Black Ops II
Due to a lack of competitive support in Modern Warfare 3, Quantic Gaming has chosen to terminate its sponsorship with Leverage Gaming. During MW3, the roster only participated in one tournament, the EGL 8 Manchester 2012, and then waited for the following game to see if they could get a new sponsor. Complexity Gaming has signed ACHES and TeePee, as well as FEARS and former Halo player Crimsix, for the next season, which coincides with the release of Black Ops 2. CompLexity took first place in Frag Cup IV, beating JuKeD in what was their first big online tournament. OpTic Gaming beat CompLexity in the finals of the first LAN of the season, which took place at UMG Chicago 2012. After the game, there was an argument between ACHES and Nadeshot, which ended in a fight between the two players. ACHES retained his position as team captain, while FEARS was benched in favor of TuQuick for the next competition.

TuQuick was dismissed from the squad after two fourth-place performances at MLG Dallas 2013 and the Call of Duty Championship 2013, and Clayster was brought in from UNiTE Gaming to form what would become one of the best Call of Duty teams in history. MLG Anaheim 2013 was the first event that this new team competed in, and they were victorious, beating the four-time reigning champions, Impact Wrestling. The squad would go on to win the next two competitions, Gfinity 1 and UMG Atlanta 2013. Although UNiTE Gaming would finish second to CompLexity at the MLG PAX Prime Invitational, the team would rebound to win the last three events of the season at Gfinity 2, the MLG Fall Invitational 2013, and the ESL World Championship Series 2013.
Ghosts
Despite winning MLG Columbus 2013, CompLexity was unable to maintain its dominance in Ghosts. Clayster was dropped by the squad as a result of internal disagreements rather than due to poor performance. Karma, a former Impact world champion, would be the new member, and he and the squad hit it off right away, winning the following tournament, UMG Philadelphia 2014. A decision was made to withdraw from the Call of Duty Winter Invitational after just two matches by the squad. The reasons behind this were inadequate organization and the fact that we were not permitted to broadcast on Twitch. The squad has set its eyes on the Call of Duty Championship 2014 competition. They qualified for the tournament by finishing in second place in the Call of Duty Championship 2014: United States Regional Final in September.
When it came to winning the Call of Duty Final in 2014, CompLexity went undefeated in group play while also taking home every series in the championship bracket. Their victory against Team EnVyUs in the global championship finals earned them the title. As a result, Karma is the only person to have won the World Championship twice. Following the tournament, the team proceeded to demonstrate their supremacy by winning the MLG CoD League Season 1 Playoffs and then further demonstrating their dominance in the UGC Niagara 2014 Championship. They were eliminated in the first round, but they battled their way through the losers bracket to take home the championship. Announcing the sale of their squad to Evil Geniuses after the tournament on May 6, 2014, the team revealed that the team had been acquired for an unknown sum. CompLexity would be gone from the scene for two years until they resurfaced with a new lineup at the start of Call of Duty: Black Ops 3.
Black Ops 3
In a press release issued on November 5, compLexity announced the addition of NAMELESS, Ricky, MiRx, and Parasite to their roster for the upcoming Black Ops III campaign. The team finished third or fourth in their debut competition, Totino's Invitational 2015. A short time after the tournament, the squad was asked to compete in the 2016 COD World League NA Pro Division Qualifying Invitational Tournament, with the winner earning a spot in the 2016 NA CWL Stage 1 Regular Season. They won their first two games against Nation and Happy Hour to earn a place in the league. CompLexity was defeated by challenger team Team Liquid at the UMG South Carolina 2016 Champion Tournament and was sent home with a 9-16th Place result in the tournament. Over the course of the following month, the squad would only achieve one top-eight result in the four online Challenger Division tournaments they participated in. It was a continuation of the team's difficulties as they finished the 2016 NA CWL Stage 1 Regular Season in sixth place with a 10-12(41-50) record, which included losing their last six games. During the 2016 NA CWL Stage 1 Playoffs, FaZe Clan beat compLexity 4-0, and they would go on to place 5-8th overall. Following the incident and months of internal turmoil, the team decided to part ways with Parasite and recruit Goonjar, a former member of the demoted Team Kaliber. After just a month, this move failed to provide any noticeable improvement, and Parasite was reinstated to the roster in lieu of NAMELESS.