Archive | Sports

Bayesians, Frequentists, and Lance Armstrong

This is a guest post by Nathan Paxton.


Lance Armstrong has returned to the news, and the Tour de France is upon us in just a few more days. For those of you who don’t follow professional cycling, most likely the first thing that comes to mind about the sport is doping. Indeed, that’s why Armstrong popped up in sports pages again, since the United States Anti-Doping Agency (USADA) has begun an investigation of him (after the Justice Department dropped its case against him last February).

Rather than consider whether all these charges, counter-charges, and counter-counter charges are true, let’s talk about a couple of different ways that social scientists might think about l’affaire Armstrong. (As justification for the break in election programming, I’d like to note that one of the founders of this blog was just a bit of a cycling nut.)

As social scientists, at least as regards what we can empirically assess, we tend to make statements of probability rather than fact. So rather than say that Armstrong did or did not use performance enhancers, we would talk about how likely versus not likely it is that he used the substances. It frustrates many people that we rarely make categorical statements, but we’re trying to be honest about what we know and don’t know.

The two major approaches to this sort of reasoning are probabilistic/statistical in nature, and we generally refer to them as “frequentist” and “Bayesian.” A “frequentist” viewpoint is the basis of almost any basic statistics class you took in college or grad school (unless you became a social methodologist or statistician). Basically, it asks, “Given an infinite number of trials or experiments or tests, what is the probability that the results I am getting are true?” At a sufficiently small, agreed-upon threshold (1 out of 20 or 0.05 in the social sciences), a frequentist would accept or reject the “null hypothesis” (the proposition that nothing actually happened even if the data said otherwise). They’re called “frequentists” because they assess how frequently a phenomenon “should” occur.

In the case of a doping test, a frequentist would look at the number of performance enhancing substance (PES) tests that Lance Armstrong has taken (lots, and all negative, so far as we know), seen that they are all negative, and say, “The probability of a false negative is small but possible. Under repeated sampling (which is what each drug test is in essence), we become more and more sure that we are getting the ‘true’ result.” This understanding of probability is what underlies the case from Armstrong’s camp: he’s had ALL of these tests over years, they have ALL been negative, and so it is virtually impossible that he could have been using performance enhancers. The frequentist perspective relies upon holding probabilities for some event constant, like getting positive test results, but those probabilities are based upon specific conditions or assumptions that may not hold.

Bayesians, on the other hand, look at evidence differently. The world, for them, can be divided into “priors” (what you know or educatedly guess the world is like), “data” (information you collect and assess), and “posteriors” (your revised beliefs about the world, which can be thought of as the combination of priors and data). Posteriors come from the combination of priors and data.

Bayesians also like to “iterate.” Posteriors beliefs from a situation can become the prior beliefs for another round of data examination.

Bayesian-inclined cycling fans might look at the brouhaha this way. Armstrong has never failed a drug test, of which he has taken more than 500. Armstrong was at the very top of this grueling sport for many, many years (7 Tour de France titles). Armstrong’s greatest, most consistent competitors — like Italian Ivan Basso, German Jan Ullrich — and potential American heirs — like Tyler Hamilton or Floyd Landis — have all been found to have used PES. If these are the only people who have been able to keep up with Armstrong over the years, and they have been found to use some form of performance enhancement, then we may have more reason to think that something doesn’t quite add up.

  • Prior: LA did not use performance enhancers because the tests show super-low probability.

  • Data: All significant competitors used performance enhancers and tested negative, until they were caught (sometimes via a test, sometimes via old-fashioned police work).

  • Posterior: Perhaps the tests’ probability of sussing out those who use performance enhancers are wrong. Revise those probabilities, in light of what we now know, make them the new “priors”, run the tests on the data, and assess how probable it is that Armstrong used those substances.

My own interpretation: If Armstrong did not use performance enhancers, then that means he’s even more extraordinary than previously reported, since he won unassisted against those with PES assistance. It seems more plausible that there’s either something wrong with the tests or that LA used performance enhancing substances than that he becomes an even greater statistical anomaly.

Why can we say this? Given what you might call the “hard” results of LA’s tests and the “soft,” circumstantial results of his competitors, iterating the posteriors and making them priors is exactly what we want to do.

The tests that these cyclists take tell us something not only about the cyclists, but about the tests too. Since we know that many of these riders were being regularly tested and passed the tests until they did not, and we gain a better appreciation of how well the tests detect people who are doping. It’s pretty commonly accepted in sports discussion that the EPO test has a high false negative rate (athlete tests “clean” even if using PES), even if no one seems to know the exact rate. The updated/iterated prior confirms that idea.

A Bayesian perspective can more easily contend with a world where athletes are actively trying to mislead, hide, and evade detection. When we know that competitors are trying to hide, that they did use banned PES, and that previous tests didn’t catch them, we can use the collective information about the population of athletes to make more real-world accurate  statements about the probability a particular athlete’s results are right.

Importantly, I think, this “light” Bayesian perspective on cycling and Armstrong gives us better leverage for thinking through the problem. Adopting the perspective does not mean that you think Armstrong used PES. But it does mean that one has to take into account more information about the world (of cycling, at least) than just how likely a particular test result is — one also needs to know how well the system is being gamed, and how well the tests caught demonstrated users. We can get some indication of that by looking at Armstrong’s peers.

Even if it turns out that Armstrong used performance enhancers, it may not diminish his Tour de France accomplishments. If he won using these substances while all his significant competitors did too, that still may mean that he’s the better cyclist. On the other hand, given how much he has made of never using banned substances and competing clean, it could significantly hurt his charitable works on behalf of cancer patients.

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8020 Games…

…and the Mets have a no-hitter! Congratulations, Johan Santana! And thank you!

[Photo Credit: Joshua Tucker, staring in awe at his TV as he realized that this moment had finally arrived…]

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Political Scientists are Concerned with Ethics

Or at the very least, University of Michigan political scientist Jenna Bednar is! Her question appeared in the NY Times Magazine’s The Ethicist column this weekend, when she asked:

Given the mounting evidence of long-term and even fatal effects of brain injuries incurred by professional football players, is it ethical for us to watch the games?

The answer is too long too summarize here (and can be read in its entirety here), but intriguingly contains a politics analogy(!) in its conclusion:

But somewhere between those extremes lies an option that has the virtue of being both ethical and simple: If you think the action on the field is unfair to players, just don’t watch. Just choose not to participate. ([Malcolm] Gladwell predicts that in 15 years or so, no reasonable person will admit to watching football.)

Turning off the TV won’t do much. Only as much, perhaps, as voting, an act which in the singular is so small, it’s almost meaningless, but which in the aggregate can change history. Your act may or may not help change football, but if you feel as your letter suggests, it will keep you from directly participating in something at odds with your own personal values.

Just another way political scientists are helping to shape important public debates!

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Mascotology, Not Bracketology

This is a guest post from political scientist and mascotologist Tobin Grant.  The image is mine.


Since I like being part of an NCAA bracket pool but hate to lose money, I’ve often entered a “mascot” bracket because most people let me put in for free. Consider it the worst possible bracket.

Slate has just put up their own take on whose university would beat whose in a real fight.  The real fun in all this is figuring out what some of the weirder nicknames are. In grad school some friends and I took this a little too seriously. We came up with a general ranking from winner to loser nicknames:

  1. Supernatural (Demon Deacons is the highest, drawing upon both good and evil)

  2. Acts of God (e.g., Hurricanes)

  3. People with Weapons—Ranked from most lethal (e.g., Mountaineers with rifle) to least lethal (e.g., Gaels, Seminoles)

  4. Large carnivores, though sometimes these can kill a human with a weapon

  5. Unarmed people (e.g., Boilermakers, Hoosiers)

  6. Other animals, ranked from Large Herbivores (e.g., Longhorns), Small Carnivores (e.g., Wildcats), Raptors, and other small animals

  7. Inanimate objects.  (e.g., Buckeyes)

  8. Colors and other adjectives (e.g., Orange, Crimson)

Sometimes you can’t figure it out from a team’s name or tradition. No one—I mean no one—can give a definitive definition of a “hoya.” It’s lost in history, just like a Virginia Tech “hokie” or Virginia “wahoo.” Apparently students in the Commonwealth like weird cheers and think they make great nicknames. In our rankings, we use the original meaning of the nickname. Occasionally, a mascot is used to figure things out.

Here are some of the more interesting ones in this year’s tourney:

  • St. Bonaventure Bonnies are just short for the name of the school. Being known as a lovely lass isn’t the best name, but it’s better than one of the least PC names ever: The St. Bonaventure Brown Indians (1927-1992).

  • St. Louis University Billikens is a classic early nickname. In the early 1900’s, one of the first trademark dolls was the Billiken. Made in St. Louis, it was a kind of good luck doll. Very creepy looking—kind of a mix between a fat Buddah and an elf. Apparently the football coach also looked like a fat Buddah and an elf, so he and the team started being called the Billikens.

  • Duke Blue Devils aren’t really devils. They’re named after a World War I French fighting group that was touring the U.S. for the war effort. Ever notice the little mustache and cape on the mascot? Now you know why. On the nickname ranking, this drops Duke from supernatural down to armed humans—though as a French WWI soldier, they’re arguably even lower. Relatedly: DePaul Blue Demons aren’t really demons—they used to have big blue “D”’s on their jerseys. Blue D-Men. Get it?

  • Both Missouri Tigers and Kansas Jayhawks are named for armed groups that fought before/during the Civil War. The Jayhawks were free state armed groups; the Tigers were a militia in Columbia that organized to defend against confederate raiders. Both Tigers and Jayhawks later came to mean anyone from the respective states. In the pool, both are treated like armed humans, not animals (this avoids having to figure out what a jayhawk would really be).

  • North Carolina Tarheels is also a civil war reference for their resistance to retreat (but this is debated).

  • Long Beach 49ers. It’s partially a reference to the gold rush, but really it’s because the school was founded in 1949.

  • Wisconsin Badgers. Not the animal. Wisconsin lead miners working in Galena, IL used to live in homes carved in the hillside, so they were nicknamed “badgers.” It was derogatory but it stuck.

  • Michigan Wolverines. Since no wolverine ever lived in Michigan, it’s a mystery. Most common explanation was that it, too, was a derogatory name given to Michiganders by Ohio during a dispute over the Michigan-Ohio border (wolverines are known for their appetite and fierceness). Ohio won, by the way, if you consider Toledo a victory.

  • Vanderbilt Commodores. This is reference to Cornelius Vanderbilt, who made his money in shipping and was known as the Commodore. Not frightening at first blush, but I’m guessing Vanderbilt had more power than all the Earth’s bears, wildcats, and eagles combined.

  • Western Kentucky Hilltoppers. Simple: the school’s set on some hills. The former teaching college used to go by the Pedagogues.

  • Wichita State Shockers. Like a cornhusker but for wheat. They shock the wheat. Shockers. Get it?

One thing I’ve learned looking at nicknames for years: The best nicknames were chosen in the 1920’s; the worst were chosen by committees who decided the originals weren’t PC (which they often weren’t).  Case in point: Wheaton College (Illinois).  Students latched on to the Crusaders, which caused real problems when students went to the middle east.  So, the school changes it to Thunder!  As a friend put it, it’s the only thing that scares people but can’t actually hurt you.  The college has now introduced a mascot Tor, a mastodon (long story).  The name Tor is supposedly short for “stertorous.”  The college says that stertorous is “a synonym for loud and cacophonous and also meaning heavy snoring” but it really means ONLY a snoring sound and when it doesn’t, the “loud and cacophonous” sound is usually something like flatulence, not thunder.  Leave it to a committee to give us a sound with no fury as a nickname and name the mascot after snoring.  But I digress.

Here is a full list of mascots and the resulting pool.

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I remember when I heard that Ronald Reagan had appointed a guy named Ling to be Secretary of Agriculture, I thought, Cool—-he appointed an Asian. Then it turned out that it was actually a white guy named Lyng.

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Magic Johnson and Public Opinion about AIDS

Twenty years ago today, Magic Johnson announced that he was HIV-positive.  In my newest post at 538, I discuss how this affected public opinion, drawing on a 1994 paper by political scientist Philip Pollock.  The upshot: Johnson’s announcement led the public to think about HIV and AIDS in terms of opinions about heterosexual sex, rather than just opinions about homosexual sex.

The post is here.

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Baseball World Champions

I just wanted to clarify Josh’s post on the baseball “world series” for our non-American audience. Josh was not writing about the improbable run that the Dutch national honkbal team made last week to defeat Cuba, the US, and others to become the first European world champion in baseball since 1938. No, Josh was referring to the improbable win by the team from St. Louis from the state Missouri in the North American baseball championships. See, we’re always helpful this way at the Monkey Cage. Go honkballers!

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