Subscribe: iTunes |Download |RSS |Video

You can stream or download the full episode above. You can also find us by searching “fivethirtyeight” in your favorite podcast app, or subscribe using the RSS feed. Check out all our other shows.

If you’re a fan of the elections podcast, leave us a rating and review on iTunes, which helps other people discover the show. Have a comment, want to suggest something for “good polling vs. bad polling” or want to ask a question? Get in touch by email, on Twitter or in the comments.

When on the court together for the Warriors this season, Steph Curry, Klay Thompson, Andre Iguodala, Harrison Barnes and Draymond Green scored the most points per offensive chance (1.26) of any five-man unit in the NBA,¹ allowed the 13th-fewest points (0.83), and had the best per-chance scoring margin (+0.43).

And that’s only the deadliest variation of the Death Lineup. Golden State also owned five of the next 10 best lineups by per-chance point differential, all of which contained a variation of Curry, Green and either Thompson or Iguodala or both. Four of those additional lineups featured one of Golden State’s traditional centers, Andrew Bogut or Festus Ezeli, as the lone conventional big; the other was a small lineup that swaps out Iguodala for guard Shaun Livingston.

With Curry injured for most of the first two rounds, those Lineups of Death haven’t spent much time fully assembled in the postseason. The Warriors’ most crucial three-man combos — Curry, Green and Thompson, and Curry, Green and Iguodala — have logged only 94 total minutes together in 10 playoff games thus far. (They still outscored opponents by 61 points in that limited playing time!) But after Curry returned for the closing two games of Golden State’s series against Portland, at least one of those trios was on the floor for 62 minutes — a total in line with the 27.7 minutes per game they spent on-court together during the regular season.

All this is bad news for the Thunder because the Warriors have a history of going small to combat good teams with lumbering big men: According to the Lineup of Death’s origin story, the tactic was only fully realized last year when head coach Steve Kerr had an epiphany during the NBA Finals and moved Iguodala into the starting lineup. That’s when the record-setting Warriors really took off, first against Cleveland and then against the rest of the league. An inability to match up with the same strategy could end up being Oklahoma City’s undoing as well.

But we shouldn’t assume the Thunder’s big lineup won’t be able to hold its own. During the regular season, only 19 five-man units² broke even against Warrior lineups containing both Curry and Green. OKC had two of them — No. 7 and No. 13 — and both were of the big variety that the team has been using extensively during the playoffs: Russell Westbrook, Kevin Durant, Ibaka and Adams, with either Andre Roberson or Dion Waiters on the wing. So in the matchup of preferred lineups, the Thunder might not be quite as outgunned as it seems at first glance.

Of course, there are a bunch of caveats to tack on here. We’re talking about only 60 to 70 chances of track record from the regular season, and lineup data is notoriously noisy anyway. Plus, even though the Thunder’s big lineup did stick with the Warriors, the Dubs swept the regular-season series anyway.

But as an exercise in figuring out how a 31 percent underdog could fight those odds, things might begin with Oklahoma City’s ability to slow down Golden State’s Lineups of Death. And what extremely limited data we have right now suggests that they could fare better than most.

Check out our latest NBA predictions.

But if this year’s contest were run under Eurovision’s old rules, the winner among the 26 participants would have been Australia.

In Eurovision, countries rank one another, and points are awarded accordingly. In each country, both residents and a panel of judges rank participants. Previously, the rankings of the public and the experts were pooled and then points were awarded based on the combined ranking. This year, rankings-based points from judges and from voters were awarded separately.³

I reran this year’s numbers to see what the results would have been under the old system.⁴ Ukraine would still have beaten Russia, but Australia — with its sparkly-but-bland number — would have beaten them both. Eurovision results lend themselves to analysis of geopolitical intrigue, but Ukraine’s song lyrics (“They kill you all and say / We’re not guilty” — referring to Russian soldiers in 1944) made it pretty easy to guess which nations would leave Russia or Ukraine out of their top 10 based on their current relationship with Russian President Vladimir Putin.

In Poland, which recently barred a Russian motorcycle group from crossing the country as part of a World War II memorial ride, the jury gave Ukraine’s protest song the maximum number of points, and Russia nothing.⁵ Twenty-one countries’ juries gave Russia no points, and 17 nations’ panels did the same to Ukraine. Australia was shut out of the top 10 by only three countries’ judges. If these low rankings had been combined with residents’ rankings to award points, Russia and Ukraine would have both wound up with more zeroes.

Instead, the new system prevented Australia from beating all of Europe in its second year participating in the competition. The true victor, as it has been for decades, was complicated European bureaucracy.

Spring: the city bodegas and country gardens are filled with blooms, the wedding invites are in the mail, and a young man’s fancy lightly turns to thoughts of love.

Ah, if only things were so simple for House Speaker Paul Ryan.

Washington’s most-watched May-December courtship, between Ryan and Donald Trump, is complicated and progressing slowly.

Trump went to Washington last week to meet with the speaker, sitting down privately with Ryan and Republican National Committee Chairman Reince Priebus for 45 minutes to discuss their differences (Ryan has yet to endorse Trump). Ryan was complimentary of Trump after the meeting, publicly calling him “warm and genuine,” though reports of the meeting note that Ryan asked Trump to tone down his immigration rhetoric. No peace was officially brokered, though a joint statement noted with acute literality, “This was our first meeting, but it was a very positive step toward unification.”

In other corners of the Republican universe, a number of party insiders vehemently opposed to Trump are making Hail Mary efforts to draft an independent candidate to challenge the presumptive nominee. According to The Washington Post, Mitt Romney himself has made overtures to John Kasich and Nebraska Sen. Ben Sasse. No one has yet bitten — the idea of being persona non grata in the party lacks appeal.

Speaking of party noblemen plotting against their presumptive king, Ted Cruz knows he’s not going to be president, but there seems to be every indication that he’s going to take his fighting energy to the rules committee in July in an effort to reform the party’s nomination process. Among the changes he’s seeking are an end to open primaries (i.e., no more squishy independent voters), a re-ordering of the primary calendar to allow more states from different regions to have an effect on the process, and the introduction of a conscience clause that would allow delegates who are typically bound to a candidate based on their state’s vote outcome to vote for whomever they wish if the winner’s values contradict theirs. Wonder who that one’s aimed at?

Over the weekend Cruz made an appearance at Texas’s party convention, spending his time at a podium thanking campaign volunteers and pointedly not making an argument for Republican unity. “I don’t know what the future will hold,” Cruz said. “We may face some challenging days ahead. We may face growing challenges going ahead, but I am convinced that [the] movement, the men and women gathered here, will be the remnant, will be the core of pulling this country back from the abyss.”

Listen to the latest episode of the FiveThirtyEight elections podcast.

Subscribe: iTunes |Download |RSS |Video

For those of you looking to whet your veepstakes appetite: Ben Carson gave an interview to The Washington Post in which he confirmed that John Kasich, Marco Rubio, Ted Cruz, Sarah Palin, Chris Christie and … Ben Carson — maybe? — were VP possibilities.

Anything else kicking in Trump world? Well, the Sunday edition of The New York Times led with a story about Trump’s often inappropriate interactions with women in both his private life and business dealings. “You like your candy,” he reportedly told one high-level executive in his business after she gained weight. The story notes that Trump hired women because he thought they worked harder than men (yours truly would like to note that she’s writing this column on a Sunday).

Read more:

Could An Independent Candidate Succeed In 2016? — A lot of people have been talking up the idea of an independent presidential run. So the FiveThirtyEight politics team chatted about whether there’s something about the current political climate or modern politics generally that makes a successful independent bid more likely.

When Did Trump Become Unstoppable? by Peter Keating — Just a couple of weeks ago, many political analysts were still chattering about a contested Republican convention. Then the forces opposing Donald Trump seemed to unravel. This terminal phase of the nominating season is a reminder of how much and why public opinion matters. Indeed, one theory correctly suggested that as of March 15, Trump was on his way to victory.

Don’t Worry About The Electoral College Math (Yet) by Harry Enten — We’re still six months from Election Day, and no single poll should receive much attention. It’s also best to avoid getting too bogged down in state polls — even of swing states. The truth is — with some notable exceptions — winning the national popular vote typically means winning the presidency. The Electoral College matters only in very close elections, and most of the time not even then.

2 kilometers

Last year, Milan, Italy, set the world record for longest pizza at just over 1.5 kilometers, and Naples is hella mad. Chefs in Naples have prepped to make a 2 kilometer pizza containing some two tons of mozzarella (for U.S. residents unfamiliar with the metric system, a kilometer is basically a mile that phoned it in). [NPR]

7-6

That was the score of a baseball game played on Sunday between the Texas Rangers and Toronto Blue Jays. (The Rangers won.) But that scoreline barely scratches the surface of what went down. There were ejections galore, the best punch I’ve ever seen televised and a bench-clearing brawl. You know, basically a boring hockey game. [ESPN]

18.9 percent

Percentage of Americans aged 65 and older who are working, the highest level in decades. [Bloomberg]

More than 4,000 complaints

Las Vegas was hit hard by the Great Recession and the collapse of the housing market. To this day, it is contending with the consequences, including squatters. In 2015, there were more than 4,000 complaints to the Las Vegas Metropolitan Police Department about squatters, up 43 percent compared to 2014. [The New York Times]

50 or more employees

The lower house of the French parliament passed a bill that would make it illegal for companies with 50 or more employees to send emails outside of work hours — namely, after work and on the weekend. [The Washington Post]

38,000 slots

The gaokao is China’s college entrance exam. It is basically the SAT on steroids, the kind of thing kids spend their lives preparing for. So the announcement that 38,000 slots at universities in the wealthy Jiangsu province will be saved for applicants from other, often poorer areas did not go over well. There were demonstrations in multiple cities. “In the provincial capital, Nanjing,” The Wall Street Journal wrote, “parents gathered outside of provincial offices Saturday, shouting, ‘Governor, come out!’ as riot police kept them at bay.” [The Wall Street Journal]

If you haven’t already, you really need to sign up for the Significant Digits newsletter — you can be the first to learn about the numbers behind the news! How great does that sound? You should totally do it.

And if you see a significant digit in the wild, send it to @WaltHickey.

Shit happens, except when it doesn’t. And when it doesn’t, we get worried. Over the centuries, constipation has gone by many delicate euphemisms, but the problem itself refuses to budge.

The Egyptian Ebers Papyrus, one of the oldest books in the world, promoted a theory of disease that begins with toxic, undigested food poisoning the body from the gut outward. Doctors no longer believe that, but we’re still worried about constipation. Even though most people who feel constipated never seek a doctor’s opinion on it, it still accounts for 8 million physician visits every year in the United States. The connections between the Ebers Papyrus and the modern health care industry are about culture as much as they are about the gut. Constipation is a social disease. It exists in your head and your heart, as well as in your colon.

To get a sense of what it means for constipation to be cultural, look no further than current estimations of the prevalence of constipation in the public. There are an awful lot of people who feel like they are constipated even though their doctors disagree. The rate of constipation in North America could be anywhere from 2 percent to 27 percent, according to a systematic review of the literature published in 2004. But the studies with the highest estimates tend to collect the data from patients’ self-reports, said Dr. Peter Higgins, associate professor of internal medicine at the University of Michigan and an author of that review paper. “If you look at physician discharge billing codes, it’s more like 1.2 percent to 4 percent,” he told me.

It’s the first day of this week’s series on gut science. We’ve also made a video about what poop can tell us about our health, and there’s more to come later in the week.

Unlike constipation, poop is purely biological. What you eat reaches your colon in a couple of hours but can take up to a week to make it out the other end. In the meantime, your colon is absorbing liquid, sucking up whatever nutrients it can as it uses muscle contractions to push along the stuff it can’t use.

That stuff is made up almost entirely of water — 75 percent. Of the rest, most is bacteria, dead and alive, plus indigestible fiber and other parts of food your body couldn’t break down during digestion. You will poop whether you eat or not, Higgins told me. “People are surprised by that. Your stomach secretes fluid every day, your pancreas secretes a large amount of fluid every day, your small bowel secretes fluid; you secrete in the neighborhood of 10 liters of fluid into your gut and then reabsorb most of that in the process of dissolving, emulsifying, grinding and reabsorbing nutrients,” he said.

Given that the secretion is happening constantly and you are (hopefully) eating every day, your rate of pooping should be reasonably regular. Studies suggest that almost everybody poops at least a couple of times a week (though what’s “normal” varies quite a bit from person to person). Because normal is a spectrum, though, it’s difficult to define precisely where normal pooping ends and constipation begins.

Doctors use diagnostic criteria for constipation, where patients have to experience two or more of six symptoms:

1. Straining during at least 25 percent of defecations
2. Lumpy or hard stools in at least 25 percent of defecations
3. Sensation of incomplete evacuation in at least 25 percent of defecations
4. Sense of obstruction in at least 25 percent of defecations
5. Manual maneuvers needed to facilitate at least 25 percent of defecations
6. Fewer than three defecations per week

But you can see how even that detailed guide is pretty imprecise. Have you ever paid enough attention to your poops to know what is happening 25 percent of the time versus, say, 15 percent? That’s why, when patients come in and tell Higgins that they are constipated, his first question is, “What do you mean by that?”

That imprecision matters because it gets in the way of our understanding something pretty basic: How has constipation changed over time? If even the highly quantified world of modern medicine isn’t super clear on this point, it’s safe to say that our knowledge of the constipation of the Ancients is even worse.

But here is something we do know: Since at least the Renaissance, Western cultures have fretted about their own bowels while looking back to an imagined past where mankind pooped in peace and harmony. According to James Whorton, professor emeritus of medical history and ethics at the University of Washington School of Medicine, modern life has long been considered the ultimate cause of constipation. Take, for instance, a bit of doggerel poetry from mid-1600s England:

And for to make us emulate,
The good old Father doth relate
The vigour of our Ancestors,
Whose shiting far exceeded ours.

Whorton documented that poem in “Inner Hygiene,” his book on the history of constipation in Western popular culture. More than just nostalgia, though, the belief that modern lifestyles caused constipation was viewed as a medical emergency, on the scale of what we think of the obesity epidemic today, Whorton told me.

That’s because constipation was, itself, a theory of disease. The ideas documented in the Ebers Papyrus, which dates to the 16th century B.C., persisted all the way through the 1930s, in the guise of “autointoxication” — accidental self-poisoning that begins in the bowels. Constipation, then, could literally cause any disease, from cancer to schizophrenia. And this emphasis on constipation as the cause of all disease got stronger in the late 19th century, after scientists began to understand the germ theory of disease, Whorton said. Suddenly, there was a scientific explanation for what everybody already thought to be true. Bacteria lived in your poop. Bacteria caused disease. Clearly, the longer your poop sat in your body, the more at risk you were of getting sick.

You can see this fear at play in the over-the-counter medications sold during the 19th and early 20th centuries. There isn’t an organized database of patent medicines. Even if there were, it would be difficult to cleanly categorize what each medication was “for” because they were frequently sold with multiple cure-all claims. But “a majority were laxatives of one kind or another,” said Edward Shorter, professor of history of medicine and psychiatry at the University of Toronto. Advertisements for these medicines called constipation “the monarch of all diseases,” claimed it was the “shortest road to old age, wrinkles and decay” and promised that “a clean colon is more important than a clean face.” A major feature of this time period was the idea that laxatives should be taken preventatively, not just as a treatment for existing constipation. After all, if constipation caused disease, you’d be better off if you never had it. People were encouraged to give their children daily doses of laxatives, such as castor oil. (A fun bit of history to ask your grandparents about at the next family holiday party!)

Eventually, Shorter said, the medical field lost interest in constipation as a source of disease and became more concerned about issues such as inflammation. But constipation, and the fears that surrounded it, are still important because of how they presaged pervasive popular ideas about health. Take, for instance, current beliefs about the dangers of modernity and the supposed inherently healthier lives of people who lived in the past or who live today under “more primitive” conditions. That idea existed long before the first human entered a CrossFit gym.

One of the people who bought into that hypothesis was Denis Burkitt, an Irishman who worked as a surgeon and Christian missionary in Uganda in the 1950s and ’60s and who is kind of the patron saint of bran muffins as health food. Burkitt became convinced that the people he treated in Uganda were much healthier than those in the United States and Europe and that the cause of their health was dietary fiber (and the healthy poops said fiber facilitated). Diseases of modernity, from varicose veins to cancer, could be attributed to a lack of fiber, Burkitt believed. And he promoted diets that were more fibrous and more “ancestral” as a cure-all. Far from being written off as a quack, Burkitt was a respected scholar who has a lymphoma named after him. He’s the primary reason doctors began recommending bran-heavy, high-fiber diets in the 1970s — and still do, even though, today, there’s little evidence that either bran or fiber has an impact on health. (Although they will, probably, make you less constipated.)

And patients are still concerned about the state of their poops, even if doctors are less so, Higgins told me. Look at the advertising for probiotics, he said. “They use code words like ‘good health’ or ‘good gut.’ They make these vague cultural references about regularity. They’re doing a dog whistle for the kind of 19th-century view of how your bowel should function.”

On the plus side, though, Higgins said that modern, over-the-counter laxatives aren’t really dangerous. You’d have to work very hard to hurt yourself with something like milk of magnesia or Activia yogurt. So there isn’t much of a downside to that disconnect between the frequency of constipation that patients report and the frequency reported by doctors. “You probably have perceptions of what’s normal that you’ve inherited from your parents or grandparents — perceptions that aren’t medical,” he said. “But if you’re happier with daily bowel movements instead of every other day, well, great. That’s fine.”

One of the major leaps forward in gut science began with an accidental shooting at a trading post on June 6, 1822. A fur trader named Alexis St. Martin took a bullet in the abdomen, leaving him with a hole ripped through his muscle, bone and internal organs. Nobody expected him to survive. But he did. And the hole through his body survived, too.

In the process of healing, St. Martin’s skin knit itself together in such a way that he was left with a puckered opening under his breast that went all the way through to his stomach. His doctor, William Beaumont, could literally tie a bit of food on a string, shove it into St. Martin’s stomach through the hole, and pull it back out again. Using this one weird trick, Beaumont extracted samples of the man’s gastric juices. Over eight years and more than 200 awkwardly invasive experiments, St. Martin and Beaumont gave humanity its first real understanding of how digestion works and what happens inside the black box that is the gut.

It’s the first day of this week’s series on gut science. We’ve written about why we’re so obsessed with constipation and made a video about what poop can tell us about our health — and there’s more to come later in the week.

Today, scientists around the world are carrying on Beaumont’s groundbreaking work — only this time the path to knowledge lies through not the stomach, but the bowels. Scientists and the public at large are intensely focused on intestines, the processing of food that takes place in them, and the microbial communities that live and work in their depths. Federal spending on research related to the microbiome — the communities of microbes that live in you, animals and the natural environment — is rising. In fiscal year 2012, the U.S. government spent just more than $200 million on microbiome research projects. By 2014, that had risen to more than $450 million. And just last week the Obama administration announced the National Microbiome Initiative, a $121 million federal investment for “cross-ecosystem microbiome studies,” with additional cash from private agencies.

All of the new research promises to change our understanding of the strange alchemy that links the sandwich you ate for lunch with the teeming mass of symbiotic organisms living inside you. If we know more about that relationship, perhaps we can better diagnose your body’s systemic health.

This week, FiveThirtyEight’s science team will be separating fact from hype, doing a gut check on gut science. You can already learn about the history of constipation anxiety and what it can tell us about gut health. And there’s a video waiting for you about researchers in Canada who freeze-dry human poop. On Tuesday, you’ll discover how science’s bias toward Western cultures is helping to distort our understanding of what a “normal,” “healthy” gut ought to look like. On Wednesday, you’ll find out whether probiotics are worth a damn. And finally, on Thursday, you’ll dive into the surprising connections scientists are finding between your gut and your brain.

Our goal is to make the inner workings of your bowels as visible as that stray shot made the inner workings of Alexis St. Martin’s stomach. Come on, take a peek.

This is the first day of this week’s series on gut science. We’ve also written about why we’re so obsessed with constipation, and there’s more to come later in the week.

Some scientists believe that these microbes can be the key to understanding certain diseases and conditions, such as inflammatory bowel disease, obesity and diabetes. The methods used to gather this data are an important consideration for microbiome research and yet, according to Deanna Gibson, director of the Center for Microbiome and Inflammatory Research at the University of British Columbia’s Okanagan campus, there is no across-the-board standard for how poop is prepared, handled and stored in the lab. More importantly, a small portion of the poop, or subsample, is often all that is tested.

Researchers at Gibson’s lab in Canada believe that a subsample is insufficient. Our poop is far too complex for a small piece to give us the information we need. So to reduce the variability of microbiome data, her team has devised a method called homogenization. It’s a protocol that requires poop, liquid nitrogen, a mortar and pestle, and a sense of humor. Watch how it happens in the video above.

But the Oklahoma City Thunder shocked the Spurs, knocking San Antonio out of the playoffs with a 113-99 victory Thursday night. After all the buildup and all the hypotheticals, there will be no epic Warriors-Spurs showdown. And given the Spurs’ preseason hype — as well as the extraordinarily high level at which they operated all season long — San Antonio’s second-round ouster has to be seen as an historic disappointment. But NBA fans can take solace: The Thunder ought to give the Warriors a terrific series, too.

I have a point system for rewarding playoff success based on how far a team advances in the playoffs (and how many teams it had to beat out to get there). Every team starts with 33 initial points, or 1,000 times one-thirtieth (there are 30 teams, so at the beginning of the season every team has a 1-in-30 chance of winning the title). By qualifying for the postseason, a team increases its chances from 1-in-30 (3.3 percent) to 1-in-16 (6.25 percent), so it gets a 29-point bonus just for making the playoffs. And from there, it’s all about advancement. Win a first-round series? Get 63 bonus points. Advance to the conference finals? Tack on 125 more. Make it to the NBA Finals? Grab 250 points. And win the chip? That’s a 500-point prize. (This means the NBA champion gets exactly 1,000 points for its playoff run.)

So San Antonio only gets a playoff score of 125 points for all its trouble this season — an absurdly low total for a team with its +11.3 efficiency differential. Excluding the 2015-16 Spurs, teams with an efficiency margin of +10 or better since 1983-84 averaged a playoff score of 859.6, which is somewhere between a championship victory and a Finals loss. The previous low playoff score for a +10 team was 250, achieved by the 2008-09 Cleveland Cavaliers, but even they managed to make the conference finals. San Antonio didn’t even get that far.

VIDEO: Neil Paine explains how disappointing the Spurs’ loss was

So NBA fans are going to be deprived of that long-anticipated Warriors-Spurs battle. But look on the bright side: the Warriors-Thunder series is also shaping up to be a classic. In fact, according to the pre-series Elo ratings (which estimate each team’s strength at any moment), it’s the single best-looking conference finals matchup since 1984:

(To give credit to series where both teams were strong — instead of cases where one of the teams propped up the overall average — I used the harmonic mean, a special type of average that penalizes low outliers.)

Not every series that looks great on paper ends up delivering on its promise. But with Kevin Durant and Russell Westbrook facing a healthy Steph Curry and the rest of the record-setting Dubs, nobody outside Texas should complain about the Spurs’ early absence from the playoffs.

Check out our latest NBA predictions.

“Momentum” is one of the most misused terms in politics — very often it’s false signal in noisy data, especially in general elections. But primaries are different. Because they’re held sequentially, winning one state may encourage voters in subsequent states to jump on the bandwagon because they want to back a winner. Winning also provides candidates with other resources, such as money and favorable media coverage. In short, there are advantages to being the front-runner: Pluralities tend to turn into majorities.

Indeed, one theory of momentum correctly suggested that as of March 15, Republican voters would start breaking toward Trump, and that he would surge to victory.

To see why, we have to start with a research paper called “The End Game in Presidential Nominations,” written in 1981 by Donald Collat, then a Yale law student, and political scientists Stanley Kelley and Ronald Rogowski. (We will call them CK&R for short.) CK&R were interested in bandwagon calculations. When political stakeholders seeking influence, patronage or other spoils choose a candidate, they must endorse someone early enough to make a visible difference, but they also have to wait long enough to be reasonably sure they are picking a winner. So when does support turn into a stampede?

To find out, CK&R studied American political conventions from 1848 to 1948. In those days, before mass communication and transportation, conventions had important substantive functions. They gave governors, members of Congress and big-city bosses a unique chance to gather, size one another up, cut deals, hammer out issues — and to battle over choosing presidential nominees, sometimes over many ballots. CK&R found that as conventions progressed, changes in delegate counts held crucial signals about when candidates became inevitable: Once they passed a particular threshold of momentum, their bandwagons started to roll. CK&R looked at a metric they called the “gain-deficit ratio”: the change in a candidate’s support from one ballot to the next, divided by the support the candidate still required to clinch the nomination. As CK&R put it, “The ratio takes account of where a candidate is, how close victory is, and how fast the candidate is progressing toward it.” And they found that at every majority-rule convention over that 100-year period (the Democrats required a two-thirds vote until 1936), the candidate who surpassed a gain-deficit ratio of 0.36 went on to win the nomination. This held true even when the eventual winner started far back, and his ultimate victory wasn’t obvious.

For example, at the 1940 Republican convention, 501 delegates were needed for nomination. Thomas E. Dewey of New York led on the first ballot with 360 votes, while businessman Wendell Willkie was in third place with 105. On the third ballot, Willkie moved from 171 votes to 259, giving him a gain-deficit ratio of (259-171)/(501-259), or 0.364. He then took the lead on the fourth ballot, and was nominated on the sixth.

The gain-deficit ratio isn’t the only way to measure bandwagon effects, and 0.36 isn’t necessarily a magic number. But the fact that it persisted as a threshold from the time of the Whig Party through Dewey’s nominations in 1944 and 1948 suggested something powerful was at work. CK&R concluded that over time, different delegates made decisions based on similar kinds of evidence, and that trends, not just levels, of candidate support mattered to them.

Now, here’s where things get really interesting. After 1952 (when it took the Democrats three ballots to pick Adlai Stevenson), parties began nominating candidates exclusively on the first ballot. That meant delegates had to make their bandwagon calculations before conventions — before they all met in one place to slug out a nomination battle round by round, and to put their support up for bid. But the gain-deficit ratio kept working anyway. CK&R looked at contested nominations from 1952 to 1976, tracking preconvention changes in support by using surveys of delegates from The Associated Press and The New York Times. Again, once a candidate passed the critical threshold, he always went on to win the nomination. In 1960, John F. Kennedy’s gain-deficit ratio hit 0.672 two and a half weeks before the Democratic convention, into which he went unsure if he had a majority of delegates. In 1968, Richard M. Nixon’s gain-deficit ratio passed 0.36 for the first time in the AP’s 11th poll of GOP delegates, reaching 0.519 the day before the Republican convention.

Even when nominations seemed to hinge on technicalities, conventions ended up favoring the candidates with the most momentum. It’s true, for example, that in 1952 Dwight D. Eisenhower prevailed on the first ballot of the Republican convention only after waging an extensive, bitter floor fight to unseat delegations that supported his opponent, Sen. Robert Taft. And that in 1972, George McGovern had to fight to preserve the winner-take-all results of the California primary, an idea most of his own followers disliked, before he could lock up the Democratic nod. But it’s also true that before their conventions ever started, both Eisenhower and McGovern had reached the point where a candidate had never been denied nomination.

After 1972, both parties shifted toward allocating delegates by primaries and caucuses. Now it’s up to every voter to decide how much and how early it matters to be on a winning team. Yet the gain-deficit ratio has remained an accurate predictor. (That’s one finding of research by political scientist Barbara Norrander, who updated CK&R’s work to look at the endgame of presidential nominations in the post-reform era.) For instance, in 1996, Bob Dole passed the 0.36 mark on March 12, when he vaulted from 276 to 737 delegates, with 996 needed to nominate, by winning all seven Super Tuesday primaries. In 2008, Barack Obama and Hillary Clinton both exceeded the 0.36 threshold on Feb. 5, when they split the large trove of delegates chosen by 22 states. Obama’s gain-deficit ratio after those contests was 0.71, while Clinton’s was 0.67, foretelling a narrow but eventual Obama victory.

Even though voters now have the power to select nominees, they seem to be subject to the same bandwagon calculations that affected delegates at the old conventions. And perhaps those delegates, and their bosses, always paid at least some attention to public opinion, in addition to their own judgment. Probably both. So the decision-makers are different today from 60 or 160 years ago; primaries and caucuses essentially fill the role that convention ballots used to. But much of the psychology and many of the incentives involved in decision-making remain similar. And the analytics of momentum, expressed in measures such as the gain-deficit ratio, still make sense. Candidates still win nominations when they close enough of the gap toward their goal that the next round naturally goes their way. Sufficient momentum attracts breakaway support. And then overperformance wins over even more undecideds, and discourages rivals.

Which appears to be just what happened with Trump. On March 15, he won 228 delegates across six contests, including four large, geographically diverse states. That gave him a total of 691 delegates, and with 1,237 needed to nominate, his gain-deficit ratio was 228/(1237-691), or 0.418, beyond the 0.36 threshold. What happened next would have been more predictable if Trump weren’t so singularly divisive, or if Ted Cruz hadn’t won Wisconsin, or if the gap between Trump’s and Cruz’s organizational skills hadn’t raised doubts about Trump’s hold on his delegates. But once the campaign moved beyond the last set of states demographically unfavorable to Trump, his bandwagon started to roll.

On April 19, Trump won a majority of votes in a state for the first time, with 60 percent in New York. Every day thereafter, his average support among Republicans in national polls held steady or set a new high. After Trump dominated primaries across the Northeast on the 26th, Cruz’s support among delegates began to wobble. By May 3, Trump was able to win Indiana by 16 percentage points and knock Cruz out of the race, even after trying on the morning of the primary to link Cruz’s father, Rafael, with Lee Harvey Oswald. Cruz quit that night, followed by John Kasich the next morning.

The gain-deficit ratio has presaged another unlikely development: that the Democratic race would last longer than the Republican contest. Hillary Clinton came close to passing the 0.36 threshold this year on March 15, when she swept five big states, and again on April 26, when she won four of five in the Northeast. But she hasn’t quite left orbit, thanks to proportional delegate allocation on the Democratic side and Bernie Sanders’s persistence.

The idea of Donald Trump winning the Republican nomination seemed crazy to a lot of smart people for a long time. (Although it’s an interesting question whether Trump actually represents more of a break with his party than George McGovern did in 1972, or than Barry Goldwater did in 1964.) But plurality support matters, tending to turn into majority support. And Trump may have been following a winning path all spring.

If he could beat rival Harumafuji — himself a winner of seven Grand Tournament championships — Hakuho would win a record 36th Emperor’s Cup, about the equivalent of a 24th major in tennis or golf.⁸ If he lost, he would have to wrestle again (almost immediately) in a tiebreaker against 13-2 ozeki⁹ Kisenosato, who was waiting ringside.

The shikiri (pre-match ritual) takes several minutes. The wrestlers clap to attract the attention of the gods, lift their hands to show they are unarmed, stomp the ground to scare away demons and throw salt in the ring to purify it. They repeatedly crouch as if about to start the match and then stand up after a few moments of glaring at each other. When they are finally ready, they creep toward their starting stance.

There is no bell. The match starts with a tachi-ai (initial charge), which generally happens the instant the opponents are set.

Harumafuji lunged from his crouch, low, exploding toward Hakuho in an effort to take control of the bout early. Instead, he caught a quick palm to the face — and then air. His momentum carried him clear out of the other side of the ring, like he’d tried to bull-rush a ghost.

The match had lasted one second.

Kisenosato scowled and walked out of the ring area. Commentators didn’t quite know what to say; one of the English announcers let out a long “hmmmmm.” The crowd booed its champion.

This is not normally how a match of this scale plays out. Side-stepping an opponent’s charge is legal but considered beneath the dignity of top sumotori. The move is known derisively as a henka (変化), which translates to “change” or “changing,” while connoting the root “strange” (変). That it would be used by an all-time great in one of the most consequential matches of his career was strange indeed.

With all Hakuho has accomplished, his greatness is unquestionable, but his legacy is an enigma. It is already beyond being measured by wins and losses, or even by yusho (tournament wins) or sansho (special prizes), so incidents like this now take on particular importance. But judging him by heel turns would be reductive. The best way to measure Hakuho’s legacy is to pit it against legend.

Enter thunder and lightning.

Before Hakuho (born in 1985), before Taiho (born in 1940), before Hitachiyama (born in 1874), before Jinmaku (born in 1829), before the United States of America (born in 1776), there was Raiden.

A legend of Japan’s Edo period, Raiden set a standard for greatness in the sport that would last hundreds of years. With centuries separating the two legends’ careers, Raiden vs. Hakuho may be one of the most time-bending sports comparisons imaginable.

Fortunately, we have data.

The visual history of sumo

As far back as the 18th century, a banzuke listing each wrestler’s rank in the hierarchy of professional sumo has been made before each honbasho (official tournament), often with elaborate detail. Some have visual guides to the various wrestlers and act as a kind of program to the events; others resemble intricate box scores. These collectibles have preserved vital information about which wrestlers were involved in each tournament, including their shikona (ring names), ranks (seedings) and hometowns.

Banzuke are the backbone of sumo stats-keeping; other information such as tournament and match results that are gathered from historical newspapers or books all tie back to them. Alexander Nitschke (a German sports data nerd) has a website called Sumo Reference where he has combined banzuke information with other sources of tournament data — including by hand-parsing thousands of lower-division match results for years — to make the most comprehensive sumo data set on the internet. It includes tournament results for most contestants going back to 1761 and individual match results for bouts back to mid-1909. He has let us use that database for this article.

Below is a chart that outlines the entire recorded history of Makuuchi division (top-level) professional sumo, from the 1761 Fuyu (winter) Basho through the now-infamous 2016 Haru (spring) Basho.

Although the discipline of sumo wrestling may have existed in various forms for well over a millennium, it isn’t the sport stuck in time that it is sometimes made out to be. It has experienced controversy throughout its history. In the 17th century, the unseemly practice of samurai wrestling each other for money was banned, only to be brought back with official sanction and standardized rules.

The first known professional tournament was held in 1684, and the first sumo organizations began issuing written rankings in the mid-1700s — just in time to document the rise of sumo’s most legendary figure.

Raiden was born Seki Tarokichi in 1767 — about 100 years before the Edo period ended — and competed under the shikona of Raiden Tameemon. Raiden is a combination of “thunder” (雷) and “lightning” (電) and translates roughly to “thunderbolt.” Mentored by the first non-posthumous yokozuna, Tanikaze, Raiden was a legend trained by a legend. He went undefeated in 24 out of the 35 tournaments he entered, and despite a much shorter tournament structure that had no method for breaking ties, Raiden finished with the most wins outright in 17 tournaments and tied for the most wins in 11 more. As there were no official tournament winners until 1909, none of these are considered official “yusho” or tournament wins, but no one would top 28 tournaments (officially or unofficially) for more than 150 years.

The Thunderbolt was an absolute monster among men — 6-foot-6 and 373 pounds — large enough to physically overpower opponents of the day. His top-division win-loss record of 254-10 (96 percent) is easily the best in recorded sumo history.¹⁰ Hakuho has won 85 percent of his upper-division matches, leading modern-era wrestlers.

Raiden’s career — like Hakuho’s — didn’t pass without controversy. It’s said that on account of Raiden’s dominance, some of his favored techniques were at least temporarily banned from the sport. And for reasons that appear to be lost to history, he was never awarded the title yokozuna. The Yokozuna Stone at the Tomioka Hachiman Shrine — home of the first professional sumo tournament — has the names of every yokozuna inscribed on it, plus one: the “peerless rikishi”¹¹ Raiden.

This is the burden of Hakuho’s dominance: He is no longer competing with his peers; he’s competing with the peerless.

A quarter-millennium of Sumo evolution

Hakuho vs. Raiden isn’t a story of a sport that has stayed the same for hundreds of years, allowing us to make clean, crisp comparisons between the two champions. But it isn’t a story of a sport changing every couple of years either.

Although there have been significant structural changes — like the setting of tournaments at 15 matches long, the introduction of tiebreakers, and the treatment of yokozuna as an official rather than ceremonial rank — the sport is always fundamentally about knocking the other guy down or getting him to step out of the ring first. Many trends happen over decades or centuries, caused by whims of history that can be hard to pick up in a data set.

But some simple metrics — like wrestler height and weight — can tell a pretty interesting story. And to understand how Raiden and Hakuho match up with each other, it helps to understand how they compare physically to their eras.

Hakuho — born Monkhbatyn Davaajargal and given the shikona Hakuho Sho — is the son of a six-time Mongolian wrestling champion and Olympic silver medalist in freestyle wrestling. Despite his pedigree, Hakuho was an undersized sumo prospect — weighing only 137 pounds when he started training at age 15 — and almost went unrecruited. Although he would eventually reach 6-foot-4 and competes at around 330-340 pounds today, he is lighter and thinner than the majority of his opponents. Taller, heavier wrestlers win (a little) more often — hence sumo wrestlers tend to be, well, big. But the relationship between size and success isn’t nearly as strong as you might think, and it gets weaker if you control for division and era.¹² However, the sample sizes are large enough to pick up meaningful trends.

For this chart, I’ve compared the relative importance of height and weight for predicting top-division wrestlers’ win-loss rate in a given tournament. Values above 2 are roughly “significant” for a given five-year period.¹³

Before around 1900, height and weight had a fairly tenuous relationship with winning. It has gotten stronger in the past century, but size advantages have never been much of a guarantee of success. For a modern example: In the 1980s and 90s, Konishiki — an ozeki who topped 600 pounds — often faced off against Wakanohana, a future yokozuna who was an inch or so shorter and more than 300 pounds lighter. Konishiki went 2-8 against him.

Sumo styles can broadly be broken down into two types: Oshi-sumo, or “thrusting” style, and Yotsu-sumo, or “grappling” style. The former is about brute force and pushing your opponent out of the ring; the latter is more about forcing your opponent to the ground or using their momentum against them.

As one might expect because of their sizes, Raiden preferred the Oshi-sumo style, and Hakuho the Yotsu. The trade-off for height and weight is pretty basic: Being big makes a wrestler harder to move, but less agile; being small can make it easier for a wrestler to maneuver but leaves him vulnerable.

In the 20th century, there appears to have been a period in which larger-than-average wrestlers were more successful than they had been in the past (or are today), at a time in which the average wrestler was growing larger than ever.

In this chart, I’ve plotted the height and BMI for each of the top-division wrestlers for each tournament, colored by country of origin:

The average height of sumo wrestlers appears to have declined between the mid-1700s and late 1800s but has been rising fairly steadily since.¹⁴

In the latter half of the 20th century, this upward trend has been aided by the arrival of non-Japanese wrestlers, who have tended to be tall. Note the non-red dots on the charts; they tend to be well above the overall trend.

For BMI, we see a similar rise for all rikishi, but with a clear divergence between the tall and heavy Americans and the tall but relatively slender Mongolians.

The American (green) wrestlers, all from Hawaii and of Pacific island ancestry, have tended to be huge — both tall and hefty for their height — and had a pretty good run for a while between 1989 and 2002. Konishiki won a few tournaments and then yokozuna Akebono and Musashimaru solidly contended for top honors (becoming the first two non-Japanese yokozuna in the process).

But the Mongolians — who have had four yokozuna — tend to be less hefty than their Japanese counterparts, defying the trend of the past 50 years.

Compared with the other top-level sumo wrestlers who have been active during his career, Hakuho, at 6 foot 4, is about 3 inches taller than average, but his top tournament weight (in our data) of 340 pounds is 5 pounds lighter than average (putting his BMI well below par).

Raiden, on the other hand, was well above average in height, weight and BMI. At 6-foot-6, he was just about 6 inches taller than his typical opponent, and his 373-pound weight gave him an 80-pound advantage. But there’s an important factor here: Relatively speaking, Raiden isn’t that much bigger than Hakuho. Raiden was about an inch and a half taller and 25 to 35 pounds heavier. Hakuho, by virtue of being less massive than many opponents, is especially strong and/or skilled for his size. In other words, because of the size difference across eras, Hakuho has the advantages of a smaller, more agile fighter without the disadvantage of being that much smaller than Raiden.

Note that this is a minor variation from the standard “people get better over time” argument, because it applies relative to their era. It’s not only that Hakuho has been as dominant as he has been in a likely tougher era, but also that his dominance is a product of qualities (strength/speed/skill) that also would be likely to advantage him against Raiden.

The growing international talent pool

If a hypothetical tale of the tape across a couple of centuries is a little too abstract for you, consider that the dramatic shift in the balance of power in sumo’s demographics that has been taking place of late also has implications for our matchup.

Before 1972, no non-Japanese wrestler had ever won a basho. The first was Takamiyama, a Hawaiian sekiwake (the third rank, behind yokozuna and ozeki) who otherwise had a relatively undistinguished career as a sumotori. But he then founded the Azumazeki stable — one of the regimented groups of wrestlers who live and train together and to which all active rikishi belong. There he recruited and trained Chad Rowan — a former high school basketball all-star from Hawaii — who took the shikona Akebono, became the first non-Japanese yokozuna and won 11 Emperor’s Cups.

Today, international wrestlers have taken over the sport. In January 2016, then-31-year-old Japanese ozeki Kotoshogiku won his first tournament. This might have been an unremarkable event, except that it was the first tournament won by any Japanese wrestler since January of 2006. Of the 58 tournaments in between, 56 were won by Mongolians; the other two were won by a Bulgarian (Kotooshu) and an Estonian (Baruto).

Here’s how this has played out since 1970:

Note that Japan’s share of champions will improve by at least a tick in 2016, while Mongolia’s will decline, after the country’s three-year stretch of winning all the tournaments.

Mongolia has had all this success with only a small fraction of the sport’s wrestlers — around a quarter of those in the top (Makuuchi) division and less than 5 percent of those who compete overall. This likely is because the Nihon Sumo Kyokai (the sport’s governing body) limits each stable to one non-Japanese wrestler, so the standards for foreign prospects are extremely high.

This carries some likely implications:

Most obviously, the non-Japanese pool of sumo talent is likely growing faster than the number of slots for non-Japanese talent. This probably advantages Hakuho’s strength of competition in our matchup because it implies that he could be the best of a much bigger talent pool than sumo wrestlers of the past. It also implies that while the non-Japanese wrestlers make the talent pool stronger than it was, limited roster slots for them keep it weaker than it could be.

On the other hand, the sumo talent from Japan may be declining. Sumo requires major physical (putting on weight) and time (years of non-stop training) commitments. Sumotori lead rigid and structured lifestyles year-round, the potential for fame and fortune isn’t that great, and Japan has an advanced economy that may afford better opportunities to athletic Japanese youth.

But even a relatively weak Japan today could be stronger than a relatively strong Japan more than 200 years ago. The population of Japan is now about five times the size of what it was when Raiden was active, making the pool of potential sumotori that much richer.¹⁵

Fish scales of greatness

There is perhaps no more intricate ritual among sports fans than debating the relative merits of greats across eras.

Over time, athletes get stronger, faster and better-trained, and benefit from accumulated institutional knowledge. NFL kickers, for example, have been getting better at a nearly constant rate for 80-plus years. So we have meta-debates about whether athletes should get more credit for dominating the competition in an earlier, top-heavy era or for excelling in a mature sport with a broader talent pool. For example, who’s the more impressive outlier, Dan Marino or Peyton Manning?

If we want to imagine athletes from different times competing, do we assume they would have enjoyed all the advantages and disadvantages of the comparison era, or do we focus on strict time-traveling scenarios? And, crucially, in time-traveling scenarios, are you bringing present-day athletes into the past, or are you snatching past legends and bringing them to the present?

From what we know about his career, Raiden won more often than Hakuho on a bout-by-bout basis. Yet though Raiden’s career was longer in years, it was short on matches. Here’s every Makuuchi division sumo career for comparison:

Tournaments grew in size, length and quantity throughout the 1900s, and in 1958, sumo adopted the current structure of six grand tournaments per year (one every two months), with 15 matches each. Both Raiden and Hakuho are clearly the top wrestlers in their given eras, but how good are they relative to how good we expect top wrestlers in their eras to be?

For this chart, I’ve plotted historical win percentages for wrestlers ranked ozeki or higher, with the number of years they competed at those ranks represented by bubble sizes:

Also, each bubble is colored to show how many “wins above replacement ozeki” (WAROZ) each wrestler would be expected to win over the course of their career, based on their win percentage relative to their era and projecting as if they’d wrestled 90 bouts per year as healthy wrestlers do today. By this metric, Hakuho leads all with 182 WAROZ (and counting), with second-place going to Tachiyama (who had 115 wins and eight ties in 128 bouts between 1909 and 1918) at 175. Raiden finishes eighth with 143 WAROZ.

Here we can see that top ozeki winning a huge percentage of their matches seems to have been almost expected hundreds of years ago. This is consistent with a number of things we know about sumo tournaments back then: With less focus on “winning,” they were a bit more like exhibitions. And we know that opponents were sometimes literally picked out of the crowd.¹⁶ Hakuho, however, competes in an environment in which losses for top-level wrestlers are considerably more common than they were in Raiden’s time, but he has maintained an extremely high win percentage nonetheless.

Behold the henka

Yokozuna face a lot of pressure to retire the instant they start to decline. It’s considered dishonorable to hold the rank of yokozuna and not be among the best in the sport.¹⁷ So although we’ve made the argument that Hakuho might have an advantage over Raiden in both prowess and résumé, recent events raise a third, more fraught point of comparison: legacy.

After Hakuho’s win by henka at the Haru basho, Mark Buckton of The Japan Times — a former amateur sumo wrestler who has covered professional sumo for 18 years — called for the White Peng’s exit. Addressing Hakuho directly, he writes:

At its lowest ebb, following the hazing death of Tokitaizan and former yokozuna Asashoryu feigning injury the only yokozuna worth his salt in both performances on the dohyo and behavior off it was yourself.

True, you are still the best there is in a mawashi.

And that is how you should be remembered.

Not as a man who resorts to a final day henka against a fellow yokozuna, on his way to yusho No. 36.

Go now and you go in true Japanese fashion, falling on your sword for that Day 15 performance so unworthy of your name.

In a phone interview, Buckton said that he thought Hakuho’s henka was disgraceful and that he was confident most Japanese sumo fans felt the same way. He said he believes the move was akin to an act of desperation — Hakuho sees his skills slipping and is resorting to dirty tactics in a last-ditch effort to stay on top of a sport that isn’t merely competitive exhibition but has its roots as a martial art in Shinto.

That’s fair enough. But for cold-blooded empiricists obsessed with win-maximization, this may all seem strange. If henka aren’t banned, not using them is just bad game theory, right?

Unfortunately, henka are hard to analyze with data. They aren’t considered a winning move themselves, and only winning moves are recorded. Hakuho’s win was scored as a tsukiotoshi (“thrust down”). What even constitutes a henka is not clear-cut — particularly in instances in which they fail.

However, what little evidence we have suggests that they work. Lon Howard of Sumo Fan Magazine attempted to crowd-source some henka data by having readers nominate matches that contained possible henka and then asking the readership to vote on whether they actually were. Overall, the possible henka led to victory 63 percent of the time; among a subset of moves that voters were certain were henka,¹⁸ that figure rises to 92 percent.

Although that data isn’t conclusive, it makes sense. If you’re playing rock-paper-scissors and your opponent does nothing but throw rock for 250 years, throwing paper may be very effective.

Stigma-based policing of the sport’s standards is defensible. Normalizing the henka might fundamentally change the sport’s dynamics too much, but outlawing it may create a havoc of gray areas. But such a defense should anticipate that sternly discouraging the move may not prevent its selective employment by a wily rikishi with a New England Patriots-style commitment to winning.

In a tear-soaked post-match interview, Hakuho appeared to express regret for the tournament ending the way it did. But he did not clarify his side-step’s strategic underpinnings, such as whether it was planned, or a response to something he saw while the wrestlers were getting set, or a reflexive reaction to Harumafuji’s charge itself.

But regardless of premeditation, consider the story told on the faces of the competitors:

Snatch Hakuho from his peak, shove him into your DeLorean and send him into any point in the past — including the 1790s — and he will almost certainly be a favorite to stay in the ring, on his feet, against any human or human-like god-giant that he runs into. We know this.

But considering his unprecedented domination of his competition, his broad skill set and, yes, even his controversial willingness to push boundaries in pursuit of victory, he can likely match any sumotori legend for legend as well.

See more: A History Of Sumo, an interactive graphic by FiveThirtyEight showing centuries of sumo wrestlers, and The Sea of Crises, a 2014 Grantland article on sumo and Japanese culture.

CORRECTION (May 13, 5:30 p.m.): An earlier version of this article included a photograph that was incorrectly described as portraying Hakuho. It has been replaced with the correct photo.

Many births are scheduled, either as induced deliveries or cesarean section. And given the choice, lots of parents would rather not take their chance with a date that delivers a double whammy of superstitious bad luck, tying together longstanding fears about Fridays and the number 13.

Births on the 13th of the month are lower than you’d expect, but especially on Fridays; the effect is smallest when the 13th falls on a weekend, when delivery wards are staffed more thinly and tend to schedule fewer births.¹⁹

As I wrote a few months ago, lots of parents-to-be try to avoid Feb. 29 births so that their children won’t have a birthday only once every four years. Reasons given on parent forums for avoiding Friday the 13th are vague. One mom wrote on a pregnancy website forum, “The office lady said yea sorry it’s on a bad luck day if I can change it I will. Since then it’s been bugging me. I’m not superstitious at all but her saying that just bugs me.” Another, who said she isn’t superstitious, wrote on another site, “When I asked the [obstetrician] about scheduling my [cesarean section] on the 13th, he just laughed and said he didn’t think the OR would be booked :)”

The belief that Friday the 13th births are bad luck isn’t universal. “Friday the 13th has become a very good day in this household,” said one mom on the second parent forum who had given birth on a Friday the 13th and had another such birthday in her family. Neel Shah, assistant professor of obstetrics and gynecology at Harvard Medical School, said by email that “our schedule for planned cesareans and planned inductions of labor looks full” for this Friday.

In 2012, computational scientist Aki Vehtari and statistician Andrew Gelman developed a more complex method for teasing out calendar birth effects, separating monthly patterns and long-term trends from attempts to avoid or land on certain dates. Their findings based on U.S. births data from 1969 to 1989 — an extension of a previous analysis by other researchers covering the birth effects of Valentine’s Day and Halloween — made the cover of a textbook they co-wrote with several other authors, “Bayesian Data Analysis” (third edition).

I sent Vehtari and Gelman the more recent births data, from 2000 to 2014, and they reran the analysis. They found that the more recent generation of parents had more say on when they gave birth: The effect for the 13th and for other key dates typically was twice as high as it had been in the 1970s and 1980s, as we’d expect since births were scheduled less often then. They also ran an analysis specifically for Friday the 13th and found results consistent with ours. Here’s their finding over the whole calendar; notice that Christmas and other holidays suppress births far more than leap days and the 13th of the month do.

Andrew Flowers contributed analysis.

Over the last few months, the lab-testing startup Theranos has endured a relentless stretch of bad publicity, morphing from a health tech darling to a Silicon Valley cautionary tale. It started last October, when The Wall Street Journal published an investigation of the company’s much-hyped technology, which promised it could run a host of lab tests (including those for diabetes, high cholesterol and prostate cancer) from just a few drops of blood taken from a finger. Its proprietary technology and lower prices, the company said, would democratize blood testing and encourage its use for routine health monitoring. But the Journal reported that the proprietary device wasn’t all it was cracked up to be, and that the company was running most of its tests on conventional lab machines. Since then there has been news of dissolved business partnerships, problems with regulators, criminal and civil probes and just this week, personnel changes. Founder and CEO Elizabeth Holmes, the Stanford dropout who was the subject of much positive media coverage before the WSJ’s report, could be banned from the industry for two years.

Much of the debate over the last few months has been about whether Theranos’s technology can actually do what the company has said it can. But there’s a dubious assumption at the heart of Theranos, arguably just as damning as the questions about its technology. Theranos wants us to believe that ostensibly healthy people can get healthier by having more tests. But the science suggests that is far from true.

To see why, let’s go deep into Holmes’s pitch for why Theranos was so important. Let’s use her 2014 TEDMED talk, which has been viewed more than 380,000 times, as a proxy for her elevator pitch:

We define diagnosis today as the determination of the presence of disease from its signs and symptoms. Yet diseases often begin so much earlier than when symptoms first appear. We see a world in which every person has access to actionable health information at the time it matters. A world in which no one ever has to say, “If only I’d known sooner.”

It seems obvious: Finding a disease as early as possible would lead to fewer deaths than finding it late. But as more and more research is showing, it’s not as simple as going exploring in healthy people to see what turns up, then treating what you find. “The reservoir of abnormalities is bottomless,” said Dr. Brenda Sirovich, co-director of the Outcomes Group at the VA Medical Center in White River Junction, Vt. “And we don’t know anything about what those things mean in an asymptomatic vacuum.”

For example, levels of prostate-specific antigen in the blood are elevated in men with prostate cancer, so a logical leap suggests that we might be able to detect nascent disease by looking for it in seemingly healthy men. But the PSA test (available from Theranos on its own or as part of a set of routine men’s health tests) is questionable as a way to screen for prostate cancer. Screening with PSA provides at most a small benefit in preventing mortality from prostate cancer, and some studies suggest it harms more men than it helps through the side effects of treatment, which can include impotence and incontinence.²⁰

The effectiveness of screening for a given disease before signs and symptoms appear depends on a host of conditions, said Dr. John Ioannidis, director of the Stanford Prevention Research Center — including whether there’s an effective treatment for whatever is found, and whether people will fare better if they get treatment without waiting for symptoms. He added that a successful screening test needs to be accurate, without too many false positives or false negatives.

But depending on the prevalence of a disease or condition in a given population, false positives can outnumber true positives, even for a test that’s quite accurate.

The wider the pool of people being tested, the greater the chance of false positives, which is why screening guidelines generally limit the population to be screened. The more independent tests you do at once, each with its own chance of error, the larger the chance that at least one of those tests produces an incorrect result, said Rebecca Goldin, director of STATS.org and a professor of mathematical sciences at George Mason University.

Screening may also find disease that would never have caused a problem if it had been left alone — what researchers call “overdiagnosis.”²¹ “There are a zillion things that are a disaster to screen for,” said Ioannidis. Last year, he was an author of a study that reviewed the evidence behind screening for 19 potentially deadly diseases²² and found it was “uncommon” for targeted screenings to lead to reductions in death from the disease being screened.

Holmes’s talk also advocates that individuals should have more power to order blood tests on their own:

And today I can go buy a deadly exotic animal, a venomous viper, a military truck or armored vehicle … but I can’t order a blood-based pregnancy test or an allergy test because that could be dangerous. God forbid I stop eating peanuts.

She elaborates on this point in a 2014 New Yorker profile, noting that Theranos’s direct-to-consumer vision would require changes to state laws and regulations, some of which prohibit blood tests without a prescription.

Holmes doesn’t get into details about the full range of tests that the company would like to see available without a prescription or expert guidance. (Theranos didn’t respond to emails requesting comment.) Other companies are also pursuing this direct-to-consumer vision. But there are reasons people generally can’t order tests themselves. For one thing, some screening tests merit a discussion ahead of time about whether the potential benefits outweigh the potential harms.²³

Tests are also hard for consumers to interpret. Few lab results are inherently binary. “Very few blood tests give you a ‘Yes, you have this condition,’ or ‘No, you don’t,’” said Dr. Kenny Lin, an associate professor of family medicine at Georgetown University Medical Center. Context — symptoms, personal and family medical history — is essential to interpret those results. Dr. Eleftherios Diamandis, division head of clinical biochemistry at Mount Sinai Hospital in Toronto, wrote in a 2015 opinion paper about Theranos that a layperson whose PSA value was 20 micrograms per liter “will assume, based on statistics, that he would have a more than 50 percent chance of harboring prostate cancer; and ask for a biopsy.” But if his PSA was 1 microgram per liter a few days earlier, he likely has benign prostatitis, not cancer.

Even something as seemingly straightforward as the allergy test Holmes mentions is fraught. A 2015 study found blood-based allergy tests in kids usually resulted in misdiagnosis and overly restrictive diets. There are real consequences to telling people they are allergic to things they aren’t.

One other idea is central to Holmes’s talk: that giving people more information about their risk of disease will cause them to make meaningful and beneficial changes.

When individuals have access to the information about their bodies, they can begin to change outcomes. Type 2 diabetes alone, which drives 20 percent of our health care costs, can be reversed through changes in lifestyle, in diet, in exercise. Yet today there’s 80 million Americans who are prediabetic and 90 percent of them don’t know that they are.

Certain people probably are motivated to make positive lifestyle changes merely by getting more comprehensive information about their health. But in the aggregate, data alone doesn’t seem to fuel better decisions. For example, almost 35 percent of American adults are obese, which is likely quite apparent to them, yet many have great difficulty losing weight. A review of studies published in March concluded that communicating genetic risk for diseases does not change people’s health behaviors, including smoking, diet, exercise, alcohol use and sun protection. And a study published last year found that screening for Type 2 diabetes didn’t change total physical activity, smoking habits or alcohol consumption.

As for prediabetes, while there is an awareness campaign to identify those who have it (about 86 million, according to the Centers for Disease Control and Prevention), there’s little evidence that that doing so will change outcomes. And identifying someone as “sick” can change self-image and cause stress, even though most people with prediabetes will not actually develop diabetes, said Gabriela Spencer Bonilla, who conducts health services research at the Mayo Clinic. It will also funnel millions more people into lifestyle management programs that are already strained by the needs of people with full-blown diabetes.

Not all of Theranos’s vision is misguided. Making lab tests cheaper, expanding access to tests used for diagnosis, and reducing the pain of traditional blood tests are “clearly worthy goals,” Ioannidis wrote in a critical look at Theranos published last year. But the vision of giving everyone widespread access to more blood tests in the belief that more information is always better is naïve at best, and harmful at worst.

Mull it over on your commute, dissect it on your lunch break, and argue about it with your friends and lovers. When you’re ready, submit your answer using the form below. I’ll reveal the solution next week, and a correct submission (chosen at random) will earn a shoutout in this column. Important small print: To be eligible, I need to receive your correct answer before 11:59 p.m. EDT on Sunday — have a great weekend!

Before we get to the new puzzle, let’s return to last week’s. Congratulations to 👏 Enrique Treviño 👏 of Lake Forest, Illinois, our big winner. You can find a solution to the previous Riddler at the bottom of this post.

Now here’s this week’s Riddler, a cocktail puzzle that comes to us from a philosophy professor who wishes to remain anonymous. Cin cin!

It’s Friday. You’ve kicked your feet up and have drunk enough of your martini that, when the conical glass (🍸) is upright, the drink reaches some fraction p of the way up its side. When tipped down on one side, just to the point of overflowing, how far does the drink reach up the opposite side?

To submit your answer, click here.

Need a hint? You can try asking me nicely. Want to submit a new puzzle or problem? Email me.

And here’s the solution to last week’s Riddler, concerning the buttons pushed in a crowded elevator.

Given N people equally likely to press any one of M elevator buttons, you can expect M-M(1-1/M)^N of the buttons to be lit up when the elevator begins its ascent. Here’s one way to get there: First, consider the probability that a given button is not pushed by anyone. The probability that any one rider doesn’t select a given floor is (M-1)/M, so the probability that a given floor is selected by no one is ((M-1)/M)^N. Put another way, the probability that any given floor is pressed by someone is 1-((M-1)/M)^N. This is true for all the buttons, independently of one another, so the expected number of pressed buttons is M multiplied by that probability, or M-M((M-1)/M)^N. A little rearranging for simplicity’s sake and we arrive at our answer: M-M(1-1/M)^N.

You can see a couple of other approaches at the blog of Laurent Lessard, and Andrew Plumb cooked up a nifty elevator simulator. The expected fraction of the buttons pushed, as a function of M and N, looks like this:

Some great extensions this week, too. Randi Goldman turned the problem upside down, and explored how the number of people affected long, Tower of Terror-style elevator drops.

In his answer submission, Don Barkauskas noticed cleverly that if riders are willing to walk one flight of stairs, and so won’t press a button if the button for an adjacent floor is already pressed, the problem morphs into the misanthropic neighbors Riddler!

But the 🏆 Coolest Riddler Extension Award 🏆 this week goes to Seth Weinberg. Seth writes: “My extension of the elevator problem is to answer the age-old question: ‘Who is worse to be on an elevator with, an obnoxious kid who pushes all of the buttons or a bunch of adults who are glued to their phones?’” With some probability p, an obnoxious kid presses all the buttons right before he exits the elevator, while a phone-glued adult might miss his floor and have to push his button again. For sparsely populated elevators, the kid is the bigger threat, but for crowded elevators, it’s the phone-obsessed adult you’ve got to watch out for. Here’s Seth’s illustration:

Happy Friday the 13th, and may your weekend be un-obnoxious and phone free. It’s beautiful outside!

U.S. manufacturing jobs, I argued a few weeks ago, are never coming back. But that doesn’t stop politicians from talking about them. Donald Trump scored his knockout blow in Indiana in part by railing against the decision by Carrier, a local air-conditioning manufacturer, to shift production to Mexico. Bernie Sanders and Hillary Clinton have sparred throughout their race over who would best protect manufacturing jobs. And the man they are all trying to replace, President Obama, pledged during his reelection campaign to create a million manufacturing jobs during his second term; he’s still about 700,000 jobs short of that goal.

Candidates talk about manufacturing because of what it represents in the popular imagination: a source of stable, well-paying jobs, especially for people without a college degree. But that image is rooted more in nostalgia than in reality. Manufacturing no longer plays its former role in the economy, and not only because there are far fewer factory jobs than in the past. The jobs being created today often pay less than those of the past — sometimes far less.

A new report this week from the Labor Center at the University of California, Berkeley, found that a third of production workers — non-managers working on factory floors and in related occupations — earn so little that their families receive some form of public assistance such as food stamps or the Earned Income Tax Credit. Many of those workers are temps, who account for a growing share of factory employment. The median wage for a manufacturing production worker, according to separate data from the Bureau of Labor Statistics, was $16.14 an hour in 2015, below the $17.40 an hour for all workers.

On average, manufacturing jobs still pay better than most jobs available to people without a college degree. The median manufacturing worker without a bachelor’s degree earned $15 an hour in 2015, a dollar more than similarly educated workers in other industries.²⁴ But those averages obscure a great deal of variation beneath the surface. Average manufacturing wages are inflated by high-earning veterans; newly created jobs tend to pay less. And there are substantial regional variations. The average manufacturing production worker in Michigan earns $20.80 an hour, vs.$18.86 in South Carolina, according to data from the Bureau of Labor Statistics.

Why do factory workers make more in Michigan? In a word: unions. The Midwest was, at least until recently, a bastion of union strength. Southern states, by contrast, are mostly “right-to-work” states where unions never gained a strong foothold. Private-sector unions have been shrinking across the country for decades, but they are stronger in the Midwest than in most other parts of the country. In Michigan, 23 percent of manufacturing production workers were union members in 2015; in South Carolina, less than 2 percent were.²⁵

Unions also help explain why the middle class is healthier in the Midwest than in the Southeast, where manufacturing jobs have been growing rapidly in recent decades. A new analysis from the Pew Research Center this week explored the state of the middle class in different parts of the country by looking at the share of households making between two-thirds and double the national median income, after controlling for the local cost of living. In many Midwestern cities, 60 percent or more of households are considered “middle-income” by this definition; in some Southern cities, even those with large manufacturing bases, middle-income households are now in the minority.

Even in the Midwest, however, unions are weakening and the middle class is shrinking. In the Indianapolis metro area, where the Carrier plant Trump talks about is located, the share of households in the middle tier of earners has shrunk to 54.8 percent in 2014 from 58.9 percent in 2000. And unlike in some parts of the country, the decline in the middle class there has been primarily driven by people falling into the lower tier of earners, not moving up. The Carrier plant, where workers make more than $20 an hour, is unionized.

Cause and effect here is complicated. Unions have been weakened by some of the same forces that are driving down wages overall, such as globalization and automation. And while unions benefit their members, economists disagree over whether they are good for the economy as a whole. Liberal economists note that overall wages tend to be higher in union-friendly states; conservative economists counter that unemployment tends to be higher in those states, too.

But this much is clear: For all of the glow that surrounds manufacturing jobs in political rhetoric, there is nothing inherently special about them. Some pay well; others don’t. They are not immune from the forces that have led to slow wage growth in other sectors of the economy. When politicians pledge to protect manufacturing jobs, they really mean a certain kind of job: well-paid, long-lasting, with opportunities for advancement. Those aren’t qualities associated with working on a factory floor; they’re qualities associated with being a member of a union.

#FedSoWhite

When the Federal Reserve’s policy-making Open Market Committee meets next month to decide whether to raise interest rates, every one of the 10 voting members will be white. Eleven of the 12 regional Fed bank presidents, who rotate voting responsibility, are white, and not one is black or Latino. (Minneapolis Fed President Neel Kashkari is Indian-American.) The Fed does a bit better when it comes to gender balance — Chair Janet Yellen is a woman, as are three other voting FOMC members. But overall, the people making U.S. monetary policy are disproportionately white men.

Does that matter? More than 100 members of Congress think so. In a letter to Yellen on Thursday, 11 senators and 116 members of the House of Representatives — all of them Democrats — wrote that they are “deeply concerned that the Federal Reserve has not yet fulfilled its statutory and moral obligation to ensure that its leadership reflects the composition of our diverse nation.” The letter is only the latest effort to draw more attention to the Fed’s lack of diversity: A report earlier this year from the liberal Center for Popular Democracy highlighted the issue, and several members of Congress also asked Yellen about it when she testified on Capitol Hill in February. (Bernie Sanders signed the letter. Hillary Clinton, who wasn’t eligible to sign since she isn’t in Congress, said she agreed with the message.)

It isn’t clear whether policy would be any different if the Fed were more diverse. But the letter writers and their allies argue that at the very least the Fed’s lack of representation could be skewing the way policymakers view the economy. By law, the Fed must balance two competing goals: maintaining stable prices (which the Fed defines as inflation of about 2 percent per year) and promoting full employment. In recent months, Yellen and her colleagues have begun the process of raising interest rates — concluding, in effect, that with the unemployment rate down to 5 percent, the “full employment” part of their mandate is largely complete. But the unemployment rate for African-Americans was 8.8 percent in April, as high as the white unemployment rate was in the middle of the recession. For them, “full employment” remains a long way off.

The long road back

Last week I noted that Americans who graduated from college during the recession are still struggling to make up for the slow start to their careers. The Wall Street Journal this week told the even more harrowing tale of people who lost jobs during the recession, many of whom still bear deep financial and psychological scars.

That isn’t surprising. Losing a job is a significant setback in any context, but it is far worse when a bad economy makes it hard to get back to work quickly. People who are laid off in a recession are far more likely to become unemployed for more than six months, which can then make it harder to find a job even once the economy improves. One estimate cited by the Journal found that people who lose jobs during a recession continue to make 15 to 20 percent less than their peers who kept their jobs, even a decade or more after the recession ended. And that is just in the typical recession; the most recent downturn was far worse.

Number of the week

Just under 8 million Americans were looking for work in March, and employers had 5.8 million jobs available to be filled. Economists look at the ratio of those numbers as a gauge of the health of the labor market, and by that measure, the economy is looking good: There were 1.4 unemployed workers for every open position in March, the fewest since 2001.

Don’t take the workers-per-job ratio too literally, though. The official definition of “unemployment” leaves out plenty of people who want jobs, and the government count of job openings is also incomplete, counting only positions for which companies are actively recruiting. But alternative measures of both unemployment and openings show the same trend: There are more jobs and fewer workers to fill them. That’s good news for workers who want jobs, and also for those who already have them — at some point, companies that want to attract workers will have to start offering higher pay.

Elsewhere

Americans are having fewer babies. Janet Adamy looks at the causes and consequences of the U.S. “baby lull.”

Eduardo Porter argues the government should do more to create good jobs for those displaced by the transition toward a service-based economy.

Timothy O’Brien, who saw Donald Trump’s tax returns as part of a lawsuit a decade ago, provides some hints as to what voters might learn if Trump ever releases the documents publicly.

Lam Thuy Vo and Josh Zumbrun dive into the data on the jobs created since the start of the recession.

In much of the country, poor people don’t have access to broadband internet, according to a Center for Public Integrity investigation.

15 medal winners

Grigory Rodchenkov, a doctor who ran Russia’s anti-doping testing laboratory during the Sochi Olympics, has come forward with claims that he provided banned substances to dozens of Russian athletes competing at the games, including 15 medal winners. [The New York Times]

Nearly 40 percent

It appears that psychologists are just as susceptible to psychological tricks as the rest of us: After the Center for Open Science announced that it would award badges to scientific papers that used transparent methods and shared their data, the percentage of such papers appearing in the journal Psychological Science jumped tenfold to nearly 40 percent of papers published. You get a gold star, Center for Open Science. [FiveThirtyEight]

55-22

The Brazilian Senate voted 55 to 22 to suspend and impeach President Dilma Rousseff over allegations of manipulating finances. The decision comes shortly before Brazil is set to host the Olympics this summer. [BBC]

$187 million

The Bill and Melinda Gates Foundation sold its entire $187 million stake in BP. [The Guardian]

$800 million

The U.S. activated an $800 million ballistic missile defense site in Romania on Thursday. The U.S. and NATO argue that the shield is meant to prevent attacks from rockets originating in Iran, but Russia is peeved. [Reuters]

$63 billion

How much money would be saved in health care costs next year if 1 in 10 U.S. smokers surreptitiously stopped smoking, according to a study from the University of California, San Francisco. [Science News Journal]

If you haven’t already, you really need to sign up for the Significant Digits newsletter — you can be the first to learn about the numbers behind the news! How great does that sound? You should totally do it.

And if you see a significant digit in the wild, send it to @WaltHickey.

Depending on whom you ask, it’s also a hotbed of geopolitical intrigue. Participating countries rank all the acts, which leads to suspicions that Europe’s factionalism rules its pre-eminent talent show. Russian twins on a teeter-totter were booed in 2014 after Russia invaded Crimea, for example. Will their acts keep being punished for as long as Russia holds on to Ukraine’s territory? Have the threats of a Grexit and now a Brexit doomed Greece and the U.K.’s chances with their European peers? And what will this year’s rule change mean for these alleged feuds and alliances?

An analysis of Eurovision voting published in the Journal of Artificial Societies and Social Simulation in 2006 by Derek Gatherer, a former lecturer at Liverpool John Moores University, compared the voting results to ones generated in random simulations to see whether certain nations agreed more often than chance would suggest. And sure enough, Gatherer found past voting patterns suggested that countries often did appear to be voting in blocs (among the most powerful lately: what he calls the Balkan Bloc, including nations such as Croatia, Macedonia and Slovenia; and the Viking Empire of Sweden, Denmark, Norway, Iceland and Estonia). But that may not be a smoking gun. Neighbors may vote together because they share similar taste in music, not because they’re nursing grudges over who invaded whom in the 1800s.

Still, some countries’ residents remain convinced that the fix is in. According to a 2013 poll of seven European nations by YouGov, Brits were the most likely to believe that other regions were conspiring to deny them victory.²⁸ Seventy-five percent of Great Britain’s residents thought that politically motivated voting kept the best countries from winning Eurovision. Only 33 percent to 48 percent of residents of six other countries²⁹ were similarly pessimistic.

This year offers better opportunities than ever for post-loss carping and conspiracy theories, because the scoring rules are changing. Previously, the Eurovision score a country awarded was a combination of two rankings — one given by a panel of judges from that country and one from its residents watching at home. Those two were averaged into one overall score for the performer. (The same process would happen with dozens of other countries, all evaluating the same performance.)

At the end of the finals, each country takes turns announcing its top 10 performers, along with the points awarded. So France would stand up and say its top 10 was Denmark, Holland, Switzerland and so on. The trouble is, this made for boring TV. It was often clear early who would win, as favorites emerged.

This year, Eurovision changed the rules in order to introduce a little more suspense. Now, the judges’ scores and the home voters’ scores aren’t averaged together. The scores from the judges will still be announced one by one, but the people’s scores from every country will be added together and tacked on at the very end.

This is basically Eurovision’s equivalent of the snitch in Quidditch: A huge number of points being awarded at the very end means anything could happen.

I wanted to know whether these new rules would change who wins Eurovision (instead of just the drama of the process of finding out). So I reran the results from 2014’s and 2015’s competitions, using the new scoring scheme.³⁰

The good news for the integrity of Eurovision is that the winner didn’t change under alternative rules. But there were some notable shifts. In 2015, the rules change would have bumped Russia from second place to third. And the United Kingdom’s aggressively art deco rendition of “Still In Love With You” would have gone from a forgettable fourth to last to dead last.

In 2014, the top five would have stayed in the same order, but Malta’s “Coming Home” (which I would have assumed was from the Country Music Awards) would have jumped 10 slots from 23rd to 13th, while Denmark’s “Cliché Love Song” (somehow even worse than the name suggests) would drop out of the top 10 to 14th. Those big swings tend to happen when the judges and the people disagree. For example, Malta was ranked in the top 10 by 22 nations’ judging panels, but only four countries’ at-home voters. Under the old rules, averaging the judges’ and the people’s scores dragged Malta down.

So here’s your cheat sheet for blaming the new rules if your favorite entry gets shafted. Just give a very European, ennui-laden sigh and say that judges and everyday people should have to mingle, and so should their scores. But now either the snooty elites or the xenophobes at home have too much influence over the outcome.

To make this complaint in true Eurovision style, deliver it while on a unicycle, dressed like a disco cadet or, failing that, as a duet with a hologram of yourself.

Scherzer also gave up two home runs in the game. That means that his performance would be considered good, but not necessarily great, by single-game starting-pitcher metrics like Bill James’s game score, or the custom variant we use in our own Elo rating algorithm. Our ratings even adjust for the quality of competition a pitcher faces, and they still rank Scherzer’s gem 119th among the 212 9-inning games with 15 or more strikeouts since 1913.

(As measured by game score, Scherzer’s no-hitter over the Mets last October — his second no-hitter of 2015 alone — was a far more impressive accomplishment.)

Scherzer also threw his 20 Ks in an era when strikeouts are more common. So far this season, Tiger batters have struck out in nearly a quarter of their plate appearances, fourth-most in MLB. Based on that number and the fact that Scherzer faced 33 Tigers Wednesday, we’d have expected an average pitcher to sit down 8.2 Tigers on strikes, meaning Scherzer struck out 11.8 more batters than expected. Among historical 15+ K games, that number also ranks surprisingly low, checking in at No. 39 since 1913:

However, for all the ways in which Scherzer’s 20-K game was strange and perhaps less impressive than it seemed at first glance, his command of the strike zone was impeccable. He didn’t walk a batter, and although he gave up six hits and two home runs, Deadspin’s Tom Ley makes the great point that those blemishes were a product of aggressive pitching. Scherzer threw a ton of strikes — only 23 of his 119 pitches failed to find the zone — and that’s the game plan of somebody who’s challenging batters to hit his stuff. Some of them did, but most were sent back to the dugout shaking their heads.

It had been a long time since the last 20-K game, and the game has changed a lot since Randy Johnson struck out 20 Cincinnati Reds in 2001. Modern pitch-counting managers won’t let today’s versions of Roger Clemens stick around for 151 pitches, for instance. So maybe Scherzer’s combative plan is the new path to huge strikeout games — even if that means they aren’t as statistically impressive as similar outings from the past.

But on June 8, 2000, Cleveland’s powerful batters looked like a bunch of grade-schoolers facing the hard-throwing kid who was held back a year, reduced to scrounging for baserunners and hoping to string together a few lucky hits. Pedro Martinez was on the mound, and that meant opposing hitters didn’t stand a chance.

Against Cleveland, Martinez pitched eight innings of one-hit, shutout ball, striking out 10 batters and walking only one. It wasn’t even his best outing of the season to that point — on May 12, he’d struck out 15 Orioles, and walked none, in a complete-game shutout — but it was a classic example of how unhittable Martinez was in his prime. When Hall of Famer Roberto Alomar reached base in the first (on a throwing error by the catcher after Alomar tapped a weak dribbler in front of home plate), he was Cleveland’s sole baserunner until late in the 5th inning. In six separate innings, Martinez set down the Indians in order, 1-2-3. As if to add emphasis, he capped off four of those perfect frames with a strikeout to retire the side.

Nobody quite knew it at the time, but the game had long-lasting historical significance as well. According to the pitching component of our new Elo ratings, Martinez’s performance against Cleveland stands as the absolute peak moment for any starting pitcher since 1911.³¹ Here’s a table of the highest historical pitcher peaks (one per pitcher)³² from the introduction to our MLB Elo ratings:

Our Elo algorithm works by assigning each starting pitcher a Pitcher Score rating representing the expected effect he’ll have on opponents’ hitting in his next start. Rookie pitchers start with a relatively low Pitcher Score, but they can build it up by posting strong starts according to the game score formula, which rewards pitchers for quality performances (with a slight bonus for greatness in the fielding-independent categories of strikeouts, walks and home runs).³³

When Martinez made his debut in 1992, Boston’s Roger Clemens had the highest Pitcher Score of any active player in baseball. A few years earlier, Clemens had even briefly come within striking distance of the all-time leader — the underappreciated Dazzy Vance, who peaked four starts into his 1929 season and had never been surpassed in the more than six decades since — and he was still pitching at one of the highest levels any starter had ever attained. But by the mid-’90s it became clear that Martinez would need to climb over more than just Clemens and Vance to reach the all-time pitching summit.

In 1994, Atlanta’s Greg Maddux staged an all-out assault on big-league batters. At the time of the season-ending players’ strike, Maddux had a microscopic 1.56 ERA, the lowest WHIP in the majors by a mile — and he was within decimal points of becoming the new all-time leader in Pitcher Score. Finally, after Maddux allowed only one run to the Houston Astros in eight innings on June 3, 1995, baseball had a new Greatest Starting Pitcher Ever™ (according to our stat). But Maddux’s reign at the top of the pitcher rankings was short-lived — Seattle’s Randy Johnson, who had the best strikeout-to-walk differential of the expansion era that year, also passed Vance, and then Maddux, before season’s end.

Over the next few seasons, Maddux and Johnson would jockey for position atop the Pitcher Score rankings. Meanwhile, Martinez slowly built his résumé in the background, cracking the top 25 in 1995 and the top 16 by 1996. Then, in 1997, Pedro made a major breakthrough, posting a 1.90 ERA and finishing the season as the third-best pitcher in the game, according to Pitcher Score. At the same time, Clemens bounced back from a handful of comparatively down seasons to make his own run at Maddux and Johnson. Baseball suddenly had a quartet of all-time great starters operating at or near the peak level of any pitchers who’d ever played the game.

Against that backdrop, Martinez kept edging closer to the top of the Pitcher Score leaderboard, spending most of the 1998 season cruising in second place behind Clemens. But in 1999, his performance took yet another huge leap — and he embarked on the most dominant stretch of pitching the sport has ever known. On Sept. 21, 1999, after shutting out the Toronto Blue Jays, with his ERA sitting at 2.11 in a league where average was 4.86, Martinez had done it: He’d broken Maddux’s record, establishing a new historical high-water mark for Pitcher Score greatness.

Somehow, Pedro was just getting started. In 1999, he’d shown the best pure stuff in baseball history — the lowest fielding-independent pitching numbers ever, before we even knew that fielding-independent pitching was important (or even, you know, a thing). In 2000, he would couple another great FIP with a high rate of outs on balls in play to generate the lowest ERA (relative to the league) of anybody, ever. The two seasons are so ridiculously good that there are actual Internet arguments over which campaign was better, with the answer pretty much determining whether you grab your wins above replacement from Baseball-Reference or from FanGraphs.

We’re certainly not going to weigh in on that battle here. But for what it’s worth, Pedro had a higher per-start average game score in 2000, and he also set the all-time peak Pitcher Score that year, during his aforementioned masterpiece against the Indians. Then again, Martinez also came close to surpassing his own record early in the 2001 season, when he put up the second-highest Pitcher Score in history after a game against the Tampa Bay Devil Rays. In fact, the list of greatest peak Pitcher Score “moments” is so thoroughly dominated by Pedro that he left little room for anybody else:

Martinez finally started to fall from his perch in 2003, but he left a collection of the greatest performances of all-time in his wake. Taking a cue from stories where we ranked all-time Elo seasons in other sports, we rated the greatest pitching seasons³⁴ according to Pitcher Score by blending three metrics for each season: a pitcher’s peak rating, his average rating throughout the entire season, and his final, end-of-season rating. Here are the leaders:

This year’s crop of starting pitchers is pretty amazing, between the ongoing dominance of such hurlers as Clayton Kershaw and Jake Arrieta, and performances like the one Max Scherzer put together Wednesday night. But even at their best, no current pitcher is within 10 Pitcher Score points of Martinez’s peak mark. The top-ranked Arrieta, for instance, would need a breakthrough like the one Martinez made between 1998 and 1999, in order to start making real progress toward Pedro’s all-time record. It’s yet another piece of context that puts Martinez’s best years in perspective — and helps us appreciate the staggering heights to which he pushed the bar for starting-pitcher greatness.

Check out our latest MLB predictions.

Subscribe: iTunes |Download |RSS |Video

Some people daydream about becoming professional baseball players. Ben Lindbergh and Sam Miller daydream about being general managers. The two co-host the “Effectively Wild” podcast for Baseball Prospectus (Ben is also a writer for this site), and last summer they learned that one of their listeners was the media relations director for the Sonoma Stompers, an independent minor-league baseball team in California. Lindbergh and Miller floated the idea that the Stompers should let them act as general managers for the team, advising on player personnel and strategy. The Stompers bit.

Their new book, “The Only Rule Is It Has To Work,” chronicles a summer spent trying out their weirdest analytics-driven ideas on the actual playing field.

On this week’s What’s The Point, Ben Lindbergh discusses his summer with the Stompers, and the larger lessons about what it’s like to try to use data to change a team’s culture.

Stream or download the full episode above, or subscribe using your favorite podcast app. Read an excerpt from the book here. Here is a transcript of a highlight from the conversation.

Ben Lindbergh: These players were far enough from the majors that they were willing to mix things up. Someone who is at AAA, one step from the big leagues, would’ve said, “I’ve gotten this far with what I’ve done, and I’m not willing to do something new.” But these guys were getting desperate enough that they were willing to listen.

Jody Avirgan: That’s the key — you have to find a community that is desperate enough to listen to what you have to say. That’s actually the key to this podcast.

But, what was your relationship with Sam [Miller] like? You host the podcast every day, I assume that you’re friends. Now all of a sudden you were thrust into a working relationship.

Lindbergh: There was some tension. Usually we are separated by a continent and we get along just fine. But when we were in the same place, running this team and writing this book, we definitely had some philosophical differences.

I remember on Opening Day I wanted to march into the manager’s office and say, “Here’s the batting order for today’s game.” Sam didn’t want to do that because he thought we would alienate the manager, and it would have a ripple effect, and we’d be fighting for the rest of the season. I thought we had to assert our authority [right away].

Avirgan: And who won that battle?

Lindbergh: I don’t know if there was a conclusive winner. Eventually Sam moved towards my side of the spectrum, but there were things he saved me from doing throughout the season.

Avirgan: Overall, do you feel like this project was a success, not just in that it was fun … but in that it taught you larger lessons about the work that you’re going to continue to do?

Lindbergh: I think it taught us about selling yourself, and storytelling. We probably could have packaged this book as “what baseball can teach us about business” or something, and sold a million more copies.

Avirgan: You could have done a TED Talk!

Lindbergh: Shoot, we should have done that. But, really — it is about management and finding a way to present your message to people who may or may not be receptive to it. You may have the spreadsheets, but don’t always show the spreadsheets. Make it fun and exciting.

Take your conclusion, one that’s sound and driven by the data … but don’t always show your math. Know your audience. So we learned a lot about how to present our findings, and that can be applicable in any field.

If you’re a fan of What’s The Point, subscribe on iTunes, and please leave a rating/review — that helps spread the word to other listeners. And be sure to check out our sports show Hot Takedown as well. Have something to say about this episode, or have an idea for a future show? Get in touch by email, on Twitter, or in the comments.

What’s The Point’s music was composed by Hrishikesh Hirway, host of the “Song Exploder” podcast. Download our theme music.