We’ve already looked at the three trades that were most influential in shaping the White Sox’ rebuild — Chris Sale, Adam Eaton and Jose Quintana.

The fourth one isn’t the biggest in terms of impact, but it’s the biggest in terms of the number of players involved. On the evening of July 18, the White Sox and Yankees cobbled together a megadeal in traditional slow-rollout #hugwatch fashion. When the smoke cleared, seven players found new homes, the Yankees had bolstered their bullpen for a postseason push, and the White Sox pared down their payroll while pursuing upside.

The White Sox traded...

*Tommy Kahnle, who was the true centerpiece of the deal, even if he was the least recognizable of the three.

Entering the season, it looked like his game had clicked over his last 16 games of 2016, as he allowed just one run and 13 baserunners to 18 strikeouts over 16 innings. He started the year in Triple-A because the White Sox had too many out-of-options relievers elsewhere, but he quickly returned when Jake Petricka hit the disabled list during the first week with a strained lat.

Kahnle may never go back to the minors. With a triple-digit fastball, a wicked changeup and improved command with both, the Latham product quickly became the White Sox’ best reliever, giving Rick Renteria true swing-and-miss stuff before David Robertson. He recorded at least one strikeout in 36 of his 37 games with the White Sox, and he recorded at least two in 22 of them.

He carried a 1.29 ERA, a .141 average against and a 51.3 percent strikeout rate into June, which made him a potential All-Star and a candidate for world’s best reliever. Regression set in shortly afterward to knock him down a peg. Over his last 15 games with the White Sox, he allowed a .300/.313/.417 line against, and only struck out a piddly 32.3 percent of batters faced.

If that’s what a struggling Kahnle looked like ... well, the Sox have seen worse. As the deadline rolled around, he became quite a trade candidate. Yet there were also compelling reasons to keep him — he was under team control for another three years, the lack of career saves made him unlikely to see a huge spike in salaries through his arbitration-eligible years, and the Sox bullpen would need high-leverage types. Any drop in trade value because of his approaching free agency would be offset by the bolstering of his track record.

That said, the Sox dealt Kahnle back to the team that drafted him. Kahnle remained an effective reliever in his first stint with the Yankees, even though he walked more batters as Yankee (10) than he did with the White Sox (seven) in 9 1⁄ 3 fewer innings. The strikeout rate also settled into the low 30’s.

Kahnle saved his best stuff for the postseason, when he rattled off six scoreless outings, with six of them requiring six or more outs. He closed out Game 4 of the ALDS with a five-strikeout performance over two scoreless innings. Alas, his season crashed into the barrier, as he gave up three of the four runs the Yankees allowed in their Game 7 loss to Houston in the ALCS. That outing notwithstanding, he’s still in a very good position to be a very good reliever at a reasonable cost the next three seasons.

*David Robertson, who warded off signs of decline in 2016 by showing a more dominant streak in 2017. He converted 13 of 14 save opportunities with the White Sox, and they were easier to watch because 15 of his 33 1⁄ 3 innings were of the three-up-three-down variety.

He contributed to and benefited from the curveball revolution. After throwing them 30 percent of the time over his first two years with the Sox, his usage jumped up to 43 percent. The strikeout rate rebounded to 37.1 percent, matching his last year with the Yankees, and the walk rate dropped three points as well.

Over the winter, it looked like the White Sox might have to chip in some cash to offset the remaining $25 million on the final two years of his deal. However, his first half alleviated concerns on both the performance and financial fronts, which made it seem like he could be a standalone trade piece.

Instead, he was packaged with Kahnle and Frazier in a return to New York, where he took it up a notch as a setup man. He posted a 1.03 ERA over 36 innings, allowing just 14 hits and 12 walks to 51 strikeouts. Opponents hit just .119/.205/.195 against him after the trade, and he became Joe Girardi’s chief fireman in the postseason afterward.

Robertson started October by throwing a career-high 3 1⁄ 3 innings -- scoreless -- in the Wild Card game, carrying the game from the third to the sixth and picking up the win in the process. It was the first of eight appearances over 13 postseason games, five of them requiring more than three outs. He did give up a game-tying homer in Game 2, but he picked up the win in Game 5 with 2 2⁄ 3 scoreless innings.

He was less successful in the ALCS, although the five runs he gave up did not affect the games in any meaningful way.

Robertson’s a somewhat counterproductive fit for the Yankees because his $13 million will only be good for the second-highest salary in the bullpen, and it’s a team trying to get under the luxury tax. Then again, it may be fine as long as that money is cleared by the 2018-19 free agent class, of which Robertson will be a part.

*Todd Frazier, who continued slugging away as a low-average home-run threat with reliable defense at third base. He hit just .207 with the White Sox, although an uptick in walks and a rebound in his defensive metrics ultimately made him a decent starter. He had racked up 48 walks when the White Sox traded him, and that was good enough to make him the team leader despite missing the last two-plus months.

The market for corner infielders was limited — especially for teams needing a rental — but fortunately two teams lacking production from third base happened to be direct rivals. The Red Sox chose Eduardo Nunez and Rafael Devers, while the Yankees acquired Frazier. Frazier walked even more frequently as a Yankee, but otherwise his production mirrored his time with the Sox. This even extended into the postseason. Frazier hit just .186 with a .255 on-base percentage, coming up with a couple timely hits — including a very ugly three-run homer against Houston -- but also going 0-for-10 over the last three games.

He’s now a free agent who will turn 32 around the time pitchers and catchers report.

White Sox received...

*Blake Rutherford, whose draft status (18th overall pick in 2016) and prospect status (top-50) hinged on his fundamentally sound left-handed swing developing more pop as he matured.

One year in, the power remains a theory. He hit .260/.326/.348 with just two homers over 101 games between South Atlantic League affiliates Charleston and Kannapolis, and the Yankees saw the best part of it.

Charleston: .281/.342/.391, 24 extra-base hits over 71 games

.281/.342/.391, 24 extra-base hits over 71 games Kannapolis: .213/.289/.254, five extra-base hits over 30 games

At the time of the trade, it looked like Rutherford had found gap power, which is a step on the way to genuine power. After the trade, doubles were mostly a dream.

Rutherford spent the instructional league working on improving his launch angle, although the Sox don’t like using that word with players. This development is vital for him because he profiles more as a corner oufielder who can occasionally cover center, which is why Ryan Sweeney often comes to mind. Sweeney had his own power outage in the minors, hitting just one homer as a 20-year-old. The difference is that Sweeney was a 20-year-old in Birmingham, where fly balls go to die unless you’re Eloy Jimenez.

Rutherford still has time on side. He’s also got plenty of work cut out for him, especially in a crowded low-minors outfield situation.

*Ian Clarkin, who has had a difficult time staying healthy over his five professional seasons. The Yankees drafted him with a compensatory pick in the 2013 draft (right after Aaron Judge), and the lefty has a 3.16 ERA in the minors since, which reflects the quality of his pitch mix in A-ball.

He’s also never thrown 100 innings in a season due to a variety of DL stints. He came to the Sox with ankle, elbow and meniscus injuries in his past, and he added an oblique strain to the list after the deal. He was limited to just 11 innings with Winston-Salem.

If he can stay healthy, he profiles as a command-oriented lefty groundballer who has enough on his fastball to sit in the low-90s. He’ll be eligible for the Rule 5 draft, which is another reason why he was expendable to the Yankees, who have their own 40-man roster crunch. The White Sox probably don’t have to protect him, but since he’s a lefty, one can’t quite be sure.

*Tito Polo, an undersized spark plug of an outfielder whose production has exceeded scouting reports. After a breakout year in A-ball between the Pirates and Yankees organizations in 2016, Polo maintained his standing by hitting .289/.346/.434 with 20 steals for High-A Tampa. That warranted a promotion to Double-A Trenton, where he hit .382/.460/.545 in 14 games before a trade sent him to Birmingham.

Adjusting for the difficult hitting environment, and there’s nothing wrong with Polo’s .278/.342/.389 line with the Barons. It would’ve been nice if Polo played more than 21 games, but a DL stint interrupted the start of his time with the White Sox. Polo headed to the Arizona Fall League for reps, but was replaced a few days ago by Charlie Tilson because he needed a tooth pulled.

Assuming Polo is in full working order in 2018, he could grab some playing time in a very open center field situation for the White Sox. Before then, he’s eligible for the Rule 5 draft, and his skill set is potentially versatile enough to warrant a selection. Like Clarkin, though, the time missed might have been enough to suppress enthusiasm about his immediate prospects.

*Tyler Clippard, who wasn’t going to have a spot in the Yankees’ postseason bullpen, and had a little more than $2 million remaining on his deal. Given the White Sox sent their two best relievers and two of their bigger annual contracts to New York, it made sense to get some veteran ballast back.

This part of the deal was basically an accounting move. Clippard pitched well enough for the White Sox -- two runs over 10 innings, many of them adventuresome — to find his way back to a contender. In this case, the Astros picked him up, paying the White Sox $1 million in mid-August, which covered most of his remaining salary.

The White Sox fared...

... well, it’s a poor first impression. There’s still plenty of time for development, but the early returns have thus far reinforced the prospects’ fatal flaws (Rutherford can’t find power, Clarkin can’t stay healthy), and they’re not even out of A-ball yet. It’s pessimistic but realistic to predict that none of these players will reach the majors with the White Sox, which is something that can’t be said about the other deals we’ve examined (for Jimenez, it’d be pessimistic bordering on masochistic).

Of course, Sale, Eaton and Quintana had insanely valuable contracts while Robertson and Frazier earned the market rate. Moreover, while one could envision Sale, Eaton and Quintana playing for the next good White Sox team before their contracts expired, the windows of relevance were over for the two veterans dealt here. The Sox lacked leverage.

Kahnle was the exception as somebody who had a potential future with the Sox -- he would’ve made a fine extension candidate if he were amiable to a deal -- and so it surprised me to see him packaged with Robertson and Frazier. Then again, if the Sox really wanted Rutherford, Kahnle was the only player they had to get him, and a top-50 prospect was a strong return for a volatile reliever’s first good half-season.

But that assumed that Rutherford had established a trajectory, which didn’t turn out to be true. A few months later, Kahnle has a good full season under his belt with three affordable salaries ahead while Rutherford’s progress reversed in Kannapolis. Take a step back and recalibrate, and it looks like Rick Hahn sold Kahnle too soon.

Speaking of “too soon,” one can’t yet draw a conclusion about this deal, but that can be said for every prospect trade. For the time being, it’s a counterweight to the excitement from the Eaton trade. In that move, the White Sox received three pitchers whose collective progress would be hard to top. In this trade, the White Sox are still waiting for even one of these players to make a clear step forward.