Decision Graphs: When You Can’t See the Forest for the Trees

DeciViggiani's tree of strikession trees are sometimes derided by practitioners of historical fencing; after all the chaos of a fencing match rarely allows the luxury of time for complex decision making, and even a relatively simple decision tree can have multiple recursive branches and layers.  As a result even a relatively sedate exchange gives precious little opportunity the complexities of long term diagram driven decision making.  In this article we’ll take a deeper look at decision making processes, and how decision trees can be used to great effect to improve our fencing.

In doing so we will focus on how decision trees can be used to generate rich generalised representations of a given fencing style, and how fencers can use trees to create drills which hone the skills and tactics their fencing style focuses on.

Trees for All Occasions 

Tactical decision trees are visual representations of how a series of fencing techniques unfold over time.  They capture stimulus-response pairings, and decision points which govern the flow of a flight – if my opponent does action A, I respond with action X, whereas if they performed action B, I should respond with Y.

These kinds of diagrams are widely used to represent  tactics in a modern military context.  For example, the actions of combat pilots (and more importantly for the air-warfare-officers who actually make the tactical decisions for them), are enacted as decision trees.  These trees exist not simply for actual in-flight combat tactics, but also for decision making surrounding rules of engagement, threat avoidance, and even refuelling decisions.

On important consideration is the related concepts of tactics and strategies.  Formally speaking a strategy is a high-level description of a broad general approach to a situation.  It might break down a top level problem into a series of goals.  A tactic, by comparison, is an instantiation of how a particular subgoal is to be achieved in a given set of circumstances.  Put more simply, the strategy is the overall “game plan”, whereas the tactics is what you do “in the moment” based on an opponent’s actions.

From an academic perspective there are a variety of formalisms for diagramming tactical and strategic decision making, from simple flowcharts through to the Tactical Decision Framework (TDF) formalism put forward by Thangarajah & Everstz [1] which captures the Goals of an individual Actor in a scenario, and maps them to plans, actions, and other interactions through a formal set of symbols and diagram structures.  The method you use isn’t important; it’s the process of stepping back from the trees and seeing what they represent that counts.

However you write them down, there are a number of criticisms leveled at decision trees.

Common Criticisms:

When discussed in combat sports the idea of tactical decision trees generally come under a handful of main criticisms. The main criticisms are

1.  We Don’t Make Decisions that Quickly

Realistically our brains simply don’t process decisions quickly enough to reason through a decision tree in real time.  Fencing times can sometimes be measured in a handful of milliseconds, whereas the rational decision making processes of the brain operate orders of magnitude more slowly.  A fencer who learns from the texts exclusively & repeats the movements sequentially will surely understand the movements of a given technique series, yet when they try to put this into practice they are inevitably outpaced by even a novice fencer who has swiftness and resoluteness of purpose to call upon.

Neurologically this can be related to the sequence of neurons through which a decision must be processed before it can be acted upon.  A visual movement, for example, passes from the eye through the visual cortex, prefrontal cortex and so on, all the way up to the outer layer of the brain wherein the rational decision making process takes place.  Even at its fastest this chain is a dozen neurons in length, and with each neuron taking a few milliseconds the process is already slower than the movement.  Even if the fencer has practiced the motions and achieved automaticity in the body movements (which saves significant time and mental effort in guiding at technique their decision making will lag far behind the necessary speed to be effective; by the time the decision results in a movement of the arm the exchange is over.

This is one of the reasons that beginners are so easily defeated with techniques such as changing through; their brains are still trying to cope with the first intention by the time the second intention strike hits home.

2. Decision Trees are Brittle

A decision tree is a perfect map of the fight so long as the opponent provides the correct stimulus and reacts the correct way.  This is all very well in training – we can always stop and say “you’re not doing the drill right” to our opponent, but that is less than helpful in a match against an unknown opponent.  In this situation we cannot rely on our opponent to do the “right thing” so we can perform our perfect thrust from the Zornhau.  In this way decision trees are extremely brittle; once you go outside their bounds you have effectively broken them.

Let us take our Zornhau decision tree example.  Our Zornhau defeats all cuts from above by use of the cut and the point.  We can easily demonstrate this against an opponent cutting the same way we do.  Let us say, however, that instead of simply cutting in, they cut an Oberhau to Longpoint in the style of Meyer, and moreover, are using ring-guards on the hilt or are striking in with the flat as advised in the first play from Tag (High Guard).  The fencer will quickly discover that cutting over this attack is difficult to begin with, and moreover the high hand position and ring guards make the ensuing thrust extremely difficult to pull off.  Likewise the taking off above is made all but impossible to achieve, and attempting the Krieg often results in being stabbed in the face.

This is not to say it can’t be made to work, but it does immediately break the brittle decision tree of the Zornhau as represented here. This fragility is particularly a problem for those who dogmatically follow the text without stepping outside it to examine the principles underlying a technique or placing them in a free-fencing context, but more on this later.

3. Decision Trees are a Snapshot of the Art

The third criticism (and perhaps most apropos in many HEMA discussions) is that Decision Trees are simply a snapshot of the overall art.  If we slavishly practice the decision trees “as written” then we are simply aping a small subset of exemplars without developing a broader understanding of the art we are aiming to reproduce.  This is actually a valid criticism – if I practice Meyer’s second Stucke from Ochs, for example, all I’m doing is repeating a series of mindless motions without trying to understand the broader context.

Breaking through this idea of dogmatism in decision trees is the jumping off point for the genuine utility of decision trees.

So What Are Decision Trees Good For?

On the basis of these arguments it is tempting to ignore decision trees altogether.  This is throwing the baby out with the bathwater, though, and it is not by accident that so many fencing texts inherently encode their author’s syllabus in a text-based decision tree.  In his discussion on how to interpret historical fencing texts Slee [2] describes the steps in interpretation of a historical text.  To paraphrase his stages:

  1. First we establish the atomic actions which make up a system or style.  In Meyer, for example, we have the Principal Cuts, the Secondary Cuts, the Guards, the Steps, and so on.
  2. Second we uncover individual tactical actions and scenarios.  The Zornhau is just such one series of actions – a brief graph of decisions from the initial exchange through to the follow up with Abnehmen or entry to the windings in the Krieg, for example.
  3. Third, we establish the broader principles and grounds on which the text builds its system.  This kind of less can sometimes be explicit (Meyer’s description of the Provoker, Taker, & Hitter for example are an explicit technique set which can be taken as-is from the text) or more often need to be teased out of the system through analysis of the movements themselves and through assiduously experimenting with the atomic actions and tactical scenarios; crossing the centre-line to keep oneself safe, for example, is never explicitly discussed in the Liechtenauer glosses, but is a necessary precondition to success in a number of techniques.

The criticisms we’ve encountered so far assume that a we stop at stage 2 of this process.

This isn’t necessarily a bad thing. Talej’s discussion of using fuzzy collections to analyse individual techniques [3] is a wonderful example of using fuzzy sets as a means of analysing the text.  In his case-study of the Zornhau he describes perfectly the analysis of this technique on the basis of several historical treatises, using them to make a number of conclusions about the atomic movements of the Zornhau.  The same principle applies to the tactical sequencing – we can consider a literature survey of the Abnehmen from the Zornhau to decide which of the opponent’s openings we should target in the follow up, using specificity rules as a general guide just as we would in rules of formal logical reasoning from partial information (specificity is given preference in categorisation in these formalisms, so “high cut to the opponent’s right ear” would be considered more specific and accurate than a simple “high cut to the opponent”, given that all other factors are equal).

Let us take stock of what we can do with just these first two steps:

  • Practice movements in isolation to develop an appreciation of the movement, and perfect edge alignment etc.
  • Practice movements in sequence & derive the best body mechanics for a given technique – we can learn the fastest way to Zornhau, for example by simply repeating the Zornhau plays with subtle variations until we find the best implementation.
  • Learn the canonical techniques of a system (the various Haupstucke, for example) so that we are better able to pass it on to others without having to reference texts constantly to look at what we’re “supposed to do”.

These are all extremely valuable outcomes.  If we were to look at grading systems in Eastern martial arts such Kodokan Judo, Kenjutsu, or Koryu Jujutsu we see a similar process of progress through the Kyu gradings; they capture knowledge and application of core techniques (notably they do not capture “fighting ability” at all).  Another analogy commonly used in fencing is that of language: if we were learning a language this second step would be the equivalent of phrase-book conversation.  We’ve learned an array of defined exchanges extremely well, but outside these we are stilted and halting.

Deriving Meaning

In step 3 of Slee’s approach we attempt to establish broader principles of the fencing style.  As Slee points out, sometimes this is explicit in nature – in this case we are fortunate, the meta analysis of a style has been carried out for us and we can adopt a top-down approach to the system’s strategies.  If on the other hand we are not given this information, then a bottom-up approach of constructing these meta concepts for ourselves may be required.

Bottom-Up Approaches

Let’s consider the bottom up approach first.  In this case we have been given some phrases for our language of fencing which we can express as graphs using a formalism such as TDF or even simple flowcharts.  When we try to capture techniques this way then apply them to the real world scenario we rapidly discover that deriving general rules from tactical exemplars is an iterative process in which we draw semantic links between different situations, and in doing so extract shared tactical templates which can be applied more broadly. 

Given that many of the sources (especially those in the Liechtenauer tradition) are built around the idea of discrete “plays” we are given plenty of material for drawing out tactical concepts. As an example we might discover that as a general rule for a large number of cuts, be it a Zornhau or a Zwerch for example, we have three simple “core” defensive reactions that take place.

  1. They parry but are soft in the parry (i.e. their point is not forcibly online & threatening us)
  2. They parry but are strong in the parry & push us offline (i.e. their point is offline but their parry is over ours)
  3. They parry but their point remains more-or-less online

This is not a complete analysis, but this example will serve our purposes as a toy domain in which we can separate the individual parameters for training.  In each case the reaction parameters in the decision tree have somewhat similar outcomes between both the Zwerch and the Zornhau: striking/thrusting through, moving around to the other side of their blade (by Abnehman or Umbschlagen, for example), or Winden/Duplieren respectively.

By working “bottom up” in this way we extract these generic templates or models at a tactical level.

Top-Down Approaches

The alternative situation to the bottom up approach is the top-down method.  Instead of starting from the plays and finding their intersectional points, the top down approach takes the explicitly described tactical or strategic components of the system and finds the elements or decision trees to which they apply.

A Meyer practitioner, for example, may take the higher level tactical concept of the Provoker, Taker, and Hitter and see how it applies to a number of the devices from the text.  In finding which elements apply we again find the intersections between movements, except in this case the fencer has been given the conceptual groupings and doesn’t have to derive them for himself.

From “top down” we connect theory to reality; the templatised concept is demonstrated with a real-world example.

Hybrid Approaches

For many historical traditions we can usually assume that a mixture of bottom-up and top-down methodology will apply.

Often top-down methods deal with strategic principles, while bottom-up discovery of concept is much more tactical.  Between the two we have a broader fencing “theory” for our system.

Whatever the approach the goal is the same.  When using decision trees we are attempting to generate broadly applicable, flexible, and simple models of typical fencing situations. The purpose of these models will become clear later in this discussion, however in the short term the point is that we can use these methods to develop a broader set of drills targeted at addressing our new “model” of fencing.

Discovering Fluency

With our new understanding of decision trees as a means of eliciting concepts we can now expand the ideas we have generated to create fencing drills to address them.

Specifically the decision trees and plays from the text can now be expressed intersectionally – grouped by technique (e.g. Zornhau) as well as by principle (response to an opponent with a propensity to parry hard at the blade, for example). We map across time on one axis as the techniques unfold, and on related principles on the other as we connect similar movements across techniques. From this we can develop drills with a greater degree of “aliveness” than we previously would have.  Whereas we practice the individual technique to achieve technical excellence in a fixed play, our principle based drill attempts to generalise these movements and attempt them from any cut and any position.

The devices or trees thereafter become examplars for that tactical element, and the drills so derived don’t necessarily seek to emulate the atomic techniques of the drill, but rather they are flexible drills created from whole cloth by applying the tactical lessons in a more flexible and “open” structure (open in this context meaning not tied to performance of a particular atomic technique, but rather inspired by that technique).  This requires a degree of fencing maturity from participants.  It is seldom a good idea to give people a completely “open” structure for drills until they have learned the atomic elements themselves.

The transition from decision tree exemplars to fully “open” versions of the same tree can be carried out in stages, adding or altering one parameter at a time.  We might begin with a drill which directly reflects the first Zornhau play, then give a hard/soft bind decision, then change choice of incoming attack into a choice of two (Oberhau, or Unterhau, say), and so on, each time increasing complexity until we have a simple, but “open” drill –

  • Person A attacks with an unspecified cut,
  • Person B countercuts with and unspecified cut,
  • Person A is strong or weak
  • Person B reacts accordingly

The drill reflects the framework of the original Zornhau play, but is now unshackled from certain specifics.

Over time this kind of drilling produces a kind of automaticity to a fencer’s motions.  Automaticity is the degree to which a given task requires our conscious attention and focus.  When we learn to drive a car for the first time the simple elements of changing gears and staying in the correct road position take a great degree of concentration.  After a few years, however, those actions become almost automatic, requiring almost no mental attention.

The same applies to fencing.  Learning a new drill with an unfamiliar style or weapon for the first few times is awkward and difficult.  After a while, though, these particular movements become embedded as subroutines: we have achieved automaticity.

Furthermore our repeated practice has given us an innate understanding of measure and how fast we can perform fencing actions.  In the terminology of the American Psychologist J.J.Gibson[4] have effectively learned the “affordances” of the sword, and our opponent .  Again this has implications on automaticity; we no longer have to concentrate on measure as we have become automatically aware of it, we no longer need to worry about whether we’re cutting a Zornhau or a Zwerch, our knowledge of the blade’s affordances takes care of that for us.

In our linguistic analogy we have moved from phrasebooks to free conversations about specific topics, it’s only a short step from here to general conversation.

This embedding of our own behaviour, and of a model of what to do based on opponent’s behaviour, is widely recognised in tactical decision theory, and finds its best expression in the OODA loop.

Introducing the OODA Loop

The importance of deriving useful heuristic models of fencing style and behaviour is demonstrated by Boyd’s OODA loop. Boyd was a combat pilot and military consultant who was extremely influential in the field of military decision making theory. His model has been extended and modified over the decades since it was first introduced, but in its basic form it becomes a very useful basis for developing our fencing techniques.
The basic version of the OODA loop is shown below:
The OODA Loop
OODA is an acronym for the stages of the tactical reasoning process. Specifically we have:>

Observe

This is the data-gathering phase. A fencers observations can be broad reaching, from instantaneous inputs, to higher-order observations. Some examples in fencing might include a fencer’s perception of:

  • Distance/measure from the opponent
  • Feeling of the bind (soft/weak vs hard/strong)
  • Opponent reaction times
  • Visual telegraphs and triggers

We say “perception of” because everything we do is guided by our perceptions – and these perceptions are prone to being wrong, but more on that later.

Orient

The orientation phase is where we construct our mental “picture” of the situation, then tear it down and construct them anew; it’s where we make and break connections between the incoming Observations, and what we “believe” is going on.

In the orientation phase we make our own internal representation of the world, deciding for example on our opponent’s overall temperament; are they aggressive or defensive? Quick to thrust or do they prefer the cut? Are their movements typically linear or circular? Do they like to parry upward, downward, or sideward?

The more accurate and flexible our models, and the more useful models we have at our disposal, the more broadly effective we are likely to be. Where do we get our models? From the concepts derived and practiced from our decision trees, of course!

Decide

Typically our Orientation phase results in prototypes across multiple fencing dimensions. We might have an opponent who is Defensive and Linear, who prefers to parry Sideward.  The decision phase deals with the selection of a corresponding tactic or set of actions which will be most effective against our prototype opponent. In our example we might decide on a provocation changing through into a thrust just over the arms to the torso as the most effective, for example.

This decision is typically imperfect – it is a best guess from limited data. This decision making set is what many of our drills are aimed directly at addressing; creating the right decision making behaviour for given trigger prototypes.

Sometimes, of course, we have no information at all – at the start of a match we don’t know our opponent’s capabilities, and our model is far too limited for proper decision making. In this case our decision might be to perform some “reconnaissance by fire” – to give a few test cuts to see how they reaction; it’s important to remember that these decisions are not always decisive attacks; they can be utility functions to get more data, give you a moment to rest and reorientated yourself, and so on.

The decision stage is directly informed by our conceptual models, established earlier from decision trees.

Act

Finally we come to the Act phase. This is where we execute our decision in the real world; we perform our provocation and change through, we do some test cuts, whatever we chose in our Decide phase.

Importantly this feeds back immediately into the Observe phase; we need not go through the whole set of Actions; if a technique fails or something happens to confound it, we begin the loop again. Whatever happens the outcome of our Act phase creates an entirely new set of inputs for the Observe phase, and our loop begins again.

Connecting Decision Trees and OODA Loops

The connection between OODA Loops and decision trees should be fairly clear by now. As mentioned earlier a conscientious study of decision trees provides us with:

  1. An understanding of how to perform the atomic actions which make up the system (cuts, handworks, and so on).
  2. A series of exemplar tactical scenarios using atomic actions.
  3. A top-down or bottom-up analysis of how tactical or strategic scenarios that apply to given situations.

Having developed fluency from our drills we now have two elements:

  1. Automaticity of actions dealing with general tactical or strategic scenarios.
  2. Efficient and unconscious use of the sword through knowledge of its affordances.

These elements can map directly to various stages of the OODA loop. Consider:

  • Observe:
    • Our fluency in drills generalised from techniques give us experience with a variety of input patterns.
  • Orient:
    • Our understanding of the implicit and explicit tactical and strategic scenarios allow us to orient ourselves even in the case of slightly varied or unfamiliar inputs.
  • Decide:
    • Fluency drills have provided a degree of automaticity in deciding what to do in a given orientation situation.
  • Act:
    • Our knowledge of affordances and practice of atomic actions ensure efficient and effective implementation of techniques.

Leveraging the OODA Loop

The useful thing about the OODA loop is that our opponent is using something very much like it, even if they’ve never even heard of it before. It models with reasonable accuracy the kind of steps everyones’ brains seem to go through when performing activities in the real world. Because of this verisimilitude between model and action we can build our fencing drills and techniques to actively disrupt the opponent’s OODA loop, while minimising the cycle time on our own loop.

When we develop our drills based on tactical and strategic concepts we should consider at all times where they intersect with the OODA loop, and how it can be used to either disrupt the opponent’s loop, or improve our own.

We can optimise our own OODA loop in a number of ways, for example:

  • Observe
    • Develop feeling in the bind (Fuhlen)
    • Learn to look for specific triggers or behaviours which are used in later steps. For example:
      • Tells that indicate when a cut or thrust is coming
      • Indications of whether the opponent’s line is covered
  • Orient
    • Develop drills which include triggers to indicate if an opponent matches a certain model.
    • Drill against a wide variety of opponents
    • Develop coached drills where the opponent takes the role of a particular type of fencer.
  • Decide
    • Drill a subset of high percentage decision actions which can be used in a variety of scenarios – 5 high percentage drills you’ve practiced a hundred times, are better than 100 techniques you’ve studied a handful of times, or worse, simply analysed at length in conversation and text.
    • Know the measure at which different techniques are effective, and when they need second intention actions.
    • Prune your own decision tree by opening a single line of attack; you know they have to attack down that line, so all other options can be discarded.
  • Act
    • Drill body movements until automaticity is reached.
    • Practice solo to increase our understanding of the weapon.
    • Develop physical athleticism to move faster and fight longer.

Conversely interrupting our opponent’s loop can include:

  • Observe
    • Provide “noisy” input – erratic movements, reversals, changed footwork and timing – anything that interrupts clear flow of input data to the opponent.
    • Minimise your tells for particular movements.
  • Orient
    • Move in time-spans where you know your opponent cannot observe and orient themselves in a timely fashion (Force a short loop)
    • Create rhythms, then break them (Reset their Loop)
    • Change their internal prototype – vary your techniques and approach to the fight (Deceive their internal model so they have to reevaluate)
  • Decide
    • Interrupt their decision tree by forcing them to act with a provocation; this will reduce their viable decisions to hastily made responses with only partial orientation/decision completed (shorten the time they have for their OODA loop)
  • Act
    • Choose movements which are faster than theirs, this “faster” can include concepts such as:
      • Using time of the hand to beat their time.
      • Using single tempo movements against their double tempo
      • Choosing movements that are shorter in execution time than the opponent’s (a short thrust vs a cut around, for example).

Conclusions

Clearly decision trees are far more than a dogmatic series of movements which we must adhere strictly to at all time, and that we think about step by step as we fence. We should consider decision trees as templates or prototypes for concepts and movements from which we should develop small, easily adaptable drills which capture the underlying essence of the technique without necessarily mimicking it directly. These decision trees allow us to:

  • Learn the atomic techniques of a style.
  • Learn specific named scenarios where these can be applied.
  • Derive concepts from which we can generate our drills. The drills themselves should aim to:
    • Provide a knowledge of the affordances of the sword.
    • Provide fluency in recognising tactical situations.
    • Provide automaticity in responding to these situations.

When developing these drills we should always be mindful of the benefit we are trying to achieve. In this respect the OODA loop is a useful model for analysis. Whenever we consider a new drill we should think about:

  • Observe
    • What are the stimuli for the particular drill – are they well defined and parameterised?
    • Do the fencers own actions provide correct stimulus for the opponent (provocation, invitation, confusion)
  • Orient
    • What is the conceptual model or tactic we are trying to recognise?
    • Is the model flexible or brittle and overly specific?
    • Do we confound the opponent’s own orientation model with our actions?
  • Decide
    • Does the drill have decision points?
    • Have fencers practiced enough to achieve automaticity?
    • Does the drill interrupt the opponent’s intention effectively?
  • Act
    • Have fencers trained enough on the atomic elements to be effective in their act?
    • Are we using appropriate movement tempo?

If we are mindful of these ideas then a scant handful of well designed drills can result in more effective fencing than endlessly repeating the fixed plays from a text for years.


[1] Thangarajah & Evertsz (2015) A framework for modelling tactical decision-making in autonomous systems

[2] Chris Slee (2017) From Text to Training Developing a functional training plan any HEMA source text

[3] Maciej Talaga (2017) Do you even Zornhaw? A set-theoretic approach to HEMA reconstruction

[4] Gibson, J. J. (1966). The senses considered as perceptual systems.

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