fivethirthyeight--2020-06-25--Megan Rapinoe And Tobin Heath Have Opted Out. But There’s Still Lots To Root For In The NWSL.

It hasn ’ t been the smoothest road , but American team sports are almost back .
The first league set to return is the National Women ’ s Soccer League , which kicks off Saturday with the Challenge Cup , a special , COVID-designed tournament .
The NBA , NHL and MLS have similar tournament-style events planned to get their seasons back on track and likely will be watching the Challenge Cup closely for how it plays out .
Even before NWSL teams arrived at the host site in Sandy , Utah , the pandemic had already thrown the @ @ @ @ @ @ @ Monday , before the league ’ s nine teams departed from their preseason camps , the Orlando Pride announced they had to withdraw because six players and four staffers tested positive for COVID-19 .
Sources in the league have blamed Orlando players for breaking team social distancing protocols and going out to bars in a state — Florida — that has been among the earliest to reopen such establishments .
With Orlando ’ s withdrawal chalked up to irresponsible individual behavior and not insufficient league protocols , the Challenge Cup is full steam @ @ @ @ @ @ @ ’ s biggest stars , particularly members of the U.S. women ’ s national team , have opted out of the event over concerns of COVID-19 and the possibility of injury , including household names Megan Rapinoe and Tobin Heath .
This event , which will be broadcast on CBS and CBS All Access , will likely determine the champion of the 2020 season , given that there are no plans for a normal regular season afterward .
The FiveThirtyEight Challenge Cup prediction model had the Orlando Pride in dead last anyway , @ @ @ @ @ @ @ the tournament doesn ’ t clearly help any single team .
Each team will play four games in the first round set by random lottery , and no one will be eliminated from that round , now that Orlando has dropped out .
Instead , the first round will be used to determine seeding for a knockout stage with the league ’ s eight remaining teams .
FiveThirtyEight odds to win it all : 27 percent For the past two seasons , the Courage have won both the NWSL Shield for the best @ @ @ @ @ @ @ .
Just a quick glance at their roster helps explain it — there ’ s not a weak spot for the Courage , and unlike some other teams in this tournament , they won ’ t have any stars missing .
The Courage ’ s playing style is the soccer equivalent of a battering ram , relying on a breakneck pace and brute force to outscore opponents .
Indeed , the Courage have led the league in shots taken ( and shots on goal ) for the past two seasons .
Their shot @ @ @ @ @ @ @ ( that honor went to the Portland Thorns for the past two seasons ) , but that ’ s not really the point .
The sheer volume of the Courage ’ s attacking waves is difficult to defend for a full 90 minutes , and it ’ s easy to see why the Courage have led the NWSL in late goals — in the final 15 minutes of games — over the past two seasons .
There ’ s not much reason to doubt the Courage can win it all in Utah , @ @ @ @ @ @ @ Courage have the best home record over the last two years , and the looming question is whether they can be as dominant at a neutral site .
Notable inclusions : 2019 World Cup winner Lindsey Horan , No .
1 and No .
2 overall 2020 NWSL draft picks Sophia Smith and Morgan Weaver , all-time international leader in goals Christine Sinclair .
FiveThirtyEight odds to win it all : 12 percent Considered the flagship club of the NWSL , the 2013 and 2017 champions start every season with high expectations .
@ @ @ @ @ @ @ year and were eliminated in the playoffs , which prompted some serious roster reconstruction over the offseason .
Players like Midge Purce , Ellie Carpenter and Caitlin Foord , who played prominent roles at multiple positions for the Thorns , are gone .
Those exits plus the absence of Heath leave the Thorns without the potent wide players who were such a hallmark of the 2019 team .
Now questions linger about how the Thorns will play at the Challenge Cup .
Will they return to a three-back system with wingbacks , or @ @ @ @ @ @ @ Will they continue their aggressive counter-pressing , swarming defensive style or go with something a bit more conservative ?
Either way , the Challenge Cup is going to be an adjustment for the Thorns , a team that typically averages around 20,000 rowdy , chanting fans per home game .
That best-in-the-league home support is part of why the Thorns have one of the best home records every season , but the Thorns will be playing in empty stadiums in Utah .
FiveThirtyEight odds to win it all : 14 percent It ’ @ @ @ @ @ @ @ Stars without first talking about who they don ’ t have .
Last year ’ s NWSL Golden Boot winner and MVP , Samantha Kerr , signed with Chelsea in the offseason and leaves an Australia-sized hole in the Chicago attack .
There ’ s no like-for-like replacement for a player who scored 34 goals in her 40 appearances for the club , and the Red Stars will need more players stepping up goal-scoring production .
An injury to Alyssa Mautz , who the club announced tore her ACL earlier this week , @ @ @ @ @ @ @ Nagasato should contribute a few goals , as should Kealia Ohai Watt , but that still doesn ’ t get close to Kerr ’ s output .
The Red Stars have a solid roster otherwise .
Defensively , Ertz and Casey Short are two of the best in the league ( and if Ertz plays as a midfielder , she ’ s one of the best at that too ) .
Midfielders Brian and Vanessa DiBernardo , who have both battled injuries , are in their best shape over the past two years @ @ @ @ @ @ @ from ?
It remains to be seen .
FiveThirtyEight odds to win it all : 11 percent After a last-place finish in 2017 , the Spirit have slowly been on the rise , reaching fifth last year .
But they also haven ’ t come particularly close to the upper echelon , and the club added 11 players in the offseason , including former UCLA standout Ashley Sanchez , whom the Spirit selected with the No .
4 pick in this year ’ s draft .
Notably , the club said goodbye to @ @ @ @ @ @ @ still widely considered the future of the U.S. women ’ s national team but has lately struggled to hold onto a spot with the national team .
Instead , the club looked to build around players who have steadily been on the rise in Lavelle and Andi Sullivan , a duo that has built a formidable central midfield partnership for the Spirit over the years .
The Spirit tend to play a less direct style than the rest of the NWSL , with the league-best passing accuracy and the second-most passes overall in @ @ @ @ @ @ @ is whether they can convert that into attacking opportunities .
The Spirit ’ s passing accuracy plummeted in the opposing half last season , and they weren ’ t potent enough in front of goal .
FiveThirtyEight odds to win it all : 11 percent Formerly called the Seattle Reign and now owned by OL Groupe , the parent company of women ’ s soccer powerhouse Olympique Lyonnais , OL Reign has gone through more changes than just its rebranding .
Vlatko Andonovski , the team ’ s coach for the 2018 and @ @ @ @ @ @ @ the U.S. women ’ s national team , and the club brought in former Olympique Lyonnais coach Farid Benstiti , who has never coached in the United States before .
The club has also added some notable international players , including Costa Rica ’ s Shirley Cruz and Japan ’ s Yuka Momiki , and American defender Alana Cook has joined on loan from Paris Saint-Germain .
But how it all comes together is anyone ’ s guess .
It ’ s a new era for the Reign — and in unusual circumstances @ @ @ @ @ @ @ The absence of superstar Rapinoe , who has declined to play in the Challenge Cup , won ’ t help .
FiveThirtyEight odds to win it all : 10 percent Over two-thirds of the Royals ’ goals last season were scored by one of two players : Press or Rodriguez .
Unfortunately for the Royals , Press has opted out of the Challenge Cup , which seems like a big problem for the de facto home team of this tournament .
But Press and Rodriguez often seemed to be on different pages when @ @ @ @ @ @ @ a good game and score goals while the other struggled .
That could allow Rodriguez to take the reins and return to her goal-scoring form that led FC Kansas City to back-to-back championships in 2014 and 2015 .
That might be asking a lot of Rodriguez , but it ’ s the Royals ’ best hope .
The Royals would have been better off had the rumored acquisition of German star Dzsenifer Marozsan not fallen through .
But midfielder Aminata Diallo , on loan from Paris Saint-Germain , and Spanish midfielder Vero Boquete @ @ @ @ @ @ @ .
FiveThirtyEight odds to win it all : 7 percent The Dash have never quite lived up to their potential .
The second MLS-backed club to join the NWSL and the league ’ s first expansion team , Houston has perennially struggled , with a carousel of new coaches doing little to improve the situation .
It ’ s on second-year head coach James Clarkson to figure it out in Utah in a venue that could suit the Dash , who actually did better on the road than at home last year .
@ @ @ @ @ @ @ of roster changes without much time to build chemistry .
They brought in defensive veterans Megan Oyster and Katie Naughton to bolster a backline that has been a liability over the years .
Meanwhile , three of the Dash ’ s top five goal-scorers from last season are gone , with Sofia Huerta , Kealia Ohai Watts and Kyah Simon all departing in the offseason , along with longtime defender Amber Brooks .
FiveThirtyEight odds to win it all : 7 percent The New Jersey-based team has been the NWSL ’ s offseason @ @ @ @ @ @ @ turnaround in better housing conditions and facilities after players publicly lambasted the club .
But whether they can make similar progress on the field remains to be seen .
For starters , Lloyd and new addition Pugh are both injured , dealing major blows to the Sky Blue attack .
Defender Caprice Dydasco is also out .
But Midge Purce was a workhorse last year for the Thorns and can plug in most holes around the field , so she ’ ll probably carry some of the scoring burden either up top or @ @ @ @ @ @ @ don ’ t really know how Sky Blue will play .
Head coach Freya Coombe took over late last season , but it will clearly be an uphill battle .
The team conceded more shots than any other in the NWSL last year , yet was last on the other end of the field in shots taken and shot conversion .
Given their significant absences , it ’ s hard to see how they do much better this year .
CORRECTION ( June 25 , 2020 , TK : TK p.m. ) : @ @ @ @ @ @ @ the incorrect year of the Portland Thorns ’ first NWSL championship .
They won in 2013 , not 2012 .


fivethirthyeight--2020-06-26--Can You Connect The Dots?

Can You Connect The Dots?

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 .
@ @ @ @ @ @ @ follow a grid layout , running north-south and east-west .
You ’ re driving north when you decide to play a little game .
Every time you reach an intersection , you randomly turn left or right , each with a 50 percent chance .
After driving through 10 intersections , what is the probability that you are still driving north ?
Extra credit : Now suppose that at every intersection , there ’ s a one-third chance you turn left , a one-third chance you turn right and a one-third chance you @ @ @ @ @ @ @ intersections , now what ’ s the probability that you are still driving north ?
Polly Gawn loves to play “ connect the dots.
” Today , she ’ s playing a particularly challenging version of the game , which has six unlabeled dots on the page .
She would like to connect them so that they form the vertices of a hexagon .
To her surprise , she finds that there are many different hexagons she can draw , each with the same six vertices .
What is the greatest possible number @ @ @ @ @ @ @ six points ?
Extra Credit : What is the greatest possible number of unique heptagons Polly can draw using seven points ?
Congratulations to 👏 Emma Knight 👏 of Toronto , Canada , winner of last week ’ s Riddler Express .
Last week , I had a coin with a sun on the front and a moon on the back .
I claimed that on most days it was a fair coin .
But once a year , on the summer solstice , the coin always came up the opposite side as @ @ @ @ @ @ @ you were skeptical of my claim .
You initially figured there was a 1 percent chance that the coin was magical and a 99 percent chance that it was just an ordinary fair coin .
You then asked me to “ prove ” the coin was magical by flipping it some number of times .
How many successfully alternating coin flips would it have taken for you to think there was a 99 percent chance the coin was magical ( or , more likely , that I had rigged it so it always @ @ @ @ @ @ @ a lot of disagreement about this problem !
About 40 percent thought the answer was eight flips , 30 percent thought the answer was seven , 12 percent thought the answer was 15 and 8 percent thought the answer was 14 .
( The remaining 10 percent gave answers ranging from zero to 100 . )
But before revealing the correct result , let ’ s take a closer look at what was happening with these coin flips .
Suppose my first flip happened to be a sun , my second flip was @ @ @ @ @ @ @ alternating with every subsequent flip .
The more alternating flips I got in a row , the more confident you ’ d become that the coin was magical .
To quantify this level of confidence , you needed an assist from Bayes ’ theorem : Given N alternating flips in the row , the probability that the coin was magical was equal to the probability that a magic coin would generate N alternating flips , multiplied by the prior probability that the coin was magical , then divided by the prior total probability @ @ @ @ @ @ @ of these were easier to calculate than others .
For example , the probability that a magical coin would generate N alternating flips was 1 .
( That ’ s what it meant for the coin to be magical ; the flips would always alternate . )
And the prior probability that the coin was magical — prior to any flipping to prove it was magical — was given in the statement of the problem : 1 percent , or 0.01 .
The challenge was to determine the final value to plug into @ @ @ @ @ @ @ probability of getting N alternating flips .
On the ( 1 percent ) off chance the coin was magical , you would always get N alternating flips .
But even if the coin wasn ’ t magical ( the remaining 99 percent of the time ) , you could still get N alternating flips , with a probability that decreased with N. In fact , the probability was 1/2N−1 , since the first flip could be a sun or a moon , and the remaining N−1 flips each had a 50 percent chance @ @ @ @ @ @ @ .
All together , that meant the total prior probability of getting N alternating flips was 0.01+0.99/2N−1 .
At last , with all that deep thought behind us , it ’ s time to plug and chug .
Given N alternating flips in a row , the probability that the coin was magical was 0.01/ ( 0.01+0.99/2N−1 ) .
Now your task was to find the first value of N where this probability exceeded 0.99 , meaning you could be 99 percent sure the coin was magical .
Starting with the inequality 0.01/ @ @ @ @ @ @ @ careful rearrangement led to the simplified inequality 2N−1 ≥ 992 .
The smallest power of two that exceeded 992 , or 9,801 , was 214 , or 16,384 .
While many thought the answer was 14 , it was in fact N−1 that equalled 14 , meaning the answer was 15 flips .
And in calculating that tricky prior total probability of getting N alternating flips , if you forgot to account for the 1 percent of the time the coin was magic , you got the incorrect answer of eight flips ( @ @ @ @ @ @ @ to add one to the exponent ) .
Or you might have discarded the prior probability altogether and looked for the first power of 1/2 that was less than 0.01 .
No doubt this was a challenging Express .
And in case you were curious , yes , the coin really was magical .
Congratulations to 👏 Eric Widdison 👏 of Kaysville , Utah , winner of last week ’ s Riddler Classic .
Last week , King Auric was passing his most prized possession — perfect spheres of solid gold — to @ @ @ @ @ @ @ with diameters of 1 centimeter , 2 centimeters , 3 centimeters , and so on .
To be fair to his children , he wanted to give each an equal weight of gold .
After much trial and error , the king managed to divide his spheres into three groups of equal weight .
He was further amused when he realized that his collection contained the minimum number of spheres needed for such a division .
How many golden spheres did King Auric have ?
An important detail from the puzzle was that @ @ @ @ @ @ @ their weight was proportional to the cube of their diameter .
In other words , you had to find a whole number N such that 13 , 23 , 33 , … , N3 could be partitioned into three groups with the same sum .
A good place to start was to find the weights of each of those three groups .
Summing the cubes from 13 to N3 always equals N2 ( N+1 ) 2/4 , and since each group had a weight that was one-third of the total , the weight @ @ @ @ @ @ @ N+1 ) 2/12 .
You also knew that the largest sphere must have belonged to one of the three groups , and clearly its weight couldn ’ t be greater than the sum of its corresponding group .
In other words , N3 had to be less than or equal to N2 ( N+1 ) 2/12 .
With a little algebraic manipulation , this meant that N had to be 10 or greater .
Also , in order to evenly split the spheres into three groups , you knew that the total sum @ @ @ @ @ @ @ ) 2/4 , had to be divisible by three .
That meant N had to either be a multiple of three or two more than a multiple of three .
So possible values of N were now 11 , 12 , 14 , 15 , 17 , 18 , etc .
At this point , solver after solver turned to their computer for assistance .
As this week ’ s winner Eric Widdison noted , this problem appeared to be a variant of the famous knapsack problem , which is NP-complete .
So @ @ @ @ @ @ @ , Eric was able to find that the smallest possible number of spheres was 23 .
The fair division of the spheres was { 1 , 4 , 7 , 8 , 12 , 16 , 20 , 22 } , { 2 , 5 , 9 , 11 , 14 , 15 , 17 , 23 } and { 3 , 6 , 10 , 13 , 18 , 19 , 21 } .
For all three groups , the sum of the cubes was 76,176 .
That ’ s a whole @ @ @ @ @ @ @ extra credit asked you to find the smallest number of spheres that could be evenly shared among other numbers of children , like two , four , five , six , etc .
Solver Allen Gu reported several of these results , along with how long it took his computer to generate each result .
With two children , King Auric would need 12 spheres ; with four or five children , he would need 24 spheres ; with six children , he would need 35 spheres ; with seven children , he @ @ @ @ @ @ @ eight children , he would need 47 spheres .
At this point , Allen ’ s computer failed him , and he upgraded to a “ beefier ” virtual machine .
After several hours , he found that with nine children , King Auric would need 53 spheres .
Allen is still waiting to hear back from his computer in the case of 10 children .
These results formed a rather unpredictable sequence of integers : 1 , 12 , 23 ( this week ’ s answer ) , 24 , 24 , @ @ @ @ @ @ @ , and so on .
And now , thanks to the puzzle ’ s submitter , Dean Ballard , this sequence has been enshrined for all eternity in the On-line Encyclopedia of Integer Sequences as sequence A330212 .
While he was there , Dean apparently updated the related sequence , A240070 , which looks at splitting up powers other than cubes into three equal groups .
As for the computational difficulty in cranking out these integer sequences , Emma Knight put it best , concluding that “ [ a ] t this point @ @ @ @ @ @ @ would advise the royal couple to ease up on their procreation habit.
” 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 !

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
In Riddler City, the city streets follow a grid layout, running north-south and east-west. You’re driving north when you decide to play a little game. Every time you reach an intersection, you randomly turn left or right, each with a 50 percent chance.
After driving through 10 intersections, what is the probability that you are still driving north?
Extra credit: Now suppose that at every intersection, there’s a one-third chance you turn left, a one-third chance you turn right and a one-third chance you drive straight. After driving through 10 intersections, now what’s the probability that you are still driving north?
The solution to this Riddler Express can be found in the following week’s column.
Riddler Classic
Polly Gawn loves to play “connect the dots.” Today, she’s playing a particularly challenging version of the game, which has six unlabeled dots on the page. She would like to connect them so that they form the vertices of a hexagon. To her surprise, she finds that there are many different hexagons she can draw, each with the same six vertices.
What is the greatest possible number of unique hexagons Polly can draw using six points?
(Hint: With four points, that answer is three. That is, Polly can draw up to three quadrilaterals, as long as one of the points lies inside the triangle formed by the other three. Otherwise, Polly would only be able to draw one quadrilateral.)
Extra Credit: What is the greatest possible number of unique heptagons Polly can draw using seven points?
The solution to this Riddler Classic can be found in the following week’s column.
Solution to last week’s Riddler Express
Congratulations to 👏 Emma Knight 👏 of Toronto, Canada, winner of last week’s Riddler Express.
Last week, I had a coin with a sun on the front and a moon on the back. I claimed that on most days it was a fair coin. But once a year, on the summer solstice, the coin always came up the opposite side as the previous flip.
Of course, you were skeptical of my claim. You initially figured there was a 1 percent chance that the coin was magical and a 99 percent chance that it was just an ordinary fair coin. You then asked me to “prove” the coin was magical by flipping it some number of times.
How many successfully alternating coin flips would it have taken for you to think there was a 99 percent chance the coin was magical (or, more likely, that I had rigged it so it always alternated)?
Wow, there was a lot of disagreement about this problem! About 40 percent thought the answer was eight flips, 30 percent thought the answer was seven, 12 percent thought the answer was 15 and 8 percent thought the answer was 14. (The remaining 10 percent gave answers ranging from zero to 100.) But before revealing the correct result, let’s take a closer look at what was happening with these coin flips.
Suppose my first flip happened to be a sun, my second flip was a moon, and the outcome continued alternating with every subsequent flip. The more alternating flips I got in a row, the more confident you’d become that the coin was magical.
To quantify this level of confidence, you needed an assist from Bayes’ theorem: Given N alternating flips in the row, the probability that the coin was magical was equal to the probability that a magic coin would generate N alternating flips, multiplied by the prior probability that the coin was magical, then divided by the prior total probability of getting N alternating flips.
Some of these were easier to calculate than others. For example, the probability that a magical coin would generate N alternating flips was 1. (That’s what it meant for the coin to be magical; the flips would always alternate.) And the prior probability that the coin was magical — prior to any flipping to prove it was magical — was given in the statement of the problem: 1 percent, or 0.01. The challenge was to determine the final value to plug into Bayes’ theorem: the prior total probability of getting N alternating flips.
On the (1 percent) off chance the coin was magical, you would always get N alternating flips. But even if the coin wasn’t magical (the remaining 99 percent of the time), you could still get N alternating flips, with a probability that decreased with N. In fact, the probability was 1/2N−1, since the first flip could be a sun or a moon, and the remaining N−1 flips each had a 50 percent chance of being different from the previous flip. All together, that meant the total prior probability of getting N alternating flips was 0.01+0.99/2N−1.
At last, with all that deep thought behind us, it’s time to plug and chug. Given N alternating flips in a row, the probability that the coin was magical was 0.01/(0.01+0.99/2N−1). Now your task was to find the first value of N where this probability exceeded 0.99, meaning you could be 99 percent sure the coin was magical.
Starting with the inequality 0.01/(0.01+0.99/2N−1) ≥ 0.99, some careful rearrangement led to the simplified inequality 2N−1 ≥ 992. The smallest power of two that exceeded 992, or 9,801, was 214, or 16,384. While many thought the answer was 14, it was in fact N−1 that equalled 14, meaning the answer was 15 flips.
And in calculating that tricky prior total probability of getting N alternating flips, if you forgot to account for the 1 percent of the time the coin was magic, you got the incorrect answer of eight flips (or seven, if you again forgot to add one to the exponent). Or you might have discarded the prior probability altogether and looked for the first power of 1/2 that was less than 0.01.
No doubt this was a challenging Express. And in case you were curious, yes, the coin really was magical.
Solution to last week’s Riddler Classic
Congratulations to 👏 Eric Widdison 👏 of Kaysville, Utah, winner of last week’s Riddler Classic.
Last week, King Auric was passing his most prized possession — perfect spheres of solid gold — to his three children. He had spheres with diameters of 1 centimeter, 2 centimeters, 3 centimeters, and so on. To be fair to his children, he wanted to give each an equal weight of gold.
After much trial and error, the king managed to divide his spheres into three groups of equal weight. He was further amused when he realized that his collection contained the minimum number of spheres needed for such a division. How many golden spheres did King Auric have?
An important detail from the puzzle was that the spheres were solid gold, meaning their weight was proportional to the cube of their diameter. In other words, you had to find a whole number N such that 13, 23, 33, … , N3 could be partitioned into three groups with the same sum.
A good place to start was to find the weights of each of those three groups. Summing the cubes from 13 to N3 always equals N2(N+1)2/4, and since each group had a weight that was one-third of the total, the weight of each group was therefore N2(N+1)2/12.
You also knew that the largest sphere must have belonged to one of the three groups, and clearly its weight couldn’t be greater than the sum of its corresponding group. In other words, N3 had to be less than or equal to N2(N+1)2/12. With a little algebraic manipulation, this meant that N had to be 10 or greater.
Also, in order to evenly split the spheres into three groups, you knew that the total sum of the weights, N2(N+1)2/4, had to be divisible by three. That meant N had to either be a multiple of three or two more than a multiple of three. So possible values of N were now 11, 12, 14, 15, 17, 18, etc.
At this point, solver after solver turned to their computer for assistance. As this week’s winner Eric Widdison noted, this problem appeared to be a variant of the famous knapsack problem, which is NP-complete. So it was computers or bust.
Nevertheless, Eric was able to find that the smallest possible number of spheres was 23. The fair division of the spheres was {1, 4, 7, 8, 12, 16, 20, 22}, {2, 5, 9, 11, 14, 15, 17, 23} and {3, 6, 10, 13, 18, 19, 21}. For all three groups, the sum of the cubes was 76,176. That’s a whole lotta gold!
Last week’s extra credit asked you to find the smallest number of spheres that could be evenly shared among other numbers of children, like two, four, five, six, etc.
Solver Allen Gu reported several of these results, along with how long it took his computer to generate each result. With two children, King Auric would need 12 spheres; with four or five children, he would need 24 spheres; with six children, he would need 35 spheres; with seven children, he would need 41 spheres, and with eight children, he would need 47 spheres. At this point, Allen’s computer failed him, and he upgraded to a “beefier” virtual machine. After several hours, he found that with nine children, King Auric would need 53 spheres. Allen is still waiting to hear back from his computer in the case of 10 children.
These results formed a rather unpredictable sequence of integers: 1, 12, 23 (this week’s answer), 24, 24, 35, 41, 47, 53, and so on. And now, thanks to the puzzle’s submitter, Dean Ballard, this sequence has been enshrined for all eternity in the On-line Encyclopedia of Integer Sequences as sequence A330212. While he was there, Dean apparently updated the related sequence, A240070, which looks at splitting up powers other than cubes into three equal groups.
As for the computational difficulty in cranking out these integer sequences, Emma Knight put it best, concluding that “[a]t this point I (and my poor CPU) would advise the royal couple to ease up on their procreation habit.”
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--2020-06-26--Voter Registrations Are Way, Way Down During The Pandemic

Poll after poll showed a high level of enthusiasm for voting in the general election in 2020 , and in the beginning of the year , voter registration surged to match that excitement .
Then the COVID-19 pandemic hit .
New registrations have fallen off a cliff .
The spring of a presidential election year is often a busy time for adding new voters to the rolls , and a recent report from the Center for Election Innovation and Research , a nonprofit organization that aims to improve voter turnout and election security , shows registration numbers were even stronger @ @ @ @ @ @ @ But things changed dramatically in March , at least in the 12 places where FiveThirtyEight or CEIR were able to obtain data on new voters , a category that includes first-time voters , voters who recently moved to the state and , in some states ( Texas , for example ) even voters who moved between counties in the state .
Consider Florida , for example , where 109,859 new voters registered in February of this year , compared to 87,351 registrants in February of 2016 .
But in April 2020 , only @ @ @ @ @ @ @ 52,508 in 2016 .
The same pattern holds in 10 other states , plus Washington , D.C. : Each one registered fewer new voters in April 2020 than in April 2016 , including in states where online voter registration is available .
Currently , 39 states plus Washington , D.C. , offer the ability to register to vote online , and a 40th ( Oklahoma ) is expected to implement it this year .
However , in the three places for which we have the relevant data ( Florida , Maryland and Washington @ @ @ @ @ @ @ taken off during the pandemic — certainly not enough to make up for the lost in-person registrations .
Even in Washington , where online registrations have ticked up since the beginning of the year , the pace is comparable to 2016 : 2,956 people registered online in April and May 2020 , similar to the 2,771 people who registered online in April and May 2016 .
The fact that new voter registrations were outpacing the 2016 numbers in January and February was predictable , according to David Becker , the executive director and @ @ @ @ @ @ @ , population growth means that voter registration always climbs a bit , he said .
The expansion of automatic voter registration makes getting on the rolls more convenient than ever in many states , too .
Voters were also clearly interested in registering , Becker said .
“ Every piece of data we had looked at with regard to enthusiasm about engaging in this presidential election cycle indicated that we had to be prepared for the highest-turnout presidential election that almost anyone living had ever seen , ” Becker said , “ which @ @ @ @ @ @ @ April all the more striking.
” Based on the timing , it seems safe to assume that COVID-19 had something to do with the drop-off , but there ’ s data to back that assumption up , too .
In addition to how many new voters register , some states track how these new voters get their name on the books .
In 2016 and in the pre-pandemic months of 2020 , in-person registration at places like departments of motor vehicles made up a large plurality , or even a majority , of @ @ @ @ @ @ @ which we have data on how new voters are registering .
But after the pandemic caused most states to shutter many government offices , those registrations dwindled .
By contrast , remote registrations ( e.g.
, online or by mail ) held relatively steady .
“ This is completely expected , but very concerning , ” said Wendy Weiser , director of the democracy program at the Brennan Center for Justice at New York University ’ s School of Law .
“ The coronavirus shut down most of the primary avenues through which @ @ @ @ @ @ @ , and all the malls , theaters and public places where voter registration drives operate.
” Indeed , the closing of schools and public events like festivals has hindered in-person voter registration drives run by third-party organizations .
“ We had planned to go to 850 high schools leading up to graduation , but as schools closed , that work was clearly disrupted , ” said Jeanette Senecal , a senior director for the League of Women Voters who focuses on voter education .
For example , in Florida , third-party organizations registered @ @ @ @ @ @ @ huge increase from the 1,196 they registered in January 2016 .
But in April 2020 , they registered only 133 voters — down from 3,806 in April 2016 .
States and third-party groups can still get around social distancing restrictions to get more voters on the poll books , though .
Voto Latino , an organization that works to register and encourage Latino Americans to vote , has been operating digitally almost since its inception and was well prepared to continue its work during a pandemic .
It uses digital campaigns to help @ @ @ @ @ @ @ in states like Texas , which does not have online voter registration — Voto Latino created an app that makes it easy to fill out the required form , which is then emailed to the voter to print off and mail in .
Danny Turkel , the communications manager for Voto Latino , said the group has actually seen a surge in voter registration , especially since protests in response to the killing of George Floyd began .
“ Our original goal entering 2020 was to register 500,000 voters , ” said Turkel @ @ @ @ @ @ @ in and surged , we are now thinking that we could surpass 500,000.
” So what kind of people might have registered if the coronavirus hadn ’ t struck ?
Well for one thing , they ’ re probably disproportionately young .
“ In any given year , far more young people register than older people , just because 18-year-olds age in [ to being able to vote ] and young people are more likely to move ” and need to register at a new address , said Kevin Morris , a quantitative @ @ @ @ @ @ @ at the Brennan Center .
According to Morris ’ s data , 57 percent of new registrants in Florida in the first four months of 2016 were under the age of 40 , as were 65 percent of new registrants in Georgia .
While the proportions were similar in the beginning of 2020 , the total number was much lower than in the past , which means that lots of young people aren ’ t registering as usual in at least two key 2020 swing states .
Some of these delayed registrants may @ @ @ @ @ @ @ Though we don ’ t have data for how a pandemic has affected registration in the past ( since the U.S. hasn ’ t faced a similar situation for a good century ) , Weiser cited another instance when voter registration dipped due to extenuating circumstances .
In May of 2011 , Florida passed a new bill that placed tough restrictions on third-party voter registration organizations , prompting many of them , such as the League of Women Voters , to stop operating in the state .
The restrictions were suspended by a @ @ @ @ @ @ @ had been done ; a subsequent study found that about 14 percent fewer voters registered in 2011 compared to the same period in 2007 , with a notable drop following the introduction of the bill — and those registrations never completely caught up .
In 2008 , more than 1 million new voters registered in Florida .
In 2012 , fewer than 900,000 did , according to the state ’ s voter registration data .
Of course , one unusual law in Florida isn ’ t exactly analogous to a pandemic , and @ @ @ @ @ @ @ level of enthusiasm for this election will be enough to close the gap that COVID-19 created , especially as states begin to reopen and voters return to registration sites like the DMV .
So it ’ s difficult to know whether this drop in registrations is permanent .
But it is clear that despite voters ’ intense interest in this election , the coronavirus has already made it harder for new voters to participate in it .

Poll after poll showed a high level of enthusiasm for voting in the general election in 2020, and in the beginning of the year, voter registration surged to match that excitement. Then the COVID-19 pandemic hit. New registrations have fallen off a cliff.
The spring of a presidential election year is often a busy time for adding new voters to the rolls, and a recent report from the Center for Election Innovation and Research, a nonprofit organization that aims to improve voter turnout and election security, shows registration numbers were even stronger in early 2020 than early 2016. But things changed dramatically in March, at least in the 12 places where FiveThirtyEight or CEIR were able to obtain data on new voters, a category that includes first-time voters, voters who recently moved to the state and, in some states (Texas, for example) even voters who moved between counties in the state.
Consider Florida, for example, where 109,859 new voters registered in February of this year, compared to 87,351 registrants in February of 2016. But in April 2020, only 21,031 new voters registered, compared with 52,508 in 2016. The same pattern holds in 10 other states, plus Washington, D.C.: Each one registered fewer new voters in April 2020 than in April 2016, including in states where online voter registration is available.
Currently, 39 states plus Washington, D.C., offer the ability to register to vote online, and a 40th (Oklahoma) is expected to implement it this year. However, in the three places for which we have the relevant data (Florida, Maryland and Washington), online voter registration has not taken off during the pandemic — certainly not enough to make up for the lost in-person registrations. Even in Washington, where online registrations have ticked up since the beginning of the year, the pace is comparable to 2016: 2,956 people registered online in April and May 2020, similar to the 2,771 people who registered online in April and May 2016.
The fact that new voter registrations were outpacing the 2016 numbers in January and February was predictable, according to David Becker, the executive director and founder of CEIR. For one thing, population growth means that voter registration always climbs a bit, he said. The expansion of automatic voter registration makes getting on the rolls more convenient than ever in many states, too. Voters were also clearly interested in registering, Becker said.
“Every piece of data we had looked at with regard to enthusiasm about engaging in this presidential election cycle indicated that we had to be prepared for the highest-turnout presidential election that almost anyone living had ever seen,” Becker said, “which makes the decline in March and especially April all the more striking.”
Based on the timing, it seems safe to assume that COVID-19 had something to do with the drop-off, but there’s data to back that assumption up, too. In addition to how many new voters register, some states track how these new voters get their name on the books. In 2016 and in the pre-pandemic months of 2020, in-person registration at places like departments of motor vehicles made up a large plurality, or even a majority, of new registrants in the four places for which we have data on how new voters are registering. But after the pandemic caused most states to shutter many government offices, those registrations dwindled. By contrast, remote registrations (e.g., online or by mail) held relatively steady.
“This is completely expected, but very concerning,” said Wendy Weiser, director of the democracy program at the Brennan Center for Justice at New York University’s School of Law. “The coronavirus shut down most of the primary avenues through which Americans register to vote: government offices, and all the malls, theaters and public places where voter registration drives operate.”
Indeed, the closing of schools and public events like festivals has hindered in-person voter registration drives run by third-party organizations. “We had planned to go to 850 high schools leading up to graduation, but as schools closed, that work was clearly disrupted,” said Jeanette Senecal, a senior director for the League of Women Voters who focuses on voter education.
For example, in Florida, third-party organizations registered 14,144 voters in January 2020 — a huge increase from the 1,196 they registered in January 2016. But in April 2020, they registered only 133 voters — down from 3,806 in April 2016.
States and third-party groups can still get around social distancing restrictions to get more voters on the poll books, though. Voto Latino, an organization that works to register and encourage Latino Americans to vote, has been operating digitally almost since its inception and was well prepared to continue its work during a pandemic. It uses digital campaigns to help voters register, which can even work in states like Texas, which does not have online voter registration — Voto Latino created an app that makes it easy to fill out the required form, which is then emailed to the voter to print off and mail in.
Danny Turkel, the communications manager for Voto Latino, said the group has actually seen a surge in voter registration, especially since protests in response to the killing of George Floyd began. “Our original goal entering 2020 was to register 500,000 voters,” said Turkel. “As the numbers have come in and surged, we are now thinking that we could surpass 500,000.”
So what kind of people might have registered if the coronavirus hadn’t struck? Well for one thing, they’re probably disproportionately young. “In any given year, far more young people register than older people, just because 18-year-olds age in [to being able to vote] and young people are more likely to move” and need to register at a new address, said Kevin Morris, a quantitative researcher focusing on voting rights and elections at the Brennan Center. According to Morris’s data, 57 percent of new registrants in Florida in the first four months of 2016 were under the age of 40, as were 65 percent of new registrants in Georgia. While the proportions were similar in the beginning of 2020, the total number was much lower than in the past, which means that lots of young people aren’t registering as usual in at least two key 2020 swing states.
New voter registrations have nosedived during COVID-19
Some of these delayed registrants may never end up registering at all. Though we don’t have data for how a pandemic has affected registration in the past (since the U.S. hasn’t faced a similar situation for a good century), Weiser cited another instance when voter registration dipped due to extenuating circumstances. In May of 2011, Florida passed a new bill that placed tough restrictions on third-party voter registration organizations, prompting many of them, such as the League of Women Voters, to stop operating in the state. The restrictions were suspended by a judge in May 2012 but the damage had been done; a subsequent study found that about 14 percent fewer voters registered in 2011 compared to the same period in 2007, with a notable drop following the introduction of the bill — and those registrations never completely caught up. In 2008, more than 1 million new voters registered in Florida. In 2012, fewer than 900,000 did, according to the state’s voter registration data.
Of course, one unusual law in Florida isn’t exactly analogous to a pandemic, and it’s possible that the high level of enthusiasm for this election will be enough to close the gap that COVID-19 created, especially as states begin to reopen and voters return to registration sites like the DMV. So it’s difficult to know whether this drop in registrations is permanent. But it is clear that despite voters’ intense interest in this election, the coronavirus has already made it harder for new voters to participate in it.


fivethirthyeight--2020-06-26--The Latest Senate Polls Show Some Good News For Democrats

Welcome to Pollapalooza , our weekly polling roundup .
In recent days , we ’ ve seen a number of surveys of high-profile Senate contests .
On the whole , the polls indicate Democrats have a real chance of picking up some seats in battleground states .
Some of this is thanks to former Vice President Joe Biden ’ s sizable lead over President Trump ( 9.5 points ) , as the current national environment is very favorable to Democrats .
But remember many races could still go either way .
And the good news for Republicans is that they @ @ @ @ @ @ @ Democratic-held seat in Alabama and probably don ’ t have to worry too much about losing Kentucky .
With the GOP holding a 53-47 majority in the Senate , Democrats still have to pick up three seats and the vice presidency , or at least four seats without the vice presidency , to take control of the chamber .
Let ’ s start with the Republican-held seats .
Sen. Martha McSally of Arizona has long been endangered , and three new surveys confirm she ’ s in real trouble .
Last week , @ @ @ @ @ @ @ found Democrat Mark Kelly , a retired astronaut , leading McSally 51 percent to 42 percent .
Two additional polls dropped on Thursday : The New York Times/Siena College gave Kelly a 9-point edge , 47 percent to 38 percent , and Redfield & Wilton Strategies found him ahead by 15 points , 49 percent to 34 percent .
Kelly has tended to attract slightly more support than Biden in Arizona — though they were about the same in the Times/Siena poll — and that ’ s an especially good sign for Kelly @ @ @ @ @ @ @ margin there .
In North Carolina , five new polls show Republican Sen. Thom Tillis in a tight race with former Democratic state Sen. Cal Cunningham .
The New York Times/Siena College survey of the race gave Cunningham a slim edge , 42 percent to 39 percent , which echoed another poll released this week — Democratic pollster Public Policy Polling had Cunningham up 44 percent to 40 percent .
( Both leads were inside the polls ’ margin of error . )
And a Fox News poll released Thursday evening put Cunningham @ @ @ @ @ @ @ to 37 percent .
However , an OAN/Gravis Marketing poll released last Friday found Tillis with 46 percent support , ahead by 1 point .
And a Redfield & Wilton Strategies poll released Thursday morning gave Cunningham a 9-point advantage , 45 percent to 36 percent .
Still , considering Biden is only leading Trump by 3 points in our North Carolina polling average , this race is likely to be very close in November .
Meanwhile , two recent polls in Georgia suggest that Democrats have a chance of capturing a Peach @ @ @ @ @ @ @ found Republican Sen. David Perdue ahead by just 3 points over Democratic nominee Jon Ossoff , 45 percent to 42 percent , while a Public Policy Polling survey gave Ossoff a 1-point lead , 45 percent to 44 percent .
Remember , though , that in Georgia a Senate candidate must win an outright majority or the race will go to a runoff , so there ’ s definitely a possibility that neither Perdue nor Ossoff win a majority ( there ’ s also a Libertarian candidate running ) .
No news on @ @ @ @ @ @ @ , which is a special election with a jungle primary that will also take place this November , though that contest will likely go to a January runoff .
In Kentucky , though , GOP Senate Majority Leader Mitch McConnell will be heavily favored against whomever the Democrats choose ( the results of Kentucky ’ s Democratic primary won ’ t be known until next week . )
A Civiqs survey from the week of June 13 found McConnell led Democratic state Rep. Charles Booker by 14 points , 52 percent to 38 @ @ @ @ @ @ @ 2018 congressional candidate Amy McGrath by 20 points , 53 percent to 33 percent .
The poll also found Trump ahead of Biden by 20 points , so the president ’ s big advantage should help McConnell down-ballot .
But Republicans aren ’ t the only ones playing defense .
Democrats also have to defend a couple of seats in states that Trump carried in 2016 — most notably Alabama .
Democratic Sen. Doug Jones has long been seen as the most vulnerable Senate incumbent up in 2020 , but on Monday , @ @ @ @ @ @ @ May that had him down just 3 points , 44 percent to 47 percent , against former Auburn football coach Tommy Tuberville , who is seen as the favorite over former Senator and Attorney General Jeff Sessions in the July GOP primary runoff .
Of course , this was an internal poll , so take it with a grain of salt , and a mid-June poll from GOP pollster Cygnal painted a much different picture .
It put Tuberville ahead of Jones by 14 points , 50 percent to 36 percent , and @ @ @ @ @ @ @ percent to 35 percent .
The Jones campaign is arguing that Jones ’ s lead could have grown since their poll , especially since Biden ’ s standing has improved in Alabama , but in all likelihood , Jones is still a serious underdog .
After all , Trump still leads Biden by 15 points in our polling average and is likely to win Alabama by the double-digits in November .
Finally , we also have five fresh surveys from Michigan , where Democratic Sen. Gary Peters faces Republican John James , an @ @ @ @ @ @ @ ’ s 2018 Senate race , but still performed fairly well in a Democratic-leaning environment .
Yet the numbers now mostly augur well for Peters .
Thursday ’ s New York Times/Siena College poll put Peters ahead by 10 points , 41 percent to 31 percent while Redfield & Wilton Strategies had him up by 18 points , 50 percent to 32 percent .
And Peters also had double-digit leads in two polls conducted on behalf of right-leaning sponsors : The conservative Restoration PAC and GOP pollster Hodas & Associates put a poll @ @ @ @ @ @ @ by 13 points , 51 percent to 38 percent , while a survey released last week by TIPP on behalf of conservative outlet American Greatness found Peters up by 12 points , 47 percent to 35 percent .
Plus , Marketing Resource Group also released a poll last week that found Peters ahead by 6 points , albeit only 36 percent to 30 percent , with 14 percent preferring “ someone else ” and 18 percent undecided .
Bottom line : Peters seems to be cruising toward reelection , buoyed by the fact @ @ @ @ @ @ @ points in our Michigan polling average .
It ’ s too early to say that Democrats can take back the Senate , but if the national environment remains this favorable for Democrats , they ’ ll certainly stand a pretty good chance of regaining control in November .
• A new survey from Morning Consult found that 80 percent of Americans believe it ’ s “ very ” or “ somewhat ” likely that a second wave of coronavirus cases will hit in the next year .
Respondents were split as to whether @ @ @ @ @ @ @ impact of a second wave — 42 percent said yes , 45 percent no .
But only 33 percent agreed that the country was ready to handle the economic impacts of a second wave , while 53 percent disagreed .
• A new poll from Axios/Ipsos suggests that comfort with getting a haircut might signal how safe the public feels about coronavirus cases in their state .
In states where the number of new cases decreased from June 9 to 16 , the share of respondents getting their hair cut increased from 10 @ @ @ @ @ @ @ states where there was at least a 50 percent increase in new cases , the share of respondents who visited a hair salon fell from 19 percent to 13 percent .
States with small increases in cases saw the share visiting a hair salon stay at 18 percent .
• A record-high share of Americans — 40 percent — view the death penalty as “ morally wrong , ” according to a new poll from Gallup .
Fifty-four percent still said it was morally acceptable , but that ’ s the lowest share @ @ @ @ @ @ @ in 2001 .
The drop in support was driven largely by liberals and moderates , who expressed new lows in approval — 37 percent and 56 percent , respectively .
• NFL players kneeling during the national anthem to protest racism was once pretty unpopular , but as support for the Black Lives Matter movement has increased in recent weeks , fewer Americans think these protests are unacceptable .
A new survey from YouGov found that 51 percent now support sports leagues substituting the phrase “ Black Lives Matter ” in place of @ @ @ @ @ @ @ jerseys .
Only 35 percent opposed the idea , but there was a sizable partisan gap : 73 percent of Democrats approved of this compared to just 22 percent of Republicans .
• Following the U.S. Supreme Court ’ s ruling that protects gay and transgender workers from workplace discrimination , the Kaiser Family Foundation found that about 9 in 10 Americans think it should be illegal for employers to fire or refuse to hire individuals because of their sexual orientation or gender identity .
Additionally , the poll found that most respondents @ @ @ @ @ @ @ lesbian , gay or bisexual face widespread discrimination — 79 percent and 74 percent , respectively .
• The Senate has been unable to pass a police reform bill , but majorities of Democratic and Republican voters back reforms like banning chokeholds , training police on de-escalation , creating a national database of police disciplinary records and banning or increasing regulations on no-knock warrants , according to a new survey from Morning Consult .
Asked about specific reform plans from House Democrats and Senate Republicans , 48 percent of respondents felt the Democratic @ @ @ @ @ @ @ warrants — appropriately addressed police reform , while only 33 percent said the same for the GOP proposal ( which discourages the use of chokeholds and no-knock warrants , but doesn ’ t ban them outright ) .
According to FiveThirtyEight ’ s presidential approval tracker , 40.6 percent of Americans approve of the job Trump is doing as president , while 55.2 percent disapprove ( a net approval rating of -14.6 points ) .
At this time last week , 41.2 percent approved and 55.2 percent disapproved ( a net approval rating @ @ @ @ @ @ @ ago , Trump had an approval rating of 42.7 percent and a disapproval rating of 53.5 percent , for a net approval rating of -10.7 points .
In our average of polls of the generic congressional ballot , Democrats currently lead by 8.1 percentage points ( 48.7 percent to 40.6 percent ) .
A week ago , Democrats led Republicans by 7.9 points ( 48.6 percent to 40.7 percent ) .
At this time last month , voters also preferred Democrats by 8.0 points ( 48.2 percent to 40.2 percent ) .

Welcome to Pollapalooza, our weekly polling roundup.
Poll(s) of the week
In recent days, we’ve seen a number of surveys of high-profile Senate contests. On the whole, the polls indicate Democrats have a real chance of picking up some seats in battleground states. Some of this is thanks to former Vice President Joe Biden’s sizable lead over President Trump (9.5 points), as the current national environment is very favorable to Democrats.
But remember many races could still go either way. And the good news for Republicans is that they’re favored to pick up a Democratic-held seat in Alabama and probably don’t have to worry too much about losing Kentucky. With the GOP holding a 53-47 majority in the Senate, Democrats still have to pick up three seats and the vice presidency, or at least four seats without the vice presidency, to take control of the chamber.
Let’s start with the Republican-held seats. Sen. Martha McSally of Arizona has long been endangered, and three new surveys confirm she’s in real trouble. Last week, Democratic pollster Civiqs released a poll that found Democrat Mark Kelly, a retired astronaut, leading McSally 51 percent to 42 percent. Two additional polls dropped on Thursday: The New York Times/Siena College gave Kelly a 9-point edge, 47 percent to 38 percent, and Redfield & Wilton Strategies found him ahead by 15 points, 49 percent to 34 percent. Kelly has tended to attract slightly more support than Biden in Arizona — though they were about the same in the Times/Siena poll — and that’s an especially good sign for Kelly as Biden has led by a small margin there.
In North Carolina, five new polls show Republican Sen. Thom Tillis in a tight race with former Democratic state Sen. Cal Cunningham. The New York Times/Siena College survey of the race gave Cunningham a slim edge, 42 percent to 39 percent, which echoed another poll released this week — Democratic pollster Public Policy Polling had Cunningham up 44 percent to 40 percent. (Both leads were inside the polls’ margin of error.) And a Fox News poll released Thursday evening put Cunningham ahead by 2 points, 39 percent to 37 percent. However, an OAN/Gravis Marketing poll released last Friday found Tillis with 46 percent support, ahead by 1 point. And a Redfield & Wilton Strategies poll released Thursday morning gave Cunningham a 9-point advantage, 45 percent to 36 percent. Still, considering Biden is only leading Trump by 3 points in our North Carolina polling average, this race is likely to be very close in November.
Meanwhile, two recent polls in Georgia suggest that Democrats have a chance of capturing a Peach State seat. A Fox News survey found Republican Sen. David Perdue ahead by just 3 points over Democratic nominee Jon Ossoff, 45 percent to 42 percent, while a Public Policy Polling survey gave Ossoff a 1-point lead, 45 percent to 44 percent. Remember, though, that in Georgia a Senate candidate must win an outright majority or the race will go to a runoff, so there’s definitely a possibility that neither Perdue nor Ossoff win a majority (there’s also a Libertarian candidate running). No news on the state’s other Senate seat, which is a special election with a jungle primary that will also take place this November, though that contest will likely go to a January runoff.
In Kentucky, though, GOP Senate Majority Leader Mitch McConnell will be heavily favored against whomever the Democrats choose (the results of Kentucky’s Democratic primary won’t be known until next week.) A Civiqs survey from the week of June 13 found McConnell led Democratic state Rep. Charles Booker by 14 points, 52 percent to 38 percent, and former fighter pilot and 2018 congressional candidate Amy McGrath by 20 points, 53 percent to 33 percent. The poll also found Trump ahead of Biden by 20 points, so the president’s big advantage should help McConnell down-ballot.
But Republicans aren’t the only ones playing defense. Democrats also have to defend a couple of seats in states that Trump carried in 2016 — most notably Alabama. Democratic Sen. Doug Jones has long been seen as the most vulnerable Senate incumbent up in 2020, but on Monday, his campaign released an internal poll from May that had him down just 3 points, 44 percent to 47 percent, against former Auburn football coach Tommy Tuberville, who is seen as the favorite over former Senator and Attorney General Jeff Sessions in the July GOP primary runoff.
Of course, this was an internal poll, so take it with a grain of salt, and a mid-June poll from GOP pollster Cygnal painted a much different picture. It put Tuberville ahead of Jones by 14 points, 50 percent to 36 percent, and Sessions ahead by 10 points, 45 percent to 35 percent. The Jones campaign is arguing that Jones’s lead could have grown since their poll, especially since Biden’s standing has improved in Alabama, but in all likelihood, Jones is still a serious underdog. After all, Trump still leads Biden by 15 points in our polling average and is likely to win Alabama by the double-digits in November.
Finally, we also have five fresh surveys from Michigan, where Democratic Sen. Gary Peters faces Republican John James, an Army veteran. James lost the state’s 2018 Senate race, but still performed fairly well in a Democratic-leaning environment. Yet the numbers now mostly augur well for Peters. Thursday’s New York Times/Siena College poll put Peters ahead by 10 points, 41 percent to 31 percent while Redfield & Wilton Strategies had him up by 18 points, 50 percent to 32 percent. And Peters also had double-digit leads in two polls conducted on behalf of right-leaning sponsors: The conservative Restoration PAC and GOP pollster Hodas & Associates put a poll out on Thursday that had Peters ahead by 13 points, 51 percent to 38 percent, while a survey released last week by TIPP on behalf of conservative outlet American Greatness found Peters up by 12 points, 47 percent to 35 percent. Plus, Marketing Resource Group also released a poll last week that found Peters ahead by 6 points, albeit only 36 percent to 30 percent, with 14 percent preferring “someone else” and 18 percent undecided. Bottom line: Peters seems to be cruising toward reelection, buoyed by the fact that Biden leads Trump by about 11 points in our Michigan polling average.
It’s too early to say that Democrats can take back the Senate, but if the national environment remains this favorable for Democrats, they’ll certainly stand a pretty good chance of regaining control in November.
Other polling bites
Trump approval
According to FiveThirtyEight’s presidential approval tracker, 40.6 percent of Americans approve of the job Trump is doing as president, while 55.2 percent disapprove (a net approval rating of -14.6 points). At this time last week, 41.2 percent approved and 55.2 percent disapproved (a net approval rating of -14.0 points). One month ago, Trump had an approval rating of 42.7 percent and a disapproval rating of 53.5 percent, for a net approval rating of -10.7 points.
Generic ballot
In our average of polls of the generic congressional ballot, Democrats currently lead by 8.1 percentage points (48.7 percent to 40.6 percent). A week ago, Democrats led Republicans by 7.9 points (48.6 percent to 40.7 percent). At this time last month, voters also preferred Democrats by 8.0 points (48.2 percent to 40.2 percent).


fivethirthyeight--2020-06-26--FiveThirtyEight Debate Club: What’s The Correct Way To Organize Your Bookshelf?

It ’ s time for another installment of FiveThirtyEight Debate Club !
It turns out , our staffers have very @ @ @ @ @ how many books one should own , what kinds of books , and most importantly @ @ @ @ @ those books on a bookshelf .
With that in mind , we hope to answer @ @ @ @ @ episode of Debate Club .
What ’ s your preferred organizational method ?
Be sure @ @ @ @ @ or Twitter .
And while you ’ re there , let us know what you @ @ @ @ @ debate in the next episode .

It’s time for another installment of FiveThirtyEight Debate Club!
It turns out, our staffers have very strong opinions on books — how many books one should own, what kinds of books, and most importantly, how to best organize those books on a bookshelf. With that in mind, we hope to answer that very question on this episode of Debate Club.
What’s your preferred organizational method? Be sure to tell us on YouTube or Twitter. And while you’re there, let us know what you’d like us to debate in the next episode.
Do we even need political conventions anymore? | FiveThirtyEight Debate Club
Whatâs the best state in the US? | FiveThirtyEight Debate Club


fivethirthyeight--2020-06-26--What We Know About Face Masks Now

What We Know About Face Masks Now

This week ’ s episode of PODCAST-19 is all about face masks — whether they ’ re effective , why @ @ @ @ @ evolved , and what you should look for when you buy one of your own @ @ @ @ @ Rogers , two of FiveThirtyEight ’ s reporters on the COVID-19 beat , join the @ @ @ @ @ science supporting the use of face masks has really changed as the pandemic has gone @ @ @ @ @ want to miss an episode of PODCAST-19 , FiveThirtyEight ’ s weekly look at what @ @ @ @ @ we know we don ’ t know — about COVID-19 ?
Subscribe on your favorite @ @ @ @ @ , here ’ s where to do it on Apple Podcasts and Spotify .

This week’s episode of PODCAST-19 is all about face masks — whether they’re effective, why our thinking on them has evolved, and what you should look for when you buy one of your own. Maggie Koerth and Kaleigh Rogers, two of FiveThirtyEight’s reporters on the COVID-19 beat, join the show to share whether the science supporting the use of face masks has really changed as the pandemic has gone on.
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--2020-06-26--How The Pandemic Is Already Affecting The Election

On this episode of the FiveThirtyEight Politics podcast , we analyze data showing that the number of people registering to @ @ @ @ @ cliff during the coronavirus pandemic and discuss what that means for the November election .

On this episode of the FiveThirtyEight Politics podcast, we analyze data showing that the number of people registering to vote has fallen off a cliff during the coronavirus pandemic and discuss what that means for the November election.