fivethirthyeight--2020-07-08--America Is Testing For COVID-19 More Than Ever — And It Still Isn’t Enough

Expert consensus was clear early in the pandemic : To control the spread of COVID-19 , the U.S. needed to increase testing .
Four months on , we are testing more — a lot more .
The number of Americans getting tested daily is higher than at any point in this pandemic , and we ’ re testing more people per capita than almost any other country on the planet .
Yet many experts say we still need more tests .
Despite a steady increase in testing infrastructure , the U.S. is caught in a vicious cycle with no end @ @ @ @ @ @ @ leads to more cases , which leads to the need for even more tests to finally get a handle on the pandemic .
We ’ ve been playing catch up from the beginning , and , experts say , we ’ re still not close to closing the gap in most states .
In early May , for example , a group of researchers at the Harvard Global Health Institute calculated the average daily number of tests each state and Washington , D.C. , would need to conduct in order to begin reopening @ @ @ @ @ @ @ of June , the researchers adjusted those numbers .
In 18 states and D.C. , the June testing goals for mitigating the pandemic were lower than the goals first proposed in May since the pandemic had waned there .
But in the rest of the country , the testing goals were higher .
Of these 32 states with higher testing goals in June , just six had an average daily testing rate last month that met the goal , and 13 still didn ’ t have an average daily testing rate that met @ @ @ @ @ @ @ finally hitting the numbers that we needed to hit in March , but it ’ s July , ” said Dr. Thomas Tsai , a surgeon and researcher at Harvard who co-authored the testing analysis .
“ And in that interim , hundreds of thousands of new cases have erupted.
” There are lots of factors that have likely contributed to the fact that the U.S. ’ s COVID-19 case numbers haven ’ t dropped the way other countries ’ have .
But a lack of sufficient testing has made it that much @ @ @ @ @ @ @ help the country overcome those factors .
Take contact tracing , for example , a strategy deployed in South Korea early in the pandemic with great success .
Ideally , whenever someone tests positive for COVID-19 , they ’ d isolate themselves , and public health workers would contact everyone that person had contact with recently and test them for COVID-19 too .
If any of those people test positive , they isolate themselves , and then their recent contacts are tested .
None of this is possible without testing .
The Harvard @ @ @ @ @ @ @ encourage us to just randomly test 1.2 million Americans every day and hope the virus disappears .
The idea is that if we were sufficiently testing to track , trace and isolate positive cases , we ’ d be seeing daily testing numbers closer to 1.2 million , instead of 600,000 .
“ I do not want to overstate the kind of magical nature of testing , ” said Dr. Ashish Jha , director of the Harvard Global Health Institute , during an online press conference .
“ The lack of testing makes @ @ @ @ @ @ @ but even if you have adequate capacity , even if you have deployed it effectively , you ’ ve got to do something with that.
” The shortfall in testing numbers is due to two pervasive but opposite problems .
First , some labs and clinics have a shortage of supplies and a backlog of tests , sometimes running out of tests five minutes after opening , according to a report in The New York Times , other times causing a wait of seven days or more to get test results .
That @ @ @ @ @ @ @ country ’ s original missteps when it comes to testing , including the Centers for Disease Control and Prevention originally manufacturing faulty tests , and a general lack of preparedness for an epidemic , from which we never fully recovered .
The second problem speaks to a deeper , more psychological issue .
Many states have the capacity for more testing , but people just aren ’ t lining up to get tested , and contact tracers have reported difficulty getting in touch with individuals who have crossed paths with someone who later @ @ @ @ @ @ @ Hochman , a professor of clinical medicine at the University of Southern California , said this might be due to a sense of fatigue about the pandemic .
“ At a certain point , you get tested once or twice — I see this with my patients , they ’ re like ‘ oh , this was a waste of time , ’ ” Hochman said .
“ In the beginning , my patients were calling me asking to get tested .
Those calls aren ’ t coming in anymore.
” There are @ @ @ @ @ @ @ getting tested , including costs ( while tests are free , the appointment needed to get a test often isn ’ t ) , concerns about missing work , or even local limitations on who is allowed to get tested .
All of this still means we have a lack of testing , but not necessarily for a lack of trying .
The U.S. had an opportunity to close the testing gap .
During lockdown , strict social distancing helped case numbers drop and lessened the strain on health care systems .
As @ @ @ @ @ @ @ to allow businesses to reopen , cases are bound to rise .
But if , during lockdown , states had ramped up testing dramatically by creating a strong supply chain and expanding testing parameters beyond actively sick individuals , , they would have had the necessary infrastructure to address future rises in cases , according to Tsai .
Instead , states gradually increased testing while simultaneously lifting restrictions , a double-whammy that all but guaranteed the surge in cases we ’ re seeing now , with little ability to nip local outbreaks in @ @ @ @ @ @ @ a forest fire ( an analogy a few experts have been using ) .
If you have a handful of small brush fires , you can find them and control them .
If you don ’ t know they ’ re there , they can quickly turn into a raging forest fire that is much harder to control .
Without sufficient testing when cases are low , those cases can go undetected , possibly by people who have mild or no symptoms and are out in the community spreading the disease to more @ @ @ @ @ @ @ risk as cities and states start to reopen .
“ It ’ s going to be tough right now because the case numbers are so high that to do really efficient testing , tracing , and isolation , we ’ re going to need a whole lot of tests , ” said Tara Smith , an epidemiologist at Kent State University .
There are some experts who argue we don ’ t need to dramatically increase testing further , such as Hochman , who has written on the topic .
Hochman argues the @ @ @ @ @ @ @ to inform public health responses .
But the problem is we ’ re not executing those responses well , either .
“ Masks , social distancing and hygiene are the three things that make the biggest difference , and testing is probably four or five on that list , ” Hochman said .
Testing on its own doesn ’ t equal success in the battle against the novel coronavirus .
But for the U.S. , our failure to sufficiently test enough people is representative of the many challenges we face .

America Is Testing For COVID-19 More Than Ever — And It Still Isn’t Enough
Expert consensus was clear early in the pandemic: To control the spread of COVID-19, the U.S. needed to increase testing. Four months on, we are testing more — a lot more. The number of Americans getting tested daily is higher than at any point in this pandemic, and we’re testing more people per capita than almost any other country on the planet.
Yet many experts say we still need more tests.
Despite a steady increase in testing infrastructure, the U.S. is caught in a vicious cycle with no end in sight. A lag in testing leads to more cases, which leads to the need for even more tests to finally get a handle on the pandemic. We’ve been playing catch up from the beginning, and, experts say, we’re still not close to closing the gap in most states.
In early May, for example, a group of researchers at the Harvard Global Health Institute calculated the average daily number of tests each state and Washington, D.C., would need to conduct in order to begin reopening later that month. At the end of June, the researchers adjusted those numbers. In 18 states and D.C., the June testing goals for mitigating the pandemic were lower than the goals first proposed in May since the pandemic had waned there. But in the rest of the country, the testing goals were higher. Of these 32 states with higher testing goals in June, just six had an average daily testing rate last month that met the goal, and 13 still didn’t have an average daily testing rate that met the May benchmarks.
The majority of states and U.S. are lagging behind in testing The difference in the average number of tests and the Harvard Global Health Institute’s mitigation testing goal for each state, D.C. and the country JUNE testing AVERAGE HARVARD JUNE GOAL Difference Hawaii 771 192 +301% Vermont 1,060 265 +300% Alaska 2,016 520 +288% Montana 1,702 553 +208% New Jersey 22,541 7,346 +207% West Virginia 2,471 923 +168% Connecticut 7,212 2,769 +160% New York 61,704 29,591 +109% D.C. 1,694 1,002 +69% Maine 1,511 952 +59% Delaware 1,674 1,268 +32% Illinois 23,525 19,116 +23% Massachusetts 8,510 7,333 +16% South Dakota 1,199 1,041 +15% Idaho 1,420 1,363 +4% Rhode Island 2,926 2,893 +1% North Dakota 1,136 1,129 +1% New Hampshire 1,601 1,622 -1% Maryland 7,799 8,292 -6% Indiana 7,422 8,051 -8% Michigan 13,810 15,646 -12% Oklahoma 4,946 5,816 -15% Nebraska 2,567 3,133 -18% Wyoming 309 394 -21% Pennsylvania 10,284 13,326 -23% Kansas 2,726 3,574 -24% New Mexico 4,776 7,044 -32% Louisiana 11,780 17,896 -34% Minnesota 10,729 17,361 -38% Oregon 3,614 6,152 -41% Kentucky 5,239 9,523 -45% Wisconsin 10,018 19,196 -48% Iowa 4,930 9,497 -48% Virginia 10,988 22,422 -51% Nevada 4,500 9,518 -53% Missouri 5,982 13,007 -54% United States 509,782 1,165,199 -56% Washington 7,003 16,062 -56% Tennessee 11,905 27,894 -57% Ohio 13,234 35,148 -62% Colorado 4,774 12,979 -63% Arkansas 6,056 16,668 -64% Utah 4,228 11,710 -64% California 74,076 222,862 -67% North Carolina 16,458 51,305 -68% Texas 30,581 117,119 -74% Florida 30,788 142,300 -78% Georgia 12,278 64,048 -81% South Carolina 6,012 32,831 -82% Alabama 6,303 41,577 -85% Arizona 10,238 74,135 -86% Mississippi 3,857 28,835 -87% * These 16 states report the number of specimens tested, not people, in their testing reports. Because some people may be tested more than once, these numbers are probably higher than the number of people tested. Texas reports a mix of specimens and people tested. Wyoming switched from reporting data on specimens tested to people on June 19. The Idaho Department of Health and Welfare includes a small number of out-of-state residents among its counts. Source: the covid tracking project, Harvard global health institute
“We are finally hitting the numbers that we needed to hit in March, but it’s July,” said Dr. Thomas Tsai, a surgeon and researcher at Harvard who co-authored the testing analysis. “And in that interim, hundreds of thousands of new cases have erupted.”
There are lots of factors that have likely contributed to the fact that the U.S.’s COVID-19 case numbers haven’t dropped the way other countries’ have. But a lack of sufficient testing has made it that much harder to implement any strategy that might help the country overcome those factors. Take contact tracing, for example, a strategy deployed in South Korea early in the pandemic with great success. Ideally, whenever someone tests positive for COVID-19, they’d isolate themselves, and public health workers would contact everyone that person had contact with recently and test them for COVID-19 too. If any of those people test positive, they isolate themselves, and then their recent contacts are tested. None of this is possible without testing.
[Related: Where The Latest COVID-19 Models Think We’re Headed — And Why They Disagree]
The Harvard testing goals aren’t meant to encourage us to just randomly test 1.2 million Americans every day and hope the virus disappears. The idea is that if we were sufficiently testing to track, trace and isolate positive cases, we’d be seeing daily testing numbers closer to 1.2 million, instead of 600,000.
“I do not want to overstate the kind of magical nature of testing,” said Dr. Ashish Jha, director of the Harvard Global Health Institute, during an online press conference. “The lack of testing makes it difficult to control the virus, but even if you have adequate capacity, even if you have deployed it effectively, you’ve got to do something with that.”
The shortfall in testing numbers is due to two pervasive but opposite problems. First, some labs and clinics have a shortage of supplies and a backlog of tests, sometimes running out of tests five minutes after opening, according to a report in The New York Times, other times causing a wait of seven days or more to get test results. That’s partly the result of the country’s original missteps when it comes to testing, including the Centers for Disease Control and Prevention originally manufacturing faulty tests, and a general lack of preparedness for an epidemic, from which we never fully recovered.
The second problem speaks to a deeper, more psychological issue. Many states have the capacity for more testing, but people just aren’t lining up to get tested, and contact tracers have reported difficulty getting in touch with individuals who have crossed paths with someone who later tested positive for COVID-19. Dr. Michael Hochman, a professor of clinical medicine at the University of Southern California, said this might be due to a sense of fatigue about the pandemic. “At a certain point, you get tested once or twice — I see this with my patients, they’re like ‘oh, this was a waste of time,’” Hochman said. “In the beginning, my patients were calling me asking to get tested. Those calls aren’t coming in anymore.”
[Related: The Science of Mask-Wearing Hasn’t Changed. So Why Have Our Expectations?]
There are also other factors that discourage people from getting tested, including costs (while tests are free, the appointment needed to get a test often isn’t), concerns about missing work, or even local limitations on who is allowed to get tested.
All of this still means we have a lack of testing, but not necessarily for a lack of trying.
The U.S. had an opportunity to close the testing gap. During lockdown, strict social distancing helped case numbers drop and lessened the strain on health care systems. As soon as states ease restrictions and begin to allow businesses to reopen, cases are bound to rise. But if, during lockdown, states had ramped up testing dramatically by creating a strong supply chain and expanding testing parameters beyond actively sick individuals,, they would have had the necessary infrastructure to address future rises in cases, according to Tsai.
Subscribe to our coronavirus podcast, PODCAST-19
Instead, states gradually increased testing while simultaneously lifting restrictions, a double-whammy that all but guaranteed the surge in cases we’re seeing now, with little ability to nip local outbreaks in the bud.
Think of it like a forest fire (an analogy a few experts have been using). If you have a handful of small brush fires, you can find them and control them. If you don’t know they’re there, they can quickly turn into a raging forest fire that is much harder to control. Without sufficient testing when cases are low, those cases can go undetected, possibly by people who have mild or no symptoms and are out in the community spreading the disease to more people. This becomes an even higher risk as cities and states start to reopen.
[Related: How Americans View The Coronavirus Crisis And Trump’s Response]
“It’s going to be tough right now because the case numbers are so high that to do really efficient testing, tracing, and isolation, we’re going to need a whole lot of tests,” said Tara Smith, an epidemiologist at Kent State University.
There are some experts who argue we don’t need to dramatically increase testing further, such as Hochman, who has written on the topic. Hochman argues the current level of testing should be sufficient to inform public health responses. But the problem is we’re not executing those responses well, either.
“Masks, social distancing and hygiene are the three things that make the biggest difference, and testing is probably four or five on that list,” Hochman said.
Testing on its own doesn’t equal success in the battle against the novel coronavirus. But for the U.S., our failure to sufficiently test enough people is representative of the many challenges we face.


fivethirthyeight--2020-07-08--What If Kevin Garnett And Tracy McGrady Had Shot Threes Instead Of Long Twos?

Forty years and many analytic debates after the first 3-pointer in NBA history , the league finally understands the power of that arc .
Twenty-six of the 30 NBA teams have averaged more than 30 3-point attempts per game this season , and only one ( the Knicks ) has made fewer than 10 long balls a contest .
The three hasn ’ t killed the midrange game , particularly for star players , but it has wreaked havoc on the long 2-point jumper .
We saw an average of only 2.28 made 2-pointers from at least 19 feet per @ @ @ @ @ @ @ less than half the number from an average game in 2015-16 and less than a third of a typical contest from the 2007-08 season .
The jump shot is older than the pro game itself , and sharpshooters have been hitting long jumpers ever since .
The difference now is that players increasingly take one step further back to earn an extra point .
In fact , shooters almost always take that step back now .
Twenty years ago , 43.9 percent of all jumpers made from 19 feet or further were two-pointers @ @ @ @ @ @ @ league in long twos made that season , made 2.7 jumpers per game from at least 19 feet .
Only 27 percent of those shots were 3-pointers .
Twenty-seven percent !
The contrast to 2019-20 is stark .
LaMarcus Aldridge , the NBA leader in long twos made per game , is behind the 3-point line on 61 percent of his jump shots made from at least 19 feet .
And Aldridge is an outlier : On average , 91.4 percent of all shots made from at least 19 feet this season were @ @ @ @ @ @ @ Brandon who made lots of jumpers before the NBA found religion with 3-pointers ?
How many points did they leave on the table ?
To find out , I looked on Basketball-Reference.com at every regular-season 2-point jumper made from at least 19 feet since the 1996-97 season .
I filtered for players with at least 250 field-goal attempts and at least 5,000 career points total .
I then converted all of those long twos to threes and recalculated each shooter ’ s scoring totals and true shooting percentages .
Of course , this @ @ @ @ @ @ @ ’ s no way to know whether those shots would have actually gone in from the longer distance .
But this does offer us some insight into who may have most benefited from ditching long-range twos for threes .
Here are the 25 players with the greatest difference between their actual true shooting percentage and what it could have been if they had just stepped back .
In general , role players saw the largest true shooting percentage gains , while stars got smaller efficiency bumps despite adding more points to their totals @ @ @ @ @ @ @ — role players are more likely to shoot the assisted perimeter jumpers that were once long twos and are now almost exclusively threes .
But there are two fascinating exceptions : Kevin Garnett and Tracy McGrady .
Like most superstars , they both made a ton of long twos .
Unlike most superstars , they got the scoring efficiency boost in this exercise more typical of role players .
That ’ s because their games were made for today ’ s NBA , not the league in which they starred .
The fact @ @ @ @ @ @ @ their craft despite so many long twos that would have been discouraged today should be a major boost to their historical legacies .
Garnett and McGrady were prototypes of the two kinds of superstars taking over the league today .
Garnett was what we now ( ironically ) call a “ unicorn ” : a long , mobile , skilled big man who could space the floor on offense and shut down all five positions on defense .
McGrady was the platonic ideal of every top wing scorer today — more point guard @ @ @ @ @ @ @ , handles and a lanky core that allowed him to drive around and through his defender .
Put another way , KG was the precursor to Anthony Davis , while James Harden is just T-Mac 2.0 .
Like Davis , KG toiled on mediocre teams before a midcareer trade to a contender .
Like Harden , T-Mac passed up being a sidekick and became the sun that his other teammates orbited around .
Davis and Harden are fortunate enough to play in an era that properly values 3-point shots .
Their shot profiles @ @ @ @ @ @ @ feature many more threes than long twos , so they appear to be far more efficient scorers than Garnett and McGrady .
Based on that , it might be easy to think that Davis and Harden belong in a higher echelon in the NBA pantheon than Garnett and McGrady .
But the reality is far more complex .
If you turn every long two made by those four players into made 3-pointers , the efficiency gap among each pair of superstars significantly shrinks .
Davis and Harden still have an advantage over their @ @ @ @ @ @ @ .
And that ’ s before considering that Garnett and McGrady had far less room to get their shots and drives than Davis and Harden see today , in an era of pristine spacing .
KG would ’ ve been more open if he stood here : Instead of here : And you think T-Mac wouldn ’ t have relished attacking his man off the dribble with the floor spaced like this ?
Instead of this ?
Perhaps it ’ s assuming too much to say McGrady and ( especially ) Garnett would @ @ @ @ @ @ @ behind the 3-point line instead of one step inside it .
But their reluctance to make that change has more to do with their era than their own qualities .
That ’ s worth keeping in mind when comparing the statistics of current superstars with past legends , especially amid the 3-point revolution .
They may play alike , but they weren ’ t playing the same game .

What If Kevin Garnett And Tracy McGrady Had Shot Threes Instead Of Long Twos? The NBA has ditched the long 2-pointer — but not in time to boost the point totals of past stars.
Forty years and many analytic debates after the first 3-pointer in NBA history, the league finally understands the power of that arc. Twenty-six of the 30 NBA teams have averaged more than 30 3-point attempts per game this season, and only one (the Knicks) has made fewer than 10 long balls a contest. The three hasn’t killed the midrange game, particularly for star players, but it has wreaked havoc on the long 2-point jumper. We saw an average of only 2.28 made 2-pointers from at least 19 feet per game this season. That’s less than half the number from an average game in 2015-16 and less than a third of a typical contest from the 2007-08 season.
The jump shot is older than the pro game itself, and sharpshooters have been hitting long jumpers ever since. The difference now is that players increasingly take one step further back to earn an extra point.
NBA players aren’t making as many long twos Total regular-season 2-point shots made from at least 19 feet since 1996-97, plus each season’s leader Long TWOS made Season Total Per game Season leader 2019-20 2,212 2.28 LaMarcus Aldridge 2018-19 3,593 2.92 J.J. Redick 2017-18 4,841 3.94 J.J. Redick 2016-17 5,216 4.24 J.J. Redick 2015-16 5,828 4.74 J.J. Redick 2014-15 6,315 5.13 Avery Bradley, LaMarcus Aldridge 2013-14 6,437 5.23 LaMarcus Aldridge 2012-13 6,840 5.57 LaMarcus Aldridge 2011-12 5,877 5.94 Josh Smith 2010-11 7,865 6.39 LeBron James 2009-10 8,115 6.60 LeBron James 2008-09 8,725 7.09 Dwyane Wade 2007-08 9,536 7.75 Tracy McGrady 2006-07 8,547 6.95 Tracy McGrady 2005-06 8,633 7.02 Kobe Bryant 2004-05 8,533 6.94 Tracy McGrady 2003-04 7,528 6.33 DeShawn Stevenson 2002-03 7,940 6.68 Desmond Mason 2001-02 7,517 6.32 David Wesley 2000-01 7,570 6.37 Mike Bibby 1999-00 9,004 7.57 Terrell Brandon 1998-99 5,116 7.06 John Starks 1997-98 8,326 7.00 Ron Mercer 1996-97 5,209 4.38 Mahmoud Abdul-Rauf Source: Basketball-Reference.com
In fact, shooters almost always take that step back now. Twenty years ago, 43.9 percent of all jumpers made from 19 feet or further were two-pointers. Terrell Brandon, who led the league in long twos made that season, made 2.7 jumpers per game from at least 19 feet. Only 27 percent of those shots were 3-pointers. Twenty-seven percent!
The contrast to 2019-20 is stark. LaMarcus Aldridge, the NBA leader in long twos made per game, is behind the 3-point line on 61 percent of his jump shots made from at least 19 feet. And Aldridge is an outlier: On average, 91.4 percent of all shots made from at least 19 feet this season were threes.
[Related: The Winners And Losers In Our Updated NBA Forecast]
So what about players like Brandon who made lots of jumpers before the NBA found religion with 3-pointers? How many points did they leave on the table? To find out, I looked on Basketball-Reference.com at every regular-season 2-point jumper made from at least 19 feet since the 1996-97 season. I filtered for players with at least 250 field-goal attempts and at least 5,000 career points total. I then converted all of those long twos to threes and recalculated each shooter’s scoring totals and true shooting percentages.
Of course, this is just a thought experiment — there’s no way to know whether those shots would have actually gone in from the longer distance. But this does offer us some insight into who may have most benefited from ditching long-range twos for threes. Here are the 25 players with the greatest difference between their actual true shooting percentage and what it could have been if they had just stepped back.
Players have left a lot of points on the court NBA players since 1996-97 with the biggest difference in true shooting percentage after adjusting the value of their long 2-pointers* to 3 points Career points True Shooting % Player Long TWOs Total Adjusted CAREER Adjusted DIFF. Eddie House 567 5,356 5,923 50.77% 56.14% +5.37 Ron Mercer 549 5,892 6,441 47.01 51.39 +4.38 José Calderón 597 7,921 8,518 57.35 61.67 +4.32 Mike Bibby 1,177 14,698 15,875 53.62 57.91 +4.29 Raja Bell 545 6,998 7,543 54.39 58.62 +4.24 Derek Fisher 844 10,713 11,557 51.41 55.46 +4.05 DeShawn Stevenson 481 5,930 6,411 48.72 52.68 +3.95 David Wesley 885 11,842 12,727 52.55 56.48 +3.93 J.J. Redick 707 11,589 12,296 60.23 63.91 +3.67 Travis Best 382 5,376 5,758 51.45 55.11 +3.66 Channing Frye 515 7,786 8,301 54.65 58.27 +3.61 Avery Bradley 469 6,712 7,181 51.53 55.14 +3.60 Travis Outlaw 379 5,273 5,652 50.03 53.63 +3.60 Brevin Knight 391 5,342 5,733 47.57 51.05 +3.48 Wally Szczerbiak 559 9,195 9,754 57.26 60.75 +3.48 Ben Gordon 693 11,084 11,777 54.63 58.04 +3.42 Kirk Hinrich 632 9,594 10,226 51.58 54.97 +3.40 Steve Blake 363 5,662 6,025 52.14 55.49 +3.34 Lucious Harris 370 5,784 6,154 50.70 53.94 +3.24 Tracy McGrady 1,134 18,381 19,515 51.92 55.12 +3.20 Caron Butler 751 12,430 13,181 52.29 55.45 +3.16 Kevin Garnett 1,484 26,071 27,555 54.62 57.73 +3.11 Luke Ridnour 462 7,740 8,202 51.87 54.96 +3.10 Mike Miller 584 10,973 11,557 57.63 60.70 +3.07 Damon Stoudamire 703 11,763 12,466 50.49 53.51 +3.02 *Long 2-pointers are those from at least 19 feet. Players include only those with at least 250 field-goal attempts and 5,000 career points. Regular season only. Source: Basketball-Reference.com
In general, role players saw the largest true shooting percentage gains, while stars got smaller efficiency bumps despite adding more points to their totals. That shouldn’t surprise anyone — role players are more likely to shoot the assisted perimeter jumpers that were once long twos and are now almost exclusively threes.
But there are two fascinating exceptions: Kevin Garnett and Tracy McGrady. Like most superstars, they both made a ton of long twos. Unlike most superstars, they got the scoring efficiency boost in this exercise more typical of role players. That’s because their games were made for today’s NBA, not the league in which they starred. The fact that they were near the top of their craft despite so many long twos that would have been discouraged today should be a major boost to their historical legacies.
Garnett and McGrady were prototypes of the two kinds of superstars taking over the league today. Garnett was what we now (ironically) call a “unicorn”: a long, mobile, skilled big man who could space the floor on offense and shut down all five positions on defense. McGrady was the platonic ideal of every top wing scorer today — more point guard than small forward, with shooting range, handles and a lanky core that allowed him to drive around and through his defender.
Put another way, KG was the precursor to Anthony Davis, while James Harden is just T-Mac 2.0. Like Davis, KG toiled on mediocre teams before a midcareer trade to a contender. Like Harden, T-Mac passed up being a sidekick and became the sun that his other teammates orbited around.
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Davis and Harden are fortunate enough to play in an era that properly values 3-point shots. Their shot profiles — Harden’s especially so — feature many more threes than long twos, so they appear to be far more efficient scorers than Garnett and McGrady. Based on that, it might be easy to think that Davis and Harden belong in a higher echelon in the NBA pantheon than Garnett and McGrady.
But the reality is far more complex. If you turn every long two made by those four players into made 3-pointers, the efficiency gap among each pair of superstars significantly shrinks. Davis and Harden still have an advantage over their prototypes, but not by as much.
How do KG and T-Mac compare to the next generation? Career shots made and differences in true shooting percentage after adjusting the value of long 2-pointers* to 3 points for Anthony Davis vs. Kevin Garnett and James Harden vs. Tracy McGrady Career shots made True Shooting % Long twos Threes Actual Adjusted Diff. Anthony Davis 266 246 58.82% 60.07% +1.25 Kevin Garnett 1,484 174 54.62 57.73 +3.11 Difference -1,218 72 4.20 2.34 -1.86 James Harden 176 2,296 60.99 61.51 +0.52 Tracy McGrady 1,134 1,081 51.92 55.12 +3.20 Difference -958 1,215 9.07 6.39 -2.69 *Long twos are since 1996-97, Garnett’s second season in the NBA, which is as far back as play-by-play data goes. Source: Basketball-Reference.com
And that’s before considering that Garnett and McGrady had far less room to get their shots and drives than Davis and Harden see today, in an era of pristine spacing. KG would’ve been more open if he stood here:
Instead of here:
And you think T-Mac wouldn’t have relished attacking his man off the dribble with the floor spaced like this?
Instead of this?
Perhaps it’s assuming too much to say McGrady and (especially) Garnett would have shot as accurately from one step behind the 3-point line instead of one step inside it. But their reluctance to make that change has more to do with their era than their own qualities.
That’s worth keeping in mind when comparing the statistics of current superstars with past legends, especially amid the 3-point revolution. They may play alike, but they weren’t playing the same game.


fivethirthyeight--2020-07-09--Biden’s Polling Lead Is Big — And Steady

The race between President Trump and Joe Biden is verging on a landslide .
That ’ s not a word we use lightly .
Over the past month , Biden ’ s lead over Trump has been both incredibly stable and unusually large .
Amidst Trump ’ s unpopular handling of the protests that followed the police killing of George Floyd , Biden ’ s lead has hovered within a tight band of 8.9 to 9.6 percentage points since mid-June , according to FiveThirtyEight ’ s national polling average .
This is a sizable enough lead that Trump ’ s @ @ @ @ @ @ @ .
Take what CNN analyst and FiveThirtyEight alum Harry Enten found earlier this month when he looked back at presidential elections where an incumbent was running since 1940 .
He calculated , on average , a 7-point difference between the final national popular vote margin and the polls conducted four months out .
That might sound like a lot of movement — and it is — but the problem for Trump is even if the polls swung toward him by 7 points , he would still trail Biden by about 2 to 3 @ @ @ @ @ @ @ found , 4.5 points , would leave Trump in even worse shape .
Of course , if the polls did swing 7 points in Trump ’ s favor , leaving him only 2 to 3 points behind Biden nationally , Trump could still win — after all , he won in 2016 despite losing the popular vote by about 2 points .
But this isn ’ t an easy reelection path , particularly if Biden ’ s lead holds .
New national surveys mostly confirmed Biden ’ s sizable lead .
This week @ @ @ @ @ @ @ points , 49 percent to 40 percent , and last week a survey from Research Co. found the same .
Rasmussen Reports/Pulse Opinion Research , a pollster Trump often cites in support of his presidency , this week found Biden up 10 points , 50 percent to 40 percent .
But not every recent poll has been quite so bullish for Biden — a new poll from Reuters/Ipsos found Biden up 6 points , while a survey last week by Yahoo News/YouGov put him up by just 5 points , 45 percent to @ @ @ @ @ @ @ from The Hill/HarrisX found Biden up by just 4 points .
Additionally , Trump got a few favorable polls in Florida and Pennsylvania .
In surveys conducted just before the Fourth of July , Trafalgar Group found Trump tied with Biden in Florida and trailing Biden by just 5 points in Pennsylvania .
That might not sound like particularly good news for Trump in Pennsylvania , but considering Biden ’ s average lead there is more than 7 points , anything that shows that lead waning is a win for Trump .
However @ @ @ @ @ @ @ Republican pollster with a slight bias toward the GOP isn ’ t great news for Trump , as in many ways these polls offer his best-case scenario , and that scenario still isn ’ t very good .
It has Trump either barely breaking even ( Florida ) or still underwater ( Pennsylvania ) .
Elsewhere , state-level polls didn ’ t offer Trump much of a silver lining .
Democratic pollster Public Policy Polling found Biden up by 17 points in Colorado , which Trump lost by 5 points in 2016 , @ @ @ @ @ @ @ , which Trump lost by just 3 points last time .
The pollster has a slight Democratic bias , but Biden ’ s lead in these polls are sizable enough to suggest that Trump will have a difficult time competing in these states .
In fact , although the battleground states skew slightly more Republican than the nation as a whole — as you can see in the table below — Biden continues to lead in nearly every one of them , including places like Georgia , which The Cook Political Report just @ @ @ @ @ @ @ .
If Biden won all the states that the election handicapper rates as solidly or slightly Democratic , it would now give him more than 270 electoral votes because of his advantage in these key states .
As always , there ’ s still time for the electoral environment to shift in Trump ’ s direction and narrow his polling deficit .
The national party conventions and Biden ’ s vice presidential pick are big events that could still change the race , and there ’ s always the possibility that some unexpected @ @ @ @ @ @ @ .
But unfortunately for the president , recent polls have shown simply more of the same — he ’ s treading on thin electoral ice .

The race between President Trump and Joe Biden is verging on a landslide. That’s not a word we use lightly.
Over the past month, Biden’s lead over Trump has been both incredibly stable and unusually large. Amidst Trump’s unpopular handling of the protests that followed the police killing of George Floyd, Biden’s lead has hovered within a tight band of 8.9 to 9.6 percentage points since mid-June, according to FiveThirtyEight’s national polling average.
This is a sizable enough lead that Trump’s reelection chances are in a precarious position. Take what CNN analyst and FiveThirtyEight alum Harry Enten found earlier this month when he looked back at presidential elections where an incumbent was running since 1940. He calculated, on average, a 7-point difference between the final national popular vote margin and the polls conducted four months out. That might sound like a lot of movement — and it is — but the problem for Trump is even if the polls swung toward him by 7 points, he would still trail Biden by about 2 to 3 points nationally. The median difference Enten found, 4.5 points, would leave Trump in even worse shape.
[Related: Our 2020 National Polling Averages]
Of course, if the polls did swing 7 points in Trump’s favor, leaving him only 2 to 3 points behind Biden nationally, Trump could still win — after all, he won in 2016 despite losing the popular vote by about 2 points. But this isn’t an easy reelection path, particularly if Biden’s lead holds.
New national surveys mostly confirmed Biden’s sizable lead. This week, The Economist/YouGov found Biden up 9 points, 49 percent to 40 percent, and last week a survey from Research Co. found the same. Rasmussen Reports/Pulse Opinion Research, a pollster Trump often cites in support of his presidency, this week found Biden up 10 points, 50 percent to 40 percent. But not every recent poll has been quite so bullish for Biden — a new poll from Reuters/Ipsos found Biden up 6 points, while a survey last week by Yahoo News/YouGov put him up by just 5 points, 45 percent to 40 percent. Plus, a survey from The Hill/HarrisX found Biden up by just 4 points.
[Related: How Popular Is President Donald Trump?]
Additionally, Trump got a few favorable polls in Florida and Pennsylvania. In surveys conducted just before the Fourth of July, Trafalgar Group found Trump tied with Biden in Florida and trailing Biden by just 5 points in Pennsylvania. That might not sound like particularly good news for Trump in Pennsylvania, but considering Biden’s average lead there is more than 7 points, anything that shows that lead waning is a win for Trump. However, the fact that Trafalgar is a Republican pollster with a slight bias toward the GOP isn’t great news for Trump, as in many ways these polls offer his best-case scenario, and that scenario still isn’t very good. It has Trump either barely breaking even (Florida) or still underwater (Pennsylvania).
Elsewhere, state-level polls didn’t offer Trump much of a silver lining. Democratic pollster Public Policy Polling found Biden up by 17 points in Colorado, which Trump lost by 5 points in 2016, and ahead by 11 points in Maine, which Trump lost by just 3 points last time. The pollster has a slight Democratic bias, but Biden’s lead in these polls are sizable enough to suggest that Trump will have a difficult time competing in these states.
[Related: Our Pollster Ratings]
In fact, although the battleground states skew slightly more Republican than the nation as a whole — as you can see in the table below — Biden continues to lead in nearly every one of them, including places like Georgia, which The Cook Political Report just moved into its “toss-up” category. If Biden won all the states that the election handicapper rates as solidly or slightly Democratic, it would now give him more than 270 electoral votes because of his advantage in these key states.
Biden continues to lead in national and battleground polls FiveThirtyEight polling averages as of 5:15 p.m. Eastern on July 8, 2020 State Biden Trump Biden Margin Lean Relative to Nation Colorado 55.1% 37.8% +17.4 D+7.8 New Mexico 54.3 40.4 +13.9 D+4.3 Maine 53.4 40.8 +12.5 D+2.9 Virginia 50.8 39.5 +11.2 D+1.7 Minnesota 54.3 43.7 +10.6 D+1.0 Michigan 50.0 40.3 +9.7 D+0.1 National 50.7 41.1 +9.6 EVEN Nevada 48.5 39.8 +8.7 R+0.9 New Hampshire 50.1 41.8 +8.3 R+1.3 Wisconsin 49.5 41.4 +8.1 R+1.5 Pennsylvania 49.6 42.0 +7.5 R+2.0 Florida 48.8 42.6 +6.3 R+3.3 North Carolina 47.8 44.6 +3.2 R+6.4 Arizona 47.3 44.2 +3.1 R+6.5 Ohio 48.1 45.5 +2.6 R+7.0 Georgia 47.6 45.8 +1.7 R+7.9 Iowa 45.7 45.7 +0.0 R+9.6 Texas 46.0 47.3 -1.3 R+10.9 “Lean relative to nation” is how much more pro-Biden or pro-Trump a state’s polling average is than the national polling average.
As always, there’s still time for the electoral environment to shift in Trump’s direction and narrow his polling deficit. The national party conventions and Biden’s vice presidential pick are big events that could still change the race, and there’s always the possibility that some unexpected news will break between now and November. But unfortunately for the president, recent polls have shown simply more of the same — he’s treading on thin electoral ice.
‘(Masks) might wind up helping Trump’s poll numbers’: Nate Silver


fivethirthyeight--2020-07-09--Politics Podcast: Conservatives Didn’t Get The SCOTUS They Wanted This Term

The U.S. Supreme Court wrapped up a lengthy and consequential term on Thursday with a ruling that rejected President Trump @ @ @ @ @ immunity .
In this installment of the FiveThirtyEight Politics podcast , Amelia Thomson-DeVeaux and Galen @ @ @ @ @ that ruling and look back at other key decisions throughout the term .
They also @ @ @ @ @ ’ s role on the court and ask whether justices are influenced by public opinion @ @ @ @ @ the episode by clicking the “ play ” button in the audio player above or @ @ @ @ @ , the ESPN App or your favorite podcast platform .
If you are new to @ @ @ @ @ listen .
The FiveThirtyEight Politics podcast publishes Mondays and Thursdays .
Help new listeners discover @ @ @ @ @ a rating and review on iTunes .
Have a comment , question or suggestion for @ @ @ @ @ polling ” ?
Get in touch by email , on Twitter or in the comments @

The U.S. Supreme Court wrapped up a lengthy and consequential term on Thursday with a ruling that rejected President Trump’s claims to legal immunity. In this installment of the FiveThirtyEight Politics podcast, Amelia Thomson-DeVeaux and Galen Druke unpack the implications of that ruling and look back at other key decisions throughout the term. They also consider Chief Justice John Roberts’s role on the court and ask whether justices are influenced by public opinion.
You can listen to the episode by clicking the “play” button in the audio player above or by downloading it in iTunes, the ESPN App or your favorite podcast platform. If you are new to podcasts, learn how to listen.
The FiveThirtyEight Politics podcast publishes Mondays and Thursdays. Help new listeners discover the show by leaving us a rating and review on iTunes. Have a comment, question or suggestion for “good polling vs. bad polling”? Get in touch by email, on Twitter or in the comments.


fivethirthyeight--2020-07-09--An Interview With Dr. Anthony Fauci

An Interview With Dr. Anthony Fauci

Dr. Anthony Fauci , the director of the National Institute of Allergy and Infectious Diseases , talks to PODCAST-19 host @ @ @ @ @ , how America ’ s response to COVID-19 compares with other countries ’ , and @ @ @ @ @ .
Don ’ t want to miss an episode of PODCAST-19 , FiveThirtyEight ’ s @ @ @ @ @ know — and what we know we don ’ t know — about COVID-19 ?
@ @ @ @ @ app !
For example , here ’ s where to do it on Apple Podcasts @ @ @

Dr. Fauci On How The U.S. Is Doing And The Timeline For A COVID-19 Vaccine
Dr. Anthony Fauci, the director of the National Institute of Allergy and Infectious Diseases, talks to PODCAST-19 host Anna Rothschild about political partisanship, how America’s response to COVID-19 compares with other countries’, and the search for a vaccine.
Don’t want to miss an episode of PODCAST-19, FiveThirtyEight’s weekly look at what we know — and what we know we don’t know — about COVID-19? Subscribe on your favorite podcasting app! For example, here’s where to do it on Apple Podcasts and Spotify.


fivethirthyeight--2020-07-09--Fauci: ‘I Don’t Think You Can Say We’re Doing Great. I Mean, We’re Just Not.’

For this week ’ s episode of PODCAST-19 , we interviewed Dr. Anthony Fauci , the director of the National Institute of Allergy and Infectious Diseases , and a leader in the United States ’ COVID-19 response .
As you ’ ll hear in the podcast and read in selected excerpts below , we covered a lot of ground in the 30 minutes we had to talk , including how the U.S. is doing compared to other countries , how American partisanship has influenced our recovery efforts , and how a COVID-19 vaccine might influence the future of vaccine acceptance @ @ @ @ @ @ @ want to miss an episode of PODCAST-19 , FiveThirtyEight ’ s weekly look at what we know — and what we know we don ’ t know — about COVID-19 ?
Subscribe on your favorite podcasting app !
For example , here ’ s where to do it on Apple Podcasts and Spotify .
On why we ’ re seeing a surge in cases : Anna Rothschild : So are you saying that in these states , are you saying that it ’ s a mix of politicians not following guidelines and people @ @ @ @ @ @ @ : Yes .
It is both .
I mean , it ’ s not a unidimensional thing .
It ’ s complicated .
There are some governors and mayors that did it perfectly correctly .
They stayed exactly .
They wanted to open up , so they went through the guidelines of opening up their state .
But what happened is that many of the citizenry , said , “ You know , well , I ’ m either going to be locked down or I ’ m going to let it all @ @ @ @ @ @ @ just looking , documented on TV and in the papers of still photos of people at bars and congregations , which are a perfect setup , particularly if you don ’ t have a mask .
Yeah , then there are some times when despite the guidelines and the recommendations to open up carefully and prudently , some states skipped over those and just opened up too quickly .
AR : Do you think that Florida and Arizona opened up too quickly ?
AF : You know , I think in some respects @ @ @ @ @ @ @ not always .
But I think that that certainly is contributing to that .
Certainly Florida I know , you know , I think jumped over a couple of checkpoints .
Fauci on why we ’ re seeing a surge in cases l FiveThirtyEight On whether partisanship makes fighting COVID-19 more difficult : AR You know , for a few months , masks were quite a partisan issue , though in the past few weeks politicians on both sides have advocated for their use .
Do you think America ’ s hyperpartisan environment @ @ @ @ @ @ @ the virus ?
AF : You know , I think you ’ d have to admit that that ’ s the case .
We live , I mean , you have to be having blindfolders on and covering your ears to think that we don ’ t live in a very divisive society now , from a political standpoint .
I mean , it ’ s just unfortunate , but it is what it is .
And you know , from experience historically , that when you don ’ t have unanimity in @ @ @ @ @ @ @ re not as effective in how you handle it .
So I think you ’ d have to make the assumption that if there wasn ’ t such divisiveness , that we would have a more coordinated approach .
Fauci on whether partisanship makes fighting COVID-19 more difficult On how the U.S. is doing : AR : How do you think the U.S. is doing right now ?
If you ’ re looking across the world , what are your feelings about how we ’ re doing right now ?
AF : Well @ @ @ @ @ @ @ of the United States , like where you live right now [ in New York ] , that are doing really well , that you ’ ve been through something really bad and you have things under control .
And you have a governor and mayor in the city who understand what it means to go by the guidelines for the gateway , phase one , phase two , phase three .
So you ’ re doing well .
Other cities are doing well .
But as a country , when you compare @ @ @ @ @ @ @ ’ t think you can say we ’ re doing great .
I mean , we ’ re just not .
AR : We ’ re at this weird place now where the EU and some other European countries are opening their borders , but they ’ re still banning travel from the United States .
Do you think that ’ s a justified decision on their part ?
AF : You know , I wouldn ’ t use the word justified .
I would say it ’ s understandable .
Because , @ @ @ @ @ @ @ there were many cases in Europe and in China , we banned travel from the European Union , from the U.K. , to us .
So right now , they have their infection rate very low , much lower than we do .
So they ’ re looking at us and they ’ re saying the same thing that we said to them .
I wish that that were not the case .
I wouldn ’ t be recommending that .
I think we need to get back to some sort of normality @ @ @ @ @ @ @ re saying to us , “ Why are you still banning travel from Europe ?
” Which we are .
I mean , so I ’ m all for America and I back what we do .
But if I were a European , then I ’ d be looking at us .
I ’ d say , “ Why are you still banning Europeans from coming to the United States ?
” Fauci on travel restrictions during the pandemic and the EU ban l FiveThirtyEight On whether we can get control of @ @ @ @ @ @ @ : Without a vaccine , how hopeful are you that we ’ ll get this pandemic under control in the U.S. ?
AF : I think we can get it under control .
But keeping it under control is going to be the real problem .
Because this virus is not like other viruses that we ’ ve experienced , like the original SARS from 2002 .
That was a coronavirus .
It caused an outbreak , a pandemic — there were 8,000 cases and 800 deaths .
So in magnitude alone , @ @ @ @ @ @ @ what we ’ re doing now .
But it was not really very well and efficiently transmissible , whereas this virus , to our dismay , is spectacularly efficient in transmitting from person to person .
So that makes me skeptical whether we would get permanent , sustained control of this without having a vaccine .
Fauci on whether we can get control of the virus without a vaccine | FiveThirtyEight On how anti-vaxxers affect what will happen once a vaccine is discovered : AR : One thing I ’ ve been thinking @ @ @ @ @ @ @ know , with any vaccine , even after it goes through extensive clinical trials , there is always some risk of adverse effects .
And even if the side effects with the COVID vaccine , whatever it may be , are extremely small , it ’ s going to get more media attention than probably any other vaccine in history .
At the same time , we also have a growing anti-vaccine movement in this country and around the world .
So I ’ m wondering whether you and other other public health @ @ @ @ @ @ @ long term impact of this moment on vaccine acceptance ?
AF : That ’ s a great question , Anna .
Because what it really tells us is that we got to get it right .
We really do .
Because if we don ’ t , it might have a real negative impact in the long range , in the long term , on how people approach and respond to the need for vaccination , which is the reason why we ’ re taking so seriously that even though we ’ re @ @ @ @ @ @ @ not compromising the safety and nor are we compromising the scientific integrity .
So as we go into the phase three trials , not only are we going to be looking at efficacy , but we ’ re going to be really paying attention : Is there anything there that we ’ re seeing that ’ s even suggestive of a negative impact ?
That ’ s going to be really very important .
So that ’ s a really important question you asked .

For this week’s episode of PODCAST-19, we interviewed Dr. Anthony Fauci, the director of the National Institute of Allergy and Infectious Diseases, and a leader in the United States’ COVID-19 response. As you’ll hear in the podcast and read in selected excerpts below, we covered a lot of ground in the 30 minutes we had to talk, including how the U.S. is doing compared to other countries, how American partisanship has influenced our recovery efforts, and how a COVID-19 vaccine might influence the future of vaccine acceptance in our country.
Don’t want to miss an episode of PODCAST-19, FiveThirtyEight’s weekly look at what we know — and what we know we don’t know — about COVID-19? Subscribe on your favorite podcasting app! For example, here’s where to do it on Apple Podcasts and Spotify.
On why we’re seeing a surge in cases:
Anna Rothschild: So are you saying that in these states, are you saying that it’s a mix of politicians not following guidelines and people not following orders?
Dr. Anthony Fauci: Yes. It is both. I mean, it’s not a unidimensional thing. It’s complicated. There are some governors and mayors that did it perfectly correctly. They stayed exactly. They wanted to open up, so they went through the guidelines of opening up their state. But what happened is that many of the citizenry, said, “You know, well, I’m either going to be locked down or I’m going to let it all rip.” And you could see from just looking, documented on TV and in the papers of still photos of people at bars and congregations, which are a perfect setup, particularly if you don’t have a mask. Yeah, then there are some times when despite the guidelines and the recommendations to open up carefully and prudently, some states skipped over those and just opened up too quickly.
AR: Do you think that Florida and Arizona opened up too quickly?
AF: You know, I think in some respects, in some cases, they did not always. But I think that that certainly is contributing to that. Certainly Florida I know, you know, I think jumped over a couple of checkpoints.
Fauci on why we’re seeing a surge in cases l FiveThirtyEight
On whether partisanship makes fighting COVID-19 more difficult:
AR You know, for a few months, masks were quite a partisan issue, though in the past few weeks politicians on both sides have advocated for their use. Do you think America’s hyperpartisan environment has made it more difficult to suppress the virus?
AF: You know, I think you’d have to admit that that’s the case. We live, I mean, you have to be having blindfolders on and covering your ears to think that we don’t live in a very divisive society now, from a political standpoint. I mean, it’s just unfortunate, but it is what it is. And you know, from experience historically, that when you don’t have unanimity in an approach to something, you’re not as effective in how you handle it. So I think you’d have to make the assumption that if there wasn’t such divisiveness, that we would have a more coordinated approach.
Fauci on whether partisanship makes fighting COVID-19 more difficult
On how the U.S. is doing:
AR: How do you think the U.S. is doing right now? If you’re looking across the world, what are your feelings about how we’re doing right now?
AF: Well, let me say there are parts of the United States, like where you live right now [in New York], that are doing really well, that you’ve been through something really bad and you have things under control. And you have a governor and mayor in the city who understand what it means to go by the guidelines for the gateway, phase one, phase two, phase three. So you’re doing well. Other cities are doing well. But as a country, when you compare us to other countries, I don’t think you can say we’re doing great. I mean, we’re just not.
On travel restrictions:
AR: We’re at this weird place now where the EU and some other European countries are opening their borders, but they’re still banning travel from the United States. Do you think that’s a justified decision on their part?
AF: You know, I wouldn’t use the word justified. I would say it’s understandable. Because, you know, when we saw that there were many cases in Europe and in China, we banned travel from the European Union, from the U.K., to us. So right now, they have their infection rate very low, much lower than we do. So they’re looking at us and they’re saying the same thing that we said to them. I wish that that were not the case. I wouldn’t be recommending that. I think we need to get back to some sort of normality. Just the same as they’re saying to us, “Why are you still banning travel from Europe?” Which we are. I mean, so I’m all for America and I back what we do. But if I were a European, then I’d be looking at us. I’d say, “Why are you still banning Europeans from coming to the United States?”
Fauci on travel restrictions during the pandemic and the EU ban l FiveThirtyEight
On whether we can get control of the virus without a vaccine:
AR: Without a vaccine, how hopeful are you that we’ll get this pandemic under control in the U.S.?
AF: I think we can get it under control. But keeping it under control is going to be the real problem. Because this virus is not like other viruses that we’ve experienced, like the original SARS from 2002. That was a coronavirus. It caused an outbreak, a pandemic — there were 8,000 cases and 800 deaths. So in magnitude alone, you see how different it is from what we’re doing now. But it was not really very well and efficiently transmissible, whereas this virus, to our dismay, is spectacularly efficient in transmitting from person to person. So that makes me skeptical whether we would get permanent, sustained control of this without having a vaccine.
Fauci on whether we can get control of the virus without a vaccine | FiveThirtyEight
On how anti-vaxxers affect what will happen once a vaccine is discovered:
AR: One thing I’ve been thinking a lot about is that, you know, with any vaccine, even after it goes through extensive clinical trials, there is always some risk of adverse effects. And even if the side effects with the COVID vaccine, whatever it may be, are extremely small, it’s going to get more media attention than probably any other vaccine in history. At the same time, we also have a growing anti-vaccine movement in this country and around the world. So I’m wondering whether you and other other public health officials are concerned about kind of the long term impact of this moment on vaccine acceptance?
AF: That’s a great question, Anna. Because what it really tells us is that we got to get it right. We really do. Because if we don’t, it might have a real negative impact in the long range, in the long term, on how people approach and respond to the need for vaccination, which is the reason why we’re taking so seriously that even though we’re doing this quickly, we’re not compromising the safety and nor are we compromising the scientific integrity. So as we go into the phase three trials, not only are we going to be looking at efficacy, but we’re going to be really paying attention: Is there anything there that we’re seeing that’s even suggestive of a negative impact? That’s going to be really very important. So that’s a really important question you asked.


fivethirthyeight--2020-07-09--We’re Not Going To See Trump’s Tax Returns Anytime Soon

President Trump is one of the only presidents in modern memory who has kept his tax returns private , and attempts to force their release have sparked a mountain of litigation , reaching all the way to the Supreme Court .
But the Supreme Court ’ s verdict on whether Trump ’ s banks and accounting firm can be required to release his personal financial records is a bit of a mixed bag .
On the one hand , the court delivered Trump a major defeat , dismissing his most expansive claims to presidential immunity .
Trump has argued that @ @ @ @ @ @ @ can ’ t be criminally investigated .
But the court ruled in a 7-2 decision written by Chief Justice John Roberts that New York prosecutors do have the authority to subpoena his business records , sending the case back to the lower court .
But in the second ruling on Trump ’ s tax returns — which was also a 7-2 decision written by Roberts — which involved three House committees ’ subpoenas for his records , the court essentially punted .
The justices emphasized the House does have the authority to issue @ @ @ @ @ @ @ branch , but they said lower court judges didn ’ t properly weigh the separation of powers issues inherent in the requests — suggesting that Congress ’ s power to investigate the president is not unlimited .
The ruling also sent that case back to the lower courts for further consideration .
That means Trump ’ s much-sought-after tax returns will almost certainly remain under wraps until after the election in November .
In essence , neither side quite got what it wanted , which is why untangling the legal and practical implications @ @ @ @ @ @ @ In both sets of cases , Trump ’ s lawyers made extraordinarily far-reaching claims about what it means to be commander in chief .
And those arguments did not find an especially receptive audience with most of the justices — including Neil Gorsuch and Brett Kavanaugh , who Trump appointed to the court .
( Justices Clarence Thomas and Samuel Alito were the two dissenting votes in both cases . )
In the case involving the New York prosecutor ’ s subpoena for his financial records , Trump ’ s legal team contended @ @ @ @ @ @ @ t touch him while he was president — a claim that the justices roundly rejected .
“ Two hundred years ago , a great jurist of our Court established that no citizen , not even the President , is categorically above the common duty to produce evidence when called upon in a criminal proceeding , ” Roberts wrote in his opinion .
“ We reaffirm that principle today and hold that the President is neither absolutely immune from state criminal subpoenas seeking his private papers nor entitled to a heightened standard of need.
@ @ @ @ @ @ @ Congress , Trump ’ s lawyers argued that the House couldn ’ t subpoena his financial records because they didn ’ t serve a legitimate legislative purpose .
House Democrats had argued that the documents were necessary to shed light on possible foreign entanglements by Trump and money laundering by Trump and his family .
Trump ’ s arguments didn ’ t get much traction here either , although the court also suggested that it was wary about the breadth of House Democrats ’ subpoena .
Bottom line : Congress emerged from the @ @ @ @ @ @ @ branch oversight mostly intact , but in the short term , Trump got a big practical win , because it ’ s now virtually guaranteed that his tax returns will stay out of the public eye until after the election .
That ’ s because even though the court ruled that Trump ’ s arguments about sweeping presidential immunity don ’ t hold water , Roberts noted that Trump could still try to fight the subpoenas as an ordinary citizen , so the case could continue for some time .
And even if @ @ @ @ @ @ @ in a relatively timely way , they ’ ll remain under wraps as the criminal investigation moves forward , which is almost guaranteed to keep them out of public view at least until after the election , if they ’ re ever made public at all .
Meanwhile , the legal battle between Trump and House Democrats certainly won ’ t be resolved before November either as the cases are returning to the lower courts for more litigation .
And ultimately that ’ s a significant electoral victory for Trump , even if @ @ @ @ @ @ @ mostly dismissed .
Because with four months until the election , the last thing Trump probably wanted was a news cycle devoted to the contents of his tax returns .
But it is striking that seven Supreme Court justices , including Roberts , Kavanaugh and Gorsuch , weren ’ t on Trump ’ s side when he claimed broad immunity from prosecution and investigation while in office .
Throughout his presidency , Trump has pushed an expansive view of presidential power that could reverberate long past his own time in the White House @ @ @ @ @ @ @ ’ t buy it .

President Trump is one of the only presidents in modern memory who has kept his tax returns private, and attempts to force their release have sparked a mountain of litigation, reaching all the way to the Supreme Court.
But the Supreme Court’s verdict on whether Trump’s banks and accounting firm can be required to release his personal financial records is a bit of a mixed bag.
On the one hand, the court delivered Trump a major defeat, dismissing his most expansive claims to presidential immunity. Trump has argued that while in the White House, he can’t be criminally investigated. But the court ruled in a 7-2 decision written by Chief Justice John Roberts that New York prosecutors do have the authority to subpoena his business records, sending the case back to the lower court.
But in the second ruling on Trump’s tax returns — which was also a 7-2 decision written by Roberts — which involved three House committees’ subpoenas for his records, the court essentially punted. The justices emphasized the House does have the authority to issue subpoenas related to oversight of the executive branch, but they said lower court judges didn’t properly weigh the separation of powers issues inherent in the requests — suggesting that Congress’s power to investigate the president is not unlimited. The ruling also sent that case back to the lower courts for further consideration.
That means Trump’s much-sought-after tax returns will almost certainly remain under wraps until after the election in November.
In essence, neither side quite got what it wanted, which is why untangling the legal and practical implications of the two rulings is important. In both sets of cases, Trump’s lawyers made extraordinarily far-reaching claims about what it means to be commander in chief. And those arguments did not find an especially receptive audience with most of the justices — including Neil Gorsuch and Brett Kavanaugh, who Trump appointed to the court. (Justices Clarence Thomas and Samuel Alito were the two dissenting votes in both cases.)
In the case involving the New York prosecutor’s subpoena for his financial records, Trump’s legal team contended that the criminal legal process couldn’t touch him while he was president — a claim that the justices roundly rejected. “Two hundred years ago, a great jurist of our Court established that no citizen, not even the President, is categorically above the common duty to produce evidence when called upon in a criminal proceeding,” Roberts wrote in his opinion. “We reaffirm that principle today and hold that the President is neither absolutely immune from state criminal subpoenas seeking his private papers nor entitled to a heightened standard of need.”
Similarly, in the case involving Congress, Trump’s lawyers argued that the House couldn’t subpoena his financial records because they didn’t serve a legitimate legislative purpose. House Democrats had argued that the documents were necessary to shed light on possible foreign entanglements by Trump and money laundering by Trump and his family. Trump’s arguments didn’t get much traction here either, although the court also suggested that it was wary about the breadth of House Democrats’ subpoena. Bottom line: Congress emerged from the case with its authority to conduct executive branch oversight mostly intact, but in the short term, Trump got a big practical win, because it’s now virtually guaranteed that his tax returns will stay out of the public eye until after the election.
That’s because even though the court ruled that Trump’s arguments about sweeping presidential immunity don’t hold water, Roberts noted that Trump could still try to fight the subpoenas as an ordinary citizen, so the case could continue for some time. And even if the New York prosecutors get the documents in a relatively timely way, they’ll remain under wraps as the criminal investigation moves forward, which is almost guaranteed to keep them out of public view at least until after the election, if they’re ever made public at all. Meanwhile, the legal battle between Trump and House Democrats certainly won’t be resolved before November either as the cases are returning to the lower courts for more litigation.
And ultimately that’s a significant electoral victory for Trump, even if his claims to sweeping executive power were mostly dismissed. Because with four months until the election, the last thing Trump probably wanted was a news cycle devoted to the contents of his tax returns. But it is striking that seven Supreme Court justices, including Roberts, Kavanaugh and Gorsuch, weren’t on Trump’s side when he claimed broad immunity from prosecution and investigation while in office.
Throughout his presidency, Trump has pushed an expansive view of presidential power that could reverberate long past his own time in the White House. Today, the Supreme Court didn’t buy it.


fivethirthyeight--2020-07-10--Can You Make 24?

Can You Make 24?

Welcome to The Riddler .
Every week , I offer up problems related to the things we hold dear around here : math , logic and probability .
Two puzzles are presented each week : the Riddler Express for those of you who want something bite-size and the Riddler Classic for those of you in the slow-puzzle movement .
Submit a correct answer for either , 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 .
@ @ @ @ @ @ @ of mathematical fluency .
In the Riddler version of the game , your goal is to make a numerical expression that equals 24 , using each of four given numbers once , along with parentheses , addition , subtraction , multiplication , division and exponentiation .
For example , if I gave you the numbers 1 , 2 , 3 and 8 , then valid solutions would be 8×3× ( 2−1 ) and ( 3+1 ) × ( 8−2 ) , since they both equal 24 .
However , concatenation is not an @ @ @ @ @ @ @ ) ×1 is not a solution — that is , you can ’ t smush the 3 and the 2 together to get 32 .
Given the four numbers 2 , 3 , 3 and 4 , how can you make 24 ?
From Austin Shapiro comes a story of stacking that may stump you : Mira has a toy with five rings of different diameters and a tapered column .
Each ring has a “ correct ” position on the column , from the largest ring that fits snugly at the bottom @ @ @ @ @ @ @ at the top .
Each ring she places will slide down to its correct position , if possible .
Otherwise , it will rest on what was previously the topmost ring .
For example , if Mira stacks the smallest ring first , then she can not stack any more rings on top .
But if she stacks the second-smallest ring first , then she can stack any one of the remaining four rings above it , after which she can not stack any more rings .
Here are a four different stacks @ @ @ @ @ @ @ thinking .
How many unique stacks can she create using at least one ring ?
Extra credit : Instead of five rings , suppose the toy has N rings .
Now how many unique stacks can Mira create ?
Congratulations to 👏 Bram Carlson 👏 of Fort Lauderdale , Florida , winner of last week ’ s Riddler Express .
Last week , my swimming pool was opening soon , with its five swimming lanes ( and no general swim area ) .
It seemed likely that social distancing regulations would prevent swimmers @ @ @ @ @ @ @ to know what would happen if a queue of swimmers arrived at the pool when it opened at 9 a.m. One at a time , each person randomly picked a lane among the lanes that were available ( i.e.
, the lane had no swimmer already and was not adjacent to any lanes with swimmers ) , until no more lanes were available .
At this point , what was the expected number of swimmers in the pool ?
This was a simplified version of a previous Riddler , which looked at the @ @ @ @ @ @ @ week ’ s extra credit — but in the context of misanthropes and houses .
First off , it was helpful to label the lanes — say , 1 , 2 , 3 , 4 and 5 , in that order .
Whenever the first swimmer chose lane 2 , the second swimmer had to choose either lane 4 or 5 .
At this point , there would be no more available lanes , meaning there were exactly two swimmers in total .
This same reasoning applied to lane 4 as well .
@ @ @ @ @ @ @ choose lane 3 , the second and third swimmers would choose lanes 1 and 5 , meaning there would be exactly three swimmers in total .
A trickier case was when the first swimmer chose lane 1 .
The second swimmer could then choose from lanes 3 , 4 and 5 , each with a one-third probability .
If the second swimmer chose lane 3 or lane 5 , then there would be three swimmers in total ( lanes 1 , 3 and 5 ) .
But if the second swimmer chose lane @ @ @ @ @ @ @ be no more available lanes , meaning there would be two swimmers in total .
And when the first swimmer chose lane 5 , the math worked out the same , with the second swimmer choosing from lanes 1 , 2 and 3 .
So when the first swimmer chose lane 1 or 5 , there was a two-thirds chance of having three swimmers and a one-third chance of having two swimmers — an average of 8/3 swimmers .
Overall , that meant there was a 40 percent chance of two swimmers ( @ @ @ @ @ @ @ or 4 ) , a 20 percent chance of three swimmers ( when the first swimmer chose lane 3 ) and a 40 percent chance of 8/3 swimmers ( when the first swimmer chose lane 1 or 5 ) .
Putting these probabilities together , the average number of swimmers was 37/15 , or about 2.467 .
And what if there are more than five lanes ?
In the best-case scenario , about half of the lines would be occupied — when swimmers are in alternating lanes .
And in the worst-case scenario @ @ @ @ @ @ @ be occupied — when swimmers have two empty lanes on either side of them .
As previously explored on this column , the exact answer is ( 1−e−2 ) /2 , or about 0.432 , which falls neatly between the extremes .
To see where this limiting behavior comes from , check out the explanations from Josh Silverman and Enrique Treviño .
And if you ever happen to be first in line at my local pool , be a good sport and choose lane 3 .
Congratulations to 👏 Josh Rosenbluth 👏 of @ @ @ @ @ @ @ week ’ s Riddler Classic .
Last week , you were arranging the stars on the American flag .
The 50 stars on the current flag form two rectangles : The larger rectangle is 5 stars wide , 6 stars long ; the smaller rectangle is embedded inside the larger and is 4 stars wide , 5 stars long .
This square-like pattern of stars is possible because the number of states ( 50 ) is twice a square number ( 25 ) .
Now that the House of Representatives has passed legislation @ @ @ @ @ @ @ the 51st U.S. state , a natural question was how to aesthetically arrange 51 stars on the flag .
One pleasing design had a star in the middle , surrounded by concentric pentagons of increasing side length .
The innermost pentagon had five stars , and subsequent pentagons were made up of 10 , 15 and 20 stars .
All told , that ’ s 51 stars .
It just so happened that when N equaled 50 , N was twice a square and N+1 was a centered pentagonal number .
After 50 @ @ @ @ @ @ @ with this property ?
First off , any number that was twice a square could be written as 2x2 , where x is an integer .
But what about centered pentagonal numbers ?
For example , the seventh centered pentagonal number is 1 + 5 + 10 + 15 + 20 + 25 + 30 .
Other than the 1 , every other term in the sum is a multiple of 5 .
Factoring out that 5 gives us 1 + 5 ᐧ ( 1 + 2 + 3 + 4 + 5 @ @ @ @ @ @ @ inside the parentheses is something we can work with — it ’ s the sixth triangular number !
For many solvers , this connection between centered pentagonal and triangular numbers unlocked a formula : Centered pentagonal numbers can be written as 1 + 5y ( y+1 ) /2 , where y is an integer .
Now all you had to do was find integers x and y such that 2x2 was one less than 1 + 5y ( y+1 ) /2 , meaning 2x2 = 5y ( y+1 ) /2 , or 4x2 @ @ @ @ @ @ @ around this point , most solvers started cranking through values on their spreadsheets or writing some code to do this for them .
But there were a few brave souls who tried to solve this analytically .
Solver Grant Larsen noticed that the left side of that last equation was the square of 2x — an integer — which meant 5y ( y+1 ) was also a square .
Since 5 is prime and y and y+1 are guaranteed to be relatively prime , there were two possible cases : either ( 1 @ @ @ @ @ @ @ were both square numbers , or ( 2 ) y+1 and 5y were both square numbers .
The first value of y to satisfy one of these cases — the former , as it turned out — was 4 , since 4 and 5 ( 4+1 ) are both squares .
But this corresponded to N = 50 , the value given in the problem .
Trying out different squares , Grant found that the next solution — which happened to satisfy the latter case — was when y was 80 , since @ @ @ @ @ @ @ both squares .
This corresponded to N = 16,200 .
You read that right .
The next time our flag can go from its current square-like arrangement to a centered pentagonal number is when the 16,201st state joins the Union .
Here ’ s what the flag would look like : Now it ’ s true that the above solution had an element of “ guess and check.
” Some solvers , like Gareth McCaughan and Laurent Lessard ( admittedly out of his comfort zone with this puzzle ) ventured deeper into number @ @ @ @ @ @ @ equations .
These are well studied , and Gareth and Laurent used them to find a closed-form solution for all such values of N. Solver Emma Knight further extended the problem , looking for square-like numbers that were one greater than a centered pentagonal number .
Oh , and in case you were curious , the next value of N that worked was 5,216,450 .
And after that , it was 1,679,680,800 .
Even the United Federation of Planets doesn ’ t have a flag with that many stars .
Well , aren @ @ @ @ @ @ @ 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 !

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. Two puzzles are presented each week: the Riddler Express for those of you who want something bite-size and the Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either, 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
The 24 Game is a fun test of mathematical fluency. In the Riddler version of the game, your goal is to make a numerical expression that equals 24, using each of four given numbers once, along with parentheses, addition, subtraction, multiplication, division and exponentiation.
For example, if I gave you the numbers 1, 2, 3 and 8, then valid solutions would be 8×3×(2−1) and (3+1)×(8−2), since they both equal 24. However, concatenation is not an allowed operation, which means (32−8)×1 is not a solution — that is, you can’t smush the 3 and the 2 together to get 32.
Given the four numbers 2, 3, 3 and 4, how can you make 24?
Extra credit: Can you find another way to make 24?
The solution to this Riddler Express can be found in the following week’s column.
Riddler Classic
From Austin Shapiro comes a story of stacking that may stump you:
Mira has a toy with five rings of different diameters and a tapered column. Each ring has a “correct” position on the column, from the largest ring that fits snugly at the bottom to the smallest ring that fits snugly at the top.
Each ring she places will slide down to its correct position, if possible. Otherwise, it will rest on what was previously the topmost ring.
For example, if Mira stacks the smallest ring first, then she cannot stack any more rings on top. But if she stacks the second-smallest ring first, then she can stack any one of the remaining four rings above it, after which she cannot stack any more rings.
Here are a four different stacks Mira could make:
This got Mira thinking. How many unique stacks can she create using at least one ring?
Extra credit: Instead of five rings, suppose the toy has N rings. Now how many unique stacks can Mira create?
The solution to this Riddler Classic can be found in the following week’s column.
Solution to last week’s Riddler Express
Congratulations to 👏 Bram Carlson 👏 of Fort Lauderdale, Florida, winner of last week’s Riddler Express.
Last week, my swimming pool was opening soon, with its five swimming lanes (and no general swim area). It seemed likely that social distancing regulations would prevent swimmers from occupying adjacent lanes.
I wanted to know what would happen if a queue of swimmers arrived at the pool when it opened at 9 a.m. One at a time, each person randomly picked a lane among the lanes that were available (i.e., the lane had no swimmer already and was not adjacent to any lanes with swimmers), until no more lanes were available.
At this point, what was the expected number of swimmers in the pool?
This was a simplified version of a previous Riddler, which looked at the general case of N lanes — last week’s extra credit — but in the context of misanthropes and houses.
First off, it was helpful to label the lanes — say, 1, 2, 3, 4 and 5, in that order. Whenever the first swimmer chose lane 2, the second swimmer had to choose either lane 4 or 5. At this point, there would be no more available lanes, meaning there were exactly two swimmers in total. This same reasoning applied to lane 4 as well.
But if the first swimmer happened to choose lane 3, the second and third swimmers would choose lanes 1 and 5, meaning there would be exactly three swimmers in total.
A trickier case was when the first swimmer chose lane 1. The second swimmer could then choose from lanes 3, 4 and 5, each with a one-third probability. If the second swimmer chose lane 3 or lane 5, then there would be three swimmers in total (lanes 1, 3 and 5). But if the second swimmer chose lane 4, then once again there would be no more available lanes, meaning there would be two swimmers in total. And when the first swimmer chose lane 5, the math worked out the same, with the second swimmer choosing from lanes 1, 2 and 3. So when the first swimmer chose lane 1 or 5, there was a two-thirds chance of having three swimmers and a one-third chance of having two swimmers — an average of 8/3 swimmers.
Overall, that meant there was a 40 percent chance of two swimmers (when the first swimmer chose lane 2 or 4), a 20 percent chance of three swimmers (when the first swimmer chose lane 3) and a 40 percent chance of 8/3 swimmers (when the first swimmer chose lane 1 or 5). Putting these probabilities together, the average number of swimmers was 37/15, or about 2.467.
And what if there are more than five lanes? In the best-case scenario, about half of the lines would be occupied — when swimmers are in alternating lanes. And in the worst-case scenario, about a third of lanes would be occupied — when swimmers have two empty lanes on either side of them. As previously explored on this column, the exact answer is (1−e−2)/2, or about 0.432, which falls neatly between the extremes.
To see where this limiting behavior comes from, check out the explanations from Josh Silverman and Enrique Treviño.
And if you ever happen to be first in line at my local pool, be a good sport and choose lane 3.
Solution to last week’s Riddler Classic
Congratulations to 👏 Josh Rosenbluth 👏 of Oxnard, California, winner of last week’s Riddler Classic.
Last week, you were arranging the stars on the American flag. The 50 stars on the current flag form two rectangles: The larger rectangle is 5 stars wide, 6 stars long; the smaller rectangle is embedded inside the larger and is 4 stars wide, 5 stars long. This square-like pattern of stars is possible because the number of states (50) is twice a square number (25).
Now that the House of Representatives has passed legislation that would make the District of Columbia the 51st U.S. state, a natural question was how to aesthetically arrange 51 stars on the flag.
One pleasing design had a star in the middle, surrounded by concentric pentagons of increasing side length. The innermost pentagon had five stars, and subsequent pentagons were made up of 10, 15 and 20 stars. All told, that’s 51 stars.
It just so happened that when N equaled 50, N was twice a square and N+1 was a centered pentagonal number. After 50, what was the next integer N with this property?
First off, any number that was twice a square could be written as 2x2, where x is an integer. But what about centered pentagonal numbers? For example, the seventh centered pentagonal number is 1 + 5 + 10 + 15 + 20 + 25 + 30. Other than the 1, every other term in the sum is a multiple of 5. Factoring out that 5 gives us 1 + 5 ᐧ (1 + 2 + 3 + 4 + 5 + 6). Now that expression inside the parentheses is something we can work with — it’s the sixth triangular number! For many solvers, this connection between centered pentagonal and triangular numbers unlocked a formula: Centered pentagonal numbers can be written as 1 + 5y(y+1)/2, where y is an integer.
Now all you had to do was find integers x and y such that 2x2 was one less than 1 + 5y(y+1)/2, meaning 2x2 = 5y(y+1)/2, or 4x2 = 5y(y+1). Right around this point, most solvers started cranking through values on their spreadsheets or writing some code to do this for them. But there were a few brave souls who tried to solve this analytically.
Solver Grant Larsen noticed that the left side of that last equation was the square of 2x — an integer — which meant 5y(y+1) was also a square. Since 5 is prime and y and y+1 are guaranteed to be relatively prime, there were two possible cases: either (1) y and 5(y+1) were both square numbers, or (2) y+1 and 5y were both square numbers.
The first value of y to satisfy one of these cases — the former, as it turned out — was 4, since 4 and 5(4+1) are both squares. But this corresponded to N = 50, the value given in the problem. Trying out different squares, Grant found that the next solution — which happened to satisfy the latter case — was when y was 80, since 5(80) and 80+1 are both squares. This corresponded to N = 16,200.
You read that right. The next time our flag can go from its current square-like arrangement to a centered pentagonal number is when the 16,201st state joins the Union.
Here’s what the flag would look like:
Now it’s true that the above solution had an element of “guess and check.” Some solvers, like Gareth McCaughan and Laurent Lessard (admittedly out of his comfort zone with this puzzle) ventured deeper into number theory and into the realm of Pell equations. These are well studied, and Gareth and Laurent used them to find a closed-form solution for all such values of N. Solver Emma Knight further extended the problem, looking for square-like numbers that were one greater than a centered pentagonal number.
Oh, and in case you were curious, the next value of N that worked was 5,216,450. And after that, it was 1,679,680,800.
Even the United Federation of Planets doesn’t have a flag with that many stars.
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 Zach Wissner-Gross at riddlercolumn@gmail.com.


fivethirthyeight--2020-07-10--Confidence Interval: Could Trump Win If He Replaces Pence?

Welcome to another episode of Confidence Interval , where we make a persuasive case for a hot take … and @ @ @ @ @ really feel about the idea .
This time , elections analyst Geoffrey Skelley wonders whether @ @ @ @ @ would help President Trump ’ s chances of reelection in November .

Welcome to another episode of Confidence Interval, where we make a persuasive case for a hot take … and then reveal how confident we really feel about the idea. This time, elections analyst Geoffrey Skelley wonders whether replacing Vice President Mike Pence would help President Trump’s chances of reelection in November.