Any time statistics, advanced or otherwise, come into the discussion of sports, one of the biggest issues can come from a small sample size. So when I approached this article, my first concern was that. As such, all points made are meant to show small trends that have occurred over the first three matches (the Community Shield is included). Extrapolating that data over the course of a season would be unwise. For example, one would not expect West Ham to allow 133 goals this year, despite their early season struggles. Basically, take everything as observation and not guarantees for how the year will play out.

THE OBVIOUS

    To start simple, Arsenal (statistically) look great. Speaking within the Premier League, they lead the league in both shots per game (22.5) and possession (67.5%). Compare those numbers to last season, when they posted season averages of 14.9 and 56.5%. Meanwhile, they’ve allowed only 24 shots over their first three matches, 11 of which were on frame. They’ve seen only one card – Bellerin in the early stages against Chelsea. Nothing jumps out as a hint that they have done less than ideal.

These are early figures, but certainly point to Arsenal walking away with six points from the first two. Yet, would it be surprising if they had one? Zero, even? There’s a disconnect within the numbers.

UNLUCKY OR POOR PERFORMANCE?

    One of the best statistical judges of “luck” within football is PDO. This isn’t an acronym, it was the online handle of the man who invented the stat. It was originally created for use with hockey, but easily translates across sports. It is not a difficult calculation – simply, it is save percentage + shooting percentage (multiplied by 100). Put another way, how often are we putting our shots (that are on target) in the goal and saving the shots our opponents put on frame?

    Intuitively, this does not seem like a great way to judge luck. Yet, PDO – with extreme consistency – regresses to mean. That’s a fancy way of saying that over the long haul, it averages out to the mean within the league (theoretically 100, since a shot on target either goes in or is saved). That research has been done numerous times over and does not need to be repeated here.

    However, it is also worth noting that the elite clubs in the world steadily outperform this metric. In theory, this is because they have the best goalkeepers and best finishers in the world. Over the past four seasons in the EPL, only three teams have been over the league average each season: Chelsea, Manchester United, and of course, Arsenal.

    So, we can reasonably expect that Arsenal be within the top half of PDO scores for the league by having better than average forwards and Cech in goal. Through three games, their PDO is a shocking 79.5. For reference, that would be the lowest in the Premier League in the past five seasons.

    As mentioned earlier, this is not a sustainable number. In fact, based on what we know, we can reasonably assume that Arsenal will both improve closer to the league average and continue above that based on the talent. So let’s take a deeper look and see if anything pops out about the early goings.

A LOOK AT THE ATTACK

    We start with the forwards. The league average goal rate – which we will define as a shot on target that goes in – is roughly 31% historically. Furthermore, we can establish a finishing rate – the odds of any shot to go, whether off target or on – is 10%. All these numbers are based on the past four years in the Premier League. How have Arsenal’s group done so far?

A combined 56 shots, 20 of which have been on target. Of those, five have been goals. That gives them a goal rate of 25% and a finishing rate of 9%. Individually, Giroud leads all players. He's taken only two shots, one of which was a goal, giving him rates of 100% and 50%.On the flip side, Oxlade-Chamberlain has taken nine shots, with only two finding the frame and neither going in.

    I want to again bring up the issue of small sample size. That is no more obvious than here. For example, Ox has yet to score in nine shots. However if he puts his next in the back of the net, he would meet the league average finishing and goal rate. Draw conclusions on individuals at your own risk.

    However, the last two team numbers are noteworthy. While both numbers are below what we might expect, they aren’t substantially less – certainly within the margin of error. This is something we can attribute to “bad luck,” though that phrase is always scary when talking numbers.

A LOOK AT THE DEFENSE

    If the offense is performing close to what is expected, then the issue must be on the opposite side. League wide save percentage is typically around 68%. One could reasonably expect Cech to do better than that with his reputation as a world class keeper. And he has, with an average of 73% over his time with Arsenal.

    So far this year? He’s faced 11 shots on goal, saving six of them. That puts his save percentage at an equally shocking 54.5%. Clearly, this is where Arsenal is performing significantly below expectations. Even below what the bottom of the league would expect. Does this fall on Cech or the defense?

    The answer lies somewhere in between. First, when judging a keeper you should consider save percentage, but it’s not the whole story. That said, Leicester’s opener is a knock against Cech, where he followed the ball past the post and was beat when it was headed back across goal. Their second was poorly dealt with by all, while the third is dismal marking on a corner. The goals in the Stoke match and Community Shield come from the defenders getting beat behind, but they are saves Cech has made before. There’s plenty of blame to go around.

WHAT DOES IT ALL MEAN?

    The numbers teach us something most Arsenal fans have reasonably assumed on their own; the defense is poor, but the Gunners will continue to control games and will score enough goals to have a top four finish. Whether or not the defense will match is another story.