Neverauskas is a native of Vilnius, Lithuania, where he learned to play baseball on rocky soccer fields. When he signed with Pittsburgh as an amateur free agent in 2009, he was the first Lithuanian to sign a professional baseball contract.
Neverauskas put up unimpressive numbers in his first five seasons in the minors as a starter but he quickly advanced through the Pittsburgh system after being moved to the bullpen in 2015. He was invited to participate in the MLB Futures Game during the All-Star Game last season.
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Neverauskas had a 1.207 WHIP and struck out 8.7 batters per nine innings across two levels last season. He did not allow an earned run in 8 1/3 innings this season at Triple A.