Drake is a graduate of Northfield Mount Hermon School, earning letters in baseball and hockey while a student there. He was a first-team All-CNEPSL as a junior and a senior, winning the Thompson Blanket, Ralph E. Jillson and Nettie M. Johnson Memorial awards as the latter. After high school, Drake attended the United States Naval Academy and played for the Navy Midshipmen baseball team. He had one of the best freshman pitching seasons in school history, going 3-3 with a 3.22 ERA. He went 6–3 with a 3.70 ERA as a sophomore, having an 8.74 K/9 ratio. After two years at Navy, Drake was drafted in the 43rd round of the 2008 Major League Baseball draft by the Orioles.
Professional career
Baltimore Orioles
Drake was assigned to Rookie-league Bluefield, then the Bluefield Orioles, pitching in 7 games, going 1–0 with a 0.77 ERA before being promoted to Low-A Aberdeen, pitching in 5 games with a 0.87 ERA. His totals in 2008 were 12 games, going 1–0 with a 0.82 ERA. He spent all of 2009 with Single-A Delmarva, going 8–9 with a 4.34 ERA over 25 games, 24 of them starts. He played all of 2010 with High-A Frederick, going 6–6 with a 4.36 ERA over 24 games. He also played in the Arizona Fall League with Scottsdale, going 1–3 with an 8.38 ERA. He split 2011 with Frederick and Double-A Bowie, while also playing 1 game with Triple-A Norfolk, going 11–8 with a 3.32 ERA over 27 games. He was added to the Orioles' 40-man roster following the season. He had shoulder surgery in 2012. Entering 2014, he was rated the Orioles' 24th-best prospect by Baseball America. Drake signed a major league deal with the Baltimore Orioles on November 18, 2014. In 2015, in 18 innings for Norfolk, he had a 0.96 ERA. On May 23, 2015, Drake was promoted to the Major League team and made his pitching debut that day. Entering the game in the ninth inning of a scoreless tie against the Miami Marlins, Drake pitched three scoreless innings, allowing only two hits and striking out two in a game the Orioles eventually lost 1-0 in 13 innings. By making his big-league debut, Drake became the second former Naval Academy pitcher to make his Major League debut during the 2015 season, along with Navy alum Mitch Harris of the St. Louis Cardinals. Drake pitched in five games and 7.2 innings for the Orioles with a 3.52 ERA. On June 3 he was optioned back to the AAA Norfolk Tides. Drake pitched in 13 games for the Orioles in 2015, pitching to a 2.87 ERA in 15 innings. He struck out 17 batters. On September 23, 2016, Drake pitched one inning of relief in extra innings out of the bullpen for the Orioles. The Orioles would walk it off in the bottom half of the inning, giving Drake his first career victory.
Milwaukee Brewers
On April 13, 2017, Drake was designated for assignment. Later the same day, the Orioles traded him to the Milwaukee Brewers for a player to be named later or cash considerations. On March 28, 2018, Drake made the Opening Day roster for the Milwaukee Brewers. Drake posted a 5.11 ERA, 1.7 WHIP and a 7:7 K:BB across 12.1 innings in Spring Training leading up to the 2018 season. After struggling to begin the season, he was designated for assignment on May 1st.
Cleveland Indians
On May 5, 2018, Drake was traded to the Cleveland Indians in exchange for cash considerations. He was later designated for assignment on May 26.
Los Angeles Angels
On May 31, 2018, Drake was claimed off waivers by the Los Angeles Angels. Drake was designated for assignment on June 16, 2018 and again on July 23.
Toronto Blue Jays
On July 26, 2018, Drake was claimed by the Toronto Blue Jays. He was designated for assignment on July 30.
Minnesota Twins
On August 3, 2018, Drake was claimed off waivers by the Minnesota Twins. When Drake entered the game on August 4 against the Kansas City Royals, he set the MLB record for most teams played for in a single season with five.
Tampa Bay Rays
On November 1, 2018, Drake was claimed off waivers by the Tampa Bay Rays. He was designated for assignment on November 20.
Toronto Blue Jays (Second Stint)
On November 26, 2018, Drake was claimed off waivers by the Toronto Blue Jays.
Tampa Bay Rays (Second Stint)
On January 4, 2019, Drake was traded back to the Rays for cash considerations. On January 18, 2019 the Rays designated Drake for assignment, and he was outrighted to the Durham Bulls on January 24. He was called up by Tampa Bay on May 26 as Tyler Glasnow was added to the 60-day injured list. On August 12, Drake recorded his first career hit, an RBI single at Petco Park against the San Diego Padres.
