Barnum also packs a punch at the plate, as he hit .491 as a junior.
"We tried to play the board the way that we could, and got a lot of middle infielders and young kids," Laumann said. "You kind of have to do what the draft dictates by what's available, and I didn't think the college crop was real good this year."
One of those middle infielders was New Mexico State shortstop Zachary Voight, who the White Sox selected in the 20th round. Voight hit over .300 his junior and senior years, adding eight home runs his senior year after hitting just two during his junior season.
"It was really nothing to prove that I had the power," Voight said. "I finally got the freedom, getting to hit in the four-hole rather than the two-hole. I got to look for the pitches to drive rather than look to get the runner over."
Though Laumann said he wasn't as fond of the college class this year as in years past, 29 of Chicago's final 39 picks came from the college ranks. In the later rounds, the White Sox shifted toward selecting more seasoned collegiate players who may be easier to sign.
"Once you get to the 25th, 30, 35th round, you're not going to be able to be expected to go get a high school kid or even like a college junior that's got some leverage and the ability to go to college and get better," Laumann said. "The type of money we pay these guys in the lower rounds, you almost have to stick with the college seniors."
Regardless of age, the White Sox finished with depth at every position in the draft. The South Siders selected three catchers and third basemen, while grabbing four first basemen, outfielders, second basemen and shortstops.
The remaining 19 selections were pitchers, including 22nd round pick Cory McGinnis, a senior from Auburn University at Montgomery who was also looked at by the Padres a day earlier.
"I'd been drafted before, but when you're a senior and you know you're gone, you're just kind of hoping you get a chance," McGinnis said.
The White Sox turned their attention to pitching on the second day of the Draft, selecting pitchers with nine of their 14 selections on Tuesday. Of the 19 total pitching selections, 15 were right-handers.
The club's second and fourth-round picks were both right-handers with high upside. Laumann said Chris Beck, who was selected 76th overall, could be a first-round talent if he can find the stuff he had last summer as a Cape Cod League All-Star.
Brandon Brennan, the club's fourth-round pick (141st overall), was 11-1 with a 1.25 ERA at Orange Coast College in California.
Laumann said previously that when deciding between a pitcher and a position player, he normally leaned toward taking a hurler. The club took another 10 pitchers on the final day of the draft on Wednesday.
"Typically at the end of the Draft you can find certain positions," Laumann said. "There's always a lot of pitchers."
The White Sox didn't select a third baseman until the 18th round in Kentucky senior Thomas McCarthy, a first-team All-SEC player in 2011 who hit .310 with five home runs and 33 RBIs this year. They went with third basemen again in consecutive rounds in the 31st and 32nd, with college seniors in East Carolina's William Thompson and Temple's Steven Nikorak, respectively.
Thompson hit at least .315 in each of his final two seasons, while the versatile Nikorak, who pitched, and played first base and third base in his time at Tulane, hit .304 with seven home runs.
With the amount of college seniors selected in the later rounds and early high school picks, the South Siders should be able to sign a significant amount of players.