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Advanced statistics predict Arsenal to finish third, Liverpool fourth

Two precious European places are still up for grabs in the English Premier League. Chelsea and Manchester City have their Champions League berths nearly clinched, but below them the table is crowded. Only five points separate Arsenal in third from Southampton in seventh, with Manchester United, Liverpool and Tottenham in between.

While truly it is anyone's race to win, statistics can help point out some favourites and underdogs. In the top-four race by the numbers, two clubs look precariously perched for a fall and one clear favourite for a Champions League berth rises above the rest.

Three key indicators drive the statistical analysis. These are (1) the points the club have already accrued, (2) the underlying quality of the club and how well they are expected to play down the stretch, and (3) the difficulty of the schedule remaining.

To reflect the quality of the club, I will use "expected goals" to estimate team quality. This statistic measures the quality of chances created and conceded based on location, assist type, speed of attack and a variety of other factors. This is listed as expected goals ratio, which is calculated as expected goals created divided by the sum of expected goals created and conceded. More than 0.500 is above average, more than 0.600 is good, and title contenders tend to run closer to 0.700.

For strength of schedule, I will list the club's number of home matches remaining and number of matches remaining against other clubs in the top seven.

Based on the statistics, Arsenal are the likeliest to qualify for the Champions League of the five Premier League clubs vying for the top four.

Third place: Arsenal


Key statistics: 54 points, 0.627 expected goals ratio, 6/10 home matches, 3/10 vs. top seven

Arsenal lead the pack in the current table with 54 points. Further, that 0.627 expected goals ratio is also the best of the contending sides. When Arsenal started the season slowly, they still had excellent underlying expected goals statistics. Now as Olivier Giroud has hit a rich vein of finishing form and opposition clubs have ceased stealing clutch goals with perfect strikes, the results have caught up to the statistics. Arsenal's third-place position is backed up not only by expected goals but by an excellent 0.634 goals ratio as well.

If that weren't enough, the Gunners also have the easiest schedule remaining. Arsenal are the only contending side with six home matches left. Everyone else has either four or five. And of those three difficult matches (Liverpool, Chelsea and Manchester United), two are at the Emirates. No other top-four contender can beat Arsenal for this combination of beatable opposition and lack of travel. If there is one nailed on Champions League side in the race, it is Arsene Wenger's club.

Fourth-sixth places: Liverpool, Manchester United, Southampton


Liverpool key stats: 51 points, 0.573 expected goals ratio, 4/10 home matches, 3/10 vs. top seven
Man United key stats: 53 points, 0.539 expected goals ratio, 5/10 home matches, 5/10 vs top seven
Southampton key stats: 49 points, 0.610 expected goals ratio, 4/10 home matches, 3/10 vs. top seven

It is likely that one of these three clubs will take the remaining Champions League position, but picking a favourite is not simple. Manchester United have fourth place now and a small lead, but they also face the most difficult remaining schedule remaining and their expected goals statistics are the weakest of this group. Southampton have the best xG numbers but the fewest points, and Liverpool fall in between.

So how much will Manchester United's schedule doom them? To estimate this, I wrote a simulation program and I tested how many points a typical fourth-sixh place Premier League team (a 65-70 points club) would take if they faced any of the remaining schedules of these clubs. So in the graph below, more points means an easier schedule.

Manchester United have the most difficult remaining schedule of those fighting for a top-four finish in the Premier League.

Manchester United's schedule cost them, on average, about a point over 10 matches compared to Liverpool and Southampton. Every point matters at this stage of the season, but just on the basis of schedule the Red Devils should not drop out of fourth.

Liverpool have an edge in this race, then, mostly because of their projected quality. Manchester United have been squeaking by all season, hanging on for results in matches in which they were not the better side. United have attempted only 13 more shots from the danger zone than their opponents on the season, while Liverpool have attempted 46 more than they've conceded. Further, Liverpool's 0.573 expected goals ratio does not fully capture their likely form.

Ever since Brendan Rodgers switched to a 3-4-2-1 formation and gave the keys of the attack to Philippe Coutinho, Liverpool's football has clearly improved. Their expected goals ratio in matches started with a three-CB formation is an excellent 0.640. That number is slightly better than Manchester City's xGR for the season. On the basis of this established form since December and an easier remaining schedule, Liverpool should be able to overtake United.

For Southampton, in my projections four points is just too steep a hill to climb. Unless they can steal a win from matches away to Chelsea and Manchester City, the Saints would need to be nearly perfect in the other eight to grab a place in the Champions League. It is certainly possible they could rattle off another hot streak, but it is not as likely.

Seventh place: Tottenham Hotspur


Key stats: 50 points, 0.479 expected goals ratio, 4/10 home matches, 3/10 vs. top seven

Tottenham Hotspur combine the problems of Manchester United (poor underlying statistics) with those of Southampton (just too far behind to be favourites). Tottenham's goal difference of plus-seven is the worst of the contenders, and the deeper you look at the statistics the worse they get. Spurs have conceded 30 more shots from the danger zone than they have attempted. This figure trails Crystal Palace (minus-25) and West Brom (minus-26). Only a string of clutch late game-winners by Christian Eriksen has kept Spurs in the race this far. Statistically, Tottenham are clearly the odd team out in this race.

Now, Spurs certainly have not been eliminated. All of these teams have the talent to win eight of 10 down the stretch if everything clicks, and any of them might collapse. Statistics are never a guarantee. But the indicators all point to Arsenal seizing a Champions League berth, Tottenham falling short, and the final slot falling to one of the closely matched bunch of Liverpool, Southampton and Manchester United.

Michael Caley is a writer bringing a statistical approach to football analysis. Follow him on Twitter: @MC_of_A.

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