​A few weeks ago, I took a look at Arsenal’s first few games through a statistical lens: I introduced a luck rating called PDO, broke it down offensively and defensively, and concluded that Arsenal had been extremely unlucky during their first four matches and fully expected those numbers to drastically improve over the coming weeks. Let’s look at where we stand now:

PDO ​

To recap, PDO is a largely regressive statistic, implying that there is a high luck factor to it. However, we also established how the top clubs in any given league should out-perform PDO: with better than average strikers and keepers, their PDO should be above the 100 league average. When we examined the first few matches, Arsenal was at a shocking 79.5 – this would have been the lowest EPL PDO in over five years. ​

Not surprisingly, the Gunners now find themselves at a respectable 94.2, just below the league average. Starting at such a low point, it is not surprising to find them still below 100, and we can reasonably expect them to continue to climb closer to 100 and even surpass as the league rolls on. Arsenal has averaged a PDO of 108 over the past five seasons.

​So clearly improvements have been made. When we examined the stat last time, we looked at three numbers that make up PDO: save percentage, finishing rate, and goal rate. Save percentage is straight forward, while finishing rate is the percentage of all shots that go in, with goal rate being the percentage of shots on target that go in. Leagues averages are 68%, 10%, and 31% respectively. ​

Cech’s save percentage has sky rocketed from 54.5% to 69.2% - above league average and closing in on his 72% career average with Arsenal. The finishing rate has rose from 9% to 13% - again, above the league average. Goal Rate is right at the average at 31%, up from 25%. None of this is surprising: Arsenal is a better than average team and therefore should have better than average PDO. They are still below it now – mostly due to a small sample size and higher-than-sustainable numbers from some clubs - but everything is headed in the right direction.

POWER RANKINGS ​

Power rankings are a popular way to order teams, though almost always it is extremely arbitrary and often comes down to a matter of opinion. In this section, I’ll look at a more statistical approach to judge teams. I’m including a variety of statistics, but I’ll focus on three main “sections” of numbers to avoid over-explaining the methodology here. ​

PDO is included. Yes, it does have a high correlation to luck, however it’s also worth noting that good teams tend to over-perform it, while bad teams underperform. These aren’t hard and fast rules, but PDO does a good job at explaining what has happened when other numbers may struggle. ​

Also included is shot ratio. Shot ratio has been a staple of the statistics of football for some time because it is simple and obvious: if you shoot more times than your opponent, you should score more often. Clearly the quality of shots is important (I’ll discuss that in a minute), but as a broad statement, it will be true more often than not. ​

Our third and final section focuses on shot quality: are we getting good opportunities and forcing our opponents into low percentage chances? This ties everything up nicely and makes these rankings easy and logical: are we getting more shots than our opponent, with better quality chances, and scoring more of those chances? In total, there are 23 inputs for this formula.

THE RESULTS ​

To start, Arsenal checks in 5th. Considering that is also their place in the table, this is an encouraging start. In fact, our top three in the power rankings are exactly like the table: Manchester City, United, and Spurs. We also have two of the three clubs currently in the relegation zone in the bottom three: Swansea and Crystal Palace. There’s significant correlation between the league table and these rankings. There is only one significant outlier in the comparisons: Burnley currently checks in at 6th in the league, yet next-to-last in the rankings. They are being outshot nearly two and half times their output and long term this is not sustainable to stay in the top half. ​

It also tells us some things that you could probably assume if you have been watching: the Manchester clubs are a class above the rest of the league, coming in rated significantly higher than even third place Spurs. Also, there’s a large gap between the top seven – which includes the aforementioned clubs, Liverpool, Chelsea, and Newcastle – and everyone else. Burnley and Watford are unlikely to keep their form up, and a European spot seems unlikely. Finally, Swansea and Crystal Palace are performing like two of the worst clubs in the history of the league. In fact, through predictive modeling, we give these clubs a COMBINED 12% chance to stay up. ​

The predictive modeling gives these rankings a lot more value. Currently, Arsenal has a 5.4 rating – technically this is on a 10 point scale, but the highest score over the past six years in the EPL would be a 6.3 for Man City in 2013-14. Additionally, every club with a 5.4 or higher has finished in the top four in their respective season. The sample size here is still small – the Manchester clubs both have ratings above 7, with City at 7.4. In all likelihood, these numbers are unlikely to hold over 38 matches, but there is plenty of early indication of who the real contenders are.

FOR ARSENAL ​

Fifth seems like an appropriate spot for the Gunners. After dropped points to start the year, the turning point seemed to be the Liverpool blow out. Since, they have won six of seven matches across all competitions, with the only dropped points being a road draw with Chelsea. If this continues, a top four finish seems likely and the Europa League title is a possibility.