As Stefan Reinartz's career as a tidy holding midfielder in the Bundesliga began to stall due to various injuries, his curiosity about the machinations of the game only grew bigger.
"I always enjoyed thinking about numbers and probability models," the 27-year-old, who retired from active duty in May, told ESPN FC. "But I really became interested in the field after hearing a lecture on football stats at the German Sports University in Cologne. It discussed a study that showed that most common statistical numbers -- possession, passing success rates, one-on-ones -- had no relevance to the end result. So me and my [Bayer Leverkusen] teammate Jens Hegeler thought: 'let's see if we can do better.'"
Reinartz and Hegeler decided to look at passing; more specifically, they searched for a way to assign a numerical value to effective passing. Over the course of 18 months, they came up with a system that counts the number of opponents taken out of the game by a pass (or a successful dribble) and called it "Packing." Their innovation has proved so successful that it is being employed by analysts at Borussia Dortmund, Leverkusen and the German FA as well as by German state broadcaster ARD, who used it as an on-screen metric during Euro 2016.
"The correlation between getting the ball past opponents and winning is between 0.3 and 0.4," Reinarzt explained, "with one being a 100 percent correlation. If you then drill down into the numbers of defenders that were taken out, the correlation rises to 0.6, which is statistically very significant."
Out of 51 games at France 2016, 34 were won by teams with higher Packing numbers for getting past defenders. Fourteen of the remaining 17 games were drawn, and only three games were lost by those who got beyond defenders more often than their opponents. That much all seems quite intuitive, but the bigger attraction of the system, perhaps, is that it reveals who exactly is responsible for getting the ball past opponents and into dangerous spaces.
With an average of 82 opponents taken out in each game, Real Madrid's Toni Kroos was the most effective passer at the Euros, according to Reinartz. Switzerland's Granit Xhaka amassed the fifth-best Packing rate (55 opponents, on average), which could explain why he was valued so highly by Arsenal coach Arsene Wenger, who sanctioned a €45 million transfer from Borussia Mönchengladbach.
"Our numbers for the Bundesliga show that Xhaka was the second-best holding midfielder after Xabi Alonso in the league, too, when it comes to verticality," Reinartz said. (Bayern Munich centre-back Jerome Boateng was the best player in Germany in 2015/16, taking out 75 players on average per game thanks to his excellent passing from the back.)
Crucially, the model also measures the effectiveness of pass recipients. While Italy's Graziano Pellè was the best target man at the Euros, collecting balls that took out an average of 82 players per game, Mesut Ozil's ability to find space in the opposition half as an outlet to teammates was equally remarkable. Passes to the German playmaker took out 63 players per game on average. This is the kind of insight that traditional statistics didn't provide; Ozil's passing skills were well-known, but his movement perhaps wasn't as valued.
"Ozil enables you to get the ball past players," Reinartz said. "He's the best in the world between the lines... that's why he's an automatic starter under any coach even if the public don't always appreciate him. I believe the importance of attacking players as pass recipients is the greatest insight we have gathered over the last couple of years."
Packing numbers reveal that Antoine Griezmann is the perfect package: the Frenchman didn't just score six goals at Euro 2016, he also had the fifth-best stats for playing/going past defenders and was also among the 10 best vertical pass collectors.
Individual stats aside, Packing offers an interesting perspective on teams' playing styles, strengths and weaknesses, too. Belgium, for example, appeared as by far the best side when it came to getting past defenders -- Eden Hazard alone managed to take out nine defenders on average per game, no one else was as effective at the Euros -- but they were very bad at dealing with counter-attacks and thus extremely vulnerable to balls/players getting behind their defensive lines. (Wales, France and Portugal, by contrast, had the fewest players taken out on average per game.)
England's failure to create much of note against Iceland is also neatly captured by Reinartz's model: Roy Hodgson's men only got past 28 defenders over the course of the 90 minutes vs. Iceland in Nice, whereas their opponents were far more effective going forward, beating 41 defenders.
"England played without a sense for the dangerous spaces," Reinartz said. "They took up positions on the pitch rather than positions in space. They constantly [had] to rely on athleticism and one-vs-one situations because their passing and positional game [wasn't] good enough. That's the biggest advance in knowledge in Germany: we produce players and coaches who understand the importance of space."
Nevertheless, the World Cup winners couldn't bring their strong passing game fully to bear in France. They only got behind a total of 21 defenders in the semifinal against France (just over half their average number in previous games) and had problems defending. "They allowed more through-balls and opponents going past their defenders than the other semi-finalists," Reinartz noted. "Germany could do better in terms of counter-pressing and positioning themselves to prevent counter-attacks."
Like other analytical tools, Packing will never fully supplant traditional scouting and non-quantitative analysis. But as a means to identify effective attacking players and, beyond that, "to explain football better to people" (according to Reinartz), it opens up some interesting perspectives. Among other things, the data underlines what successful coaches the world over have always known: your style of play is not really relevant as long as it regularly gets you past defenders.