They aren't random, there's a plethora of metrics that suggest a greater level of success in football that we've clearly regressed in. Our average possession under Carrick, for example, is 49% (an average significantly aided by matches against 10 men, if we only include matches against 11 men it drops to 46.5%). The only team to win the Premier League in the past 20 years with a lower average possession is Leicester, which is a clear anomaly. Other areas we've regressed include xG for (1.72 vs 1.41) and against (1.18 to 1.28), big chances for (2.8 vs 2.6) and against (1.85 vs 2.15), touches in the opposition box, opposition touches in our box, etc.
Changes to our approach have been reflected in statistics immediately, it's why we've dropped off in so many because we've abandoned the ambition of controlling matches to focus on defensive solidity. Which has worked in results, but that's mostly through opposition profligacy as we're giving up more and better chances since the change.
Carrick got the results, and that was his remit for this ~half season, so there's no doubting he's been a great success as interim manager. But those results aren't sustainable, and without changes to our approach and performance levels we'll inevitably see a downturn in results next season.