The Good/Lucky Matrix

It’s early October, and the league tables around Europe are starting to shape up. If you want to see how your team’s doing, it is tempting to check the league table, but you may well fool yourself into an opinion by doing so. With just over a handful of games played, league tables tend to lie. So, how can we do better without overcomplicating things?

Here’s where the Good/Lucky Matrix comes in. The brilliant Benjamin Pugsley released this very fitting name for a plot with a straightforward design. The Good/Lucky Matrix depicts exactly the type of information we are looking for, without additional fancy complicated stuff. In fact, it is a sublime graphical representation of the concepts that have shaped football analytics here and elsewhere over the past years, shot ratio and PDO, separating skill and luck.

Good - Lucky Matrix Eredivisie 2014-15 05 oktober 2014

The Good/Lucky Matrix consists of two simple, yet crucial elements: ExpG ratio and PDO.



The horizontal bar presents how good teams have performed to date. Ben prefers the ‘Shots on Target Ratio’(SoTR), but to best evaluate team performance, I prefer the Expected Goals Ratio. The method behind my ExpG formula is explained here. In return for the added complexity that ExpG has over a simple shots count like SoTR, it adds more detailed shot information and a better appreciation of shot quality. It’s a matter of taste, but if you have an ExpG at hand, then why not use it?



The vertical bar represent an acronym called ‘PDO’. Most readers will probably be familiar with PDO, but for those who are not, it’s a simple addition of a team’s save percentage and scoring percentage. The league average PDO will always be 1000, since one team’s goal is another team’s goal conceded.

As a rule of thumb, the best teams in a league will have a PDO around 1020, while the worst teams don’t drop below 980 in the long-term. In other words, PDO’s outside that zone indicate under- or over performance that won’t hold up long-term. For practical reasons, we shall call this luck, and for now skip the philosophical debate whether over performance is indeed luck or not.

The red line in the Good-Lucky Matrix indicates a roughly normal PDO for a given performance. In the present Matrix it is in fact the regression line between ExpG ratio and PDO.


Same PDO, different luck

Please take a look at the Matrix and locate, from left to right, Go Ahead Eagles (ExpG-R 0.285 ; PDO 987), AZ (ExpG-R 0.527 ; PDO 988) and Feyenoord (ExpG-R 0.752 ; PDO 1001). Here are three teams with vastly different performances: very poor, upper mid-table and elite. A simple look at the PDO would say they are all well within the 980-1020 zone where we would assume they have neither been lucky, nor unlucky.

But, based on the correlation between performance and PDO, I would say that Go Ahead Eagles have been a bit lucky, AZ a slight bit unlucky, and Feyenoord quite unlucky so far.


The extremes

On the extreme sides of the PDO axis are Heracles (unlucky) and PSV (lucky).

Heracles, who have just won their first game this weekend after an 0 for 7 start, were never as bad as their start to this season indicated. Their results seem mainly driven by an extremely low PDO (872) that will soon find its way to a more sustainable zone. Heracles’ ExpG ratio of 0.445 on the low end of the mid table bunch of the league, and if their performance stays like it is, it is to be expected that their league table position will reflect that in time.

PSV, who lead the league table with 18 points from 8 matches, should be happy and worried at the same time. Happy that they won over two points per match while two teams with better underlying performance (Feyenoord and Vitesse) trail them by 7 points already. Worried, that their underlying performance does not indicate title winning form, which generally requires an ExpG ratio over 0.650.


In the end

The Good/Lucky Matrix, with all credit to Benjamin Pugsley, will make frequent appearances here, if I don’t find the time for extensive pieces, but feel the need for a quick analytical glance. For me, it’s a perfect tool to grasp the actual state of teams.

One thought on “The Good/Lucky Matrix

  1. Pingback: Visualising the Championship: Good-‘Lucky’ matrix over time. | stats and snakeoil

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