Though we will be looking at some of his best individual performances, football is a team sport, and Carrick's contributions have often been the kind to go under the radar. Those efforts, though, have been channelled into a great deal of silverware.
Five Premier League titles, three League Cups, a UEFA Champions League and a FIFA Club World Cup were added to over the past two seasons with an FA Cup and the UEFA Europa League to complete the spectacular set.
We asked United fans on Twitter to pick out some of their favourite Carrick games, and though many responded with examples, there was also a common theme in the replies. Plenty of people drew attention to his general, long-term contribution, which adds up to more than the sum of its parts.
For some reason, Sir Alex Ferguson could never quite crack the central-midfield nut during his last few seasons as United boss, and this left Carrick with a heavy burden to carry. It might not quite have been half his United career, but there were a few seasons wherein injury to the Geordie was the thing United fans feared most.
He was never the team's best player over the course of a season, but he was the least replaceable in a squad that was short of talent in the middle of the park.
It seemed apt to include a contribution from a Tottenham Hotspur fan, who saw firsthand how the loss of Carrick affected his side's performances. Spurs rebounded in time, but his absence was keenly felt.
The most mentioned performance is also the earliest in the chronology. It is, unsurprisingly, United's 7-1 win over AS Roma in the second leg of the Champions League quarter-final in April 2007. The back end of Carrick's first season at United saw him put in one of his finest displays:
United were scintillating that day. It served as a kind of announcement they were once again ready to compete at Europe's highest level and that Ferguson's decision to back Cristiano Ronaldo and Wayne Rooney as players around whom to build a side was about to be seriously vindicated.
It also served to suggest that giving Roy Keane's No. 16 shirt to Carrick was not as controversial as it seemed. Though their styles could hardly have been more different, there was plenty of evidence of the new incumbent's quality. He scored two goals, something of a rarity during the years to follow, but he demonstrated that he met the standard.
The 7-1 did not take place in a Champions League-winning season, but they corrected that at the next time of asking, winning the 2007/08 competition by beating Chelsea on penalties in Moscow:
Carrick played in three Champions League finals for United but was only on the winning side in that first one. He was solid in midfield, and as Simpson points out, his penalty in the shootout displayed nerves of steel. United were on top of the world, and their No. 16 was at the heart of that.
Following the 0-0 draw in the Champions League round-of-16 first leg away against Inter Milan, Mark Ashenden of BBC Sport described Carrick and Ryan Giggs as "dominant in the middle in the opening exchanges" of the clash.
The day after the second leg, Henry Winter wrote in the Daily Telegraph: "Wayne Rooney’s display against Inter yesterday and Michael Carrick's first-leg contribution highlighted the Premier League's irresistible blend of maturity and adventure."
United were on their way to defeat in the final, but along the way, they showed they could still mix it with the best sides in Europe—this was the Jose Mourinho-managed Inter side that won the Champions League the following season, and Carrick was brilliant against them on their turf.
We will return to those Chelsea games, but the point about his ability to snuff out opposition threats is well made. United's defence in this era, with goalkeeper Edwin van der Sar behind Rio Ferdinand and Nemanja Vidic was best in class. Carrick gave them a lot of support. In 2014, Ferdinand described Carrick as "the best holding midfielder England have," per The Independent.
Ferdinand would be well-placed to judge, having played behind him for so many years.
United won the league and made it back to the Champions League final in 2010/11. Carrick was exceptional during that run.
In that quarter-final away leg against Chelsea, he made a remarkable seven interceptions. Then, in the return leg at Old Trafford, he completed eight of his nine attempted tackles, a huge number for a player not primarily known for his tackling. He helped nullify the Blues as an attacking threat in both legs, ensuring United's safe passage to the semi-final.
Against Schalke 04 in the first leg of that semi-final, he completed 99 of his 113 attempted passes, and all of his five attempted tackles resulted in United winning the ball back. United took control of the tie, and Carrick was a huge part of why.
He was unable to compete with Xavi, Andres Iniesta and Sergio Busquets in the final, but in a two-man midfield alongside a 37-year-old Giggs, he never stood a chance.
It is not necessarily fair to say this game changed the trajectory of his United career given his contributions at the back end of the 2010/11 season were so noticeable, but the away game against Queens Park Rangers in December 2011 did mark the moment United's away support embraced Carrick.
The "It's Carrick, ya know; it's hard to believe it's not Scholes" chant had been written long before, but this was the game when it got its first sustained airing. The next game at Old Trafford saw the Stretford End sing it too, and for the next couple of seasons, it was an ever-present in the rotation. It was a defining moment in the player's relationship with the club's support.
One of the reasons his song was sung so often in the years that followed that QPR game is the player's performances remained consistent. The aforementioned Newcastle United performance was particularly memorable thanks to his brilliant assist for Javier Hernandez's winner, but he was the club's second-best performer behind Robin van Persie across the season. It was vital that he was too, as United's midfield resources were at their most stretched during that campaign.
This run of games in early spring 2015 saw Louis van Gaal rejig his midfield as part of a 4-3-3 formation, with Ander Herrera and Marouane Fellaini free to attack while Carrick held down the fort. United beat Spurs, Liverpool, Aston Villa and Manchester City in succession, and he was superb throughout.
It was in his absence that Mourinho's Chelsea ended that winning run, able to take advantage of a United side that was much less balanced without their long-serving midfielder.
It seemed appropriate to include this game. Northampton Town were no match for United, but this was the moment when Mourinho reintroduced Carrick into the fold, and his side's fortunes changed dramatically. The Northampton game was in the EFL Cup, which United won, and the player was equally important during this phase of their Europa League run. Again, Carrick at the base of a 4-3-3 proved a winning formula.
It remains to be seen what kind of contribution Carrick can make in the season ahead. His performances tailed off last season after that good spell. He has had a long career, and his most important role—as club captain and an experienced older head—might just be ambassadorial. Whether he can roll back the years on the pitch remains to be seen.
But regardless of whether he does, plenty of United fans will always appreciate all he gave to their club during his time at Old Trafford.
Advanced data per WhoScored.com.