All right I'm changing the rules a little because this is kinda fun. I'm changing 1 draft pick. Only 1.
With the 23rd pick in the 2009 MLB Draft, the Chicago White Sox select...Mike Trout, Millville Senior High School, New Jersey. Assume he follows the same path and the White Sox don't accidentally trade him in 2010 for an overpaid pitcher.
2011...Alex Rios, Alejandra De Aza play a fair amount of CF. Rios has an utterly awful season, so there's plenty of room for experience for Trout. The team still finishes a few games below .500 because Trout isn't a difference maker. Ozzie Guillen still quits on the team, Robin Ventura is hired.
2012. White Sox finished 3 games behind 88 win Detroit Tigers for AL Central, most common CF is Alejandro De Aza who puts up 2.3 rWAR. White Sox are a 90+ win team and a legitimate one, also beating Detroit on WAR. They struggle down the stretch again as their pitchers tire, but their lead was substantial by midseason and the White Sox win the AL Central by several games. Robin Ventura gets his contract extended here.
2013: Disaster. Pitchers get hurt, offense falls apart. Team originally won 63 games - now they're a 71 win team. Jake Peavy is still traded midseason to Detroit for Avisail Garcia.
2014: Now here's where it gets really interesting. They draft 6th, just before the Philadelphia Phillies. Carlos Rodon is off the board, let's assume he went to the Cubs. The White Sox have a choice between Aaron Nola and Jeff Hoffmann, who fell due to TJS. The White Sox go ahead and draft Nola (you want to run this the other way, you go ahead). The White Sox still need a 1b and the Yankees and Red Sox are still out, so they still sign Jose Abreu. Unwilling to sign a $100 million deal, they choose not to sign Trout to the same extension that the Angels gave him. The trade for Adam Eaton, involving Hector Santiago, still makes sense for the White Sox, so they acquire him as a corner OF, effectively moving De Aza and Viciedo out of the lineup. Garcia still gets hurt as Ventura is still the coach. The White Sox finish as a .500 team.
2015: Trout's first arbitration year. The White Sox are convinced they have a shot in the AL Central. Rick Hahn is still alive and Robin Ventura is still the manager. Therefore, in the offseason they trade Bassitt and Semien to the A's for Jeff Samardzija. They sign Adam LaRoche to DH, but they do not sign Melky Cabrera as they don't need an extra OF. Aaron Nola is rushed to the big leagues as soon as the extra year of FA is available in April, he's a little more effective than Rodon but not much. They no longer have the least effective position players in baseball, but they total about 35 fWAR. They finish a couple games above .500.
In an alternative universe - Rick Hahn retires and Jerry Reinsdorf passes ownership to his family, ,the White Sox realize they need to be aggressive with only 3 years of control left on Trout, and rather than trading for Samardzija, they take the money they would have spent on Samardzija + Cabrera and go for a big pitching splash. Both Lester and Scherzer were available. In the process, the White Sox hold onto Semien and Bassitt. The draft really doesn't help unless the White Sox strike gold and select walker Buehler, who was the only good pick in the 2nd half of the first round.
2016: Trout's second arbitration year. They have 2 years left before he signs the biggest contract in MLB History. In the real world, Cleveland won 94 games with a huge winning streak midseason, they put up 42 fWAR. The White Sox put up 32. But, Eaton moves to RF, Trout moves to CF, Nola struggles a fair amount in the rotation. The Wild Card winners that year only won 89 games. With Trout in the lineup, the White Sox make it a 3-way tie for the Wild Card, with the team still underperforming some. The White Sox still make a midseason deal for James Shields, correctly thinking they need pitching help. Shields continues to be awful and it's the worst deal any of us have ever seen.
In the second alternate universe with a new owner, the White Sox signed either Lester or Scherzer in 2015. They hold onto Semien, Bassitt still gets hurt, but they know they need additional offense on the IF and they know they need a LH bat somewhere in their lineup. Rather than Frazier, they acquire Chase Headley, who was dealt to the Yankees the year before (and the Yankees still wind up rebuilding for a year in 2016, they got themselves out of the multi-year penalties around then). Semien takes over an IF slot and while he struggles on defense it isn't a killer. In this universe, the White Sox take the AL Central. Cubs White Sox world series is possible if both teams advance. Oh, and a kid SS who no one has seen play has a breakout campaign in their minor leagues.
2017: Trout's last year with the White Sox. Avisail Garcia has a breakout season, 5 WAR. Chris Sale has a 7 win season. Aaron Nola has a breakout season. Jose Quintana is still ok. Jose Abreu has his best season. Tim Anderson is working into the IF. Adam Eaton gets hurt in the OF, I don't have a good candidate to replace him. This team is strong even if they still made the Rick Hahn moves. If they made the "not Rick Hahn" moves and signed a Scherzer, held onto a Semien, and therefore never traded for a Shields...Cleveland and Chicago both win in the high 90s in games, and who knows if a trashcan is enough for the Astros to win that title? And oh, the next year the White Sox have the #1 prospect in baseball.
2018: Garcia and Abreu struggle. Trout has departed for the Yankees. Nola puts up his best season, Sale starts showing some injury issues at the end of the year. Anderson is up and has taken over SS, while Semien has moved to a different IF spot. Quintana falls apart. This team misses the playoffs.
2019: Chris Sale goes down for TJS and then re-signs with the team for a short term deal. Aaron Nola isn't as good as the previous year. But the White Sox's infield is now Semien, Anderson, Tatis, Abreu from 3b to 1b. Robin Ventura is still managing this team.