Dodgers select Wisconsin high school shortstop Gavin Lux with first-round pick

With four choices in the top 65 picks in Thursday’s Major League Baseball draft, the Dodgers selected a shortstop and a catcher with solid defensive reputations and a pair of pitchers with Tommy John surgery in their past.

The team chose shortstop Gavin Lux, an 18-year-old from Indian Trail Academy in Kenosha, Wis., with the 20th pick. They followed that up with University of Louisville catcher Will Smith at No. 32 and Vanderbilt right-handed pitcher Justin Sheffield at No. 36. To wrap up the day, the team picked Santa Clara right-hander Mitchell White at No. 65.

Lux has committed to Arizona State, but he sounded enthusiastic about signing with the Dodgers.

“I want to play professional baseball,” Lux said on a conference call. “I’m kind of set on doing that. So for me, right now, I just want to get out there and get going as soon as possible. I’m pumped up to start my career right now.”

The two compensatory picks resulted from unforeseen outcomes. The Dodgers received the No. 32 selection when Zack Greinke signed with Arizona.

The Dodgers missed the chance for two more picks when Brett Anderson accepted a $15.8-million qualifying offer and when Howie Kendrick, his market collapsed due to requiring draft-pick compensation, re-signed for two years and $20 million.

The Dodgers were granted the No. 36 choice after failing to sign first-round choice Kyle Funkhouser, a pitcher from Louisville. Funkhouser rejected the Dodgers’ offers and returned for his senior season. Walker Buehler, the team’s other first-round pick in 2015, needed Tommy John surgery and has yet to pitch in a professional game.

Lux hit .531 as a senior and was the Gatorade player of the year for Wisconsin. His uncle, Augie Schmidt, was selected with the second-overall pick in 1982 by Toronto. Schmidt coaches baseball at Carthage College in Kenosha.

“We really think he’s got a chance to be a good hitter at the major league level,” Dodgers scouting director Billy Gasparino said. “It’s a nice mix of talent and skill, and a kid who comes from a baseball family.”

Smith, 21, hit .380 with seven home runs, eight doubles and a 1.049 on-base plus slugging percentage during his junior season for the Cardinals. Gasparino referred to him as a “little bit of a late bloomer.”

“He can really receive,” Gasparino said. “He can really throw. And he had a really good year this year. He started to hit with power.”

Sheffield, a 6-foot 21-year-old, underwent Tommy John surgery as a senior at Tullahoma High in Tullahoma, Tenn. He is the nephew of former Dodger Gary Sheffield.

Gasparino said the team was pleasantly surprised to see Sheffield still available at No. 36.

After pitching for most of 2015 in the bullpen, Sheffield made 16 starts for the Commodores this season. He struck out 113 batters in 1012/3 innings with a 3.01 earned-run average.

“He’s a highly competitive kid,” Gasparino said. “He knows the game. He understands professional baseball.”

Vanderbilt starter Jordan Sheffield pitches against Xavier in the first inning of an NCAA regional tournament game.

(Mark Humphrey / Associated Press)

Like Sheffield, Mitchell also needed Tommy John surgery in 2013. He also spent the entirety of 2015 as a reliever. He converted to Santa Clara’s rotation this season and made 15 starts with a 3.72 ERA. He struck out 118 batters in 92 innings.

His fastball touched 95 mph in the second half of this season, Gasparino said. The team also believes in his slider. He stands 6-4, and his physicality aids him on the mound.

“We feel like he’s trending up,” Gasparino said. “And he has a chance to be a mid-rotation starter.”

andy.mccullough@latimes.com

Twitter: @McCulloughTimes