Olympic Games – Small is not beautiful

Olympic-logoThe Olympic Games came to an end a little bit more than a week ago. Beyond the last-minute logistic annoyances, the United States showed the rest of the world that one more time they were dominant in the Olympic arena. Good surprise came from team GB, which benefited from years of investment and the partial ban of the Russian delegation to clinch the runner-up spot. On the other end of the rankings, almost 100 countries will fly back with no medal.

The question is what is the best predictor of a nation’s performance at the Olympics? First, we need to be clear about what we mean by ‘performance’. Limiting myself to countries which have managed to take a medal home, I have used the official medal table and I have allocated 5 points for a gold medal, 3 points for a silver medal and 1 point for a bronze medal – I could have used the gold medals only but this would have created an ‘edge effect’ as many countries have won no or very few gold medals. The official ranking (taking only gold medals into account) is largely preserved: only exceptions in the top 10 are France (with its famous ‘fear of winning’) and the Republic of Korea.

Points ranking according to our methodology.
Top 10 countries according to our methodology.

We can use a few macroeconomic indicators to assess whether they are correlated to the success of a given country. It is important to note here that a regression only enables us to conclude about the presence or absence of correlation and not about the presence of a causality effect. For instance, if we plot population on the X axis, we see that the bigger a country is, the more medals it tends to gather – with the notable exception of India, circled in red, whose poor performance has been largely documented throughout the event. So what we can conclude is that there is a correlation, but we cannot state that ‘a higher population leads to a higher number of medals’ (which is nonetheless probably true) or that ‘a higher number of medals leads to a higher population’ (if so we would have baby booms in the US every 4 years).

Regression log(population) (X) - log(points) (Y).
Regression log(population) (X) – log(points) (Y).

The Economist argues that the most significant driver is actually GDP. The correlation effect is also significant.

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Regression log(GDP) (X) – log(points) (Y).

What it means, interestingly, is that GDP per capita correlates poorly with the ultimate country performance – contrary to what the same Economist article may assert. The nominal sizes of the economy and of the population thus prevail. This is understandable: more money overall tends to mean more investment in infrastructures, training etc. However, we would need to dig further as wealth created is not evenly allocated to the development of sports in each country.

Log(GDP per capita) (X) - log(points) (Y)
Regression log(GDP per capita) (X) – log(points) (Y).

Goldman Sachs performed a forecasting exercise using its proprietary Growth Environment Score (GES), which captures “important features of the economic, political and institutional environment that affect productivity performance and growth across countries”. Simply said, Goldman Sachs uses a multi-variable correlation instead of relying on one macroeconomic driver as we have done so far. The algorithm grants extra points for the last two hosts (i.e. Brazil and the UK) to acknowledge the important investment and support of the crowd. The accuracy obtained is remarkable.

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Number of gold medals for top 10 countries: Goldman Sachs forecast vs. actual.

In its paper, Goldman Sachs states that “a country is more likely to produce world class athletes in a world class environment”. I took the statement seriously and checked for a correlation between the number of medals and the Human Development Index, which accounts for human well-being beyond economic considerations by including data on life expectancy and education, among other factors. A high correlation would be fantastic news: sports excellence would be a ‘by-product’ of the improvement in life standards. The result can be found below.

Regression HDI (X) - log(points) (Y)
Regression HDI (X) – log(points) (Y)

Although we could advocate for a slight correlation, the effect of human development remains limited compared with the one of money. This conclusion highlights a fact that is widely shared throughout the sporting world (including football, which we will deal with in a later post): human effort alone only returns sweat, but only with a wallet will it be worth its weight in gold.

Brexit: How tight is it, really?

brexit-ballot-boxWith the official referendum expected in less than two months, the latest polls on Brexit show a narrower than ever gap between both camps. The Financial Times’ Brexit poll tracker shows that the June referendum could go either way. However, as mentioned in an earlier post, bookmakers such as Betfair have barely adjusted their odds over the last few weeks and still predict a victory for the ‘Bremain’ side with a 65% probability – and even closer to 75% following Barack Obama’s visit to the UK last week. How can we reconcile those two facts?

Evolution of implied ‘Bremain’ success odds according to Betfair.

First, to reiterate an argument already developed on that blog, bettors and bookmakers believe that, unconsciously or not, individuals positioning themselves in favour of Brexit do not reveal their real vote intention to pollsters. A similar bias can be observed in voters’ behaviour towards the most extreme parties prior to an election. A share of the self-declared ‘extremist’ electorate will actually revise their intentions just before putting the ballot in the box.

Result of the first round of the 2002 French Presidential Elections

That being said, the reverse trend used to be true in some countries such as France – i.e. individuals planning to vote for the Front National were fearful of revealing their real intentions and hid it to pollsters – and partly explained the 2002 French Presidential Election upset where Front National’s Jean-Marie Le Pen unexpectedly ousted Parti Socialiste’s Lionel Jospin from the second round. Being able to identify and quantitatively assess behavioural biases has become part of survey institutes’ core job, especially in tight contests such as the one we are witnessing today.

Unconscious behaviours nonetheless do not fully explain the discrepancy between polls and bookmakers. Statistics also come into play. In the context of the Brexit referendum, the Bremain camp has indeed managed to maintain a small, although very narrow, lead in most of the polls. As a consequence, the odds of the Bremain camp winning are actually greater than the gap could lead us to believe. To illustrate this fact, let us assume that the distribution of vote shares in favour of ‘Bremain’ follows a normal distribution – the infamous ‘bell curve’.

This distribution is centred around an average of 52% – i.e. on average Bremain wins by a 52-48 margin. Let us also assume that we are almost certain (with a 95% certainty to be perfectly exact) that the Bremain camp will score between 44% and 60% on D-day. The resulting bell curve is drawn below, with the shaded area representing the area sitting above the 50% threshold – i.e. the area where the Bremain camp wins. Although we built the bell curve around a 52% average, the shaded area represents 69% of the total area under the curve, which means that the Bremain camp has a 69% chance of winning. The parameters for this example have not been chosen randomly: 69% is indeed very close to Betfair’s latest estimates.

Bell curve with average of 52% and std deviation of 4%. Shaded area corresponds to p>50%.

This exercise would theoretically give us a lot of confidence on the referendum outcome. In practice, the exercise is unfortunately made much more complicated by the high share of ‘undecided’ voters, standing at roughly 30% of the voting population as of today. Given its size, this group will clearly decide on the referendum’s outcome and can overturn any statistical projection. Being able to predict the behaviour of such a heterogeneous group has therefore become the focus – and the nightmare – of all pollsters – notwithstanding the bookies.

Brexit won’t happen – Just ask the bookies

Credits: www.dnaindia.com

Recent surveys about Brexit depict a very close race between the supporters of ‘Brexit’ and ‘Bremain’. Basing itself on the last 6 polls, The Telegraph asserts that the gap has narrowed to a thin 51-49 majority in favour of remaining in the UK. The Week has drawn similar conclusions: the 2% difference between ‘In’ and ‘Out’ supporters is insignificant if we consider that 4% of voters admitted to be unsure about their vote.

Source: Telegraph.co.uk
Source: Telegraph.co.uk

The question now becomes: to which extent can we trust surveys? And are there alternative, more reliable sources of wisdom? In the UK, the answer is ‘definitely yes’ and is in the hands of the likes of Ladbrokes, William Hill and Betfair.

James Surowiecki
James Surowiecki

As explained by James Surowiecki in his book The Wisdom of Crowds, betting markets are great ways to aggregate heterogeneous opinions across a given population. More importantly, by putting their own money at stake (by definition), bettors should not focus on their own views but predict the outcome of the vote instead. Provided that the market is liquid enough, academics such as Justin Wolfers built on Surowiecki’s work to demonstrate that, actually, those markets were the most accurate predictors of future event outcomes – and were given the name of ‘prediction markets’ as a consequence.

Betfair_logo.svgWhat are the odds then? Well, all bookmakers concur to assert that the situation is much clearer than the polls suggest. The odds of a ‘Bremain’ on Betfair, the leading betting exchange platform (i.e. a platform where players take bets against each other), have been fluctuating between 1.30 and 1.60 over the last few days, which translates into a probability range of 62% to 77%. This takes into account the recent bombings in Brussels which slightly revived the ‘Eurosceptic’ sentiment – see green arrow in the chart below. According to the same bookmaker, the exact split as of yesterday was 65-35 in favour of ‘Bremain’, with more than £2.7m worth of matched bets.

Historical evolution of ‘Bremain’ odds. Source: Betfair.com

Beyond bookmakers, the world of finance also provides us with a number of prediction markets. The evolution of the GBP/USD exchange rate, for instance, is another way to assess the relative ratio of power between the two sides if we believe that a Brexit would translate into a significant depreciation of the pound. This type of analysis, however, does not allow us to deduct a precise probability of ‘Brexit’ happening but can only track its relative evolution.

Historical evolution of USD/GBP FX rate. Sources: Oanda, author analysis.
Historical evolution of USD/GBP FX rate, with selected time averages.
Sources: Oanda, author analysis.

Given the high stakes, the political establishment will undoubtedly keep a close eye on these indicators over the next few months. Will they prove accurate?

For those unfamiliar with Betfair, here is a short corporate video presenting the basics of the betting platform.