Gott was born in Lexington, Kentucky. He was a pitcher on the Southeast Lexington team that went to the Cal Ripken 12-and-Under World Series in 2005. During one game in that series, he struck out nine batters in three innings. Gott attended Tates Creek High School. In 2010, a writer with The State Journal referred to him as "one of the best pitchers in the state." As a senior, he was 6-0 with a 1.12 ERA and 76 strikeouts in 47.1 innings, and batted.382 with two home runs and 13 RBIs. He was the Gatorade Kentucky High School Player of the Year.
College career
Gott played college baseball at the University of Kentucky for the Wildcats from 2011 to 2013. After his freshman year, he pitched in the Cape Cod Baseball League, where he was the winner of the Russell Ford Award as the league's reliever of the year. As a sophomore in 2012, Gott set the Kentucky record for saves in a season with nine. Before the start of the 2013 season, Gott had recovered from a minor bout of bursitis and he was on the preseason watch list for the NCBWA Stopper of the Year Award. That year he broke his own single-season save record, finishing with 12, and he also set the school's all-time saves record with 20.
In early 2013, Baseball America named Gott as the second-best draft prospect from the University of Kentucky behind Corey Littrell. The San Diego Padres drafted Gott in the sixth round of the 2013 Major League Baseball draft. He signed with the Padres for a $200,000 signing bonus and made his professional debut with the Eugene Emeralds of the Class A-Short SeasonNorthwest League. After making four appearances with Eugene in which he pitched to an earned run average of 2.08, walked three, and struck out eight in innings with no decisions, he was promoted to the Fort Wayne TinCaps of the Class AMidwest League. He finished the season with the TinCaps, making 27 appearances for them and pitching innings in which he walked 12, struck out 33, posted a record of 2–2 and an ERA of 2.56, and recorded his first four professional saves in five opportunities. He finished the 2013 season with 31 appearances and a 2.50 ERA overall, with 15 walks, 41 strikeouts, four saves, and a record of 2–2 in 36 innings of work. Gott started 2014 with the Lake Elsinore Storm in the Class A-AdvancedCalifornia League and was named a California League All-Star. He pitched innings in 29 games for Lake Elsinore, striking out 31, walking nine, posting a record of 2–2 and an ERA of 3.16, and recording 16 saves in 20 opportunities. He was promoted to the San Antonio Missions of the Class AATexas League in July 2014. In 10 appearances for San Antonio, he had no decisions, but he struck out 11, walked nine, and pitched to a 4.63 ERA in innings of work.
On July 19, 2014, the Padres traded Gott, along with Huston Street, to the Los Angeles Angels of Anaheim in exchange for Taylor Lindsey, R. J. Alvarez, José Rondón, and Elliot Morris. The Angels sent him to the Arkansas Travelers of the Class AA Texas League, where he finished the season. He had a record of 2–1 and an ERA of 1.53 at Arkansas with 18 strikeouts, seven walks, and two saves in four opportunities, pitching innings in 13 games. Overall in 2014, he made 52 appearances for three minor-league teams, pitching innings, striking out 60, walking 25, posting a record of 4–5 and an ERA of 2.97, and recording 18 saves in 24 opportunities. In the fall of 2014, Gott played for the Mesa Solar Sox in the Arizona Fall League. He made eight appearances for the Solar Sox with no decisions, posting an ERA of 6.14 in innings of work, walking two, striking out four, and recording one save. He also was honored as an Arizona Fall League Rising Star and represented Mesa on the East team in the league′s Fall Stars Game that year.
2015
Gott started the 2015 season with Arkansas, pitching innings in 18 appearances with a record of 1–0 and an ERA of 3.20, striking out 20, walking seven, and going 8-for-8 in save opportunities. He was a Texas League mid-season all-star in 2015. Promoted to the Salt Lake Bees of the Class AAAPacific Coast League on May 24, he blew his only save opportunity but gave up no earned runs in seven appearances for the Bees, striking out 10 and walking five in innings of work with no decisions, giving him overall minor-league statistics for 2015 of 28 innings pitched in 25 games with a record of 1–0, an ERA of 2.25, 30 strikeouts, 12 walks, and eight saves in nine opportunities. The Angels selected Gott's contract from the Bees on June 13, and he made his major-league debut with the Angels on June 14, 2015. Later in the season, he became an important part of the Angels' bullpen after closer Huston Street and pitcher Joe Smith both suffered injuries. He finished the season with the Angels, appearing in 48 games for them, going 0-for-4 in save opportunities but striking out 27, walking 16, and posting a record of 4–2 and an ERA of 3.02 in innings pitched. On December 10, 2015, the Angels traded Gott, along with Michael Brady, to the Washington Nationals in exchange for Yunel Escobar.
Washington Nationals
2016
The Nationals assigned Gott to the Syracuse Chiefs in the Class AAA International League to start the 2016 season. He went on the 7-day disabled list on June 6 with elbow inflammation, and remained out of action until July 25, when he was sent to the Gulf Coast League Nationals of the rookie-level Gulf Coast League for a rehabilitation assignment. He took the loss in his only appearance for the Gulf Coast League Nationals, giving up two earned runs and striking out two in two innings pitched. On July 27, he reported to the Auburn Doubledays of the Class A-Short Season New York-Penn League to continue his rehabilitation assignment and made one appearance for them, giving up an earned run and striking out two in two innings of work. He was reactivated to play for Syracuse August 1. Overall, Gott made 33 appearances for Syracuse in 2016, pitching innings, posting a record of 3–3 and an ERA of 4.35, striking out 31, walking 13, and recording one save in three opportunities. After major-league rosters expanded to 40 men, the Nationals called Gott up on September 2. Gott posted a 1.50 ERA in six innings over nine appearances for Washington, striking out six and walking three with no decisions.
2017
Gott began the 2017 season with Syracuse. The Nationals called him up to the majors on June 12 when Washington needed bullpen reinforcements. He earned his first win with the Nationals on June 13, but he ended up as the team′s "sacrificial lamb" in a 13–2 loss to the Atlanta Braves the next day, needing 52 pitches to get through innings, striking out two batters but giving up five runs – all earned – on five hits and two walks before he was relieved. Washington optioned Gott back to Syracuse after the game. The Nationals recalled Gott on July 14 after they optioned Sammy Solis to the minors and placed Joe Ross on the disabled list with a torn ulnar collateral ligament of the elbow. Appearing in the ninth inning of a game against the Cincinnati Reds the next day in which Washington led 10–2, Gott proceeded to give up five earned runs without recording an out before de facto closer Matt Grace entered to record the save. The Nationals again optioned Gott to Syracuse on July 18. On July 24, he went on the 7-day disabled list retroactive to July 22, and did not return to action in 2017, subsequently being shut down for the season to undergo hernia surgery. Overall in 2017, Gott made 30 appearances for Syracuse, pitching innings, striking out 35, walking 13, posting a record of 2–0 and an ERA of 3.86, and going 4-for-4 in save opportunities; for Washington, he made four appearances, with a 1–0 record and three strikeouts in three innings of work, but he also walked three and his major-league ERA for the season was 30.00.
2018
After a standout performance in spring training in which he posted a 1.54 ERA in innings over 11 appearances, Gott began the 2018 season on the Nationals′ 25-man roster. To start the season, he appeared in five games, pitching five innings and giving up three earned runs for a 5.40 ERA before he was optioned to Syracuse on April 16. The Nationals recalled Gott on April 21 when they placed reliever Matt Grace on the disabled list. Gott slipped on the mound and sprained his ankle at Nationals Park in Washington, D.C., on May 5 during the sixth inning of a 7-3 win over the Philadelphia Phillies, throwing 17 pitches and getting one out but giving up a single, two home runs, and three earned runs before exiting. He remained with the Nationals after the incident and without a stint on the disabled list. He had a 5.28 ERA, an 0–2 record, seven walks, and 12 strikeouts in innings over 17 major-league appearances on the season when the Nationals optioned him to Syracuse again to make room on their roster when they activated reliever Ryan Madson from the disabled list. The Nationals again recalled Gott from Syracuse along with reliever Wander Suero on June 11 when they placed starting pitcher Stephen Strasburg and reliever Brandon Kintzler on the disabled list, and on June 13 – by which time he had lowered his major-league ERA for the season to 4.96 but had given up eight walks along with striking out 12 in the majors for the year – again optioned him to Syracuse when they called up starting pitcher Erick Fedde from the Chiefs.
San Francisco Giants
On February 13, 2019, after being designated for assignment, Gott was acquired by the San Francisco Giants in exchange for cash. Pitching for the Giants in 2019 he was 7-0 with one save and a 4.44 ERA, as in 50 relief appearances he pitched 52.2 innings and struck out 57 batters.
