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COSTAS final medal standings

  August 15, 2012 06:15 AM

Here are the final COSTAS medal standings, complete through the end of Olympic play on August 12. For an explanation of the methodology behind COSTAS, click here, and here for the COSTAS standings after the first week of the Olympics.

First, the standings as represented by the traditional medal table:


Now, for the final COSTAS count:


Though the U.S. made up substantial ground in the COSTAS standings in the second week of competition, we still could not overturn the early advantage built up by the Chinese. The American sweep of the gold medals in basketball and wins in beach volleyball and women’s soccer boosted our COSTAS total, but China's mastery of badminton, table tennis, and diving created a deficit too large to surmount. Though the U.S. won handily in the traditional medal table, their advantage came at the very end of the Olympics, largely through track and field, the individual events of which are heavily discounted by COSTAS due to the sheer number of them.

The COSTAS standings also see Great Britain knocked from their third-place perch, supplanted by Russia. Many of Team GB’s medals, in particular their golds, came in sports with many events, like cycling, rowing, and boxing, reducing the number of points they received. Ironically, the cold, stern Russians gained their advantage from two sports that share more in common with dance than athletics: synchronized swimming and rhythmic gymnastics, in which they won four out of a possible four gold medals.

And with that, the Games of the 30th Olympiad are concluded. COSTAS will now enter hibernation, to be awakened only by the cold Russian sun of Sochi in 2014.

The five most dominant Olympians of all time

  August 12, 2012 01:48 PM

Following the exploits of Michael Phelps and Usain Bolt in London, the word “greatest” has been getting thrown around quite a bit. As with any time this word comes out, one has to question just how much of it is driven by recency bias; that is, these are the greatest athletes currently in front of our faces, and suddenly the leap to greatest of all time doesn’t seem so far anymore.

I prefer a bit more definitiveness to my debates than these discussions about “greatest” often provide, so I developed my own methodology for deciding the question, with one twist: I’m not necessarily looking for the greatest Olympian of all time, but instead the most dominant. I want to celebrate unyielding, unflappable, and unstoppable Olympic excellence, measured primarily in its weight in gold.

To determine my rankings, I used the following basic criteria:

Individual events only. I didn’t count any medal won with the help of another athlete, meaning I ignored relays, doubles sports, and team events (sorry, Misty and Kerri). The only medals tallied here are those earned by the athlete, and no one else.

More points for shinier medals. As in my COSTAS medal tally, I used a 4-2-1 point system for crediting gold, silver, and bronze medals. I’m looking for the most dominant Olympian of all time, not just the one with the most staying power, so those who remained at the very top of their sport for multiple Olympics and amassed a large collection of golds are rewarded accordingly.

Fewer points for more medal chances. To finalize the rankings, I divided the medal score derived from the above point system by the number of different events (i.e. the 200m butterfly and the 400m individual medley) in which an athlete participated. To determine how truly dominant an athlete was, the number of medal chances he or she had to secure his or her final haul should be taken into account. It can be argued that medaling in a variety of different disciplines should be rewarded and not penalized, but I think participating in a diversity of events reflects “most talented” rather than “most dominant.” To me, the question of dominance essentially boils down to who won the most golds given the fewest opportunities.

And with that, I give you the five most dominant Olympians of all time:

5. Greg Louganis (1976-1988), diving, United States
4 Golds, 1 Silver; competed in two individual events; Dominance Score: 9

Had politics not gotten in the way, Louganis could be even higher on this list. After winning his first medal—a silver, his only non-gold—in 1976 at the age of 16, Louganis missed the 1980 Games in Moscow as part of the United States’ Cold War boycott, despite being one of the primary contenders for gold in the 10m platform and 3m springboard. However, he made the most of his final two Olympic appearances, winning four golds in the aforementioned events in 1984 and 1988 and finishing off the greatest diving career of all time.

4. Michael Phelps (2000-2012), swimming, United States
11 Golds, 1 Silver, 1 Bronze; competed in five individual events; Dominance Score: 9.4

Given that he has already been anointed the greatest Olympian of all time by most media outlets, fourth is a controversial position for Phelps. Though he certainly boasts the most impressive raw medal haul, Phelps is hurt by the number of events in which he competed, which gave him greater chances to earn that total.

Whether this is fair or not, it remains that Phelps was not uniformly dominant in all of his events. When history reflects on his career, I think it will decide that he was otherworldly at one stroke (the butterfly, in which he won five of his individual golds), good at one stroke (the freestyle, which allowed him to participate in relays, more than anything), and competent at the other two, though “competent” might be an all-time understatement for someone who won five gold medals in individual medleys. Still, his record medal total could never have been reached without the diverse menu of events swimming offers its athletes, and for that, Phelps remains fourth, just out of the medals.

3. Carl Lewis (1984-1996), athletics, United States
7 Golds, 1 Silver; competed in three individual events; Dominance Score: 10

Unfortunately for my generation, Lewis is now known more for his anthem butchering than his achievements on the track, despite being the second-most decorated track and field Olympian of all time. Lewis was Bolt before Bolt, winning back-to-back 100m golds—though one was awarded only after a doping disqualification leveled against Canadian Ben Johnson—to go with a gold and a silver in the 200m.

But Lewis’ true dominance did not lie in sprinting. His best event was the long jump, in which he won gold at four consecutive Olympics, including one at age 35 in Atlanta. This is what separates him from Bolt; both were elite sprinters, but Lewis made the extra effort to convert that ability into long jump glory, something it has been suggested that Bolt could also have attained had he set his mind to it. Should Bolt successfully defend his 100m and 200m titles in 2016, he would surpass Lewis on this list, but given his present ambivalence, coupled with the rise of Yohan Blake, that seems increasingly unlikely.

2. Gert Fredriksson (1948-1960), canoeing, Sweden
5 Golds, 1 Silver, 1 Bronze; competed in two individual events; Dominance Score: 11.5

What? You hadn’t heard of Gert Fredriksson, the greatest canoeist of all time? I hadn’t either, but that says more about his sport’s place in our consciousness than it does about Fredriksson’s accomplishments. For four straight Olympics, Fredriksson ruled the 1,000- and 10,000-meter kayak races, taking gold in five of the seven races he entered, including two golds as a 37-year-old at the 1956 Melbourne Games. Plus, if someone builds you a statue to commemorate your status as a canoeing hero, you must have done something pretty remarkable.

1. Ray Ewry (1900-1908), athletics, United States
10 Golds; competed in three individual events; Dominance Score: 13.3

You know what Louganis, Phelps, Lewis, and Fredriksson all have in common? They didn’t have polio.

It was uncertain that Ray Ewry, the most dominant Olympian of all time, would even walk again after coming down with the disease at the age of seven. This was over seventy years before Jonas Salk pioneered the polio vaccine, so young Ewry took the next best course of treatment for his legs: jumping. And jumping, and jumping some more. Eventually, Ewry jumped all the way into an athletic career at Purdue University, where he played track and football. It was here that he began to excel in the three events that would ultimately bring him Olympic fame: the standing high jump, the standing long jump, and the standing triple jump.

From 1900 to 1908, Ewry didn’t lose a single Olympic event, winning ten golds in the three disciplines in which he competed. In 1900, Ewry set the world record in the standing high jump with a jump of 1.65 meters…which means that, in 1900, a 6’3” white guy had a 65-inch vertical. Tragically, basketball was still being played with peach baskets.

Though the standing jump events were removed from the Olympic catalog after the 1912 Olympics, Ewry’s exploits still live on in history; his record for individual gold medals stood for 100 years before Phelps passed him this summer. And for his perfect mark of ten golds in ten tries, Ewry earns the distinction of the most dominant Olympian of all time.

Dream over: How the U.S. could lose

  August 7, 2012 01:17 PM


On Wednesday, the U.S. men’s basketball team begins its gold medal defense in earnest as they square off against Australia in the quarterfinals, a contest the U.S. has been given 1/100 odds to win, according to various online sportsbooks. I happened to be in the stands for Australia’s second-to-last preliminary game, a 106-75 victory over Great Britain in which the Aussies actually trailed by 15 points in the third quarter. In the span of three minutes, a wild barrage of three-pointers from Australia, led by San Antonio Spurs point guard Patty Mills, tied the game at 53. The Aussies’ hot shooting continued into the fourth quarter, transforming the one-time deficit into a lead of ten, then 20, then finally 30 points. As I watched the Australians bring the rain down from the ceiling of the Basketball Arena, I couldn’t help but think that there was nothing the British, or anyone, could have done to stop that team-wide shooting performance. It was just their day.

The same can be said of the United States’ 83-point victory over Nigeria. Though Nigeria is the worst defensive team at these Olympics, allowing opponents to shoot 59 percent on twos and 46 percent on threes, there was no preventing the tsunami of threes that the Americans poured in on Thursday night. The U.S. went 29-for-46 from beyond the arc, ten of which came from Carmelo Anthony alone. Sometimes, you get hot.

But sometimes you’re not. In their following game, the Americans made only ten of 33 three-pointers and nearly lost to a plucky Lithuanian team, which shot a sterling 58 percent from the field. It was the type of March Madness-like near-upset that makes fans of any favorite sick. Your team clearly has the better talent but plays well below its potential, allowing the underdog to hang around for a chance to snatch away victory at the end.

In a 2009 piece for the New Yorker, Malcolm Gladwell laid out the conditions under which Davids can beat Goliaths. In mathematical terms, Gladwell suggests that underdogs pursue a risky, high-variance strategy. Given infinite trials (or games), the better team beats the worse team a majority of the time, and the gap between them exactly corresponds to the gap in talent between the two. But given one trial, like the knockout round of a basketball tournament, the role of random chance becomes much stronger. A beneficial swing in luck can then allow a team with substantially less talent to contend, and on a few rare occasions, upset Goliath.

Of course, there’s a reason these strategies are risky. If the calculated gamble doesn’t pay off and one’s team simply cannot throw the ball in the ocean, a game can get ugly very quickly. The flip side of the U.S.’s record-setting win over Nigeria was their opponent’s inept shooting performance; the Nigerians made only six of the 27 threes they jacked up (22 percent). Had they hit a few more of these (okay, maybe about 20 more), they could have kept the score within a respectable margin.

In his piece, Gladwell seems to regard the failure of Goliaths to adopt risky strategies—in his example, the full court press—as a detriment to their success. In fact, just the opposite is true. Favorites want to take as few risks as possible because they have no need for them. More often than not, their talent advantage will be enough to secure a victory, without introducing the luck factor that comes with high-risk strategies.

Due to the large talent gap between the U.S. and the rest of the world, an upset of the Americans will likely require a would-be David to pursue such a high-variance strategy. The problem, which stems in part from the composition of the team, is that the United States’ strategy this Olympics resembles that of the world’s puniest David. The Americans have attempted more threes (168) than any other team, by a considerably wide margin; the next closest is Great Britain with 126. They play a frantic style of defense, jumping every passing lane and forcing an Olympics-best 20.2 turnovers per game, but they also allow a lot of easy buckets. The U.S. is allowing opponents to shoot 54 percent from two-point range, ahead of only Tunisia, Nigeria, and Great Britain.

The danger for the United States heading into the knockout rounds lies in the potential confluence of two extremes of luck: if the Americans can’t find the basket from outside and their opponents get hot, the game will be a lot closer than it otherwise should be. In almost every instance, the Americans’ talent advantage will still be enough to paper over any disparity in luck; after all, they possess the nine or ten best players in the entire tournament. But not always—in 2004, the United States undoubtedly had a more talented team than Argentina, but in the semifinals, the Americans shot 3-for-11 from three and 42 percent overall, while Argentina made 54 percent of their attempts, including 11 of 22 threes, on its way to the gold medal game.

With a less risky strategy, the U.S. would be virtually unbeatable, but unfortunately, the personnel on the team is more suited to the open, breakneck pace we’ve seen from them so far. Perhaps, with a frontline of Dwight Howard and Andrew Bynum, the Americans could pound the ball inside for easy, high-percentage (and thus, low-variance) shots, but Tyson Chandler and Kevin Love aren’t capable of the same sort of reliable, low-post scoring. Instead, Kobe Bryant, Carmelo Anthony, and Kevin Durant are heaving up shots from all over the perimeter, which, for the most part, works just fine—they’re the best players in the world. But it leaves the door a crack further open than it should be for the rest of the world, one we can be sure they will do everything in their power to barge through.

The teams most likely to pull off the upset? Probably the pair of South American powers, Brazil and Argentina, which boast a bevy of dangerous long-range shooters in addition to a positive turnover margin. With its size down low, Brazil is better suited to keep the U.S. off of the offensive glass, but it doesn’t have quite as much offensive firepower as the Argentinians. However, don’t count out big, steady teams like Spain, Lithuania, and Russia. All three have the ability to score down low and keep the game close against a cold-shooting American team—just long enough to steal gold away from the favorites.

COSTAS standings, week one

  August 5, 2012 07:03 AM

As promised, here are the COSTAS standings for the first week of Olympic competition. To learn more about how COSTAS is calculated and what it intends to measure, read my original post here. Medal figures are current as of Saturday afternoon’s competition.

First, we have the medal standings as traditionally recorded:


Now here are those same standings, revisualized by COSTAS:


Like in 2008, China has opened up a giant lead over the rest of the field. Though they do not have a substantial advantage in gold medals, the Chinese have swept entire sports, like badminton, table tennis, and diving. The vast majority of the U.S.’s medal haul to this point has come in swimming (14 golds, eight silvers, and six bronzes), so our COSTAS total is discounted due to the large number of swimming events. The U.S. is actually far closer to third-place South Korea, which won big in archery and fencing, than to our red rivals.

An American comeback is certainly within the realm of possibility, however, given the upcoming opportunities the U.S. will have to follow China’s example and dominate in sports in which not many medals are available. The U.S. is heavily favored to take gold in men’s basketball, women’s basketball, and women’s soccer, and have looked dangerous in both men’s and women’s water polo. Medals in any of these would be rewarded heavily by COSTAS. There are also many individual gymnastics events still to come, which promise even more American gold.

But the U.S. may need all that and more to catch China, whose medal score is already a time and a half greater than the Americans’. Though we’ve just nosed into the lead according to the official standings, there’s a long way to go to match the supremacy in multiple disciplines enjoyed by the Chinese.

The bodies of champion gymnasts

  August 3, 2012 09:33 AM

Four feet, eleven inches, and 90 pounds is hardly the prototypical physique of a world-class athlete, but as American gold medalist Gabrielle Douglas proved yesterday, it’s more than enough to perform extraordinary feats on one of sport’s biggest stages: the women’s gymnastics individual all-around. Of course, the sight of pixie-sized girls tumbling and flying through the air is the norm for Olympic gymnastics; while a 4’8” girl might draw a few sidelong glances at the mall, there’s nothing peculiar about her when she’s on the mat.

Today, atypical body types are expected of female gymnasts, but that wasn’t always the case—in fact, no competitor under five feet medaled in the women’s individual all-around until Maxi Gnauck in 1980. How have the best gymnasts’ bodies evolved through the years? I examined the heights, weights, and ages of all medal winners in the individual all-around since 1956 to find if any notable changes have occurred in the last half-century.

(Note: I was unable to find height and weight figures for three gymnasts over this time period: 1992 gold medalist Tatiana Gutsu, 1992 and 1996 bronze medalist Lavinia Miloşovici, and 1956 silver medalist Ágnes Keleti).


The chart illustrates that champion gymnasts’ heights have remained relatively constant over the last sixty years—78 percent are within three inches of five feet tall. Their weights have been subject to a little more fluctuation as time has advanced, however. The data suggests a downward trend from an average of about 120 pounds in the 1950’s and 1960’s to well under 100 pounds in the modern gymnastics world.

The age of world-class gymnasts is often as mind-boggling as the twists and turns they execute on the floor. One can only marvel at the mental fortitude of a 16-year-old, most of whose peers would fold under the pressure of a speech class performance, exhibiting their talents in her sport’s most intense microscope, before an audience of millions.

Though controversy has surrounded the participation of early teen performers in the Olympics, most recently with the Chinese team in 2008, they are not a new phenomenon. Nadia Comeneci, the first champion gymnast under 100 pounds, is most well-known for her series of perfect 10.00 scores in the 1976 Montreal Games, but under today’s rules, she wouldn’t even have been allowed to compete, as her gold in the all-around came at the age of 14.

Older gymnasts are relics of the past. Only four gymnasts over the age of 19 have won medals in the individual all-around since 1976, and stardom in the sport is becoming increasingly fleeting. Shawn Johnson, the silver medalist in Beijing, chose to retire at 20 years old rather than attempt to compete in London, and Nastia Liukin, who won the gold in ’08, failed to even qualify for the Olympic team.

According to this analysis, the average medal-winning gymnast in the all-around is 19.6 years old, measures 5’1” and weighs 103 pounds. This puts them in about the tenth percentile for height and fifth percentile for weight among girls, based on statistics from the CDC. But as anyone who has watched these girls perform can attest, there are multiple connotations of the word “exception.”

Slowly but surely, international basketball catching up to US

  July 30, 2012 06:00 AM

One of the biggest yawn-fests of a story in the buildup to this year’s Olympic basketball tournament was the idle bantering between this year’s US team and the original Dream Team from 1992. It seemed fitting that the playground-style argument (“We would win!” “No, we would!”) must inevitably have no definitive answer; the point has no bearing on the current Games and serves only to ruffle a few pages in reporters’ notebooks.

The fact is that the NBA will always have the best of the best basketball players in the world, the vast majority of which come from the United States. The more interesting question, in my view, is how the rest of the world has improved since its nuclear destruction at the hands of the ’92 squad, which stomped through Olympic play with an average margin of victory of 43.75 points. As the years have advanced, it’s clear that American teams have faced much sterner tests than their predecessors—USA’s shocking sixth-place finish in the 2002 FIBA World Championships and its bronze medal in Athens attest to that fact.

Of course, the relative quality of some of these teams certainly isn’t constant—no one would confuse Raef Lafrentz with a Dream Team member (except perhaps Christian Laettner), so it’s somewhat difficult to evaluate just how much the rest of the world has improved in relation to the US.

Thankfully, we have numbers to take care of that problem. Using data available at basketball-reference.com, I added up the Win Shares per 48 minutes for every member of each United States team that competed at a major tournament (Olympics or FIBA World Championships), with the exception of the 1998 World Championships, from which NBA players were excluded due to a work stoppage. In order to assure that I fairly evaluated each team, I used the players’ Win Shares per 48 minutes in the NBA season immediately preceding the major tournament in which they competed. For instance, Larry Bird’s game, while transcendent in 1986, had lost much of its luster by the Olympic year of 1991-92, a difference that should be acknowledged when assessing his team’s talent level.

Next, I looked at how each US team actually performed on the court, recording their average margin of victory at each of the major tournaments. This is the number I used to represent the quality of their competition, the rest of the world; the closer USA’s opponents kept games, the better basketball I assumed they were playing.

But to discern anything about the change in the standard of international basketball, I needed a constant baseline with which to compare it. This is where the Win Shares data comes in; using the measures of quality for each US. team as weights, I adjusted the US margin of victory numbers to produce a single number that represented how tough of a fight the Americans’ competition put up in each event.


By this measure, the 1994 US team actually put on a more impressive on-court display than the original Dream Team. The ’94 team was far from the most talented America would assemble in the coming decade and a half, but they won games by nearly as much as the ’92 team, defeating opponents by an average of 37.75 points.

Surprisingly, this analysis suggests that international basketball has actually regressed at every tournament since Yugoslavia’s breakthrough victory at the 2002 World Championships. I think, however, that the better conclusion to draw is not from the single year-to-year changes, which are subject to quite a bit of variation in the teams’ performances, but from the general downward trend in the magnitude of USA's dominance, represented on the chart by the dashed trendline. Slowly, the rest of the world is closing the gap.

This is not a perfect proxy for international quality, of course. The US doesn’t play the same teams at every tournament, and the numbers are based on a very small sample of games per tournament, certainly not large enough to give us a totally accurate picture of the various international teams’ talent levels. But it does shed a little light on a question that has typically been reduced to hand-waving generalizations: how far is the rest of the world from catching up? I don’t think there’s any doubt they are moving in the right direction; if you need more evidence, note that the number of non-American players in the NBA has increased from 21 to 89 since 1992.

If this trend continues at the constant rate implied by the trendline, the rest of the world would finally catch up to the US in time for the 2042 World Championships, which assumes quite a bit about the increasing popularity and participation in the sport around the world. And even so, that suggests a lot of American gold in the interim 30 years.

COSTAS: the weighted Olympic medal count

  July 27, 2012 05:42 AM

A couple of days ago, I wrote about a different way to think about the traditional Olympic medal standings, which reflected the unevenness of the playing field from which athletes from all over the world come to the Games. But there’s another distortion to the medal count that is never accounted for in the usual tally and has a similarly large effect on the final standings: the differences in medals available in each sport.

In the spirit of PECOTA, KUBIAK, VUKOTA, and all other gratuitous acronyms by which sports analysts refer to their pet models, I now bring you COSTAS: the Congruent Olympic System for the Tabulation of Accolade Statistics.

First developed by Harvard student David Roher for the 2010 Winter Olympics, I adapted his model for the Summer Games to get a clearer view of the spectrum of international sporting supremacy. In the words of its founder:

“I wanted to develop a weighted medal count that not only adjusted for the importance of gold over silver over bronze, but also for the relative importance of one event over another. I also wanted its abbreviation to be COSTAS. I admit that the latter was the first requirement I thought of.”

As alluded to by Roher, the model is based on a couple of assumptions. The first is that, for the purposes of the medal standings, gold, silver, and bronze should not possess equal weights. Traditionally, every medal counts for one point for its winner’s home country, regardless of its hue, confusing the performances by which those medals were awarded in the first place.

For the debut of COSTAS at the Vancouver Olympics, Roher chose a 4-2-1 scoring system for gold, silver, and bronze, which I extended to the Summer Games. Admittedly, these weights are arbitrarily chosen—it could be argued that a 5-3-1 or a 3-2-1 system are just as valid—but they do successfully get across the main point, that medals should be treated as having different values in the medal standings, as they do on the playing fields.

The second assumption is that all sports should be treated as having equal importance. Swimming has a total of 34 events for its male and female participants, while basketball has only two. It doesn’t seem fair to conclude from this that swimming, as an Olympic sport, is 17 times more important than basketball, and yet, for the purposes of the medal count, that’s exactly how the two are treated. It’s simply the respective natures of the sports that cause the difference in each is organized; swimming wouldn’t make as much sense with the athletes of just two countries playing against each other, and basketball doesn’t have a series of disciplines in which its athletes can compete for multiple medals.

Under COSTAS, every sport is valued equally, so the total medals for swimming are worth the same amount as the total medals for basketball. By applying weights for the number of events in each individual sport, we get a clearer picture of the relative worth of each medal.

I recognize that the lines between different “sports” are sometimes hazy—for instance, trampolining doesn’t seem much different from gymnastics—so I used the official distinctions laid out by the IOC, which can be found here. I did make one exception to this: the IOC includes all track and field events under the umbrella of “Athletics,” so I separated the track events (those that consist in exclusively running) from the field events (all other events, including the decathlon and heptathlon) for the purposes of the weights. The final step in the process was to scale the COSTAS numbers into a format that looks more like the traditional medal count, so I made the total number of COSTAS points add up to the total number of medals available at the Summer Olympics (958).

So without further ado, here are the standings for the 2008 Summer Olympics in Beijing, as measured by traditional medal count:


Now here are the COSTAS standings for those same Olympics:


The country that receives the biggest boost from COSTAS is China, due to its impressive haul of gold medals and its dominance of whole events like table tennis, diving, and badminton. Under this system, the Chinese ascend firmly into first place, outpacing the second place Americans by about 28 "medals"—a humbling revelation for the red, white, and blue. Many of the Americans’ medals came from events with an enormous number of medals available, like swimming and track and field, providing them with a much smaller increase in points.

I’ll be updating the COSTAS standings for the London Olympics at various times during the Games, so stay tuned to see if the USA can wrest the mantle of supreme Olympic champions from the Chinese.

Winning golds without gold: an economic analysis of the medal standings

  July 24, 2012 03:43 AM

The Olympics are, to a large extent, rigged from the outset. The countries that have made regular appearances at the top of the medal standings at the last few Summer Olympics—the United States, Germany, France, and Great Britain—also happen to be among the world’s giants in economic power. It would seem that wealthy countries that have resources to spare toward the development of their athletes produce much greater hauls of gold, silver, and bronze than do nations that wield lesser economic clout.

However, there’s nothing particularly interesting about the “Goliath bludgeons David” narrative, so let’s focus on David’s more endearing characteristics: he doesn’t have much to work with, but he tries hard, and every so often, he enjoys a dramatic morsel of success.

So it is with many of the nations that compete in the Olympics. They send fewer athletes with less access to world-class training and facilities than the familiar characters at the top of the medal standings, but occasionally, they produce a transcendent talent, like Jamaica’s Usain Bolt, or establish long-term dominance in a particular discipline, like Kenya in long-distance running.

To find out who does the most with the least, I took the official medal count from the last three Summer Olympics—Beijing in 2008, Athens in 2004, and Sydney in 2000—and adjusted it for each country’s GDP per capita in each of the three Olympic years. The rankings, now measured in medals controlled for per capita GDP (in 2011 USD), look very different from the traditional standings.

(The weights for per capita GDP are in billions of dollars per million citizens, which amounts to thousands of dollars per person. I divided the countries’ total medal counts by this figure to get the weighted medal score.)

gdp2008.png gdp2004.png


One might think that countries with large raw populations have an advantage simply by virtue of the law of large numbers: with more people living within a country’s borders comes a greater chance that one or two of them will possess unique athletic ability.

But population doesn’t mean nearly as much without the ability to finance and foster its latent talent. India, a nation of over a billion people, has enjoyed little Olympic glory, which may be because many of its people are entrenched in poverty (and cricket isn’t an Olympic sport).

The counterexamples to India, however, are the successes of China and Russia, countries that rank 88th and 52nd, respectively, in GDP per capita, yet regularly enjoy places at the top of the medal standings. For better or worse, both of these nations have made Olympic success a priority, perhaps at the expense of more pragmatic allocations of those resources. They use their capital to find the outliers within their vast populations and give them the chance to shine on the international stage alongside their more privileged peers.

Despite having relatively low GDP per capita figures, both nations have enormous productive capacity, ranking among the highest in the world in raw GDP. In fact, in correlating both raw GDP and population with total medal count in separate tests, I found that the relationship between GDP and medal count was consistently much stronger (for the last three Summer Olympics, average correlation coefficient: 0.71) than the relationship between population and medal count (average correlation coefficient: 0.37). Of course, to some extent, levels of GDP and population go hand in hand—large countries are likelier to produce more economic output by virtue of their larger labor supplies—but the preceding analysis does suggest that national output is a better predictor of Olympic success than the size of the pool of athletes from which a country can pick. Even with a population over one billion, India is only ninth in raw GDP.

A love of sport is not unique to places like the United States, China, and Germany, but as these nations begin their inevitable ascents of the medal podium over the next few weeks, consider that there are larger forces at play behind the athletes’ individual feats. Just like life, the Olympics are not particularly fair. National differences in economic output, culture, and even geography, greatly affect the ultimate results of the Games, something to keep in mind each of the many times we hear the strains of ol’ Francis Scott Key.

Swimming on steroids: the suits that brought down records

  July 6, 2012 03:22 PM

The 2008 Summer Olympics in Beijing were remarkable for many reasons—the opening ceremonies, the human rights controversies, the Redeem Team—but the signature moments many Americans will remember came in the Water Cube, during the swimming events. Who could forget Michael Phelps out-touching Milorad Cavic by 0.01 seconds in the 100m butterfly, or Jason Lezak’s heroic charge in the 4x100m freestyle relay to overtake France’s Alain Bernard and keep Phelps’ pursuit of eight gold medals alive?

Of course, the asterisk with which those events will be tagged by history was the technology: the polyurethane Speedo LZR Racer suit. The space-age, NASA wind tunnel-tested garment increased buoyancy and allowed its wearer to glide through the water with significantly diminished drag. With a life span of only a dozen races and a small army of assistants needed to even put it on, the suit certainly didn’t seem like just a piece of clothing, and the performance it generated in the pool reinforced that impression. A combined 140 world records fell at the hands of swimmers wearing the new suits between February 2008 and July 2009. Finally, in January 2010, the international swimming federation FINA prohibited the wearing of non-textile suits like the LZR and its successor, the Arena X-Glide, in competition.

The results of the suits still stand, however, in the world records they produced. So just how much did they contribute to the swimmers’ successes over this two-year period? I set out to find the answer by isolating the effects of the suit and analyzing the distortions they created on record swimming times.

To start, I examined the progression of world record times in men’s swimming from the last 50 years—a more modern era of swimming, which includes the introduction of the flip turn and half body suits for men—and looked at how frequently, and by how much, world records fell over time. I focused on the freestyle, a stroke that has remained mostly consistent stylistically over this time span, in five different distances: the 50m, 100m, 200m, 400m, and 800m. As an example, here's the world record progression for the last 20 years of the 200m, which is pretty typical of the general trend.


The rate at which the world record times fell was remarkably consistent across the five events. Since 1962, all five world records dropped at between 0.26 and 0.36 percent per year, which I treated as the baseline rate at which all swimming times improve, due to average advances in technique, athletic development, pool design, etc. One way to separate the effects of the polyurethane suits, then, is to compare the rate at which world records fell in 2008-09 to the average up to that time for each event.


*WRs only kept since 1976

As shown by the table, world record times for most of the events fell at a rate about two to five times greater than the average, with the exception of the 400m, which was curiously immune to the effects of the polyurethane suits. This last example says less about the effects of the swimsuit than it does about the greatness of Australian swimmer Ian Thorpe, the previous world record holder in the 400m. At this distance, the Thorpedo was a Speedo LZR unto himself, carving 3.7 seconds (1.7 percent) off the world record time between 1999 and 2002, during which he broke his own world record four separate times. It’s surprising that any equipment, outside of a speedboat, could allow someone to better Thorpe’s time.

Overall, the world records fell by, on average, 1.06 percent in excess of the average rate during the two-year polyurethane reign, which I believe to be mostly attributable to the change in equipment. This, then, is the magnitude of the swimsuits' effects; a one percent drop in time may mean only one or two seconds, but that can be the difference between a very good race and a world record time. If the progression of records resumes its average rate after the ban on polyurethane suits, many of these won’t fall for another five or ten years. Only two world records have been set in men’s swimming since January 2010: the 1500m freestyle, a distance event in which the effects of the suit aren’t as pronounced, and the 200m individual medley, set by Ryan Lochte, perhaps the candidate most likely to produce a record-setting time. I limited my analysis to freestyle, but, as this summary of the 2009 world championships shows, the fact that so many records in other events were broken with the use of these suits suggests that the pattern is fairly uniform.

While the swimsuit may be the most obvious explanation for this spate of world records, a couple other factors might introduce error into my estimates. The first is the evolution of swimming pools over the last half-century, the designs of which have worked to reduce drag on swimmers, with changes in depth, width, and the effects of currents—certainly a contributing factor in the drop in times, though it’s difficult to say to what degree. However, I think the effect of pool improvements, which have come steadily over the past fifty years, would be mostly accounted for by the average rate of world record progression.

The other is that, by dealing with the progression of world record times rather than average times, I've allowed the possibility of the distorting influence of outliers to creep into the analysis. It could be that a few special athletes swam incredible times, independent of their equipment, and the presence of the suits merely disguised this fact. But the rise of relatively unheralded swimmers, like German Paul Biedermann, who bested Thorpe’s record in the 400m by 0.01 seconds in 2009, leads me to believe the suits deserve most of the credit for the flood of record times. As Biedermann himself admitted, the suit was "worth about two seconds" to his times.

In London, I anticipate that we’ll see swimming times more like those at the FINA World Championships in 2011 than at the Olympics in Beijing: impressive, but not record-breaking. Still, the accomplishment of a gold-medal winning race shouldn’t be reduced just because it isn’t done in a historic time. At least now we know that, equipment-wise, the playing field is a little more level, and the champions have achieved their status without rocket fuel in their suits.

Stats Driven is powered by David Sabino, who over the last two decades has been a source of statistical analysis on the pages of Sports Illustrated, New York Times, and Chicago Tribune. David has written about all seven recent Boston-area championships for Sports Illustrated Presents commemorative issues, was the creator of such long time features as SI’s Player Value Ranking, NBA Player Rating and long running fantasy football and baseball columns.

He has also authored or made contributions to many books, including the Sports Illustrated’s 100 Fenway: A Fascinating First Century.

Now living in Marblehead, he’s focusing his attention on the Boston sports scene, specifically delving into the numbers affecting the Red Sox, Patriots, Celtics and Bruins, with the goal of informing and entertaining real fans. You can follow him on Twitter at @SabinoSports.

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