The World’s Sport

In the wake of an entertaining FIFA World Cup, many of us may be reeling in our recollections of the wide variety of memorable upsets that took place. Whether it be the Saudi Arabia team starting their tournament with a victory over eventual champions Argentina, or the Moroccan team knocking out Spain, the tournament was full of entertainment and more than a fair share of underdog wins. For those that are less interested in the World Cup, to put things in perspective, the Saudi Arabia victory over Argentina was the biggest upset in World Cup history. After an early lead by Argentina, the betting odds on the game were so skewed that one member of the betting platform FanDuel reportedly won $21,000 on an in-game bet of $1,000 on Saudi Arabia to win.

Betting odds aside, soccer tournaments like the World Cup seem rife with upsets and drama. Naturally, this can leave many trying to draw comparisons with other sports, like hockey or baseball, to think of whether the same level of outcome disparity is seen. For instance, an event like the Saudi Arabia vs. Argentina upset would be equivalent – based on the current IIHF rankings – to the Russian national hockey team losing to South Africa. And while the Saudi Arabia vs. Argentina game was a historic upset, there were many other significant underdog victories scattered throughout the tournament. From a quantitative perspective, the question regarding the statistical prevalence of large upsets in sporting events is incredibly interesting.

Now, any talk of statistical analysis in sports may remind the reader of the 2011 film Moneyball about the contrarian 2002 Oakland Athletics baseball team that used statistics and a definition of objective player value to select their best-value roster of players.[1] This at-the-time new approach turned out to work quite well in baseball. The idea was relatively simple: over a long baseball season (162 games in the current MLB season), to make the playoffs a team needs to get a certain number of wins, and to accomplish that, they need to score runs. This means that the 2002 Oakland A’s were able to select a cheap-but-effective team of players that could statistically outperform the stacked and star-studded lineups of much more wealthy teams for a much lower price. So long as those players are getting on base and scoring runs, then the system works.

One of the reasons this statistical system works so well in baseball is that, in a given baseball game, the winner is determined by the net effect of a large number of mostly independent events. Furthermore, the baseball season is 162 games (and has been since 1962), and so – over the course of an entire regular season – the teams that get on base and score most regularly will often find themselves at the top of their divisions come playoff time.[2] Now, as this whole discussion relates back to the World Cup, the question becomes: does the same rationale apply in soccer?

Broadly speaking, the answer is “no.” Ultimately, it boils down to the fact that soccer games are often determined by a much smaller number of key events, and the statistical pressures that promise success in systems like the Oakland A’s no longer apply to the same extent. For instance, if a team takes the lead in a soccer game, it is more than possible to change their style of play to be more defensive and win the game. Alternatively, while a given team can be dominating the play, a single slip in their defensive structure can result in an goal for the opposition. While this same dynamic exists across many sports, the low scores and style-dependent nature of soccer makes the impacts of these events much more pronounced. This leads to an interesting analytical problem of understanding what statistical properties play out in the world of soccer.

An old colleague of mine – a talented mathematician and avid French soccer fan – was interested in studying this question using what is known as the “Bradley-Terry model,” which, simply put, is a mathematical model for quantifying the outcomes of two-team (or two-player) contests from a probabilistic standpoint.[i] Ultimately, the findings were that, even when there is potentially a wide range of skill levels between teams, the fact that single events can have outsized impacts on the outcome of a game means that the probability that the top-ranked team wins a particular tournament is highly sensitive to the set of skill levels of all teams involved – particularly at the top-end of the rankings. Intuitively, because even a top-ranked team can lose a contest to a lower-ranked team (and because those events can be not-so-uncommon), the likelihood of the most skilled team prevailing victoriously in a soccer tournament is lower than other sporting events.

Now, with all of this discussion of soccer and baseball in hand, what is the relation of all this to the financial world? Well, in the finance world, specific and large events tend to dominate the long-term performance of a financial portfolio, much like a singular goal can impact the outcome of a soccer match. Ultimately, many of these single-event shocks to a portfolio can be the result of maintaining a financial position that concentrates too much on the performance of single assets – like a portfolio concentrated in U.S. stocks, for instance – and becomes dominated by shocks in the same way the World Cup can be determined by a few rare events. Diversification, on the other hand, lets us spread the burden of financial risk amongst many different asset classes and risk factors, ultimately morphing the equity-concentrated-and-soccer-like financial portfolio into something more similar to baseball, where a bad game by one key player (financial asset) can be compensated by their teammates. So, while the World Cup is undoubtedly an entertaining affair for us viewers, a financial portfolio that mimics the statistics of a soccer tournament is much less desirable than one that behaves more like a statistically sound nine innings at the baseball diamond.

FOOTNOTES

[1] Interestingly, this concept is nearly a direct analog to the classical “value” investing strategy prevalent across the investment world since the 1920s. In the case of value investing, individual companies are selected based on their being undervalued – priced cheap relative to their fundamental value – while overvalued companies are avoided, much like the players are in Moneyball.

[2] The story is different, however, come playoff time. With fewer games in each series, the statistical player attributes that made the Moneyball team so successful over the course of the season at making the playoffs may have little impact on whether or not they actually win the playoffs. While the Athletics won their division four out of the six years between 2000 and 2006, they have not won a World Series since 1989.

REFERENCE[i] R Chetrite, R Diel, & M Lerasle, “The number of potential winners in Bradley-Terry model in random environment”, 2015, ArXiv.