Epstein on Athletes

As a follow-up to the most recent series of posts, you may enjoy this TED talk by David Epstein. Epstein is the author of The Sports Gene and offered the claim that kicked off those earlier posts–that he could accurately guess an Olympian’s sport knowing only her height and weight.

The talk offers some additional context for Epstein’s claim. Specifically Epstein describes how the average height and weight in a set of 24 sports has become more different over time:

In the early half of the 20th century, physical education instructors and coaches had the idea that the average body type was the best for all athletic endeavors: medium height, medium weight, no matter the sport. And this showed in athletes’ bodies. In the 1920s, the average elite high-jumper and average elite shot-putter were the same exact size. But as that idea started to fade away, as sports scientists and coaches realized that rather than the average body type, you want highly specialized bodies that fit into certain athletic niches, a form of artificial selection took place, a self-sorting for bodies that fit certain sports, and athletes’ bodies became more different from one another. Today, rather than the same size as the average elite high jumper, the average elite shot-putter is two and a half inches taller and 130 pounds heavier. And this happened throughout the sports world.

Here’s the chart used to support that point, with data points from the early twentieth century in yellow and more recent data points in blue:

Average height and mass for athletes in 24 sports in the early twentieth century (yellow) and today (blue)

Average height and mass for athletes in 24 sports in the early twentieth century (yellow) and today (blue)

This suggests that it has become easier over time to guess individuals’ sports based on physical characteristics, but as we saw it is still difficult to do with a high degree of accuracy.

Another interesting change highlighted in the talk is the role of technology:

In 1936, Jesse Owens held the world record in the 100 meters. Had Jesse Owens been racing last year in the world championships of the 100 meters, when Jamaican sprinter Usain Bolt finished, Owens would have still had 14 feet to go…. [C]onsider that Usain Bolt started by propelling himself out of blocks down a specially fabricated carpet designed to allow him to travel as fast as humanly possible. Jesse Owens, on the other hand, ran on cinders, the ash from burnt wood, and that soft surface stole far more energy from his legs as he ran. Rather than blocks, Jesse Owens had a gardening trowel that he had to use to dig holes in the cinders to start from. Biomechanical analysis of the speed of Owens’ joints shows that had been running on the same surface as Bolt, he wouldn’t have been 14 feet behind, he would have been within one stride. 

The third change Epstein discusses is more dubious: a “changing mindset” among athletes giving them a “can do” attitude. In particular he mentions Roger Bannister’s four-minute mile as a major psychological breakthrough in sporting. As this interview makes clear, Bannister attributes the fact that no progress was made in the fastest mile time between 1945 and 1954 to the destruction, rationing, and overall quite distracting events of WWII. It’s possible that a four-minute mile was run as early as 1770. I wonder what Epstein’s claims would look like on that time scale?

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.

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.

Wednesday Nerd Fun: How to Win at Jeopardy

Alex: “You know Roger, you could set a new one day record.”

Roger: “What’s the old one?”

Roger Craig should have known the answer, because he held the old record.

Craig says it works like Moneyball — a reference to the book and movie about the statistical techniques used by legendary Oakland Athletics coach Billy Beane to build a winning baseball team. Craig’s system also relied heavily on statistics.

“I actually downloaded this site called the Jeopardy! Archive, which is a fan-created site of all the questions and answers that are on the show.”

“Something like 211,000 questions and answers that have appeared on Jeopardy!,” says Esquire writer Chris Jones, a self-proclaimed “game-show nerd” who’s familiar with Craig’s tactics.

Using data-mining and text-clustering techniques, Craig grouped questions by category to figure out which topics were statistically common — and which weren’t.

“Obviously it’s impossible to know everything,” Jones says. “So he was trying to decide: What things did he need to know? He prepared himself in a way that I think is probably more rigorous than any other contestant.”

You can find the full article here, and the link comes to us via Tyler Cowen. To see Roger at work play, check out these clips: