Classifying Olympic Athletes by Sport and Event (Part 3)

This is the last post in a three-part series. Part one, describing the data, is here. Part two gives an overview of the machine learning methods and can be found here. This post presents the results.

To present the results I will use classification matrices, transformed into heatmaps. The rows indicate Olympians’ actual sports, and the columns are their predicted sports. A dark value on the diagonal indicates accurate predictions (the athlete is predicted to be in their actual sport) while light values on the diagonal suggest that Olympians in a certain sport are misclassified by the algorithms used. In each case results for the training set are in the left column and results for the test set are on the right. For a higher resolution version, see this pdf.

Classifying Athletes by Sport

sport-matrices

 

For most rows, swimming is the most common predicted sport. That’s partially because there are so many swimmers in the data and partially due to the fact that swimmers have a fairly generic body type as measured by height and weight (see the first post). With more features such as arm length and torso length we could better distinguish between swimmers and non-swimmers.

Three out of the four methods perform similarly. The real oddball here is random forest: it classifies the training data very well, but does about as well on the test data as the other methods. This suggests that random forest is overfitting the data, and won’t give us great predictions on new data.

Classifying Athletes by Event

event-matrices

The results here are similar to the ones above: all four methods do about equally well for the test data, while random forest overfits the training data. The two squares in each figure represent male and female sports. This is a good sanity check–at least our methods aren’t misclassifying men into women’s events or vice versa (recall that sex is one of the four features used for classification).

Accuracy

Visualizations are more helpful than looking at a large table of predicted probabilities, but what are the actual numbers? How accurate are the predictions from these methods? The table below presents accuracy for both tasks, for training and test sets.

accuracy

The various methods classify Olympians into sports and events with about 25-30 percent accuracy. This isn’t great performance. Keep in mind that we only had four features to go on, though–with additional data about the participants we could probably do better.

After seeing these results I am deeply skeptical that David Epstein could classify Olympians by event using only their height and weight. Giving him the benefit of the doubt, he probably had in mind the kind of sports and events that we saw were easy to classify: basketball, weightlifting, and high jump, for example. These are the types of competitions that The Sports Gene focuses on. As we have seen, though, there is a wide range of sporting events and a corresponding diversity of body types. Being naturally tall or strong doesn’t hurt, by it also doesn’t automatically qualify you for the Olympics. Training and hard work play an important role, and Olympic athletes exhibit a wide range of physical characteristics.

Classifying Olympic Athletes by Sport and Event (Part 2)

This is the second post in a three-part series. The first post, giving some background and describing the data, is here. In that post I pointed out David Epstein’s claim that he could identify an Olympian’s event knowing only her height and weight. The sheer number of Olympians–about 10,000–makes me skeptical, but I decided to see whether machine learning could accurately produce the predictions Mr. Epstein claims he could.

To do this, I tried four different machine learning methods. These are all well-documented methods implemented in existing R packages. Code and data for is here (for sports) and here (for events).

The first two methods, conditional inference trees (using the party package) and evolutionary trees (using evtree), are both decision tree-based approaches. That means that they sequentially split the data based on binary decisions. If the data falls on one side of the split (say, height above 1.8 meters) you continue down one fork of the tree, and if not you go down the other fork. The difference between these two methods is how the tree is formed: the first recursively partitions the data based on conditional probability, while the second method (as the name suggests) uses an evolutionary algorithm. To get a feel for how this actually divides the data, see the figure below and this post.

 

If a single tree is good, a whole forest must be better–or at least that’s the thinking behind random forests, the third method I used. This method generates a large number of trees (500 in this case), each of which has access to only some of the features in the data. Once we have a whole forest of trees, we combine their predictions (usually through a voting process). The combination looks a little bit like the figure below, and a good explanation is here.

 

The fourth and final method used–artificial neural networks–is a bit harder to visualize. Neural networks are sort of a black box, making them difficult to interpret and explain. At a coarse level they are intended to work like neurons in the brain: take some input, and produce output based on whether the input crosses a certain threshold. The neural networks I used have a single hidden layer with 30 (for sports classification) or 50 hidden nodes (for event classification). To get a better feel for how neural networks work, see this three part series.

That’s a very quick overview of the four machine learning methods that I applied to classifying Olympians by sport and event. The data and R code are available at the link above. In the next post, scheduled for Friday, I’ll share the results.

Classifying Olympic Athletes by Sport and Event (Part 1)

Note: This post is the first in a three-part series. It describes the motivation for this project and the data used. When parts two and three are posted I will link to them here.

Can you predict which sport or event an Olympian competes in based solely on her height, weight, age and sex? If so, that would suggest that physical features strongly drive athletes’ relative abilities across sports, and that they pick sports that best leverage their physical predisposition. If not, we might infer that athleticism is a latent trait (like “grit“) that can be applied to the sport of one’s choice.

SportsGeneDavid Epstein argues that sporting success is largely based on heredity in his book, The Sports Gene. To support his argument, he describes how elite athletes’ physical features have become more specialized to their sport over time (think Michael Phelps). At a basic level Epstein is correct: males and females differ at both a genetic level and in their physical features, generally speaking.

However, Epstein advanced a stronger claim in an interview (at 29:46) with Russ Roberts:

Roberts: [You argue that] if you simply had the height and weight of an Olympic roster, you could do a pretty good job of guessing what their events are. Is that correct?

Epstein: That’s definitely correct. I don’t think you would get every person accurately, but… I think you would get the vast majority of them correctly. And frankly, you could definitely do it easily if you had them charted on a height-and-weight graph, and I think you could do it for most positions in something like football as well.

I chose to assess Epstein’s claim in a project for a machine learning course at Duke this semester. The data was collected by The Guardian, and includes all participants for the 2012 London Summer Olympics. There was complete data on age, sex, height, and weight for 8,856 participants, excluding dressage (an oddity of the data is that every horse-rider pair was treated as the sole participant in a unique event described by the horse’s name). Olympians participate in one or more events (fairly specific competitions, like a 100m race), which are nested in sports (broader categories such as “Swimming” or “Athletics”).

Athletics is by far the largest sport category (around 20 percent of athletes), so when it was included it dominated the predictions. To get more accurate classifications, I excluded Athletics participants from the sport classification task. This left 6,956 participants in 27 sports, split into a training set of size 3,520 and a test set of size 3,436. The 1,900 Athletics participants were classified into 48 different events, and also split into training (907 observations) and test sets (993 observations). For athletes participating in more than one event, only their first event was used.

What does an initial look at the data tell us? The features of athletes in some sports (Basketball, Rowing, Weightlifting, and Wrestling) and events (100m hurdles, Hammer throw, High jump, and Javelin) exhibit strong clustering patters. This makes it relatively easy to guess a participant’s sport or event based on her features. In other sports (Archery, Swimming, Handball, Triathlon) and events (100m race, 400m hurdles, 400m race, and Marathon) there are many overlapping clusters making classification more difficult.

sport-descriptive

Well-defined (left) and poorly-defined clusters of height and weight by sport.

Well-defined (left) and poorly-defined clusters of height and weight by event.

Well-defined (left) and poorly-defined clusters of height and weight by event.

The next post, scheduled for Wednesday, will describe the machine learning methods I applied to this problem. The results will be presented on Friday.

What Really Happened to Nigeria’s Economy?

You may have heard the news that the size Nigeria’s economy now stands at nearly $500 billion. Taken at face value (as many commenters have seemed all to happy to do) this means that the West African state “overtook” South Africa’s economy, which was roughly $384 billion in 2012. Nigeria’s reported GDP for that year was $262 billion, meaning it roughly doubled in a year.

How did this “growth” happen? As Bloomberg reported:

On paper, the size of the economy expanded by more than three-quarters to an estimated 80 trillion naira ($488 billion) for 2013, Yemi Kale, head of the National Bureau of Statistics, said at a news conference yesterday to release the data in the capital, Abuja….

The NBS recalculated the value of GDP based on production patterns in 2010, increasing the number of industries it measures to 46 from 33 and giving greater weighting to sectors such as telecommunications and financial services.

The actual change appears to be due almost entirely to Nigeria including figures in GDP calculation that had been excluded previously. There is nothing wrong with this, per se, but it makes comparisons completely unrealistic. This would be like measuring your height in bare feet for years, then doing it while wearing platform shoes. Your reported height would look quite different, without any real growth taking place. Similar complications arise when comparing Nigeria’s new figures to other countries’, when the others have not changed their methodology.

Nigeria’s recalculation adds another layer of complexity to the problems plaguing African development statistics. Lack of transparency (not to mention accuracy) in reporting economic activity makes decisions about foreign aid and favorable loans more difficult. For more information on these problems, see this post discussing Morten Jerven’s book Poor NumbersIf you would like to know more about GDP and other economic summaries, and how they shape our world, I would recommend Macroeconomic Patterns and Stories (somewhat technical), The Leading Indicators, and GDP: A Brief but Affectionate History.

Visualizing the Indian Buffet Process with Shiny

(This is a somewhat more technical post than usual. If you just want the gist, skip to the visualization.)

N customers enter an Indian buffet restaurant, one after another. It has a seemingly endless array of dishes. The first customer fills her plate with a Poisson(α) number of dishes. Each successive customer i tastes the previously sampled dishes in proportion to their popularity (the number of previous customers who have sampled the kth dish, m_k, divided by i). The ith customer then samples a Poisson(α) number of new dishes.

That’s the basic idea behind the Indian Buffet Process (IBP). On Monday Eli Bingham and I gave a presentation on the IBP in our machine learning seminar at Duke, taught by Katherine Heller. The IBP is used in Bayesian non-parametrics to put a prior on (exchangeability classes of) binary matrices. The matrices usually represent the presence of features (“dishes” above, or the columns of the matrix) in objects (“customers,” or the rows of the matrix). The culinary metaphor is used by analogy to the Chinese Restaurant Process.

Although the visualizations in the main paper summarizing the IBP are good, I thought it would be helpful to have an interactive visualization where you could change α and N to see how what a random matrix with those parameters looks like. For this I used Shiny, although it would also be fun to do in d3.

One realization of the IBP, with α=10.

One realization of the IBP, with α=10.

In the example above, the first customer (top row) sampled seven dishes. The second customer sampled four of those seven dishes, and then four more dishes that the first customer did not try. The process continues for all 10 customers. (Note that this matrix is not sorted into its left-ordered-form. It also sometimes gives an error if α << N, but I wanted users to be able to choose arbitrary values of N so I have not changed this yet.) You can play with the visualization yourself here.

Interactive online visualizations like this can be a helpful teaching tool, and the process of making them can also improve your own understanding of the process. If you would like to make another visualization of the IBP (or another machine learning tool that lends itself to graphical representation) I would be happy to share it here. I plan to add the Chinese restaurant process and a Dirichlet process mixture of Gaussians soon. You can find more about creating Shiny apps here.

Playing Chicken with Your Calendar

The ever-interesting Brendan Nelson on meeting chicken:

You have a regular meeting in your calendar. It’s with just one other person. Sometimes you have things to talk to them about and sometimes you don’t. But as long as your calendar says you both have to go, you will both go.

The day of the meeting comes round. There are lots of things that need to be done that day. You look at that meeting sitting obstinately in your calendar and think how useful it would be to get that time back.

Inspiration strikes: why not cancel the meeting? A couple of mouse clicks, an automatic notification sent out, a joyously blank calendar. It seems so easy.

But you can’t bring yourself to do it, to cancel a meeting at such short notice. It would make you look disorganised, unprepared. And what about the other person?

More at the link.

Don’t Forget Your Forever Stamps

The price of a first-class US stamp is set to increase from 46 to 49 cents on January 26. Like Cosmo Kramer’s Michigan bottle redemption plan (see below), Allison Schrager and Ritchie King ran the numbers on whether it would be possible to provide from Forever Stamp arbitrage.

Could the scheme make money? Maybe–if you get the timing right and pay low interest on capital:

Assuming we sell all 10 million stamps for the bulk discount price of $0.475 each, our profit will be $150,000. Subtract out the $399 for the distributor database. Let’s also assume we spent the $3,500 for Check Stand Program plus, say, $300 to make the 100 displays for advertising in stores. That gives us $145,801.

If we do manage to shift the stamps in a month, the interest on our debt will be $29,000. That brings our profits to $116,801. Then we’ll return the equity to our shareholders, along with 50% of the profits.

That leaves us with the other 50%: $58,400.50. If you look at that as a profit on the $4.6 million initial outlay, it’s not very much: less than 1.3%. But remember, all that outlay was leveraged. So if you look at it as a return on our investment—$33.25 for shipping—it’s 175,541%.

Political Forecasting and the Use of Baseline Rates

As Joe Blitzstein likes to say, “Thinking conditionally is a condition for thinking.” Humans are not naturally good at this skill. Consider the following example: Kelly is interested in books and keeping things organized. She loves telling stories and attending book clubs. Is it more likely that Kelly is a bestselling novelist or an accountant?

Many of the “facts” about Kelly in that story might lead you to answer that she is a novelist. Only one–her sense of organization–might have pointed you toward an accountant. But think about the overall probability of each career. Very few bookworms become successful novelists, and there are many more accountants than (successful) authors in the modern workforce. Conditioning on the baseline rate helps make a more accurate decision.

I make a similar point–this time applied to political forecasting–in a recent blog post for the blog of Mike Ward’s lab (of which I am a member):

One piece of advice that Good Judgment forecasters are often reminded of is to use the baseline rate of an event as a starting point for their forecast. For example, insurgencies are a very rare event on the whole. For the period January, 2001 to August, 2013, insurgencies occurred in less than 10 percent of country-months in the ICEWS data set.

From this baseline, we can then incorporate information about the specific countries at hand and their recent history… Mozambique has not experienced an insurgency for the entire period of the ICEWS dataset. On the other hand, Chad had an insurgency that ended in December, 2003, and another that extended from November, 2005, to April, 2010. For the duration of the ICEWS data set, Chad has experienced an insurgency 59 percent of the time. This suggests that our predicted probability of insurgency in Chad should be higher than for Mozambique.

I started writing that post before rebels in Mozambique broke their treaty with the government. Maybe I spoke too soon, but the larger point is that baselines are the starting point–not the final product–of any successful forecast.

Having more data is useful, as long as it contributes more signal than noise. That’s what ICEWS aims to do, and I consider it a useful addition to the toolbox of forecasters participating in the Good Judgment Project. For more on this collaboration, as well as a map of insurgency rates around the globe as measured by ICEWS, see the aforementioned post here.

A Chrome Extension for XKCD Substitutions

This morning’s XKCD had some fun suggestions for replacing key phrases to make news articles more fun:

Regular readers may recall my Doublespeak Chrome extension, which works on the same principle. In short order, I was able to create a new app, XKCDSub, that works the same way: install the extension, and when you click its icon it will open your current page in a new tab with the phrases replaced. Here is an example of the extension in action on Elon Musk’s Wikipedia page:

elon

The code is open source on Github. You can find it in the Chrome webstore here.

Visualizing Political Unrest in Egypt, Syria, and Turkey

The lab of Michael D. Ward et al now has a blog. The inaugural post describes some of the lab’s ongoing projects that may come up in future entries including modeling of protests, insurgencies, and rebellions, event prediction (such as IED explosions), and machine learning techniques.

The second post compares two event data sets–GDELT and ICEWS–using recent political unrest in the Middle East as a focal point (more here):

We looked at protest events in Egypt and Turkey in 2011 and 2012 for both data sets, and we also looked at fighting in Syria over the same period…. What did we learn from these, limited comparisons?  First, we found out first hand what the GDELT community has been saying: the GDELT data are in BETA and currently have a lot of false positives. This is not optimal for a decision making aid such as ICEWS, in which drill-down to the specific events resulting in new predictions is a requirement. Second, no one has a good ground truth for event data — though we have some ideas on this and are working on a study to implement them. Third, geolocation is a boon. GDELT seems especially good a this, even with a lot of false positives.

The visualization, which I worked on as part of the lab, can be found here.  It relies on CartoDB to serve data from GDELT and ICEWS, with some preprocessing done using MySQL and R. The front-end is Javascript using a combination of d3 for timelines and Torque for maps.

gdelt-icews-static

GDELT (green) and ICEWS (blue) records of protests in Egypt and Turkey and conflict in Syria

If you have questions about the visualizations or the technology behind them, feel free to mention them here or on the lab blog.