Cascades and the Future of Football (with practical examples)

It can be easy to get stuck in a deconstructive mode. Sometimes it feels like trendy fads have a stranglehold on the sport. While I think critique is still needed, I’d like to try to step into a more generative mode and talk about some ways forward. 

Sports, especially free-flowing invasion games like football, present the mystery of perception in its clearest form. Elite athletes not only move more efficiently, they seem to perceive differently as well. Anyone who’s ever stepped into a game a bit above their level has felt the heart-pounding, vision-blurring vertigo of trying to catch up with the flurry of movements and zipping passes. But what are these players seeing that you aren’t? Intuitively, it would seem that they are experiencing a matrix-like type of time dilation. 

Typically, this is where some form of internal processing or “speed of thought” is appealed to. And given the popularity of this notion, there is no shortage of professional players or coaches who have uttered pithy statements about football being played in the mind and so on. I have addressed the limitations of this view in the time dilation piece linked above so I will not get into that here. My aim here is to lay out how a new way of approaching this intuitive notion of “processing speed” may hold the future of football. 

“Perceiving gets wider and finer and longer and richer and fuller as the observer explores the environment” (Gibson, 1979, p. 244).

I love this as a description of high-level performance. Performers seem to be able to zoom both in and out at the same time. They are attentive to fine-grain details at the local level as well as longer/global structures such as tactics. But this is still just a description of something good. And if there’s one thing to watch out for in performance analysis it’s vacuous statements that boil down to “good players do good things” (this Guardian piece is filled with them). There’s something seductive about re-describing positive outcomes and passing them off as explanations. So we need to go further.   

Nesting

The key here is going to be the way that events relate to each other. Instead of thinking of events as following each other, we’re going to look at events as nested within each other. For example, the event of reading this blog is nested inside the larger event of your current browsing session which is nested within your day etc. Of course, we could also look at smaller-scale events as well. Nesting relationships stretch in both directions. 

Nesting has important implications for the dependence of events on one another. Events at one scale are built upon events at another scale. There are several ways we can test this empirically, but we’ll get to that later. On to football. 

Without dipping into a negative mode, we need to quickly contrast nesting relationships with common forms of analysis. The big question that nesting and scale relationships raises has to do with the window of analysis. In other words, what happened before we started watching, and how important is this for what we saw during the time that we were watching? Common forms of analysis (e.g. perceive-decide-execute) struggle to deal with what happened before the proposed sequence began. Take the typical scanning video:

The recent emphasis on scanning represents an initial awareness that events before the player receives the ball are extremely important. This is a great start, but I fear it just kicks the can one step farther down the road if it’s left at that. For example, we can start by looking at Xavi turning his head, but we could also ask why he is in the exact location that he is when he scans. Is it good fortune that he is positioned strategically within a pocket of space? No! He is there because he likely scanned before and moved into that space (meta-scanning?!). One instance of scanning is not independent, but nested within a larger event. Scanning isn’t the first step in a chain of events, it’s a thread running through different scales of nested events. 

How can we test this empirically? If one instance of Xavi’s scanning is nested within larger scales of scanning (perception) and action, we should expect his behaviour to relate to itself across time. I’ll spare the technical details (feel free to reach out if you’re interested in them), but various forms of fractal and multifractal analysis allow us to look at these patterns of self-similarity in unfolding events. We also use a special shuffling process (called surrogate analysis) to see how much the behavioural data relies on these cross-scale interactions. 

Adaptivity and Cascades

The takeaway from empirical research so far seems to be this: the more highly skilled a performer is, the harder it is to explain their success strictly within a local time-window. For example, Nonaka & Bril (2014) found that multifractal signatures observed in the hand movements of skilled bead craftsmen predicted the quality of their work (adaptation) when presented with a new material. 

These cross-scale relationships are called cascades, and they have been used to understand how performers relate to the nested scales of performance contexts. Cascades are actually quite intuitive to understand in football. Very simply, opportunities beget opportunities. 

There’s a very satisfying sense of things sort of “running downhill” or cascading as Ozil exploits the affordances to shoot in order to first clip the ball over the keeper and then gracefully cut the ball past the sliding defenders. 

Cascades are especially important in co-adaptive contexts like sport. Competing players have opposing intentions but their movements become coupled to one another. This brings the dyad or group closer and closer to a type of edge or tipping point. In these critical or metastable regions, we often see small fluctuations in movement. Importantly, these are not exactly just 1v1s. 

Going back to our key concept of nesting, they are the moments when all the nested scales become connected. The better the player, the deeper this self-similar nesting relationship goes. 

Look at this assist by Iniesta. 

After turning the first defender, Iniesta becomes drawn into a critical region (0:08-11 seconds). Because Iniesta has beaten the first defender, the defender he now engages (Cavani) commits momentum to recover goalside. Interestingly, Iniesta slows up. Typically this would be considered a decoy or fake and it would be understood that he was always going to carry on forward. This analysis suggests otherwise. Iniesta could have beaten Cavani outright without slowing down. By slowing down, however, he straddled a more deeply nested fork in the road. Due to the possibility of Iniesta cutting inside, the second defender, Veratti, must respect that central space. When Cavani slows up to cut off the inside, Iniesta carries on and is then also able to skip past Veratti. 

Here, we can quite clearly see the nested nature of events. Inside the affordance of beating Cavani there is also a region which affords beating the second defender, Veratti. In this case it is Iniesta’s sensitivity at an extremely fine-grain scale when he engages Cavani that triggers larger scale events and results in a goal. There’s not really a good way to talk about this without crossing scales. 

But cascades also link large events to small ones as well. This is often just as important in football. 

Consider this goal by Bergkamp

This exquisite over-the-shoulder control would typically be thought of as technical ability. Again, a cross-scale view provides deeper insights. Although we can’t see Bergkamp’s initial movement, it appears that he has run at least 20m by the time he controls the ball. Bergkamp’s positioning and momentum before De Boer even strikes the ball already impact the control. If he starts a millisecond later his momentum at the point of interception will be different and a different touch would be required. There aren’t separate components for running to the ball and controlling the ball - these movements are interdependent. And of course the touches to beat the defender and finish are also contingent. Cascades allow us to understand how movement systems flexibly constrain and release degrees of freedom as nested events unfold. 

Cascades are not reserved for magical moments in the world cup or champion’s league, however. Cascades are thought to support adaptive action-perception processes much more generally. Still, there may be a special significance for sports like football. For too long we have tried to understand the sport via linear chains at a single scale (perceive-decide-execute models). From this perspective, players have attempted to train component parts without the context they are nested within. Many players could make a similar movement in a 1v1 like Iniesta did with Cavani, or even cushion a long pass like Bergkamp but we have failed to explain the contexts these actions are situated within. 

Cascades are precisely the tool we need to look at the type of context-sensitivity that has too often been chalked up to vague and unfounded notions of natural talent or game IQ. The neglect of interactions between scales has also severely limited our understanding of tactics and decision making. 

By adding these contemporary tools to our toolbox, we might be able to grasp the sport in new ways. Indeed, an exciting recent study has provided initial support for this form of analysis. My pilot data from attacker-defender tasks also initially shows cascades supporting context-sensitivity. And we’ve only just scratched the surface. 

Note: I’ve tried to keep this piece intuitive and simple but I’d also love to discuss some of the more technical details with anyone who is interested. There are important implications of related concepts like non-ergodicity and symmetry breaking for football analysis.