Statistician’s Journal: Why there is only a 42% chance of a top four finish from Manchester United?


The battle for a UEFA Champions League spot for the next season has now become a three-way race, between Arsenal, Manchester City and Manchester United. Here, we are going to discuss why, despite being below the other two clubs, Manchester United have a real good chance to make it to the top four.

Before we go deep into this discussion, let us recall the present condition of the Premier League top table:

Team Played Win Draw Loss Points
Leicester City  37  23  11  2 80
Tottenham  36  19  13  4  70
Arsenal  36  19  10  7  67
Manchester City  36  19  7  10  64
Manchester United  36  18  9  9  63
West Ham United  36  15  14 7  59

As you can see, Leicester City have already won the league and Tottenham have ensured a spot in the top four. On the other hand, seventh placed Southampton (57 points from 36 games) and eighth placed Liverpool (55 points from 35 games) will have to be happy with a Europa League spot only. Naturally, it all comes down to Arsenal, Manchester City, Manchester United and West Ham United.

Let us now take a look at the remaining fixtures of these clubs:

Teams Remaining games
Arsenal Manchester City (A), Aston Villa (H)
Manchester City Arsenal (H), Swansea City (A)
Manchester United West Ham (A), Bournemouth (H)
West Ham United Manchester United (H), Stoke City (A)

Albeit football is a game full of surprises, let us start with the assumption that all these teams will win their last game, for no team aiming for a top four spot should slip-up against a lower table team. Should that happen, West Ham United can never finish higher than United or Arsenal. So, it all boils down to three Premier League giants and the results of two particular games – tonight’s face off between Manchester City and Arsenal, and the clash of West Ham vs Manchester United later this week.

Here are the final relative positions of the three teams based on possible results of these two games:

Possible result Final standing (relative)
Arsenal win/draw, Man Utd win Arsenal, Man Utd, Man City
Man City win Man City, Arsenal, Man Utd
Arsenal win/draw, Man Utd loss Arsenal, Man City, Man Utd
Arsenal win, Man Utd draw Arsenal, Man City, Man Utd (in goal difference)

It is clear that Arsenal will make it through unless they suffer a miraculous loss to already relegated Aston Villa. However, Manchester United will manage a top four finish if and only if these three things happen – Manchester City do not win against Arsenal, United win against West Ham and United win against Bournemouth. And thus, calculating the chances of these three events can give us an idea whether the thirteen times Premier League champions can secure a berth in the Champions League next season.

Manchester City do not win against Arsenal:

Let us take a look at all the stats from previous encounters between these two teams.

At Manchester City At Arsenal Overall
Manchester City 33 (36.7%) 15 (16.7%) 48 (26.7%)
Arsenal 36 (40%) 54 (60%) 90 (50%)
Draw 21 (23.3%) 21 (23.3%) 42 (23.3%)

Thus, overall, there is only about 27% chance that Manchester City can snatch a win against Arsenal. However, considering that it is a home game, their chance increases by ten percent. On the other hand, if we consider all matches between these two teams since 2010, then the overall record improves a bit for the blues of Manchester. In 12 games in the last five years, both the teams won four times (33% chance of a City win). Among these 12 games, five have been played at the Etihad, and City won two of them, making it a chance of 40%.

And thus, considering everything, we are going to conclude that the home side have around 30-40% chance of winning tonight.

Manchester United win against West Ham and Bournemouth:

Since there are not enough data for Bournemouth and since the Cherries are not in a good touch at the moment, we will still go with the assumption that United will win against them. But, for West Ham, let us take a look at the stats from the previous encounters:

At Manchester United At West Ham Overall
Manchester United 43 (67.2%) 16 (26.2%) 59 (47.2%)
West Ham 13 (20.3%) 26 (42.6%) 39 (31.2%)
Draw 8 (12.5%) 19 (31.2%) 27 (21.6%)

And here, we can see a stark difference in Manchester United’s performance at home and away. Their winning percentage drops down by 40% when they take a trip to West Ham. However, it does not at all reflect the recent matches and while making an educated guess, we should rely more on the data from the last few years.

In the last five seasons, these two teams met 13 times, and Manchester United hammered the opponents 8 times (61.5%) and lost only once. And so far as the away matches are concerned, even if we consider all matches since 2001, United won 7 of their 13 (53.8%) away games at West Ham. And so, we can safely assume that the winning chance for the Red Devils should be around 50-60% when they are going to face West Ham later this week.

What does that leave us?

So, based on historic data and recent performances, we can assume that there is a 60-70% chance that Manchester City will not win. At the same time, Manchester United can win against West Ham with a chance of only 50-60%. But, for United to qualify for the Champions League, both will have to happen and even if we consider the maximum chances, that makes it only a 42% chance (60%-times-70%) that United will make it to a top four.

Also, this comes with an inherent assumption that United will win surely against Bournemouth, which, based on the inconsistency Rooney and co showed this season, may well end up being a farce. Hence, all in all, it is more likely that Manchester City and Arsenal will make it to the top four at the end of the season.


Do you still think Manchester United will finish in top four? Why? Let us know in the comments below!

Photo by Sean MacEntee