When We Say 70 Percent, It Really Means 70 Percent

One of FiveThirtyEight’s goals has always been to get people to think more carefully about probability. When we’re forecasting an upcoming election or sporting event, we’ll go to great lengths to analyze and explain the sources of real-world uncertainty and the extent to which events — say, a Senate race in Texas and another one in Florida — are correlated with one another. We’ll spend a lot of time working on how to build robust models that don’t suffer from p-hacking or overfitting and which will perform roughly as well when we’re making new predictions as when we’re backtesting them. There’s a lot of science in this, as well as a lot of art. We really care about the difference between a 60 percent chance and a 70 percent chance.

That’s not always how we’re judged, though. Both our fans and our critics sometimes look at our probabilistic forecasts as binary predictions. Not only might they not care about the difference between a 60 percent chance and a 70 percent chance, they sometimes treat a 55 percent chance the same way as a 95 percent one.

There are also frustrating moments related to the sheer number of forecasts that we put out — for instance, forecasts of hundreds of U.S. House races, or dozens of presidential primaries, or the thousands of NBA games in a typical season. If you want to make us look bad, you’ll have a lot of opportunities to do so because some — many, actually — of these forecasts will inevitably be “wrong.”

Sometimes, there are more sophisticated-seeming criticisms. “Sure, your forecasts are probabilistic,” people who think they’re very clever will say. “But all that means is that you can never be wrong. Even a 1 percent chance happens sometimes, after all. So what’s the point of it all?”

I don’t want to make it sound like we’ve had a rough go of things overall.1 But we do think it’s important that our forecasts are successful on their own terms — that is, in the way that we have always said they should be judged. That’s what our latest project — “How Good Are FiveThirtyEight Forecasts?” — is all about.

That way is principally via calibration. Calibration measures whether, over the long run, events occur about as often as you say they’re going to occur. For instance, of all the events that you forecast as having an 80 percent chance of happening, they should indeed occur about 80 out of 100 times; that’s good calibration. If these events happen only 60 out of 100 times, you have problems — your forecasts aren’t well-calibrated and are overconfident. But it’s just as bad if they occur 98 out of 100 times, in which case your forecasts are underconfident.

Calibration isn’t the only thing that matters when judging a forecast. Skilled forecasting also requires discrimination — that is, distinguishing relatively more likely events from relatively less likely ones. (If at the start of the 68-team NCAA men’s basketball tournament, you assigned each team a 1 in 68 chance of winning, your forecast would be well-calibrated, but it wouldn’t be a skillful forecast.) Personally, I also think it’s important how a forecast lines up relative to reasonable alternatives, e.g., how it compares with other models or the market price or the “conventional wisdom.” If you say there’s a 29 percent chance of event X occurring when everyone else says 10 percent or 2 percent or simply never really entertains X as a possibility, your forecast should probably get credit rather than blame if the event actually happens. But let’s leave that aside for now. (I’m not bitter or anything. OK, maybe I am.)

The catch about calibration is that it takes a fairly large sample size to measure it properly. If you have just 10 events that you say have an 80 percent chance of happening, you could pretty easily have them occur five out of 10 times or 10 out of 10 times as the result of chance alone. Once you get up to dozens or hundreds or thousands of events, these anomalies become much less likely.

But the thing is, FiveThirtyEight has made thousands of forecasts. We’ve been issuing forecasts of elections and sporting events for a long time — for more than 11 years, since the first version of the site was launched in March 2008. The interactive lists almost all of the probabilistic sports and election forecasts that we’ve designed and published since then. You can see how all our U.S. House forecasts have done, for example, or our men’s and women’s March Madness predictions. There are NFL games and of course presidential elections. There are a few important notes about the scope of what’s included in the footnotes,2 and for years before FiveThirtyEight was acquired by ESPN/Disney/ABC News (in 2013) — when our record-keeping wasn’t as good — we’ve sometimes had to rely on archived versions of the site if we couldn’t otherwise verify exactly what forecast was published at what time.

What you’ll find, though, is that our calibration has generally been very, very good. For instance, out of the 5,589 events (between sports and politics combined) that we said had a 70 chance of happening (rounded to the nearest 5 percent), they in fact occurred 71 percent of the time. Or of the 55,853 events3 that we said had about a 5 percent chance of occurring, they happened 4 percent of the time.

We did discover a handful of cases where we weren’t entirely satisfied with a model’s performance. For instance, our NBA game forecasts have historically been a bit overconfident in lopsided matchups — e.g., teams that were supposed to win 85 percent of the time in fact won only 79 percent of the time. These aren’t huge discrepancies, but given a large enough sample, some of them are on the threshold of being statistically significant. In the particular case of the NBA, we substantially redesigned our model before this season, so we’ll see how the new version does.4

Our forecasts of elections have actually been a little bit underconfident, historically. For instance, candidates who we said were supposed to win 75 percent of the time have won 83 percent of the time. These differences are generally not statistically significant, given that election outcomes are highly correlated and that we issue dozens of forecasts (one every day, and sometimes using several different versions of a model) for any given race. But we do think underconfidence can be a problem if replicated over a large enough sample, so it’s something we’ll keep an eye out for.

It’s just not true, though, that there have been an especially large number of upsets in politics relative to polls or forecasts (or at least not relative to FiveThirtyEight’s forecasts). In fact, there have been fewer upsets than our forecasts expected.

There’s a lot more to explore in the interactive, including Brier skill scores for each of our forecasts, which do account for discrimination as well as calibration. We’ll continue to update the interactive as elections or sporting events are completed.

None of this ought to mean that FiveThirtyEight or our forecasts — which are a relatively small part of what we do — are immune from criticism or that our models can’t be improved. We’re studying ways to improve all the time.

But we’ve been publishing forecasts for more than a decade now, and although we’ve sometimes tried to do an after-action report following a big election or sporting event, this is the first time we’ve studied all of our forecast models in a comprehensive way. So we were relieved to discover that our forecasts really do what they’re supposed to do. When we say something has a 70 percent chance of occurring, it doesn’t mean that it will always happen, and it isn’t supposed to. But empirically, 70 percent in a FiveThirtyEight forecast really does mean about 70 percent, 30 percent really does mean about 30 percent, 5 percent really does mean about 5 percent, and so forth. Our forecasts haven’t always been right, but they’ve been right just about as often as they’re supposed to be right.

Our Organ Donation System Is Unfair. The Solution Might Be Too.

At any given time, there are about 13,000 people waiting for a liver transplant in the United States. Whether the cause is a virus, alcoholism or a bit of genetic bad luck, they’re all suffering while sick and scarred livers struggle to clean their blood. Over time, their intestines bleed. Fluid builds up in their legs and their chests. Their skin turns sallow. Confusion sets in. The only cure is to swap the old liver for a healthy one. Each year, about 8,000 people will get that chance. The rest will wait, getting sicker.

There are always more people who need a new organ than there are organs available. That’s true all over the country, but not every place has the same number of available organs. Some regions have more registered donors, which means how long you have to wait for a liver is partly determined by where you happen to live.

At the end of the month, that’s set to change. The organization that manages the national organ transplant system is trying to make the wait time for donated livers more equal nationwide. It might be a preview of what’s to come for all organ-donation systems, and it’s proving to be controversial. It’s created factions among transplant surgeons. Senators have gotten involved. At least one state has proposed legislation to keep organs donated by its citizens within state borders. It’s a fight over the definition of fairness, experts say, where a seemingly simple effort to reduce geographic inequity in organ donation could end up exacerbating even bigger inequities in health care access.

Organ donation is good and kind, but it isn’t fair. For a healthy organ to save someone’s life, another family has to have the worst day of their lives. To get a lung or a heart or a liver, somebody has to die — ideally while they are young enough that the donated organ isn’t on its last legs.

One of the best ways to do that is to get more people to agree to become organ donors before something bad happens, said David Fleming, president of Donate Life America, a nonprofit that works to increase organ donation nationwide. That way the decision is already made and not left up to grieving, shocked families. But the rate at which healthy Americans choose to sign up as potential organ donors varies a lot from state to state. In some states, like Montana and Alaska, nearly the entire adult population is registered. Others, like New York and Mississippi, hover at less than 40 percent.

Organ donation registration rates vary dramatically by state
State/territory Share of adults registered as organ donors
Montana 93%
Alaska 92
Washington 89
Oregon 79
Utah 78
Indiana 75
Missouri 73
Alabama 72
Iowa 72
Louisiana 71
Maine 69
Kansas 68
Colorado 66
South Dakota 66
North Dakota 65
Virginia 65
Arkansas 64
District of Columbia 64
Idaho 64
New Hampshire 64
Ohio 64
Minnesota 63
Wisconsin 63
Maryland 62
Massachusetts 62
Michigan 62
New Mexico 62
North Carolina 62
Arizona 61
Georgia 61
Hawaii 61
Illinois 60
Vermont 60
Florida 59
Oklahoma 59
Rhode Island 59
Wyoming 58
Delaware 56
Nebraska 56
Kentucky 54
South Carolina 51
Nevada 49
Texas 49
Connecticut 48
California 47
Pennsylvania 47
Tennessee 43
West Virginia 41
New Jersey 40
Mississippi 37
New York 32
Puerto Rico 22

Source: Donate Life America

That disparity matters because, historically, the national system of determining who gets a donated organ has been deeply regional. There are 58 Organ Procurement Organizations, nonprofits that handle the process of talking to families, coordinating with hospitals and setting up the movement of an organ from one body to another. Each of those organizations has a geographical area it covers. The United Network for Organ Sharing, a private nonprofit that contracts with the federal government to manage the national organ transplant system, traditionally uses those boundaries as part of determining which patients on the waiting list get first crack at an organ. When a donor dies, the sickest patients in the same OPO have first dibs, essentially.

There are, obviously, problems with this system, said Brian Shepard, CEO of UNOS. Not only does it put patients in states with higher donor-registration rates at an advantage, it’s also drawn up in a pretty arbitrary way. For example, Iowa and Nebraska each have their own OPOs, but both states have a county or two covered by the other’s OPO. Another OPO covers all of Kansas and an odd chunk of western Missouri that’s roughly shaped like a pair of pants with a lot of thigh gap. “Texas has OPOs that have non-contiguous pieces,” Shepard said.

It’s the kind of seemingly random inequality that ends in a lawsuit. Last July, six patients on the liver transplant waiting list sued UNOS and the federal Organ Procurement and Transplantation Network, calling the policy illegal and inequitable. Those patients were from New York, California and Massachusetts. New York and California both have comparatively low rates of donor registration, and both are in regions that have longer wait times than parts of the Midwest and South.1 For instance, a patient with Type B blood who was added to the registry between 2003 and 2006 waited a median of 1,223 days for a new liver in the New York region and a median of 303 days in the region that includes Kansas. If you’re a New Yorker, that doesn’t seem very fair.

The lawsuit is still active, but it has already pushed UNOS toward changes it had long been considering, said Keren Ladin, who is a professor of public health and community medicine at Tufts University and has published research on geographic disparities in liver distribution. Potential organ donors — people who have signed up to be on the registries — aren’t evenly distributed, but maybe organs could be.

To do that, UNOS came up with a new system that will be put into action on April 30. Under the new rules, patients get first priority for newly donated livers if they are in danger of imminent death and live within a 500-mile radius of the deceased donor — OPO borders be damned. If there aren’t any patients within 500 miles who are that sick, then the livers will be offered to the next-sickest patients within a 150-mile radius. Then those in a 250-mile radius. Then 500. That could mean a patient in New York would suddenly have access to a liver from Philadelphia, which under the OPO system would be off-limits to the New Yorker but could go to a patient from West Virginia.

But just like some New Yorkers and Californians thought the old system was unfair, people from states like Missouri and Iowa see unfairness in the new system. In January, 22 senators signed an open letter to the Department of Health and Human Services demanding answers about how the new policy would affect rural communities. In February, the Kansas state legislature introduced a bill that would allow organ donors to specify that they want their body parts to go only to in-state recipients. It has the backing of doctors at the University of Kansas Medical Center’s liver transplant center.

And that, Ladin said, also makes sense because the new plan really could be unfair. Kansas’s health care infrastructure is already inferior to New York’s. Taking its organs out of the state would only exacerbate the Kansas system’s failings.

And those inequities in health care begin with the organs themselves. Donor registration matters, but donor registration isn’t really the thing that creates donors. Deaths do. “Donors get created because of poor access to care: strokes, heart attacks, bad roads,” said Richard Gilroy, who is medical director of liver transplantation at Intermountain Healthcare in Salt Lake City and was on the UNOS liver committee that ultimately voted for the new rules, although he opposes the rule change.

Look at it this way: Kansans may be generous with their organs — 68 percent of them are registered donors. But Kansas also has a higher rate of stroke deaths than New York does, and New York has a lower rate of accidental deaths than Kansas. New Yorkers have a longer wait time for organs partly because they’re less likely to die of the kind of misfortunes that turn registrants into donors.

Moreover, residents of states with better health care systems — like New York — have a greater likelihood of being diagnosed and listed as needing an organ donor to begin with, Gilroy said. And New York has more comprehensive Medicaid coverage than Kansas does, which also means that there are people who can afford to get a liver transplant in New York but couldn’t in Kansas. “Part of the workup is a wallet biopsy,” Ladin said. Patients have to prove that they can afford the drugs needed after the operation. “So already a disparity exists in states with a weaker safety net,” she said. Ultimately, despite the shorter transplant waiting list, Kansans are more likely to die from liver disease than New Yorkers are. To Gilroy, that makes the change look less like a leveling of wait times and more like redistributing health care from people who already have less to people who already have more.

And this is what complicates the fight over liver distribution: There’s more than one thing that’s unfair about the system. That frustrates both Ladin and Fleming, who told me that they see good arguments on both sides of a gaping divide that’s only likely to get bigger because other organ transplant systems are on track for similar changes. Regardless of who is correct here, the bigger problem is that the changes are just shuffling organs around — altering which patients get a liver, not increasing the number of patients who get one. Without that, they said, there’s always going to be someone who waits, and dies.

Abolishing The Electoral College Used To Be A Bipartisan Position. Not Anymore.

Twice in the past five presidential elections, a Republican has won the presidency despite losing the popular vote. Now Democratic Sen. Brian Schatz of Hawaii has introduced a constitutional amendment to abolish the Electoral College and use the national popular vote to decide who becomes president. His proposal is among the latest efforts by Democrats and those on the left to push for structural changes to the American political system.

But Schatz’s amendment is sure to meet defeat in the Republican-controlled Senate. Today, attitudes toward the Electoral College are polarized by party, with Democrats far more likely to support a change and Republicans much more likely to defend the current system — but it wasn’t always like that.

While the controversial 2000 election was still being decided, Gallup found that 61 percent of Americans — including 73 percent of Democrats and 46 percent of Republicans5 — preferred amending the Constitution to elect the popular vote winner. Only 35 percent of respondents preferred the current system. The partisan gap widened even further after the 2016 election: A few weeks after President Trump won the presidency while losing the popular vote, Gallup found that 49 percent of Americans preferred changing to a popular vote system, compared to 47 percent who wanted to keep the Electoral College, with 81 percent of Democrats supporting a change compared to just 19 percent of Republicans.6 Even given some space after that heated election, there remains a major partisan gap in opinion over how to elect a president — Pew Research found in March 2018 that 75 percent of Democrats supported moving to a popular-vote system versus only 32 percent of Republicans.

But 50 years ago, moving on from the Electoral College had bipartisan support. In May 1968, 66 percent of American approved of the idea of amending the constitution to replace the Electoral College with a popular vote system, according to Gallup. And there was no partisan divide: 66 percent of Republicans and 64 percent of Democrats approved. Six months later, Republican Richard Nixon defeated Democrat Hubert Humphrey while only winning the popular vote by less than 1 percentage point, and a post-election Gallup survey found 80 percent of Americans approved of changing the electoral system. The bipartisan support among voters and the fact that the 1968 election nearly produced a split between the popular vote and the Electoral College7 explain why there was bipartisan support in Congress in 1969 for a constitutional amendment to elect presidents based on the popular vote. The House passed it 339 to 70, with more than 80 percent of each party’s voting members lending their support. But small-state senators from both parties filibustered the amendment and it never got an up-or-down vote in the upper chamber.

As long as one side feels disadvantaged by the Electoral College, it will be far more likely to push for a popular-vote system. Right now, that’s the Democrats. Reforming how the country elects presidents falls into the broad effort on the left to reform aspects of our electoral system, including voting access and how campaign finance works. But some who want reform believe abolishing the Electoral College should be a secondary goal. “There’s a bunch of stuff to do without amending the constitution that would have the end result of making institutions and elections more fair,” said David Faris, a political scientist at Roosevelt University, who recently argued in his book “It’s Time To Fight Dirty” that Democrats should be challenging the structural and legal boundaries of the American political system to better gain and hold power. Nonetheless, Faris sees discussion over the electoral system as a good thing in that it could soften up public opinion and make people more willing to consider alternatives to the status quo.

But we may not see a true shift in public opinion unless a Republican loses in the Electoral College while winning the popular vote. As FiveThirtyEight has argued in the past, the system is not inherently biased against either party, with one side’s seeming advantage lasting for just an election or two before it flips to the other party. But as the 1969-1970 example shows, it seems likely that only serious bipartisan support for abolishing the Electoral College system could ever change how we elect a president. Although states may figure out a way around the Electoral College with the National Popular Vote interstate compact, it would not seem as permanent as a constitutional amendment, given that only one amendment has ever been repealed. And as Faris argues, using the interstate compact method might precipitate a crisis because an outcome might be seen as illegitimate and be subject to legal challenges if it delivers a result that contravenes what the Electoral College would otherwise do.

Schatz’s proposal is unlikely to pass the Senate, but it may be a symbolic effort to influence the conversation about what we want our electoral system to look like. Nonetheless, without broader agreement, a constitutional amendment to abolish the Electoral College will pass when pigs fly.

From ABC News:
Sen. Elizabeth Warren wants to get rid of the Electoral College

The Royals Are MLB’s Fastest Team In Years

With a blazing average of 4.07 seconds to first base — that’s 15.1 miles per hour — Kansas City Royals shortstop Adalberto Mondesi was one of the fastest players in Major League Baseball last season. But this year, he’s not even the fastest player on his own team. That honor belongs to new center fielder Billy Hamilton, who runs to first in an astonishing 3.94 seconds. Fourth outfielder Terrance Gore might not be much slower, either, and none of those guys is even the reigning MLB leader in stolen bases — which K.C. right fielder Whit Merrifield happens to be. These are the 2019 Royals: The fastest baseball team assembled in years.

It was clear from the start that this team’s identity would be all about running as fast as possible: “We want to be a motion team,” general manager Dayton Moore told MLB.com in February. “We have to be elite at some aspects of the game, and defense and speed is something we can be elite at.” And Kansas City has already put that speed to good use in its season-opening games against the Chicago White Sox, with Merrifield and Chris Owings swiping three combined bases and Mondesi hitting two triples in a 2-1 series victory.

If the 2014 and 2015 Royals were an experiment in whether a talented small-ball team could win a championship in the modern game (it worked), this year’s version will be more about how much pure speed can make up for a lack of talent in other areas. The Royals might not be “good” per se — but in an era when just about every team is constructed according to the blueprint of advanced analytics, they will be different, and that might have value in itself.

Certainly last season’s Royals could not have been described as anything other than abysmal. K.C. went 58-104, the team’s worst record in 13 years, and had only five regulars1 in common with the 2015 championship club: Alex Gordon, Salvador Perez, Alcides Escobar, Danny Duffy and Mike Moustakas. (Moustakas was then traded to Milwaukee in July; Escobar signed with the White Sox over the offseason.) The Royals were sixth-to-last in scoring and fourth-worst in runs allowed, with a defense tied as the fourth-least efficient in baseball. This was far removed from the team that celebrated the franchise’s second world title just three years earlier.

This year’s team is projected to be better yet still far from first place. The preseason FiveThirtyEight forecast called for Kansas City to improve all the way to 70 wins, though most of that change could be attributed to regression toward the mean rather than any specific additions. (In fact, K.C.’s most notable roster development since last fall was the news that Perez, a six-time All-Star, would miss the whole 2019 season with an elbow injury.) The projections were also low on both the 2014 and 2015 Royals, getting blindsided entirely by their World Series runs, but at least those teams had established, scout-approved talent with some sort of a track record and upside. The 2019 Royals don’t pass the eye test any more than they impress the computers.

The projected speed in this lineup, however, is the genuine article. According to FanGraphs’ preseason depth chart projections, Royal hitters were forecast to swipe 168 bases this year, which represented 6.2 percent of the total steals predicted for all of MLB.2 If Kansas City hits that benchmark, it would become only the sixth team since 1996 to claim at least 6.2 percent of leaguewide stolen bases. The 2016 Brewers did it recently, but mostly that rate was a hallmark of teams from the 1960s, ’70s and ’80s, when gaudy steal totals were the norm and not every team had settled into similar offensive philosophies guided by sabermetrics.

The speed of these Royals emerges in other metrics as well. I filtered down every opening day lineup since 1950 for those that contained at least eight players who had logged 200 or more plate appearances during the previous year. Then, for each lineup, I averaged two numbers from its players in the season before: Speed Score — a Bill James invention that estimates raw speed by combining stolen bases (both attempts and successes), triples and runs scored as a percentage of times on base — and FanGraphs’ Base Running (BsR) statistic, which quantifies the run value of every base-running action (including steals and advancement on other events). The 2019 Royals’ average Speed Score is tied for 24th since 1950, and its average BsR per 600 plate appearances ranks 71st; only 12 opening day lineups were faster by both measures, and half of those played during the nine-season span from 1978 to 1986, a heyday for running teams.

So this is basically an ’80s-style team of burners, in the mold of the Whitey Herzog St. Louis Cardinals,3 dropped down into the modern major leagues. And Kansas City’s speedsters are off to a blazing start already, easily leading baseball in Speed Score through the first weekend of the season with an eye-popping 8.5 mark. (The MLB average is about 4.4 in recent seasons, with the leader topping out around 5.4 most years.)

The Royals’ next step, though, is turning all that speed into more tangible results. Perhaps most surprising in Kansas City’s portfolio of badness last year is that the team was somehow MLB’s fifth-worst at base running (according to BsR) despite the steals-leading presence of Merrifield atop the lineup for most of the year. The Royals’ speed was above average — if not quite as impressive as this season — but they didn’t use it well, particularly between bases in advancement scenarios. According to FanGraphs, K.C. lost 12 runs (more than an entire win) relative to the average team in base-running situations that didn’t involve steals. One of the ways K.C. can improve this year is to deploy its running game in a smarter way, using it to take advantage when opponents inevitably offer up chances to take extra bases.

That’s an area in which Kansas City might take a cue from its 2014-15 teams, which were legendary for their opportunism on the base paths. Take the famous ninth-inning play that extended Game 5 of the 2015 World Series: Eric Hosmer’s heads-up sprint from third base to home on a weak groundout, a daring piece of aggressive base running that forced an errant throw by Mets first baseman Lucas Duda and tied the ballgame. The Royals would eventually score five 12th-inning runs off New York’s beleaguered bullpen to secure the championship.

Hosmer (career Speed Score: 4.0) wasn’t even fast, so imagine how much more damage Hamilton, Mondesi, Merrifield and friends could do if they pick their base-running spots correctly. Along the same lines, Kansas City is also hoping this speedy roster can emulate the 2015 Royals’ defense, which according to FanGraphs was the best in baseball in terms of runs saved relative to average.

Larger issues, such as the team’s dismal .305 on-base percentage last season, might place hard limits on how much value Kansas City can get out of its speed this year. (Even Sunday, the team was being no-hit by Chicago’s Lucas Giolito — owner of a career 5.48 earned run average going into the game — into the seventh inning.) But no matter what, it should at least be more worthwhile to watch the fleet Royals this season, both for the entertainment of all those steals and as an experiment in against-the-grain team-building.

Check out our latest MLB predictions.

11 Senators Want To Know Why The CDC’s Gun Injury Estimates Are Unreliable

Eleven senators have sent a letter to the head of the Department of Health and Human Services, demanding answers to a series of questions about the Centers for Disease Control and Prevention’s nonfatal firearm injury estimates. The inquiry relies on the findings of an investigation by The Trace, a nonprofit news organization covering gun violence in America,1 and FiveThirtyEight, and is led by Democratic Sen. Bob Menendez of New Jersey.

The Trace and FiveThirtyEight first reported last year that the CDC’s 2016 gun injury estimate was so uncertain the agency classified it as “unstable and potentially unreliable.” Since then, the agency’s data, which in 2017 was derived from a sample of just 60 hospitals, has become even more unreliable. The CDC’s gun violence estimates are widely cited in academic articles.

“Given that the CDC is not currently conducting gun violence research,” the letter reads, “the very least the agency can do is to ensure that its gun injury numbers are accurate.”

The letter asks HHS Secretary Alex Azar to explain the CDC’s methods for tracking nonfatal firearm injuries, the cause of its increasingly unreliable estimates, and whether the agency has undertaken any actions to improve the quality of its data. The senators also ask whether the Dickey Amendment — a piece of 1996 legislation that bars the CDC from using its funding to “advocate or promote gun control” — has played any role in the agency’s continued reliance on a data source that’s ill-suited for producing firearm injury estimates.

“We as lawmakers, as every American citizen, should be able to follow and understand the latest trends on firearms injuries without the concern of coming across ‘unstable and potentially unreliable’ data,” Menendez told The Trace in an email.

The CDC has previously acknowledged its estimates have a high degree of uncertainty. “CDC continues to look into various ways to strengthen the estimates for nonfatal firearm injuries,” said spokesperson Courtney Lenard in an email.

Researchers interviewed by The Trace and FiveThirtyEight believe the CDC’s estimates are too flawed to use. Guohua Li, editor-in-chief of the medical journal Injury Epidemiology and director of Columbia University’s Center for Injury Epidemiology and Prevention, said the estimates could be improved by drawing upon a larger and more reliable source of data, such as another database administered by HHS.

Menendez makes reference to this proposed solution in the letter, writing, “There appears to be no rational reason that the CDC and HHS use different databases.”

The letter was also signed by Democratic Sens. Cory Booker, Kirsten Gillibrand, Mazie Hirono, Richard Blumenthal, Amy Klobuchar, Kamala Harris, Tina Smith, Chris Murphy and Chris Van Hollen and independent Angus King. The letter asks Azar to respond by April 20.

Significant Digits For Friday, March 29, 2019

You’re reading Significant Digits, a daily digest of the numbers tucked inside the news.

More than 300 pages

The full report of special counsel Robert Mueller is more than 300 pages long, according to the Justice Department. However, all that has been made public is Attorney General William Barr’s summary, which is four pages long. In the context of government reports, Mueller’s isn’t an outlier — the Starr report ran 445 pages, the 9/11 commission report 567 pages, and a report on how the FBI handled an investigation into Hillary Clinton’s use of a private email server was 568 pages. [The New York Times]

More than 1,000 passengers

Wow Air, a budget carrier out of Iceland, ceased operations on Thursday, stranding travelers on multiple continents and affecting more than 1,000 passengers. I’ve heard of canceled flights, but never a canceled airline. “I’m disappointed not to honor our commitments,” the Wow CEO said — those commitments being, like, getting people back across the Atlantic Ocean. [CNN]

6,227 pedestrians

More than 6,000 pedestrians died in traffic accidents in 2018, according to the Governors Highway Safety Association, the highest number in three decades. Experts, according to NPR, attribute the rise to “drivers and pedestrians distracted by their phones” along with an increase in large vehicles. [NPR]

More than $1 trillion

Amy Klobuchar — Democratic candidate for president, senator from Minnesota, and reported eater of salad with comb — wants to “break the partisan logjam” and professes to be able to do so with a $1 trillion infrastructure plan to improve America’s roads and bridges, public schools, and broadband internet. She reportedly plans to make infrastructure, the betterment of which has bipartisan support, a centerpiece of her campaign. [The Wall Street Journal]

5-point window

Despite the seemingly constant clangor from the White House and Washington, D.C., President Trump’s approval ratings remain incredibly steady. Half of his approval polls have fallen with a band of 5 points, between 39 percent and 44 percent. Only President Barack Obama rivaled that narrow range, while every other president back to Harry Truman saw wider ranges, and in many cases much wider. “As Democrats and Republicans move farther apart politically,” my colleague Geoffrey Skelley writes, “the specifics of a president’s job performance may become secondary considerations for voters in forming an opinion of how he’s doing.” [FiveThirtyEight]

184 of the 270 votes

The governor of Delaware signed a law pledging that that state’s Electoral College votes will go to the winner of the national popular vote in the presidential election, regardless of who actually wins the state itself. Delaware is the 13th state to commit to such a pledge, and those states now represent 184 of the 270 Electoral College votes needed to elect a president. [Associated Press]

From ABC News:
It's Morning, America: Friday, March 29, 2019

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If you see a significant digit in the wild, please send it to @ollie.

Can You Win A Spelling Bee If You Know 99 Percent Of The Words?

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-size and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,3 and you may get a shoutout in next week’s column. If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter.

Riddler Express

From Tom Hanrahan, a probability puzzle; or, a mini-lesson in surprising results:

You are playing your first ever game of “Ticket to Ride,” a board game in which players compete to lay down railroad while getting so competitive they risk ruining their marriages. At the start of the game, you are randomly dealt a set of three Destination Tickets out of a deck of 30 different tickets. Each reveals the two terminals you must connect with a railroad to receive points. During the game, you eventually pick up another set of three Destination Tickets, so you have now seen six of the 30 tickets in the game.

Later, because you enjoyed it so much, you and your friends play a second game. The ticket cards are all returned and reshuffled. Again, you are dealt a set of three tickets to begin play. Which is more likely: that you had seen at least one of these three tickets before, or that they were all new to you?

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Riddler Classic

From Steven Pratt, ordinal bee probability:

You are competing in a spelling bee alongside nine other contestants. You can each spell words perfectly from a certain portion of the dictionary but will misspell any word not in that portion of the book. Specifically, you have 99 percent of the dictionary down cold, and your opponents have 98 percent, 97 percent, 96 percent, and so on down to 90 percent memorized. The bee’s rules are simple: The contestants take turns spelling in some fixed order, which then restarts with the first surviving speller at the end of a round. Miss a word and you’re out, and the last speller standing wins. The bee words are chosen randomly from the dictionary.

First, say the contestants go in decreasing order of their knowledge, so that you go first. What are your chances of winning the spelling bee? Second, say the contestants go in increasing order of knowledge, so that you go last. What are your chances of winning now?

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Solution to last week’s Riddler Express

Congratulations to 👏 Eric O’Neill 👏 of Madison, Wisconsin, winner of last week’s Riddler Express!

Last week, we broke out the dice to play a century-old baseball simulation game called Our National Ball Game, wherein each roll of the dice corresponded to some baseball outcome: 2-6 was a foul out, 1-1 was a double, 6-6 was a home run, and so on — you can find the full list here. How closely does such a list and a bunch of dice throws simulate the modern iteration national pastime? Specifically, what was the average number of runs that would be scored in nine innings of dice play? What was the distribution of the runs scored?

Typically, Our National Ball Game is much higher scoring than real baseball, with about 30 runs scored per game (compared to about nine in the real sport).

This was a problem of meta-simulation: Whereas the dice game simulated real baseball, you were meant to simulate the dice game (probably using a computer to save time). Solvers Julian Gerez and Ricky Martinez did just that and blogged about their approach, finding, after 10,000 innings of play, that each “baseball team” scored about 15 runs per game, for a total of about 30 runs per game, according to the simulated distribution shown below.

The computer scientist Peter Norvig was also kind enough to share his code — after a million computer-simulated dice-simulated innings, he found an average of just over 15.1 runs per team, and was able to smooth out the distribution as shown below.

A million innings! Perhaps we’ve finally found a solution to baseball’s pace-of-play problem.

Solution to last week’s Riddler Classic

Congratulations to 👏 Tyler James Burch 👏 of Naperville, Illinois, winner of last week’s Riddler Classic!

High scoring baseball is fun and all, but let’s say you wanted your game to be more faithful to real baseball than raw excitement. How could you tweak the list of rules — the correspondence between dice rolls and baseball outcomes — to create a game that more closely matched the run distribution in real baseball?

Our winner this week, Tyler James Burch, proposed the following list of rules, which I propose to call Burchball.

(1, 1): triple

(2, 2): base on error

(3, 3): double play

(4, 4): home run

(5, 5): double

(6, 6): strike out

(1, 2): strike out

(1, 3): strike out

(1, 4): base on balls

(1, 5): single

(1, 6): single

(2, 3): fly out

(2, 4): fly out

(2, 5): fly out

(2, 6): fly out

(3, 4): fly out

(3, 5): fly out

(3, 6): strike out

(4, 5): single

(4, 6): base on balls

(5, 6): single

Again, the fidelity of this tweaked game can be measured with computer simulations. In this case, Burch says his game’s simulated scoring outcomes match real baseball quite closely, as shown his chart below, in which Burchball scores are compared to MLB data from last season.

Finally, solver Douglas Harris thought outside the cubes — and got a little theoretical. “There are approximately \(6\times 10^{23}\) hydrogens in a pair of dice,” he wrote (and we, I hope understandably, did not verify). “The proton in the center of each hydrogen can be aligned either up or down relative to the Earth’s magnetic field. Hence, I actually have a \(6\times 10^{23}\) bit random-number generator every time I roll the dice, allowing me to have an outcome table with more than \(10^{{10}^{23}}\) possibilities. I mapped a tiny fraction of this outcome table to every femtosecond of every baseball game ever played. After extensive simulations, I was able to conclusively conclude that Pedro was left in one pitch too long.”

Want more riddles?

Well, aren’t you lucky? There’s a whole book full of the best puzzles from this column and some never-before-seen head-scratchers. It’s called “The Riddler,” and it’s in stores now!

Want to submit a riddle?

Email me at [email protected]

The NCAA Tournament Has Turned Into A Dunk Contest

In one of the most intoxicating games of this year’s NCAA Tournament, the UCF Knights went toe-to-toe with the top-seeded Duke Blue Devils. Leading up to and throughout the game, considerable bandwidth was spent debating whether the soon-to-be top pick in this year’s NBA draft, Zion Williamson, would add another body to his posterized graveyard. UCF center Tacko Fall, the would-be victim, chipped in 15 points on seven made shots, each of which came in eerily similar fashion. They were all dunks. At 7-foot-6, Fall is genetically predisposed to excel above the rim, as evidenced by his ability to jam it, flat-footed.

Nobody this season dunked on Mike Krzyzewski’s squad more than Fall and the Knights. But the Blue Devils, which ultimately moved on with a win, are even more dunk crazy. And they aren’t the only team still playing in this tournament with eyes trained on the rim.

This season’s Sweet 16 features a number of teams that relish slamming the ball through the cylinder. The teams have combined to produce 1,866 dunks this season. Three of the four dunk-happiest teams this season — Florida State, Duke, and LSU — are still in the field. Another contender, Gonzaga, ranks in the top 10 while Auburn, Virginia, Tennessee and Michigan rank in the top 30 by this measure. In all, six of this year’s Sweet 16 entries have a dunk share1 exceeding 10 percent. Four years ago, only one did.

The dunkers are thriving

Division I men’s college basketball teams for whom at least 10 percent of their 2-point field-goal attempts in 2018-19 were dunk attempts

Team Share of offense from Dunks Made Tournament? Made Sweet 16?
Florida St. 16.0
Stanford 14.9
Duke 14.4
LSU 14.2
UCF 14.0
Murray St. 13.8
UCLA 13.5
Auburn 13.4
Xavier 13.2
Texas 12.8
Villanova 12.8
Eastern Michigan 12.6
Arkansas 12.5
Mississippi St. 12.3
Dayton 12.2
Arizona St. 12.0
Gonzaga 11.4
Nevada 11.3
Georgia 10.9
Maryland 10.7
Virginia 10.7
Little Rock 10.6
Alabama 10.6
Texas Southern 10.5
William & Mary 10.4
Northeastern 10.4
Creighton 10.3
Washington 10.3
Vanderbilt 10.3
Texas A&M 10.2
Marshall 10.1

Source: Barttovik.com

This is less about a few dunk-crazed teams and more a reflection of the nationwide trend in college basketball. As of Tuesday, there had been 19,550 dunks this season, the highest total of any season since at least 2010. Five years ago, for comparison, there were 17,687. Individually, the 2010 season featured 23 players who had at least 45 dunks. This season there are 36, seven of whom remain in the tournament. “We’re seeing more dunks,” Jay Bilas told The New York Times, “because there are more spectacular athletes out there.”

To be sure, some of this is intuitive. Advances in science and technology make comparing today’s college athlete to those of yesteryear a comical examination. Perhaps more than ever, basketball rewards heightand, increasingly, arm length — and athleticism. Nowadays, warm-up lines seem to be as much for the fans as for the players. Tennessee is credited for starting a choreographed dunk during warm-ups that involves the entire team. It spread around the country and even reached the NBA.

The digital market is saturated with looped clips of diminutive high-flyers, players leapfrogging multiple humans and guards audaciously double-pumping in transition. The NCAA’s official website ran a listicle of players it wants to see in a dunk contest.2 Because of his dunking prowess, Williamson eclipsed 1 million Instagram followers before he even got to college.

As the number of dunk attempts has spiked, so too has their importance. Dunks accounted for 5.4 percent of all 2-point field goal attempts this season, the highest portion since 2014-15, and the fourth consecutive season that the national dunk share has risen.

In fact, according to Bart Torvik’s website, three3 of the 12 teams with the most single-season dunks since 2010 can be found in this weekend’s regional semifinals.

Of course, there are outliers. Most noticeably, Loyola-Chicago made a surprise run into and past the Sweet 16 a season ago. The Ramblers had just 15 dunks, accumulating a 1.6 percent dunk share. Duke squares off with Virginia Tech on Friday and has a clear edge on dunking; the Hokies (62 dunks) have fewer than a third as many dunks as the Blue Devils (188). But far more often, it seems that the high-flyers are moving on.

Dunks have held a special place in the NCAA Tournament for decades. It’s how many came to know the UNLV Runnin’ Rebels. It’s where Florida Gulf Coast, a plucky No. 15-seed in 2013, became known Dunk City. They have been everywhere this season and will continue to be, particularly with the regional semifinals featuring Florida State, Duke and LSU, three teams that have already skied for at least 177 dunks. The play has elevated the entertainment of the sport by a considerable measure.

While the rise of the 3-pointer has justifiably garnered much attention, the dunk is the sport’s most marketable shot. The feat of athleticism is frequent fodder for highlight reels and commercials. And, since nearly 90 percent of all dunk attempts since 2010 have been converted into points, it’s likely the most efficient shot in basketball. What was once banned is now propelling the sport forward. So keep your eye on the rim this weekend as the Sweet 16 takes flight.


Significant Digits For Wednesday, March 27, 2019

You’re reading Significant Digits, a daily digest of the numbers tucked inside the news.

1 bracket

After the first and second rounds of the NCAA men’s basketball tournament this past weekend, only one perfect bracket remains across the major online March Madness games, and it belongs to an Ohio man named Gregg Nigl. During one crucial game, Nigl said, “I wasn’t watching. I went to bed, I was tired. I had no idea that this was even happening.” [NCAA.com]

19,500 pounds

The biggest Tyrannosaurus rex known to humans, which would’ve weighed an estimated 19,500 pounds, was announced recently by paleontologists, with its first remains unearthed nearly 30 years ago. It’s nicknamed Scotty, after a bottle of scotch used to celebrate its discovery. The skeleton is 65 percent complete and the dinosaur is thought to have lived to at least the age of 28, geriatric by Jurassic standards. [National Geographic]

410 to 192

The European parliament voted in a landslide — 410 to 192 — to eliminate daylight saving time starting in 2021. Each of the 28 member countries will get to decide whether it wants to remain on a setting of “permanent summer” or “permanent winter,” either of which seems to present its own version of hellish bleakness. [The Guardian]

12 candidates

It’s common knowledge that a caravan of Democrats are running for their party’s presidential nomination. But of those, what makes a “major” presidential candidate? According to my colleague Nate Silver, 15 candidates (including former vice president Joe Biden) qualify as major by FiveThirtyEight’s rules, but only 12 have qualified for the debates according to the rules of the DNC. [FiveThirtyEight]

$270 million settlement

Purdue Pharma, the maker of OxyContin, has agreed to a $270 million settlement with the state of Oklahoma for its role in the opioid crisis. The state argues that Purdue, among other companies, is at least partially responsible “for thousands of opioid deaths across the state, in addition to the health care, law enforcement and treatment costs of the state’s addiction crisis.” [The Washington Post]

3 16-digit integers

For decades, mathematicians have pondered, as mathematicians are wont to do, a pressing question: Can the number 33 be expressed as the sum of three cubes? And now, at long last, to the fanfare of mathematical trumpets and the serenading of mathematical angels, Andrew Booker, a mathematician at the University of Bristol, has provided an answer. Yes it can, in the form of three 16-digits integers: (8,866,128,975,287,528)³ + (–8,778,405,442,862,239)³ + (–2,736,111,468,807,040)³ = 33. I’ll never forget where I was when I heard the news. [Quanta Magazine]

From ABC News:
News headlines today: Mar. 27, 2019

Love digits? Find even more in FiveThirtyEight’s book of math and logic puzzles, “The Riddler.”

If you see a significant digit in the wild, please send it to @ollie.

MLB Is Increasingly A Father-Son Game

DUNEDIN, Fla. — Within a 30-foot radius in the Toronto Blue Jays’ cramped spring training clubhouse are locker spaces adorned with the nameplates Guerrero, Biggio and Bichette. Any baseball fan of the 1990s and early 2000s would recognize these surnames: Vladimir Guerrero, Craig Biggio and Dante Bichette combined for 20 All-Star Game appearances across two decades. But these lockers belong to Vladimir Guerrero Jr., Cavan Biggio and Bo Bichette, who have combined for zero big-league at-bats to date. They are on the cusp of the majors, prospects invited to camp in the sleepy Gulf Coast town of Dunedin, Florida.

But expectations are high for the Blue Jays’ young trio. Guerrero is the No. 1 prospect in the game according to most evaluators. Bichette is considered a top 20 prospect. And Biggio dramatically elevated his prospect status last season. Another son of a former big leaguer, pitcher Mark Leiter Jr., was also in the clubhouse before undergoing Tommy John surgery.

Second-generation prospects are not limited to the Toronto system, either. ESPN’s Keith Law has San Diego’s Fernando Tatis Jr., another legacy, as the game’s No. 1 prospect, while Pittsburgh’s Ke’Bryan Hayes — son of Charlie — is also a top 20 prospect. And numerous legacy prospects are or will soon be contributing to their big-league clubs: Adalberto Mondesi (son of Raul) is expected to be in the Royals’ starting lineup, Lance McCullers Jr. is a fixture in the Astros’ rotation when healthy, and slugger Cody Bellinger (son of Clay) has already earned an All-Star nod for the Dodgers.

If it seems like the kids of former big leaguers are taking over the sport this spring, it’s because they kind of are — they’re making the majors at rates far greater than the general population.

Whether it’s Guerrero, Bichette, Biggio or another prospect, the next child of a major leaguer to reach the majors will set a record for legacy debuts in a single decade. Entering 2019, the 2010s (44 debuts) are tied with the 1990s for most such debuts, according to Baseball-Reference.com data analyzed by FiveThirtyEight. The share of debuts by sons of major leaguers this decade is the second-highest on record (2.1 percent), and could perhaps challenge the 1990s record (2.3 percent) by the close of the season.

But it’s how the progeny of former players are reaching the pinnacle of the sport, and at increasing numbers, that is misunderstood.

“There’s a lot of misconceptions,” said Zach Schonbrun, author of the “Performance Cortex: How Neuroscience Is Redefining Athletic Genius.” “Everyone thinks two great athletes are going to come together and they are going to have a kid, and that kid is automatically going to become a superstar. It’s not so easy.”

Imitation game

When Cavan Biggio and his brother, Conor (who was drafted by the Astros in 2015), were in elementary school, Craig Biggio picked them up from school when the Astros were at home. They traveled straight to Minute Maid Park for the Astros’ pre-game batting practice. During games, Cavan and Conor didn’t spend their time in the family section; rather, they confined themselves to the Astros’ concrete bunker of a batting cage in the bowels of the stadium. They would hit off the tee and play games in the space, only vacating it if an Astros bench player came to get ready for a pinch-hitting at-bat. They observed the swings and collected the balls swatted into the nylon netting. The only other time they would pause is to watch their dad’s at-bats when their attention turned to the bubble-screen TV attached above cage.

Like his dad, Cavan has a two-handed finish in his swing. This is not a coincidence. “The only thing he would say to me, mechanically, was ‘Two-handed finish, two-handed finish,’” Cavan said. “I still hear it today ‘Two-handed finish’ OK. I know [Dad]. I got it.”

He’s not alone in mimicking what made his dad so successful. The swing of Bo Bichette is also similar to his father’s.

Vlad Jr.? Like father, like son:

It’s not just at the plate, too. In Pirates camp, Hayes is renowned for his defensive ability at third base. “My mom says that our mannerisms on defense, the way we stand and stuff like that, are exactly the same,” Hayes said.

Driveline Baseball’s Kyle Boddy studies athletic movement patterns and is on the vanguard of player development in baseball. In speaking with Boddy for reporting on the “The MVP Machine,” he said the greatest advantage in being the son of a major leaguer is in mimicking movement patterns. After all, early-life imitation is key in motor learning. He cited the throwing motion of Astros’ McCullers Jr., which closely resembles that of his father’s.

Boddy suspects the children of major leaguers succeed at abnormally high rates. With the available data it’s difficult to know exactly how their success rate compares to the general population, but there are suggestions that it’s far better.

The proportion of U.S. high school players compared to domestic-born major leaguers has stayed more or less the same. In every year since 1978, there have been almost exactly 500 high school players in the country for every one U.S.-born major leaguer, according to Baseball-Reference.com and National Federation of State High School Associations data. That’s a success rate of about 0.2 percent. We don’t know the total number of major league progeny playing baseball, so we can’t make a direct comparison. But, over the last 30 years, the sons of majors leaguers have accounted for 2 percent of all debuts, and that number has gradually risen throughout the game’s history.1

Pirates general manager Neal Huntington said Hayes’ pedigree played a role in moving him up their draft board, selecting him in the first round in 2015. Huntington is also confident the Blue Jays are “baking in” legacy considerations to their evaluation sauce.

“There’s a lot to be said for seeing how things are done at the highest level whether it’s motor learning or whether it’s how people carry themselves,” Huntington said. “They see the drive, the work ethic it takes.”

What’s also interesting about Hayes, Biggio and Bichette is not just what they observed but how they were taught.

“I never really worked on mechanics,” saya Hayes about his father’s tutelage. “ At a young age, I just kinda learned the right movement, the fundamental stuff.”

Said Bichette: “We didn’t do a lot of drills.”

Boddy is wary of burdening pitchers with too many internal cues. Similarly, Schonbrun says implicit learning is the most effective way to acquire a skill.\

“Ken Griffey Sr. probably didn’t show his son how to wiggle his bat and find that perfect arc for his swing,” Schonbrun says. “I’m guessing he probably told Ken Jr. ‘Here’s how you should get from A to B,’ and Ken developed that swing on his own. … In a lot of ways, that’s a better way for the brain to learn rather than following really detailed explicit instruction.”

‘Specialization’ is not a dirty word

A common experience shared by Biggio, Bichette and Hayes is that they all grew up with a batting cage in their backyards. They all had access to travel baseball, equipment and facilities. Tim Lee, a professor of kinesiology at McMaster University in Hamilton, Ontario, believes that those factors are perhaps the greatest advantage in having a professional athlete for a parent.

“The relationship of the model to the learner is one of the important moderating variables in observational learning,” Lee told FiveThirtyEight. “My hunch, however, is that this plays a far less important role than does the availability of practice facilities and instructional opportunities.”

While those spaces speak to the financial edge that also comes with being the son of a big leaguer, the cages, lessons and tools allowed them to be exposed to not just high-level motor patterns but enabled them to log thousands upon thousands of reps.

In the backyard of their Houston home, Hayes estimates he took “anywhere from 400 to 500 swings a day.”

Said Bichette of life in the backyard swing incubator: “At one point in my life we would go into cage and count at least 200 swings.”

For his fielding work, Biggio said his dad taught him to throw a lacrosse ball off a wall to create unusual hops to improve his hands. Hayes was also taught the practice and still tosses a lacrosse ball off of a wall when killing time in the hallways of minor league clubhouses. It’s one reason he projects as having a 70-grade glove on the 20-to-80 scouting scale.

When Bichette was a freshman in high school, he was also an excellent tennis player, but his parents urged him to choose one sport. Dante Bichette understood the importance of specialization.

While there has been research and concern about sports specialization leading to injury and burnout, Schonbrun notes it’s difficult to excel without it. Florida State professor Anders Ericsson attempted to quantify the hours of specialization needed to become an expert in 1993, which Malcolm Gladwell later dubbed the 10,000-hour rule in his book “Outliers.” Schonbrun said specialization is “necessary.”

“From a cognitive and neurological standpoint, the more you can focus on one task, the more practice that goes into it, the better you are going to be,” Schonbrun said.

Baseball-Reference.com‘s database contains father-son pairs to play in the majors but it does not include minor league family history or other family connections. That means the advantage in growing up around the game is probably even more considerable than we’re showing here. Consider the case of another consensus top-five prospect this spring, a player who could be the next teenager to reach the majors: Tampa Bay’s Wander Franco.

While he seems like a natural, dominating older competition at age 17 last summer, he is also the youngest of three brothers — each named Wander Franco — who each play in the Giants organization. His father, another Wander Franco, pitched in the minor leagues. His uncles Willy and Erick Aybar played in the majors. His neighbor growing up in the Dominican city of Bani was Cleveland Indians infielder Jose Ramirez.

Franco IV was exposed to elite-level motor patterns when he was young, but he was also around people obsessed with baseball. There was a dry river bed near his neighborhood in Bani and that became their ballpark. They used whatever scrap they could find to create bases. They wound up a sock to use as a ball.

“It was all games, every day,” Franco told FiveThirtyEight through an interpreter.

The Rays gave Franco, the No. 1 international prospect in 2017, a $3.85 million bonus. “One of the things that helped us get comfortable with that level of investment was that he had grown up around the game,” said Chaim Bloom, the Rays’ vice president of baseball operations. “You see a lot of guys who have a tremendous amount of skill but don’t know how to apply it on a baseball field. The way that Wander was able to do that as an amateur was really, really rare.”

Franco might seem like a natural, but his story might be more about nurture than nature.

Genes do play a role in success, of course. Bichette said the “bat speed” he shares with his father cannot be taught. Biggio says he has better than 20-20 vision and so does his brother and father. There are things Guerrero Jr. does with that bat that are assuredly tied to genetics.

But in some ways they are all lesser athletes than their fathers. Biggio is not nearly as fast as his father. Guerrero Jr. is not built like his father listed at a 6-2, 250 pounds, where his father was 6-3, 235. As a shortstop, Bichette has a much smaller frame than his father, who was a slugging corner outfielder.

While they are the sons of former professional athletes, there are more talented natural athletes that never reach the major leaguers. Their advantages go beyond genetics, and for a variety of reasons, the advantage of being the son of a major leaguer is growing.