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Now that these particularly memorable twenty-second Winter Olympic Games have run their course, it’s time to review with an eye on answering two big questions:

-Who won Sochi 2014?

-What factors were correlative/predictive of success at Sochi 2014? (I am staying far away from making causal claims)

Worth noting before you read further:

-You should take a look at my last three posts on this topic first.

-In addition to many graphs and charts, this post will use choropleth maps, which use color to show differences. I wanted to add cartograms, which use (distorted) land area to show differences, but unfortunately ran into technical challenges I couldn’t really resolve to my satisfaction. There may be a follow-up post with some pretty cartograms if I can get it working right; in the meantime, excuse my choropleth.

-The second half of this post will feature a lot of regression results from Stata. If you’re not sure how to read regression results, I will summarize the key points, but you should also check out some of the resources out there on the internet for interpreting basic multivariate regression. It’s interesting and a useful skill! Seriously!

– Be forewarned that this is going to be a long post, so if this isn’t your thing, you should just skip down to the one about Francisco Franco. That was a good one. You could also check out this awesome interactive map from the Wall Street Journal that makes my maps look pretty lame, frankly, and I really shouldn’t link to them except integrity. Sigh.

And if you just want to skip this whole damn thing and cut to the chase, spoiler alert:

team lannister ftw

OK, let’s dive…er, slalom in:

Who Won Sochi 2014?

This question is less about data manipulation then the nature of the question itself. To determine who won, we have to decide the criteria for winning.

Most Medals

The simplest and most-widely-used criteria is most medals won. By that one, the results are pretty clear (note that all charts in this section exclude nations that failed to medal):

total medals

Winter Olympians 2014 Total Medals

Give this one to the home team. These results aren’t too surprising, but they do point to one reason these Olympics were interesting – nobody dominated quite like the US did at Vancouver, where they won 37 total medals.

Also, as we saw with the number of competitors sent to the Olympics, a small handful of countries really ran the show. Just six countries – Russia, USA, Norway, Canada, the Netherlands, and Germany – won over 52% of the 295 medals awarded at Sochi, and just eleven countries – those six plus Austria, Sweden, France, Switzerland, and China – accounted for over 75% of the medals.

But is that the best criteria? While it is a useful starting point as a raw, unweighted barometer of achievement, there are a lot of limitations to that measure. Let’s start digging into other measures.

Most Gold Medals

The second-most-widely-used criteria is most gold medals. By that one the results are also straightforward:

total gold medals

Winter Olympians 2014 GoldMedals

These results are also unsurprising – Ruskies win again – but they do start to point towards a more complex picture.

In some sense, this is also an intuitive criteria – the point of competing is winning! But that criteria also neglects a lot of considerations, first and foremost, the other two medals.

Most Quality-Weighted Medals

A compromise between/solution to the issues with those first two is to include all medals, but to weight silver higher than bronze and gold higher than silver. This process is inherently subjective; there is no obvious right answer to which system is best, and many systems can be used, some better than others, but none definitive. After some research, I personally developed a fondness for the system suggested by Robert Banks via Mario Livio, which weights the medals by the relative density of their metals; in this system a bronze medal is assigned one point, a silver medal 1.23 points, a gold medal 2.27 points. If you have another system you’d like to test, my data is included at the bottom of this post; feel free to meddle with the medal/metal formula.

total quality adjusted medals

Winter Olympics 2014 Quality Medals

These results show outcomes that roughly split the difference between the first two measures, which is deeply unsurprising – for the Amero-centric report, the US gets edged by Norway by eight-hundredths of a medal! But now we have to address some bigger issues before we can definitively declare any country “the winner.”

Medal Efficiency

The biggest issue regards the size of each country’s Olympic teams – there is an extremely strong correlation (though far from a perfect one) between the number of Olympians any country sent to the Olympics and the number of medals they won:

medal olympian scatter

Note two things. One, the “R-squared” of the trendline – how much of the variation in the data can be explained by a straight-line projection – is over .8. That means just predicting medals won by using a straight line projection from the number of Olympians a country sends will get you pretty close. The other thing is that one of those data points is orange. Note that data point.

Fortunately, this isn’t too difficult a problem to solve – we can just divide the number of medals won by the number of Olympians sent to devise a measure of “medal efficiency.” And lo and behold, these numbers look substantially different:

medal efficiency total medals

Winter Olympics 2014 Medal Efficiency

Here is where we start to get some real answers. By this measure one team in particularly is startlingly dominant – the Netherlands.

Indeed, if we look at gold medal efficiency:

medal efficiency total medals

Winter Olympics 2014 Gold Medal Efficiency

And quality-weighted medal efficiency:

medal efficiency quality adjusted medals

Winter Olympics 2014 Quality Efficiency

The Netherlands remains the dominant performer at this Olympics (also, Belarus looks pretty good – a little more on that later).

Event-Weighted Medals and Medal Efficiency

But! There is one big problem with medal efficiency, the one identified by James Harradence on Twitter last week:

Traditional medal counts award each country one medal per event, without consideration of the fact that many events feature multiple competitors, each of whom receives a medal. A country that sends more Olympians because it is competing in team events may be disadvantaged in a medal efficiency rating system that does not take team events into account (depending, of course, on what you are trying to measure – more on that later).

To break it down, of the 98 events at Sochi 2014, 25 were team events, and in total those 98 events at Sochi 2014 had a total of 203 competitors and an average of 2.07 competitors-per-event. I’ve weighed each team’s medal counts by the number of competitors in the events – the breakdown can be seen in the attached data set. Let’s see how this affects both the medal count rankings as well as the medal efficiency rankings.

First, here are the raw medal totals adjusted for the number of medalists:

total competitor adjusted medals

Winter Olympics 2014 Total Multi

Once you award Canada 46 gold medals for hawckey instead of just two, they start to look pretty rocking.

Indeed, here are competitor-adjusted gold medals:

total competitor adjusted gold

Winter Olympics 2014 Gold Multi

And competitor-adjusted quality-adjusted medals:

total competitor adjusted quality adjusted medals

Winter Olympics 2014 Quality Multi

Behold: the power of maple.

But what if we look once more at the efficiency of these medals? This again strikes at the question of what we are trying to measure, but for now again we can table that question and look at the results:

competitor adjusted medal efficiency

Winter Olympics 2014 Multi Efficiency

And once again Team Orange is on top. And when we look at competitor-adjusted gold medal efficiency:

competitor adjusted gold medal efficiency

Winter Olympics 2014 Gold Multi Efficiency

And competitor-adjusted quality-adjusted medal efficiency:

competitor adjusted quality adjusted medal efficiency

Winter Olympics 2014 Quality Multi Efficiency

The House of Orange prevails.

How Did The Netherlands Do It?

Two words: speed skating. Of the twelve speed skating events at Sochi 2014, the Dutch won eight of them outright and won 23 of the 36 available medals. Speed skating accounted for all but one of the Dutch medals at Sochi, the only other being Sjinkie Knegt’s bronze in…short track speed skating. I’m not an expert in Olympic history, but the Dutch dominance in the event this year was pretty remarkable. It was certainly an exceptional performance for the Dutch, who had never won more than 11 medals at any prior Winter Olympics; their haul at Sochi is ~22% of all Winter Olympics medals ever won by the Netherlands.

While the Netherlands have historically been excellent at speed skating (they’re the all-time medal and gold-medal leaders in the category, the former by a vast margin; conversely, they’ve only ever won five Winter medals in non-speed-skating events, ever) they’ve never been this dominant. It’s also not a function of new events; the team pursuits were first instituted at Torino and beyond that the same suite of speed skating events has been in place since Calgary. Whether it’s a level-up of the Dutch or a collapse of traditional competitors (USA, South Korea,, Canada), other analysts have put forward the case that the Dutch speed skating performance at Sochi was the most dominant national performance in any event category ever, or at least of the modern era. Just to cement the case, no country had ever “swept the podium” more than twice in a single Winter Games; the Dutch did it four times at Sochi.

So, yeah – go the Dutch. Keep on skating.

A Digression on Medal Efficiency

I think the focus on medal efficiency and competitor adjustment is useful, but it’s worth doubling back to a more foundation question – what is a country’s goal in the Olympics? Is it to:

1) Win the most events?

2) Win the most medals?

3) Do (1) or (2) within a resource constraint?

4) Some combination of all of those?

5) Other intangible goals?

Depending on how you interpret a country’s goal at the Olympics, some of these metrics do or do not make more or less sense. Depending on your resource constraints, it may not make sense, for example, to field a hockey team at all. This year the Dutch sent their largest-ever Olympic contingent, 41 athletes; but just ten of them won 23 of the 24 medals they accumulated. So how you judge who “won” the Olympics is largely dependent on not just the numbers but what you think the purpose of the Olympics is. You know, other than international harmony and sportsmanship.

What About Belarus?

So Belarus did pretty well, too – not as well as they looked during my mid-Olympic review but well enough to still stand out. How did they do it?

Answer: biathlete Darya Domracheva, who won a rockin’ three gold medals, half of Belarus’ total medal haul at Sochi. Her performance, while not unprecedented in Olympic history, was enough to render Belarus’ small contingent highly efficient, especially if the goal was to win events outright.

What factors were correlative/predictive of success at Sochi 2014?

Let’s zoom out and see if we can look at more generally what factors were associated with achievement at Sochi 2014.

As we saw above, the best way to win a lot of medals is to send a lot of Olympians:

medal olympian scatter

This finding is resilient to pretty much every measure of medals you want to use (and if all this Stata output makes your eyes glaze over, you can skip it, I promise)…

Screen Shot 2014-02-23 at 12.21.41 PM

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And even explains a pretty large share of the variation among just those countries that won at least one medal:

Screen Shot 2014-02-23 at 12.21.03 PM

Screen Shot 2014-02-23 at 12.20.57 PM

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Screen Shot 2014-02-23 at 12.20.13 PM

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Note, though, that the association is consistently weaker when you look only at gold medals, a point we will return to later.

Now, what if we try to control for other factors? In my previous post I showed that population, GDP-per-capita, distance from the equator, and to some extent former Soviet Union status (as well as interaction terms) had decent explanatory power in terms of how many Olympians countries sent to the Olympics. And clearly the number of Olympians is highly predictive of winning medals. But do those factors, above and beyond their association with the number of Olympians, have any predictive power of medal winning?

As it turns out, not really:

Screen Shot 2014-02-23 at 6.08.18 PM Screen Shot 2014-02-23 at 6.08.13 PM Screen Shot 2014-02-23 at 6.08.05 PM Screen Shot 2014-02-23 at 6.08.00 PM Screen Shot 2014-02-23 at 6.07.54 PM Screen Shot 2014-02-23 at 6.07.47 PM Screen Shot 2014-02-23 at 6.07.42 PM Screen Shot 2014-02-23 at 6.07.34 PM Screen Shot 2014-02-23 at 6.07.27 PM Screen Shot 2014-02-23 at 6.07.21 PM Screen Shot 2014-02-23 at 6.07.15 PM Screen Shot 2014-02-23 at 6.07.05 PM

In almost all those models, we gained almost no additional explanatory power. As further evidence, here’s the F-test on the first model of all the additional variables, which in layman’s terms tests whether or not adding a group of variables to a model improved it:

Screen Shot 2014-02-23 at 6.14.41 PM

So to summarize thus far:

1) Knowing about a country’s income, population, climate, and former Soviet status can help you predict how many Olympians it sends to the Winter Games.

2) Knowing how many Olympians a country sent can help you predict quite well how many medals that country will win.

3) Above and beyond that, knowing all the stuff from (1) won’t help you predict medal outcomes.

What about medal efficiency?

Screen Shot 2014-02-23 at 6.02.50 PM Screen Shot 2014-02-23 at 6.02.56 PM Screen Shot 2014-02-23 at 6.03.02 PM Screen Shot 2014-02-23 at 6.03.08 PM Screen Shot 2014-02-23 at 6.03.14 PM Screen Shot 2014-02-23 at 6.03.19 PM Screen Shot 2014-02-23 at 6.03.25 PM Screen Shot 2014-02-23 at 6.03.30 PM Screen Shot 2014-02-23 at 6.03.35 PM Screen Shot 2014-02-23 at 6.03.39 PM Screen Shot 2014-02-23 at 6.03.44 PM Screen Shot 2014-02-23 at 6.03.48 PM

Ignore some of those low p-values; they will lead you astray. The more important thing to note is that the r-squared is generally low, meaning the model explains little of the variation, and the effect size is extremely small, so small as to predict almost no difference between the largest and smallest national teams. It does a little better in explaining the variance in competitor-adjusted models that include all countries, not just the medalling countries, but the effect size is still negligible.

Does this hold even if we include the kitchen sink? You know what; you don’t need all that Stata output. The answer is “yes, it totally holds.” You’re welcome.

Remember what I said above about the difficulty in proving gold medals? I believe that’s related to the difficulty in predicting medal efficiency. Without having much more intensive and extensive data, the models aren’t really able to explain the “x-factor” – an “x-factor” that is likely some combination of luck and national passion for a particular sport unexplainable by the other factors. There are lots of small, cold, rich countries, but none of them have specialized quite as intensively in speed skating as the Dutch. This is where Richard Florida’s conclusion, restated yesterday

The top performers, after adjusting for the size of each country’s population and economy, turn out to be smaller countries in colder climates. These countries tend to specialize in winter sports, and their Olympic programs lack the competition from big-time professional sports leagues that siphon off top athletic talent.

-really comes in in explaining why certain countries excel (or the opposite) beyond what these models would predict.

For those who want to dig more, here’s the data – have fun!

Winter Olympics Full Data Set

Moral of the story: next time my wife asks me a simple question, I will not proceed to make it so complex it requires ArcMap and Stata to answer.

I responded to this great Richard Florida post, comparing Olympic medal totals to date against various national statistics, by noting that it didn’t account for the mediating factor of number of Olympians. Then I wondered – which countries are (thus far) racking up medals in or out of proportion to their Olympian count? So here you go:

dutch out!

I’ll provide more analysis when these Games are over, but for now – wow, the Nethelands and Belarus.

On the other end, Estonia, Romania, Spain, Bulgaria, Hungary, New Zealand, Brazil, and Denmark have send double-digit contingents to Sochi and are currently empty-handed.

So I already commented on Ashok Rao’s blog re: the content of Ryan Enos’ op-ed in The Washington Postre: racial polarization and partisan preferences, but after more careful examination following Noah Smith’s call for Richard Florida to refute it, I realized that a substantial part of the op-ed is not only wrong-headed but dishonest as well. He writes:

In that same year, I examined the voting of Latinos in Los Angeles and found that those who lived near predominantly African American neighborhoods were far less likely to vote for Obama than Latinos who lived farther away — suggesting that contact with their African American neighbors may have prompted them to vote against an African American candidate.

The link is to a paper authored by Enos, which, if you read, is about the 2008 Democratic presidential primary. Putting aside (very real) questions about the paper’s internal validity, by citing it in the article without mentioning that it is about the primary and not general election vote in the context of an op-ed warning of partisan polarization, Enos can only be said to be deliberately misleading readers into believing that Latinos who live nearer to African-American neighborhoods were more likely to vote for McCain or Romney as opposed to Hillary Clinton. In fact, the same precints his paper cites as the best examples of polarization in the Democratic primary are precints that went 9-to-1 for Obama in 2012.

At the very least this calls for a substantial correction to the article.

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