Rugby is a game of options. At almost every moment of the game, we have the ability to choose between a multitude of options. Do we kick? Do we Pass? Do we look for the Offload? Do we try to avoid contact, or do we blindly run into the opposition player in front of us? These choices can be seen as one making small investments, each with a potential risk and reward, paying off in the near future. Now, isn't this remotely similar to what people do in the financial world? They will look at investment opportunities, analyze the potential risks and rewards, and then invest in the choice that will give them the greatest risk-adjusted return. Although there are glaring differences, I believe the underlying principle is too similar to ignore.
In the realm of Portfolio Theory, there exists a concept called the Capital Market Line (CML). The CML essentially shows the risk to expected return relationship of a portfolio when combining different proportions of riskless and risky assets. If one is to include more risky assets, one would move rightwards up the curve to a point with a higher risk and a higher return. If we were to include no risky assets at all, we would find ourselves at the point where the CML intersects the vertical axis. The two key points on this curve, for the sake of this analysis, is the risk-free rate (Rf) and the slope of the curve, also known as the Sharpe Ratio. The risk-free rate essentially describes the return one would expect to earn without taking on any risk, these are usually government bonds in the investment world. The Sharpe ratio, or the slope of the curve, basically shows the reward one would expect for taking on additional risk. If the Share Ratio is higher, i.e. a steeper slope, then the expected return per unit of additional risk will be higher. Therefore, in this instance, it would seem beneficial to move further along the curve, obviously depending on the level of risk the investor is willing to take. This is illustrated in the graph below. Rf is the the risk-free rate or return.
The idea behind investing is quite simple. For us to achieve a higher wealth in the future we would need to invest some wealth in an investment today. Let's call these investments, 'assets'. Now, going back to the idea of a portfolio, we can invest in many different types of assets with different risk-return relationships, and combine them together in a portfolio. Rugby, I believe, can be looked at, analogously, in a very similar way. Consider a team who currently has the ball at a lineout, 22m out from the opposition try line. Many assets (options) are available to the attacking team, each with a different level of risk and expected return. If you were the Springboks, naturally you would look to maul because, for a small degree of risk, your expected return would be quite high. For the All Blacks, the situation would likely be different because, for that same level of risk, the payoff wouldn't be as high, as the Springboks are arguably the best mauling team in the world. Assume now that the ball is mauled and it collapses. At the ensuing ruck, again, the team is presented with a multitude of potential assets. Again, different teams will invest in different assets (choose different options) depending on their strengths and weaknesses, subconsciously assessing the risk-return relationship of their decisions. If we were to scale this up, one could assume that a rugby match is simply a massive portfolio of assets (or options for the next phase). Now, depending on the number of risky, or riskless, options taken by a team, they would be able to move along the CML, as seen above with a normal investment portfolio. This is illustrated below:
This is where things get interesting. For the Springboks, their risk-free expected return would be higher than any team in the world, however, their Sharpe Ratio, of the slope of their curve, would be flatter than most of the top teams in world rugby. The risk-free return, in this case, highlights a teams ability to play well in technical, and often confrontational, situations. The Sharpe Ratio highlights a team's skill level. With a higher Sharpe Ratio, or a steeper slope of the curve above, it would make sense for a team to play expansively, as the All Blacks do. Given that this is likely to be the case, it would explain why the Springboks attempt to keep a game as tight as possible, because the additional expected return is not worth taking on the additional risk because of their relatively low skill level. This is also clearly evident from the recent statistics published by the IRB from the U20 World Cup. The Baby Boks forward pack passed the ball 45 times in the entire tournament and the backs only 141 times. That being said, they still made it to the final and only lost by 1 point. Quite simply, in rugby, teams will play to their strengths.
The only problem with this, however, is when one team plays more to their strengths than another. The graph below shows the typical case of when the Springboks play the All Blacks. If the game remains very tight, theoretically, the Boks will have the advantage. However, as soon as the game opens up beyond a certain point, the All Blacks are likely to win. Naturally, there are many other idiosyncratic risk factors which need to be considered which can change a game completely, e.g. poor referring decisions, uncharacteristic mistakes by players, etc., but we shall ignore these for now (If you were looking at multiple games, these idiosyncratic factors would cancel each other out).
The beauty of this framework, is that it becomes easier to see where our structural weaknesses lie as a rugby playing nation. It is unimaginable to think that we would lose our physical and mauling dominance in the near future, therefore giving us a somewhat sustainable riskless advantage. Now, if we were to improve our skill level and improve our Shape Ratio, or return for additional unit of risk, we would be able to have an advantage over teams even when games begin to open up. Imagine a Springbok side that still maintained its dominance in the set piece, and was able to move a ball around so as to attack space and not the man in front of them. The situation, in theory, would look something more like this:
With our current skill level, it wouldn't make sense to play an expansive brand of rugby. However, with an improved ability to move the ball around, whilst maintaining our physical dominance, we would be beating the All Blacks far more consistently. Once we have improved our skill level, it would then make more sense to include more risky assets in our match day portfolio.
Although this is a highly simplified example of the applications of portfolio theory, which ignore elements such as return correlations and optimization, it does provide valuable insight. Changing a skill set of a team does not happen overnight, but the reality is that if we do not change the style with which we play, we will continue to very rarely beat the All Blacks. This type of approach and development has to begin with the unions. The obsession with winning has destroyed the ability to play an expansive type of game, often, ironically, reducing the ability to capitalize on opportunities which will actually win the game. Skills development should be an absolute priority, with the fixation around game plans becoming a secondary concern. If this was to happen, it would allow the Springbok coaching staff to play a brand of rugby which will have the foundation of riskless strengths, and a much better ability to move the ball around when needed, giving the Boks a far better chance of beating the All Blacks on a regular basis.
