I’ve previously written about the similarities between martial arts and other arts (you can read about this here and here), especially music, as I worked as professional musician for many years.

In addition, for over a decade I worked as a university lecturer in the field of business, primarily in finance, economics and professional communication.
Since leaving university I very rarely had the opportunity or need (or desire) to revisit most of the theories I used to teach, until a random conversation with a martial arts student about a university assignment somehow got me thinking about the Law of Diminishing Returns, and I was immediately shocked at how that economic principle could be used to explain, in a way, the relationship between training and results… which opened the floodgates to many more financial theories. Here are a few from the resulting brainstorm:

1. The Law of Diminishing Returns – In economics, this theory states that, with all other things being equal or unchanged, as we add more factors to production, past a certain point, we will produce less. A good example of this is the number of instructors needed to run a class. At some point, if you add more and more instructors, they will start getting in each other’s way, confuse students and take up mat space, not to mention increase your costs, and your students will end up receiving less-than-optimal tuition, and as a result will learn less. It looks something like this, where T_Max and t^* give us the point where we maximise returns before they start dropping again:

There are a couple of great applications of this theory to training:

• There is an optimal point of production which best utilizes available resources. Stay below it, and you won’t be maximising your capacity. Go past it, and you’ll stretch yourself too thin and production will fall. This is the perfect analogy for a training routine. We go through phases of training a lot, perhaps in preparation for a competition or grading, and not training at all, perhaps because of injury, but usually there will be a balance where you still grow and develop without burning yourself out. While this point may vary throughout time, it is important for us to find that point and remain aware of it as it changes. Otherwise, much like the production process, we will improve rapidly and then get injured, or train too little and not improve at all. In other words, we need to find the point where our returns from an additional training session (however you define them) are still significant enough to warrant that extra training session. 
  
  
• Another explanation is that diminishing returns refer to the point where the returns or benefits are less than the amount of energy spent or invested. I think this is a perfect example of what happens as you improve over time. As you get better and better with training, your techniques become sharper and more accurate. As this happens you start appreciating the ‘diminished returns’. You start seeing the smaller facets and fine details, and every small improvement takes more and more work and time. In a sense, the Law of Diminishing Returns describes the unattainable perfection that martial artists seek.

2. Economies of Scale - This is almost like the opposite of the Law of Diminishing Returns. This theory states that given fixed costs (for example, rent we pay for our dojo), as we increase production we reduce the fixed cost per unit. For example, if you have to pay $5,000 in rent every month and you have 5 students in your dojo, you will have to charge each of them $1,000 per month to cover rent, but if you have 500 then you only have to charge each $10. That being said, other costs - variable costs, think of them as costs per student - can increase. For example, you may have to replace pads and equipment more regularly, buy a lot more stock, pay more in utilities (phone, water, electricity, etc.), pay additional instructors, etc. This leads to a balancing point where your costs will be at their lowest before they start climbing up again. This looks something like this, where the point C₁Q₂ represents the point where costs are lowest:


Dojo management aside, this also describes, in a way, progress and focus in training resulting from getting repetitions in. Remember the first time you did a hard pad session? Probably couldn’t move for a few days after. But as you improve technically and the subtlety of the movements is explored, your body becomes accustomed to the movements and you spend less and less energy in executing the same techniques… providing other conditions are optimal, i.e. you are not overly fatigued, sick, injured, distracted, etc. Reminiscent of the last point on diminishing returns, economies of scale is the principle that we have an optimal performance point, which is, if greatly simplified, a function of repetition and fatigue. Finding this point is up to you!

3. Capital Structure Irrelevance Principle – this theorem relates to the capital structure of a firm. In other words, it relates to how the firm raises money using debt (borrowing money) and/or equity (selling ownership). What the creators of the theory, Miller and Modigliani, asserted, was that in a perfect world – a world with no taxes, transaction costs, and where everyone has the same knowledge of the market – it should make no difference whether a company borrows money or sells shares to raise funds. This was fundamental to the development of many modern economic and financial models, and even landed Miller the Nobel Prize in Economics in 1990! 
But what stands out to me most out of this is the fact that the model only works under a very strict set of assumptions that do not hold in the real world. This, to me, is the perfect analogy of the ‘dojo syndrome’ that I talk about very often (read about it here) , and about how people often perceive a martial art or combat sport to be self-defence, when really they are practicing in an environment that eliminates the complexities of the real world. By restricting the set of assumptions, we make a system work! Examples include limiting targets, introducing rounds, rules, weight divisions and time limits, cooperative opponents, predictable responses, excluding other factors such as weapons or multiple attackers or excluding certain elements altogether (no grappling, no takedowns, no striking), etc. Every system does this, and this is indeed necessary in order to train safely and allow focus on the core skill set of the system. However, this creates a serious problem with regards to training for self-defence. It makes the model work very well in theory, but when one starts introducing real-world complexities the model fails.

4. Portfolio Optimisation Theory – Harry Markowitz developed this model, which discusses the minimization of risk when creating an investment portfolio. What Markowitz demonstrated was that, under a particular set of assumptions, by adding assets that are negatively correlated (in other words, react in opposite ways to various factors), we can create a portfolio that maximizes profits and minimizes risk. Because the assets are negatively correlated, when one would lose value, another would gain value and so the overall risk and profit will retain a particular level. In layman’s terms, this is a fancy way to say ‘don’t put all of your eggs in one basket’. 
In much the same way we can look at benefits from cross training in different styles. 
I am a staunch believer that in order to improve and grow one must seek out solutions outside of their ‘base’ system, especially in today’s world of MMA. That doesn’t mean you need to be a BJJ black belt, wrestling champion, golden gloves boxer and competition shooter, but you need to have some familiarity with a range of techniques and applications in a variety if disciplines, i.e. striking, grappling, takedowns, etc., especially if your ultimate goal is self defence or MMA competition. You never want to end up in a position that you have never been in before - in competition or in real life. But how much cross training is too much? We need to follow Markotwitz’s example and find our optimized portfolio of different skills that will allow us to best implement our strategy. For exampe, if your strategy is to stay on your feet at all costs so you can deliver devastating strikes, then you need to add some wrestling/Judo and some BJJ to your portfolio so that you can minimise the risk of being taken down by grapplers. That being said, if you spend all of your assets (time, energy, money) on your grappling, your striking skills will deteriorate. It is up to you to find the optimized portfolio of skills.

Circling back to the beginning, I find martial arts analogies in everything, as training is the main focus of my life. I believe that training is an investment, and as such we can use investment-related tools to maximise results. Some of you may read these and think ‘what is he on about?!’, and that’s fair. I think that often enough too! But I do believe that we can find applications and similarities in everything, if we only open our hearts and minds to the possibilities that are out there. If nothing else, the researchers behind these theories have dedicated their entire lives to try to find solutions to problems that affect us all, which can be considered to be a way of living the warrior code to its highest standard. And if some of those solutions can be applied outside of their original context to solve other problems – some as simple as ‘should I go to training today’ – then they are valuable tools indeed, and deserve all of the credit that has been bestowed upon them.

Stay tuned, stay safe,

Osu/Oss