# Closed and open chaos – a game theory amateur’s view on Australian Rules

As the first school term wraps up, and the footy proper begins, Lachie Gaylard traces a line between the game theory chapter in his Foundation Maths textbook and Australian Rules.

So it’s here again; another year of struggling to comprehend exactly what the commentators are yammering on about when any meaningful analysis has seemingly been exhausted: structures. These mysterious entities (are they even that?) have baffled me for years, but a new foray into the study of basic maths concepts that evidently passed me by in high school has begun to clear the haze.

Game theory

The Canadian author Adam Gopnik speaks of ice hockey loosely in terms of game theory: “how much we know, how much our opponents know, how much they know of what we know,” and so on. In this way, he analyses concepts of “‘open information’ (or perfect-information) games with ‘closed’, (or imperfect) information,” citing chess as an example of the former – given each player has exactly the same information as the other – and five-card-draw poker the latter: you only know what you have; the majority of the information is closed.

Ice hockey, he argues, is appealing primarily because of its balance between open- and closed-information aspects. He acknowledges that to the unpractised eye, hockey looks like a purely open-information sport; “a series of instinctive reactions to bouncing pucks and sliding players”, but that “crucial elements are buried or cloaked and are revealed only afterwards to the eye of experience and deeper knowledge”.

A point in the right direction

The parallels between Australian rules and ice hockey are easily spotted: free-flowing games, brutal hits, on-the-fly interchanges…this is all “open” information, as is the system of scoring. Goals count for just enough to be valued, but not so much that the kicking of a single one can be attributed to winning the match itself (except for the obvious, literal situation – the last goal scored in a nailbiter). Rather, a goal is the “spark for a comeback”, keeps a team “in touch”, the “nail in the coffin”, or a “steadier”. This in contrast to soccer, where according to the wonderful maths-themed soccerbythenumbers.com blog, a game averages around 2.68 goals per game, which adds obvious added importance to each goal scored in that sport, as opposed to a high-scoring AFL match, where the number of goals scored in a free-flowing game is far higher. The fact that they are worth five points more than a goal in soccer, then, reveals the microcosm that is any individual sport: the relative worth of a “point” in any game is purely defined within that sport’s own terms.

This much is known to most casual viewers of sport. Plainly, a goal in AFL is not worth six times that of a goal in soccer (it could in fact be said to be worth less); the worth of a “point” within the context of the sport in which it is scored is all that matters. (Indeed, there can be context within context [metacontext?] – that is, within the AFL, or any outdoor game where there are variables between matches, a goal can be “worth” far more on a muddy Kardinia Park in the middle of August than on a dry, sunny SCG).

Interestingly, it seems the closer to zero the final margin in a game gets, the more the idea of losing or winning by a point becomes quite literally the “smallest possible margin”, no matter what the context. That is, losing by one point in higher scoring sports such as basketball and Australian Rules brings up the same feelings of devastation as losing by a single point in low-scoring sports such as hockey or soccer.

So it is that in the AFL, the idea and value of a point (as opposed to the point and value of an idea) is most definitely open information. But it is the closed information that I have come to realise is beyond me: structures. Defensive, offensive, running, evolving…

Structure

The bouncing and sliding pucks and players of Gopnik’s chosen sport are absent, but the instinctive reactions to similar seemingly chaotic events remain in AFL. Such split-second decisions are occurring every second of every game, but now within the context of these mysterious “structures”. Outside of sport, a structure is generally thought of as tangible; yet I can seldom spot them within a game of footy. They are talked up as revolutionary or impenetrable. Perhaps it is so that, with enough repetition, a player’s instincts can be changed to reflect the coach’s tactics. Given the modern prevalence of them, structures no doubt have had an effect on the spontaneity of the game to this point. However it seems that, parallel to the development the structures, have come speed. The game moves apace and any player caught thinking too hard about the coach’s instructions for just such a situation would no doubt find themselves the victim of a modern tackle – the viciousness of which has been equally honed through countless hours of training.

Perhaps it is not the structures themselves, but how precisely the players can stick to them when confronted with as many split-second decisions as are present in Australian Rules that matters. Once drilled countless times, these structures are perhaps as engrained in the players’ muscle memory as, say, scrambling to a bouncing ball, or deciding whether to spoil or mark.

Order

And thus we come to the crux of what, to me, makes the modern game ever watchable; the disagreement between the chaos of the game of Australian Rules, and the structures that seek to impose order on it: the jackaroo herding outback cattle from a station the size of France (or the MCG) into a confined space. As game theory shows us, however, there is an inherent structure in the chaos, the permutations of which keep us interested in the game. So, while a standard zone defence is reasonably “spottable” by me – and thus could be defined as open information – the nuances and tweaks made to it is closed. This is information one team has, but which neither the opposing team, nor the spectators, have. It is the tension that arises from the former’s struggles to comprehend, adapt, contain or defeat this modification that keeps the game interesting for the latter. However, a structure’s lifetime is limited, and the appeal lies in watching a successful team’s structures get “found out” by opposing teams and gradually taken apart, until a further modification, or brand new structure, needs to be thought of. Refusal to adapt can be disastrous for one team, but fascinating to watch…Mick and Clarko are testament to this.

The statistics expert Nate Silver successfully predicted all but one of the winners in all 50 states during the past two US elections. He was asked recently if he could apply his prediction model to forecast the winner of this year’s AFL season. He replied, “in sports like baseball and cricket, you mostly have one player acting at a time and you can isolate the actions in a very precise way. In most football codes, everyone is on the field at once acting in a more fluid way”. Offside somewhat limits this fluidity, but in AFL, irregularity rules; this is typified by the oval ball, the fickleness of which means it can (and does) bounce anywhere, even away from Milney in a grand final.

Mathematics often seems simple enough when dealing with definites, and while coaches try to limit any outliers, it is precisely information that they don’t have, we don’t have, and/or the players don’t have that makes it so enthralling to watch. Maybe I shouldn’t bother looking out for structures. Spotting patterns and imposing order upon chaos is our human instinct, but so is throwing the coach’s instructions out the window when you can see a passage through the centre and into your forward 50. It’s these moments that rise above any stability in a game and get you out of your seat yelling; that aforementioned Milney-goalmouth scenario is not part of any structure, nor is Jesaulenko. Malthouse, Ross Lyon or a multitude of analysts may have us believe that structures harbor success, but it is the breaking of these structures in which the excitement lies.

It comes back to open- and closed-information games: you want your team to have a closed structure in an open game. To hide their tactics on a 150-metre field in front of a few million observers, a team must have some pretty advanced camouflage techniques. One constant of chaos is that it’s consistently fascinating to watch, the more so when someone attempts to impose order on it.

AFL’s one heck of an open game, and it’s a hell of an exciting one – no wonder I never could spot that bloody Cluster.

### About Lachie Gaylard

Lachie is a Melbourne teacher, musician, writer, surfer and Collingwood supporter who is eternally grateful to his parents for putting him on the MCC membership list at birth. He keeps some travel writing here: http://climbingatree.wordpress.com/ and some European writings here: https://lochieg.exposure.co/ and a little photography here: http://www.flickr.com/photos/soldered_mind/

1. Really interesting piece Lachie. So much in there. Structures is a word used to describe quite a few things in footy I reckon. It is ill-defined. Would be interesting to know how people understand it.

I agree that the breakdonw of structure and the return to chaos make for the best games – and that will occur under the capped I/C. Last year’s second Geel v Haw classic was a case in point.

2. Andrew Gaylard says:

At the risk of annoying my Collingwood-supporting son by always bringing everything back to Geelong, I suggest that the fortunes of the Cats over the last five years illustrate his article nicely. The initial success of the Cats’ 2007 model came about partly because of a remarkable core of elite-level players, but essential to it was the determination to play on in order to speed ball movement as much as possible. That made the direction of ball movement after a possession less predictable and gave opposition players both less think-time and less running time to respond, rendering previously successful defensive positional structures more difficult to establish when the situation demanded it.

This high-chaos, low-structure approach made the Cats’ footy (as the writer indirectly points out) more “fascinating to watch” than anything since the open football of the 1980s. For three years it was not seriously undone by anyone except the Cats players themselves (2008 GF), until Collingwood succeeded in 2010 with its new rule-based, highly structured strategy based around close zones and high-pressure tackling, which was only fun to watch if you barracked for Collingwood.

I don’t contend, of course, that Geelong’s 2007-2011 football was unstructured, but that whatever structure existed did not intrude on the beauty of its game. Exactly what Chris Scott “tweaked” in 2011 to regain the cup remains a mystery to me, but football-lovers should be glad he did. The tide still seems to be with the anarchists. Now even Sydney’s won a flag playing eminently watchable football!

Lastly, anyone interested in the mathematics of football – even those lately arrived at maths as a subject worthy of attention – should note that Geelong is (historically) eight times as likely to win a flag in an odd-numbered year as in an even one …

3. Great story Lachie. I observe football like I observed simultaneous equations. What is known, what I want to know and how to get there. Of course, the parallels don’t always align. A + B does not always = C.
Chaos theory reigns…
When it works it is good. When it doesn’t it is bad.
Chaos theory, in AFL terms, consumes more game time than structured play.
Well done.