Braves pitcher Kris Medlen faces another rehabilitation period of at least 12 months after having Tommy John elbow surgery Tuesday for the second time in four years. And frankly, the odds he’ll pitch again at peak level are not very good.

Medlen, 28, had the ulnar-collateral ligament reconstruction procedure, commonly referred to as Tommy John surgery, done for the second time in 41 months by Dr. James Andrews, who also did his August 2010 surgery.

“He had the surgery, and everything went well,” Braves manager Fredi Gonzalez said Wednesday after getting an update from a team trainer.

Medlen missed most of the 2011 season for a 13-month rehab following that procedure, and the average recovery period has been longer for most of the relatively few pitchers who had the surgery a second time.

The Braves now have two pitchers — Medlen and reliever Jonny Venters — recovering from their second Tommy John surgeries, and could have one more if Brandon Beachy decides to have the surgery after getting another opinion from a Los Angeles specialist this week.

Beachy has pitched in only five regular-season games since having his first Tommy John surgery 21 months ago and also had an arthroscopic procedure in September to remove a bone chip. He left his March 10 start after two innings with what he thought was only biceps tightness, but which tests revealed to be more ligament damage.

Andrews has done all six elbow surgeries — five Tommy John and the Beachy arthroscope — on those three Braves pitchers.

Venters had Tommy John surgery in May 2012 and aims for a return by June. The rehab procedure is sometimes slightly shorter for relief pitchers because they don’t have to build stamina as starters do before returning to pitch in games.

The success rate for coming back from a second Tommy John surgery has been higher for relievers than starters, in terms of pitching again at pre-surgery level. Andrews has put that overall success rate at 20-30 percent for pitchers coming back from second Tommy John surgeries to pitch at pre-surgery levels, although more than twice as many have at least made it back to pitch again in the majors.

Medlen is believed to be the 25th major league pitcher to have a second Tommy John surgery, and Oakland’s Jarrod Parker is expected to become the 26th after being diagnosed this week with a torn UCL. Parker had his previous surgery in 2009.

Both Medlen and Parker had been penciled in as opening-day starters. The Braves are expected to announce that Julio Teheran will start the March 31 opener at Milwaukee, and be joined in the rotation for the first week by veteran Freddy Garcia, second-year left-hander Alex Wood, and rookie David Hale, who has pitched in two major league games.

Ervin Santana could join the rotation on or before the Braves need a fifth starter April 12, their 11th game. The Braves signed the former All-Star last week to a one-year, $14.1 million free-agent contract after the Medlen and Beachy injuries, and he’s thrown batting practice and will make his first spring-training start Thursday.

Fourteen of the previous 24 pitchers who had multiple Tommy John surgeries have returned to pitch in the majors, according to research by Dodgers head athletic trainer Stan Conte. He has one of those pitchers, former Giants closer Brian Wilson, in the Dodgers bullpen.

Three others among those 24 — Venters, Randy Wolf, Todd Coffey — could return soon, which would put the return rate at nearly 71 percent among the two dozen pitchers before Medlen to have multiple Tommy John surgeries. But returning to pitch can be quite different than pitching at pre-surgery levels.

Medlen has been one of the majors’ best since moving from the bullpen to the rotation at the end of July 2012. He was 24-12 with a 2.47 ERA in 44 games (43 starts) since, and his 2.40 ERA since the 2012 All-Star break was the second-best among pitchers with at least 250 innings, behind only Dodgers ace Clayton Kershaw.