last two months in order to get Price. The breakout of J.D. Martinez makes things easier, but who will play center field now? Looks like it will be Rajai Davis, who is not the defender that Austin Jackson was in center. Davis has also been 25 percent worse than league average with the stick against right-handers over the course of his career. 

The Tigers have scored the fourth-most runs in the American League this year, and Jackson was scuffling with the bat. Maybe they could afford to give up what they did. That doesn't make the improvement any more impressive when seen through the light of the final two months. 

Brewers (0.3)

Out: Logan Schafer (0.2)

In: Gerardo Parra (0.5)

The surprise of baseball decided to go with a more muted approach to the trade deadline, and that's probably because their minor league system is fairly barren right now. So they turfed decent-but-not-great outfield prospect Mitch Haniger for a depth upgrade over the rest of the season. Parra will help them deal with the nicks and cuts and bruises that may befall any of their veterans, and he also gives them some flexibility should one of the outfielders be able to fake it at first base for a stretch. Not sexy, but useful. 

Nationals (0)

Out: Ryan Zimmerman (0.9)

In: Asdrubal Cabrera (0.9)

Kind of amazing, huh? The Nationals lose a slugger at third base for the rest of the season to a hamstring injury, and so they replace him with a light-hitting shortstop… and it works out almost perfectly. Mostly, the Nationals have Anthony Rendon to thank for that, as the youngster can slide over to his natural position at third base and leave second base open for the middle infielder. Now Danny Espinosa returns to being a backup, and the team shouldn't miss too much of a beat. 

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Eno Sarris writes about baseball at FanGraphs most of the time. He also started BeerGraphs for the beer nerds out there. He doesn't always play daily fantasy, but when he does, he plays it at