When Ralf Rangnick was introduced as Manchester United's temporary manager in November, there was a sense of hope. Despite the fact that the German lacked recent coaching experience, it was difficult not to be captivated by his profile in the game.

Rangnick was the mastermind behind RB Leipzig's spectacular rise through the ranks of German football's football pyramid, which began in 2005. Considering the club's financial muscle, that was hardly a fairy-tale success, but it was the method in which they ascended to prominence that captivated the imagination of hopeful United followers. Rangnick's anti-pressing ideology served as the foundation upon which the club was shaped and constructed.

When Ole Gunnar Solskjaer was in charge, he appeared to be an accomplished tactician. Under Solskjaer, Manchester United had been strategically ignored, and the Norwegian was never shy about expressing his preference for man-management and motivation. Rangnick was brought in to help stabilize the team, provide harmony to the field, and, most importantly, ensure that the club qualified for the Champions League.

With nine games remaining in the Premier League season and 124 days having passed since Solskjaer was fired, it has been 124 days since the Norwegian was fired. United have been eliminated from each of the cup competitions this season, and their chances of competing in the Champions League next season are becoming increasingly remote.

Arsenal are four points ahead of Manchester United, and they have a game in hand, putting them in strong position to finish in the top four, according to bookmakers. This scenario appeared unimaginable when Manchester United signed Jadon Sancho, Raphael Varane, and Cristiano Ronaldo in the summer of 2017.

When Solskjaer was fired, United were six points outside of the top four, and that situation hasn't improved much in the intervening time. They simply have fewer games left to play — nine to be exact — in order to make up for their four-point disadvantage. When confronted with such overwhelming evidence, it is difficult to deny that Rangnick has made a positive contribution to United. Some would argue that this is the only thing that matters, and they would be correct.

Rangnick's interim tenure will be deemed a failure if United fail to qualify for the Champions League, but it is worth looking at United's underlying metrics other than points won in order to determine whether or not appointing Rangnick was the right decision.

Solskjaer led United to a total of 17 points from 12 games this season, an average of 1.41 points per game under his leadership. Since taking over the reins, Rangnick has amassed 29 points in 15 Premier League games, an average of 1.93 points per game. However, despite the fact that Rangnick's total is far higher, it is worth noting that United had the advantage of a more relaxed schedule during the frenetic holiday time.

Nonetheless, there is evidence to support the claim that Rangnick has genuinely improved United, despite the overall picture that has been created. United have made small improvements under the German in practically all offensive measures, but the most substantial improvements have come on the defensive side of the ball under the German.

Solskjaer (left) and Rangnick (right).

United have made an average of 47 interceptions per 90 minutes under Rangnick, which is an improvement above the 42 interceptions per 90 minutes that they had previously made under Solskjaer. Following Rangnick's appointment, the players at United have been encouraged to play with greater energy, which may account for the disparity. Under Solskjaer, United's play was disjointed, and their pushing of the ball was a cataclysmic failure.

Moreover, under Rangnick, United has taken an average of 20 percent more defensive actions per 90 minutes than they did under Solskjaer. Under the previous management, United recorded an average of 132 defensive activities per 90 minutes, however they now record an average of 160 defensive actions per 90 minutes in the Premier League.

Rangnick has made a number of marginal gains, but they are not the only ones. Under Rangnick, United has become a vastly stronger team in 50-50 duels, and the disparities between the two teams are evident in those measurements. Under the interim manager, Manchester United's physicality has certainly improved.

Even though Rangnick's style of play hasn't made its way to Manchester City as anticipated in November, it was naive to believe that he would have such an impact on the club in such a short period of time given the presence of a 37-year-old centre-forward in such a dysfunctional side. The squad on the field has not been changed into a fantastic pressing unit, but Rangnick has made significant improvements on crucial measures in the direction of such transformation.

The failure of Manchester United to qualify for the Champions League in the coming months is a catastrophe. If there is one silver lining to this situation, it is that Rangnick will leave the playing squad in a better state than the one in which Solskjaer left it.

Better days are ahead for everyone.

Comparisonator is a football statistics comparison tool that draws data from 271 major leagues across the world and analyzes players and clubs based on more than 100 distinct characteristics. More information can be found here.