fivethirthyeight--2020-10-02--The Seattle Storm Have Been Here Before. Can The Las Vegas Aces Break Through?

Depending on the lens you use when looking at the WNBA Finals , with Game 1 between the Seattle Storm and Las Vegas Aces set for Friday night , any of these statements can be true : Las Vegas is the favorite ( top seed , won both regular-season meetings ) .
Or Seattle is the favorite ( 2018 champs , largely intact after a 2019 missing key pieces ) .
Or this is a true toss-up ( featuring the league ’ s two best offensive and defensive ratings ) with a pair of dramatically different playing styles .
To @ @ @ @ @ @ @ it , the duo of players he coached over several generations , Sue Bird and Breanna Stewart , offers the ultimate edge for Seattle in this best-of-five series .
“ They are the two best players at their positions right now , ” Auriemma said .
“ So that helps .
But that doesn ’ t account for all of it .
They know when it ’ s winning time .
They know how to win big games .
They ’ ve played in so many of them .
And because they ’ @ @ @ @ @ @ @ many of them , they walk into every big game knowing they ’ re going to win.
” If there is a difference between these two teams , it comes down to what Auriemma said : One side has done it before .
That ’ s not to dismiss Las Vegas ’ s ability to break through , however .
This Aces team , powered by 2020 MVP A ’ ja Wilson , had long ago circled 2020 on the calendar .
When Bill Laimbeer — no stranger to WNBA championships himself , @ @ @ @ @ @ @ Detroit Shock — took the job with the Aces in 2018 , he described his process to reporters as a three-year plan .
That placed title expectations squarely on this season .
In a year when so little else has gone according to plan , that ’ s a little reassuring sense of normalcy .
So for the two 18-4 teams this year , getting to this point has meant dramatically different shapes to their games .
The Storm took 31.5 percent of their field-goal attempts from beyond the arc , almost double @ @ @ @ @ @ @ .
And that gap only expanded further in the playoffs , 39.7 percent for Seattle , 15 percent for Las Vegas .
While the Storm rely on Bird and Stewart first offensively , the Aces use Wilson , a brutally effective power forward , and Angel McCoughtry , the longtime Atlanta Dream small forward and top option refashioned as Wilson ’ s sidekick .
Wilson made an All-Star team in her rookie year of 2018 , concluding the season as Rookie of the Year .
But Laimbeer said she has improved significantly over @ @ @ @ @ @ @ She knows her responsibility , ” Laimbeer said after the Aces ’ 66-63 win over the Sun on Tuesday to earn this trip to the WNBA Finals .
“ She has matured tremendously as a person and as a basketball player .
In the first half , you watch them try to double- or triple-team her , and she found the right people .
She didn ’ t have that last two years — she has it now : her patience.
” As for McCoughtry , the decision to come to Las Vegas @ @ @ @ @ @ @ Accordingly , she has played fewer minutes than she did during her tenure as the center of Atlanta ’ s attack , but her efficiency has improved , with a 61.1 true shooting percentage and win shares per 40 of 0.288 representing the highest marks of a career that , let ’ s remember , includes five All-Star team selections and two Olympic gold medals already .
Her mentality is a microcosm for this Aces team now .
“ I kept saying , over and over in my head , ‘ Win the @ @ @ @ @ @ @ the game , ’ ” McCoughtry said after Game 5 .
“ Just figure it out .
Win it .
I don ’ t care how it is done.
” That ’ s what the Aces did to advance , holding the Connecticut Sun to 18 points in the second half of Game 5 .
Laimbeer said he didn ’ t change much tactically , and the Aces didn ’ t even play at their typical frenetic pace .
They just managed to slow the Sun attack to a crawl .
“ For @ @ @ @ @ @ @ stops together , ” Wilson said .
“ And I think that ’ s going to be key against a good Seattle team that knows how to execute all the time.
” The Storm ’ s season is really three seasons , to hear both Bird and the numbers tell it .
Overall , the Storm posted a net rating of 15 , the best in the league since the Houston Comets back in 2000 .
Over the last 10 regular-season games , though , the Storm ’ s net rating fell to @ @ @ @ @ @ @ with Las Vegas ’ s 9.4 , and during a period the Aces beat the Storm twice .
Still , the latter of those two victories came against a Seattle team missing both Bird and Stewart , and in Seattle ’ s playoff series against a talented Lynx team , the team ’ s net rating rebounded to 12.5 .
( Interestingly , Las Vegas , in their five-game slugfest against the Sun , actually posted a negative net rating despite winning the series . )
Most encouragingly for Seattle was Game 3 @ @ @ @ @ @ @ behind vintage performances from both Stewart ( 31 points , seven assists , six rebounds , no turnovers ) and Bird ( 16 points , nine assists ) .
After it was over , Lynx coach Cheryl Reeve said that Stewart “ imposed her will on the game.
” And both players acknowledged that after fighting off late-season injuries , they felt more like their typical selves , freeing them physically to capitalize on knowing when winning time was .
“ Stewie missed the last two regular-season games , and then we had @ @ @ @ @ @ @ a little bit of a delay , that first game being postponed , ” Bird said .
“ So it was a long time to not play basketball for Stewie , for myself , for really all of us , and all that does is get you out of your rhythm a little bit.
” Even so , this is not simply the Seattle Storm from 2018 , back to reclaim what is theirs .
For one , they ’ re without their head coach-in-exile , Dan Hughes , after he wasn ’ @ @ @ @ @ @ @ to enter the bubble .
The capable Gary Kloppenburg , who has served as assistant in Seattle since 2017 amid a long career coaching , has kept the Storm playing at an elite level in Hughes ’ s stead .
In many ways , they are even better , with contributors like center Mercedes Russell developing , newcomer Ezi Magbegor providing effective minutes at the 4 , and Jordin Canada , who was more rookie change-of-pace guard than effective game manager back in 2018 , now serving as a point guard who would @ @ @ @ @ @ @ And she ’ s still fast . )
The loss of Sami Whitcomb , a combo guard and champion who has left the bubble to be with her wife as she gives birth , is the only discordant basketball note heading into this series for Seattle .
“ I think this year , towards the end of the season , we ’ re really starting to hit our stride , ” Canada said , expressing the belief that this team is better than the 2018 champions .
“ We ’ ve got a @ @ @ @ @ @ @ , and I think everything ’ s coming together at the right time.
” But Las Vegas , too , has players who are eager to prove they know when winning time is , from veteran point guard Danielle Robinson to shooting guard Kayla McBride , both of whom spent time with this franchise before it moved from San Antonio to Las Vegas .
“ Nobody really expected us to be here , ” McBride said .
“ I ’ m talking to Danielle Robinson , remembering that San Antonio group .
We @ @ @ @ @ @ @ We believe in each other , trust each other at both ends of the floor.
” And who is the favorite ?
Asked point-blank , McBride offered a response just short of a guarantee .
“ I believe in my teammates , ” she said .
“ I believe in who we are .
”

The Seattle Storm Have Been Here Before. Can The Las Vegas Aces Break Through?
Depending on the lens you use when looking at the WNBA Finals, with Game 1 between the Seattle Storm and Las Vegas Aces set for Friday night, any of these statements can be true:
Las Vegas is the favorite (top seed, won both regular-season meetings). Or Seattle is the favorite (2018 champs, largely intact after a 2019 missing key pieces). Or this is a true toss-up (featuring the league’s two best offensive and defensive ratings) with a pair of dramatically different playing styles.
To hear UConn’s Geno Auriemma tell it, the duo of players he coached over several generations, Sue Bird and Breanna Stewart, offers the ultimate edge for Seattle in this best-of-five series.
“They are the two best players at their positions right now,” Auriemma said. “So that helps. But that doesn’t account for all of it. They know when it’s winning time. They know how to win big games. They’ve played in so many of them. And because they’ve been so successful and in so many of them, they walk into every big game knowing they’re going to win.”
If there is a difference between these two teams, it comes down to what Auriemma said: One side has done it before.
That’s not to dismiss Las Vegas’s ability to break through, however. This Aces team, powered by 2020 MVP A’ja Wilson, had long ago circled 2020 on the calendar. When Bill Laimbeer — no stranger to WNBA championships himself, having won as head coach of the Detroit Shock — took the job with the Aces in 2018, he described his process to reporters as a three-year plan. That placed title expectations squarely on this season. In a year when so little else has gone according to plan, that’s a little reassuring sense of normalcy.
So for the two 18-4 teams this year, getting to this point has meant dramatically different shapes to their games. The Storm took 31.5 percent of their field-goal attempts from beyond the arc, almost double Vegas’s rate of 16.8 percent. And that gap only expanded further in the playoffs, 39.7 percent for Seattle, 15 percent for Las Vegas.
While the Storm rely on Bird and Stewart first offensively, the Aces use Wilson, a brutally effective power forward, and Angel McCoughtry, the longtime Atlanta Dream small forward and top option refashioned as Wilson’s sidekick.
Wilson made an All-Star team in her rookie year of 2018, concluding the season as Rookie of the Year. But Laimbeer said she has improved significantly over even that high initial standard.
“She knows her responsibility,” Laimbeer said after the Aces’ 66-63 win over the Sun on Tuesday to earn this trip to the WNBA Finals. “She has matured tremendously as a person and as a basketball player. In the first half, you watch them try to double- or triple-team her, and she found the right people. She didn’t have that last two years — she has it now: her patience.”
As for McCoughtry, the decision to come to Las Vegas was with a championship in mind. Accordingly, she has played fewer minutes than she did during her tenure as the center of Atlanta’s attack, but her efficiency has improved, with a 61.1 true shooting percentage and win shares per 40 of 0.288 representing the highest marks of a career that, let’s remember, includes five All-Star team selections and two Olympic gold medals already.
Her mentality is a microcosm for this Aces team now.
“I kept saying, over and over in my head, ‘Win the game. Win the game. Win the game,’” McCoughtry said after Game 5. “Just figure it out. Win it. I don’t care how it is done.”
That’s what the Aces did to advance, holding the Connecticut Sun to 18 points in the second half of Game 5. Laimbeer said he didn’t change much tactically, and the Aces didn’t even play at their typical frenetic pace. They just managed to slow the Sun attack to a crawl.
“For us, it’s just putting stops together,” Wilson said. “And I think that’s going to be key against a good Seattle team that knows how to execute all the time.”
The Storm’s season is really three seasons, to hear both Bird and the numbers tell it. Overall, the Storm posted a net rating of 15, the best in the league since the Houston Comets back in 2000. Over the last 10 regular-season games, though, the Storm’s net rating fell to 9.5 — still elite but virtually tied with Las Vegas’s 9.4, and during a period the Aces beat the Storm twice.
Still, the latter of those two victories came against a Seattle team missing both Bird and Stewart, and in Seattle’s playoff series against a talented Lynx team, the team’s net rating rebounded to 12.5. (Interestingly, Las Vegas, in their five-game slugfest against the Sun, actually posted a negative net rating despite winning the series.)
Most encouragingly for Seattle was Game 3, when the Storm swept the series behind vintage performances from both Stewart (31 points, seven assists, six rebounds, no turnovers) and Bird (16 points, nine assists). After it was over, Lynx coach Cheryl Reeve said that Stewart “imposed her will on the game.” And both players acknowledged that after fighting off late-season injuries, they felt more like their typical selves, freeing them physically to capitalize on knowing when winning time was.
“Stewie missed the last two regular-season games, and then we had a week, and then we had a little bit of a delay, that first game being postponed,” Bird said. “So it was a long time to not play basketball for Stewie, for myself, for really all of us, and all that does is get you out of your rhythm a little bit.”
Even so, this is not simply the Seattle Storm from 2018, back to reclaim what is theirs. For one, they’re without their head coach-in-exile, Dan Hughes, after he wasn’t approved, for medical reasons, to enter the bubble. The capable Gary Kloppenburg, who has served as assistant in Seattle since 2017 amid a long career coaching, has kept the Storm playing at an elite level in Hughes’s stead.
In many ways, they are even better, with contributors like center Mercedes Russell developing, newcomer Ezi Magbegor providing effective minutes at the 4, and Jordin Canada, who was more rookie change-of-pace guard than effective game manager back in 2018, now serving as a point guard who would start for many other teams. (And she’s still fast.) The loss of Sami Whitcomb, a combo guard and champion who has left the bubble to be with her wife as she gives birth, is the only discordant basketball note heading into this series for Seattle.
“I think this year, towards the end of the season, we’re really starting to hit our stride,” Canada said, expressing the belief that this team is better than the 2018 champions. “We’ve got a couple of different pieces for this team, and I think everything’s coming together at the right time.”
But Las Vegas, too, has players who are eager to prove they know when winning time is, from veteran point guard Danielle Robinson to shooting guard Kayla McBride, both of whom spent time with this franchise before it moved from San Antonio to Las Vegas.
“Nobody really expected us to be here,” McBride said. “I’m talking to Danielle Robinson, remembering that San Antonio group. We won seven games one season. … We believe in each other, trust each other at both ends of the floor.”
And who is the favorite? Asked point-blank, McBride offered a response just short of a guarantee. “I believe in my teammates,” she said. “I believe in who we are.”


fivethirthyeight--2020-10-02--Patrick Mahomes Just Doesn’t Have Bad Games

Patrick Mahomes played the best game of his young career Monday night against the Baltimore Ravens .
The Kansas City quarterback passed for 385 yards and four touchdowns with no interceptions while rushing for a fifth TD , and he did it against a Baltimore team that boasted the best defense in football through two weeks of play .
Mahomes ’ s Total Quarterback Rating ( QBR ) — ESPN ’ s signature metric that accounts for a quarterback ’ s value both passing and running the ball — was 97.7 , tied for his career high .
It ’ @ @ @ @ @ @ @ the receiving end of Mahomes ’ s best game .
By halftime against Baltimore , he had become the fastest player to reach 10,000 regular-season passing yards in NFL history , two games quicker than Hall of Fame QB Kurt Warner .
Mahomes also extended his career record against Lamar Jackson and the Ravens to 3-0 .
Yet of all the superlatives that describe Mahomes ’ s already amazing career — the 2018 league MVP , the youngest QB to win Super Bowl MVP , the highest-paid player in the NFL with a @ @ @ @ @ @ @ — perhaps the most incredible is this : Mahomes has never had a below-average game since entering the NFL .
Mahomes ’ s “ worst ” game — if you can call it that — came last season at home against the Indianapolis Colts in Week 5 .
He posted a QBR of 52.6 in the game but still passed for 321 yards and a touchdown with no interceptions in the 19-13 loss .
Another team that has given Mahomes “ trouble ” is division rival Los Angeles .
In five games against @ @ @ @ @ @ @ game of over 300 yards passing .
And in two of the five games against L.A. , he threw for less than 200 yards , earning Total QBR scores of 62.5 and 61.7 .
Still , containing Mahomes hasn ’ t translated into wins for the Chargers .
Despite holding him to merely slightly above-average performances — no small feat !
— the Chargers are just 1-4 against the Chiefs with Mahomes behind center .
The only team to consistently give Mahomes some measure of trouble — and also win — are the @ @ @ @ @ @ @ Chiefs will be playing this Sunday .
In three games against head coach Bill Belichick and the Patriots ’ defense , Mahomes and the Chiefs have won just once .
Mahomes ’ s average QBR against the Patriots is 68.8 , his second-worst rating among teams he ’ s faced more than once .
New England has been particularly adept at taking away Mahomes ’ s favorite receivers , which shouldn ’ t surprise anyone familiar with a Belichick game plan .
In the three meetings between the two teams , Mahomes has @ @ @ @ @ @ @ would expect from an average NFL QB in similar situations .
Yet despite New England ’ s previous success , our Elo model gives the Patriots only a 26 percent chance to beat the Chiefs on Sunday .
With a short week to plan for New England , perhaps the odds of Mahomes having a less-than-incredible performance against the Patriots are decent , even if it doesn ’ t lead to a win .
When facing a player like Mahomes , who ’ s never had a truly bad game in his professional @ @ @ @ @ @ @ best you can hope for .

Patrick Mahomes played the best game of his young career Monday night against the Baltimore Ravens. The Kansas City quarterback passed for 385 yards and four touchdowns with no interceptions while rushing for a fifth TD, and he did it against a Baltimore team that boasted the best defense in football through two weeks of play. Mahomes’s Total Quarterback Rating (QBR) — ESPN’s signature metric that accounts for a quarterback’s value both passing and running the ball — was 97.7, tied for his career high.
It’s no small thing to be on the receiving end of Mahomes’s best game. By halftime against Baltimore, he had become the fastest player to reach 10,000 regular-season passing yards in NFL history, two games quicker than Hall of Fame QB Kurt Warner. Mahomes also extended his career record against Lamar Jackson and the Ravens to 3-0. Yet of all the superlatives that describe Mahomes’s already amazing career — the 2018 league MVP, the youngest QB to win Super Bowl MVP, the highest-paid player in the NFL with a contract worth almost half a billion dollars — perhaps the most incredible is this: Mahomes has never had a below-average game since entering the NFL.
Mahomes’s “worst” game — if you can call it that — came last season at home against the Indianapolis Colts in Week 5. He posted a QBR of 52.6 in the game but still passed for 321 yards and a touchdown with no interceptions in the 19-13 loss.
Another team that has given Mahomes “trouble” is division rival Los Angeles. In five games against the Chargers, Mahomes has just one game of over 300 yards passing. And in two of the five games against L.A., he threw for less than 200 yards, earning Total QBR scores of 62.5 and 61.7. Still, containing Mahomes hasn’t translated into wins for the Chargers. Despite holding him to merely slightly above-average performances — no small feat! — the Chargers are just 1-4 against the Chiefs with Mahomes behind center.
The only team to consistently give Mahomes some measure of trouble — and also win — are the New England Patriots, the team the Chiefs will be playing this Sunday. In three games against head coach Bill Belichick and the Patriots’ defense, Mahomes and the Chiefs have won just once. Mahomes’s average QBR against the Patriots is 68.8, his second-worst rating among teams he’s faced more than once.
New England has been particularly adept at taking away Mahomes’s favorite receivers, which shouldn’t surprise anyone familiar with a Belichick game plan. In the three meetings between the two teams, Mahomes has a completion percentage well below what we would expect from an average NFL QB in similar situations.
Yet despite New England’s previous success, our Elo model gives the Patriots only a 26 percent chance to beat the Chiefs on Sunday. With a short week to plan for New England, perhaps the odds of Mahomes having a less-than-incredible performance against the Patriots are decent, even if it doesn’t lead to a win.
When facing a player like Mahomes, who’s never had a truly bad game in his professional career, maybe that’s the best you can hope for.
Check out our latest NFL predictions.


fivethirthyeight--2020-10-02--Can You Eat All The Chocolates?

Can You Eat All The Chocolates?

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 .
Please wait until Monday to publicly share your answers !
If you need a hint or have a favorite puzzle collecting @ @ @ @ @ @ @ on Twitter .
From Benjamin Dickman comes proof that it ’ s hip to be ( a difference of ) squares : Benjamin likes numbers that can be written as the difference between two perfect squares .
He thinks they ’ re hip .
For example , the number 40 is hip , since it equals 72−32 , or 49−9 .
But hold the phone , 40 is doubly hip , because it also equals 112−92 , or 121−81 .
With apologies to Douglas Adams , 42 is not particularly hip .
Go @ @ @ @ @ @ @ whose difference is 42 .
I ’ ll wait .
Now , Benjamin is upping the stakes .
He wants to know just how hip 1,400 might be .
Can you do him a favor , and figure out how many ways 1,400 can be written as the difference of two perfect squares ?
Benjamin will really appreciate it .
Extra credit : Can you find a general formula or approach for counting the number of ways any whole number can be written as the difference between two perfect squares ?
( Your @ @ @ @ @ @ @ the number is even or odd , its prime factorization , etc . )
From mathematician ( and author of Basic Probability : What Every Math Student Should Know ) Henk Tijms comes a choice matter of chance and chocolate : I have 10 chocolates in a bag : Two are milk chocolate , while the other eight are dark chocolate .
One at a time , I randomly pull chocolates from the bag and eat them — that is , until I pick a chocolate of the other kind .
When I @ @ @ @ @ @ @ , I put it back in the bag and start drawing again with the remaining chocolates .
I keep going until I have eaten all 10 chocolates .
For example , if I first pull out a dark chocolate , I will eat it .
( I ’ ll always eat the first chocolate I pull out . )
If I pull out a second dark chocolate , I will eat that as well .
If the third one is milk chocolate , I will not eat it ( yet ) , and @ @ @ @ @ @ @ .
Then I will start again , eating the first chocolate I pull out .
What are the chances that the last chocolate I eat is milk chocolate ?
Congratulations to 👏 Karen Campe 👏 of New Canaan , Connecticut , winner of last week ’ s Riddler Express .
Last week , you took a swing at a riddle about golf .
( See what I did there ? )
A typical hole is about 400 yards long , while the cup measures a mere 4.25 inches in diameter .
Suppose that @ @ @ @ @ @ @ the ball X percent closer to the center of the hole .
For example , if X were 75 , then with every swing the ball would be four times closer to the hole than it was previously .
For a 400-yard hole with no hazards ( water , sand or otherwise ) in the way , what was the minimum value of X so that you shot par , meaning you hit the ball into the cup in exactly four strokes ?
First , it was a good idea to work with @ @ @ @ @ @ @ yard equals 3 feet , or 36 inches .
That meant the total length of the hole — 400 yards — was 14,400 inches .
Meanwhile , the cup ’ s diameter was 4.25 inches , which meant its radius was 2.125 inches .
So once the ball came within 2.125 inches of the hole ’ s center , it fell in .
( Some readers used the diameter instead of the radius here , which led to an answer that was off by a few percentage points . )
Most solvers assumed @ @ @ @ @ @ @ variable .
As we said , the initial distance to the hole was 14,400 inches .
After one swing , it was 14,400· ( 1−X ) .
After two swings , it was 14,400· ( 1−X ) 2 .
After three swings , it was 14,400· ( 1−X ) 3 .
Finally , after four swings , it was 14,400· ( 1−X ) 4 .
You shot par when this distance , 14,400· ( 1−X ) 4 , was equal to 2.125 inches ( or , rather , just a shade less than @ @ @ @ @ @ @ meant 14,400· ( 1−X ) 4 = 2.125 , or ( 1−X ) 4 = 17/115,200 .
Taking the fourth root of both sides and solving gave a solution of approximately 0.88978 .
In other words , X had to be at least about 89 for you to make par .
Some solvers took this problem even further , calculating the value of X for holes that were longer or shorter and also for different numbers of strokes .
For example , what would it take to shoot a birdie ( a score @ @ @ @ @ @ @ this case , three strokes ) on this hole ?
To answer this question , you had to solve the equation ( 1−X ) 3 = 17/115,200 , with an exponent of three rather than four .
That gave a value of X that is approximately 95 .
In other words , to go from a par to a birdie , you would need to hit the ball about twice as close to the hole with each shot .
Anyway , the next time you ’ re out on a golf course and @ @ @ @ @ @ @ to 95 percent of the way to the hole on each shot , be respectful to those playing ahead of you and shout , “ Four !
” Congratulations to 👏 Jez Schaa 👏 of Singapore , winner of last week ’ s Riddler Classic .
Last week , you had half of a 10-inch pizza that you were cramming into your fridge .
You had circular plates of all different sizes , so to save space in your fridge , you wanted to place the pizza on the smallest plate that held @ @ @ @ @ @ @ no pizza hanging off the plate ) .
Unfortunately , the smallest plate that could hold half of a 10-inch pizza was just a circle with a 10-inch diameter .
So much for saving space .
But there was a catch — you were allowed to make a single straight cut and then rearrange the two resulting pieces on a circular plate , provided the pieces didn ’ t overlap and no pizza was hanging off the plate .
What was the diameter of the smallest circular plate onto which you could fit @ @ @ @ @ @ @ Bierre put it best : “ This [ was ] a humdinger of a geometry Riddler.
” What made this problem so difficult ?
Consider all the dimensions at play here : • First , should both endpoints of the cut have been on the circumference , or should one have been along the circumference and the other on the diameter ?
The latter was a better bet .
• Where along the circumference should the first endpoint have been ?
• Where along the diameter should the second endpoint have been ?
@ @ @ @ @ @ @ arranged the two pieces so that they were enclosed by the smallest possible circle ?
Ideally , you would have turned those last three questions into three parameters .
From there , you had to find the radius of the enclosing circle as a function of those three parameters and then minimize it ( either with calculus or computationally ) .
So yes , this was certainly a “ humdinger.
” Some readers cheated and had the two pieces overlapping .
In this case , the best you could do was to cut @ @ @ @ @ @ @ quarter-circles that could be stacked directly on top of each other .
The smallest plate each quarter-circle could fit on had a diameter of 5√2 , or about 7.07 inches .
While this was not the correct answer , it served as a good lower bound — the answer could be no less than 7.07 inches .
Tom Singer of Melbourne , Florida was able to properly fit his semicircular pizza onto a plate with a diameter of approximately 8.79 inches by assuming the cut was perpendicular to the slice ’ s diameter @ @ @ @ @ @ @ , courtesy of the puzzle ’ s submitter , Dean Ballard : But if you made a cut that was not necessarily perpendicular to the diameter , it was possible to do even better .
The best anyone was able to do was about 8.16 inches .
Again , here ’ s an illustration from Dean : And if that wasn ’ t hard enough , last week ’ s extra credit had you making two straight cuts , resulting in three pieces to fit on your plate .
Whereas the two-cut problem @ @ @ @ @ @ @ three-cut version had those same parameters , plus many more .
In particular , you had to choose which piece had the second cut , the particular edges or curves that were the endpoints of this second cut and how you could arrange all three pieces as tightly as possible .
Dean made his first cut perpendicular to the diameter , achieving a minimum plate that was about 7.737 inches in diameter ( shown below ) .
Meanwhile , Steven Trautmann of Aurora , Colorado wrote some C++ code to solve this for @ @ @ @ @ @ @ about 7.584 inches .
As far as I ’ m concerned , this remains an open problem .
If you find a plate size that works and that ’ s smaller than these answers , let me know ( preferably with an image included ! )
.
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. Please wait until Monday to publicly share your answers! If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter.
Riddler Express
From Benjamin Dickman comes proof that it’s hip to be (a difference of) squares:
Benjamin likes numbers that can be written as the difference between two perfect squares. He thinks they’re hip. For example, the number 40 is hip, since it equals 72−32, or 49−9. But hold the phone, 40 is doubly hip, because it also equals 112−92, or 121−81.
With apologies to Douglas Adams, 42 is not particularly hip. Go ahead and try finding two perfect squares whose difference is 42. I’ll wait.
Now, Benjamin is upping the stakes. He wants to know just how hip 1,400 might be. Can you do him a favor, and figure out how many ways 1,400 can be written as the difference of two perfect squares? Benjamin will really appreciate it.
Extra credit: Can you find a general formula or approach for counting the number of ways any whole number can be written as the difference between two perfect squares? (Your approach might be a function of whether the number is even or odd, its prime factorization, etc.)
The solution to this Riddler Express can be found in the following week’s column.
Riddler Classic
From mathematician (and author of Basic Probability: What Every Math Student Should Know) Henk Tijms comes a choice matter of chance and chocolate:
I have 10 chocolates in a bag: Two are milk chocolate, while the other eight are dark chocolate. One at a time, I randomly pull chocolates from the bag and eat them — that is, until I pick a chocolate of the other kind. When I get to the other type of chocolate, I put it back in the bag and start drawing again with the remaining chocolates. I keep going until I have eaten all 10 chocolates.
For example, if I first pull out a dark chocolate, I will eat it. (I’ll always eat the first chocolate I pull out.) If I pull out a second dark chocolate, I will eat that as well. If the third one is milk chocolate, I will not eat it (yet), and instead place it back in the bag. Then I will start again, eating the first chocolate I pull out.
What are the chances that the last chocolate I eat is milk chocolate?
The solution to this Riddler Classic can be found in the following week’s column.
Solution to last week’s Riddler Express
Congratulations to 👏 Karen Campe 👏 of New Canaan, Connecticut, winner of last week’s Riddler Express.
Last week, you took a swing at a riddle about golf. (See what I did there?)
A typical hole is about 400 yards long, while the cup measures a mere 4.25 inches in diameter. Suppose that, with every swing, you hit the ball X percent closer to the center of the hole. For example, if X were 75, then with every swing the ball would be four times closer to the hole than it was previously.
For a 400-yard hole with no hazards (water, sand or otherwise) in the way, what was the minimum value of X so that you shot par, meaning you hit the ball into the cup in exactly four strokes?
First, it was a good idea to work with a single set of units. One yard equals 3 feet, or 36 inches. That meant the total length of the hole — 400 yards — was 14,400 inches. Meanwhile, the cup’s diameter was 4.25 inches, which meant its radius was 2.125 inches. So once the ball came within 2.125 inches of the hole’s center, it fell in. (Some readers used the diameter instead of the radius here, which led to an answer that was off by a few percentage points.)
Most solvers assumed left the value of X as a variable. As we said, the initial distance to the hole was 14,400 inches. After one swing, it was 14,400·(1−X). After two swings, it was 14,400·(1−X)2. After three swings, it was 14,400·(1−X)3. Finally, after four swings, it was 14,400·(1−X)4.
You shot par when this distance, 14,400·(1−X)4, was equal to 2.125 inches (or, rather, just a shade less than 2.125 inches). Mathematically, that meant 14,400·(1−X)4 = 2.125, or (1−X)4 = 17/115,200. Taking the fourth root of both sides and solving gave a solution of approximately 0.88978. In other words, X had to be at least about 89 for you to make par.
Some solvers took this problem even further, calculating the value of X for holes that were longer or shorter and also for different numbers of strokes. For example, what would it take to shoot a birdie (a score of one less than par — in this case, three strokes) on this hole? To answer this question, you had to solve the equation (1−X)3 = 17/115,200, with an exponent of three rather than four. That gave a value of X that is approximately 95. In other words, to go from a par to a birdie, you would need to hit the ball about twice as close to the hole with each shot.
Anyway, the next time you’re out on a golf course and you’re hitting the ball 89 to 95 percent of the way to the hole on each shot, be respectful to those playing ahead of you and shout, “Four!”
Golf humor. Apologies.
Solution to last week’s Riddler Classic
Congratulations to 👏 Jez Schaa 👏 of Singapore, winner of last week’s Riddler Classic.
Last week, you had half of a 10-inch pizza that you were cramming into your fridge. You had circular plates of all different sizes, so to save space in your fridge, you wanted to place the pizza on the smallest plate that held the entire semicircle (i.e., with no pizza hanging off the plate).
Unfortunately, the smallest plate that could hold half of a 10-inch pizza was just a circle with a 10-inch diameter. So much for saving space.
But there was a catch — you were allowed to make a single straight cut and then rearrange the two resulting pieces on a circular plate, provided the pieces didn’t overlap and no pizza was hanging off the plate.
What was the diameter of the smallest circular plate onto which you could fit the two resulting pieces?
Reader Pierre Bierre put it best: “This [was] a humdinger of a geometry Riddler.” What made this problem so difficult? Consider all the dimensions at play here:
First, should both endpoints of the cut have been on the circumference, or should one have been along the circumference and the other on the diameter? The latter was a better bet.
Where along the circumference should the first endpoint have been?
Where along the diameter should the second endpoint have been?
Finally, how should you have arranged the two pieces so that they were enclosed by the smallest possible circle?
Ideally, you would have turned those last three questions into three parameters. From there, you had to find the radius of the enclosing circle as a function of those three parameters and then minimize it (either with calculus or computationally). So yes, this was certainly a “humdinger.”
Some readers cheated and had the two pieces overlapping. In this case, the best you could do was to cut the semicircle in half, forming two quarter-circles that could be stacked directly on top of each other. The smallest plate each quarter-circle could fit on had a diameter of 5√2, or about 7.07 inches. While this was not the correct answer, it served as a good lower bound — the answer could be no less than 7.07 inches.
Tom Singer of Melbourne, Florida was able to properly fit his semicircular pizza onto a plate with a diameter of approximately 8.79 inches by assuming the cut was perpendicular to the slice’s diameter. Here’s a similar arrangement, courtesy of the puzzle’s submitter, Dean Ballard:
But if you made a cut that was not necessarily perpendicular to the diameter, it was possible to do even better. The best anyone was able to do was about 8.16 inches. Again, here’s an illustration from Dean:
And if that wasn’t hard enough, last week’s extra credit had you making two straight cuts, resulting in three pieces to fit on your plate. Whereas the two-cut problem involved optimizing across three parameters, the three-cut version had those same parameters, plus many more. In particular, you had to choose which piece had the second cut, the particular edges or curves that were the endpoints of this second cut and how you could arrange all three pieces as tightly as possible.
Dean made his first cut perpendicular to the diameter, achieving a minimum plate that was about 7.737 inches in diameter (shown below). Meanwhile, Steven Trautmann of Aurora, Colorado wrote some C++ code to solve this for him, which gave an answer of about 7.584 inches.
As far as I’m concerned, this remains an open problem. If you find a plate size that works and that’s smaller than these answers, let me know (preferably with an image included!).
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--2020-10-05--More States Are Using Ballot Drop Boxes. Why Are They So Controversial?

When we first unveiled our guide of how to vote in the 2020 election in every state , the most common question we received was , “ What if I want to drop off my mail ballot in person ?
” Well , America , we heard you : The dashboard is now updated with information about whether you can and where to return your ballot .
The good news is almost every state allows you to drop off your mail ballot in person instead of mailing it ; the only states where you can ’ t are Mississippi , @ @ @ @ @ @ @ category of absentee ballots in Oklahoma also can ’ t be delivered in person , but this applies to only a small fraction of voters . )
Typically , you can deliver your ballot to your local election office ; at least 20 states ( plus Washington , D.C. ) also accept mail ballots at polling places , but a lot of states explicitly don ’ t , so check our guide before trying that .
But an increasingly common option is drop boxes in which voters can deposit their ballots .
Going @ @ @ @ @ @ @ regularly offered drop boxes in their elections , but with the expanded popularity of mail voting amid the pandemic , at least 38 states plus Washington , D.C. , are offering them for the 2020 general election .
However , as with seemingly every other aspect of election administration this year , drop boxes have become a controversial proposal .
To proponents , drop boxes are simply a more reliable delivery method given recent cutbacks at the U.S .
Postal Service that have slowed down mail service .
Consider states that require ballots @ @ @ @ @ @ @ .
Voters who put their ballots in the mail within a week of that deadline are really leaving it up to chance whether the ballot will arrive in time .
By contrast , any ballot deposited in a drop box by the deadline is considered to have arrived on time , providing the voter with both peace of mind and an extra few days to fill out her ballot .
Drop boxes are more secure than your average blue postal box , too : Many states require them to be under video surveillance @ @ @ @ @ @ @ designed to be indestructible ( check out this photo of a drop box that survived a head-on collision from an SUV ) .
Still , opponents — including President Trump — argue that drop boxes do not sufficiently protect ballots from being tampered with , and they have opposed the boxes ’ use in at least one swing state this year .
Over the summer , Trump ’ s campaign and the Republican National Committee sued Pennsylvania over its use of drop boxes , arguing that they were not properly monitored during the @ @ @ @ @ @ @ in the general election .
However , the Pennsylvania Supreme Court rejected their argument , and ( as of now , anyway ) drop boxes remain an option for Pennsylvania voters .
But even when both parties agree that drop boxes are safe , debates can still erupt over their proliferation .
In August , Ohio ’ s Republican secretary of state directed county election officials to set up only one drop box in each county — despite the fact that some Ohio counties have more than 1 million residents .
( By @ @ @ @ @ @ @ by mail have much more specific guidelines to alleviate overcrowding .
For example , Colorado requires counties to offer at least one drop box per 30,000 registered voters , and Washington requires one drop box per 15,000 voters . )
Furious Democrats challenged his directive in court , and on Friday a court ruled that the state can allow counties to set up more boxes ( it is unclear , however , whether the state will do so ) .
A similar fight is now unfolding in Texas , where the Republican governor @ @ @ @ @ @ @ have only one drop site each — ordering counties with more than one , including Democratic strongholds like Harris and Travis counties , to close those extra sites .
Voting-rights groups quickly sued to overturn the order .
To voting-rights advocates , the convenience and ubiquity of drop boxes is one of their chief selling points .
States like California make an effort to put drop boxes at centrally located places around town , such as libraries , civic buildings and assisted living facilities , making it easier for voters to submit their @ @ @ @ @ @ @ day .
And unlike election offices , drop boxes are often open 24 hours a day .
When they ’ re accessible , drop boxes are a hugely popular option with voters , too .
For example , in the 2016 general election , 57 percent of ballots in Washington ( which automatically mails all voters a ballot ) were cast via a drop box .
And given just how many states have expanded their use of drop boxes during the pandemic , it could become a favored method of voting across much @ @ @ @ @ @ @ remember to check our guide to see if it ’ s available to you .

When we first unveiled our guide of how to vote in the 2020 election in every state, the most common question we received was, “What if I want to drop off my mail ballot in person?” Well, America, we heard you: The dashboard is now updated with information about whether you can and where to return your ballot.
The good news is almost every state allows you to drop off your mail ballot in person instead of mailing it; the only states where you can’t are Mississippi, Missouri and Tennessee. (A special category of absentee ballots in Oklahoma also can’t be delivered in person, but this applies to only a small fraction of voters.)
Typically, you can deliver your ballot to your local election office; at least 20 states (plus Washington, D.C.) also accept mail ballots at polling places, but a lot of states explicitly don’t, so check our guide before trying that. But an increasingly common option is drop boxes in which voters can deposit their ballots. Going into this year, about 13 states regularly offered drop boxes in their elections, but with the expanded popularity of mail voting amid the pandemic, at least 38 states plus Washington, D.C., are offering them for the 2020 general election.
However, as with seemingly every other aspect of election administration this year, drop boxes have become a controversial proposal. To proponents, drop boxes are simply a more reliable delivery method given recent cutbacks at the U.S. Postal Service that have slowed down mail service. Consider states that require ballots to be received by a certain date. Voters who put their ballots in the mail within a week of that deadline are really leaving it up to chance whether the ballot will arrive in time. By contrast, any ballot deposited in a drop box by the deadline is considered to have arrived on time, providing the voter with both peace of mind and an extra few days to fill out her ballot.
Drop boxes are more secure than your average blue postal box, too: Many states require them to be under video surveillance or manually staffed, and they are designed to be indestructible (check out this photo of a drop box that survived a head-on collision from an SUV). Still, opponents — including President Trump — argue that drop boxes do not sufficiently protect ballots from being tampered with, and they have opposed the boxes’ use in at least one swing state this year.
Over the summer, Trump’s campaign and the Republican National Committee sued Pennsylvania over its use of drop boxes, arguing that they were not properly monitored during the primary and thus were susceptible to fraud in the general election. However, the Pennsylvania Supreme Court rejected their argument, and (as of now, anyway) drop boxes remain an option for Pennsylvania voters.
But even when both parties agree that drop boxes are safe, debates can still erupt over their proliferation. In August, Ohio’s Republican secretary of state directed county election officials to set up only one drop box in each county — despite the fact that some Ohio counties have more than 1 million residents. (By contrast, states that regularly conduct elections by mail have much more specific guidelines to alleviate overcrowding. For example, Colorado requires counties to offer at least one drop box per 30,000 registered voters, and Washington requires one drop box per 15,000 voters.) Furious Democrats challenged his directive in court, and on Friday a court ruled that the state can allow counties to set up more boxes (it is unclear, however, whether the state will do so). A similar fight is now unfolding in Texas, where the Republican governor decreed just last week that counties could have only one drop site each — ordering counties with more than one, including Democratic strongholds like Harris and Travis counties, to close those extra sites. Voting-rights groups quickly sued to overturn the order.
To voting-rights advocates, the convenience and ubiquity of drop boxes is one of their chief selling points. States like California make an effort to put drop boxes at centrally located places around town, such as libraries, civic buildings and assisted living facilities, making it easier for voters to submit their ballot in the normal course of their day. And unlike election offices, drop boxes are often open 24 hours a day.
When they’re accessible, drop boxes are a hugely popular option with voters, too. For example, in the 2016 general election, 57 percent of ballots in Washington (which automatically mails all voters a ballot) were cast via a drop box. And given just how many states have expanded their use of drop boxes during the pandemic, it could become a favored method of voting across much of the country this year. Just remember to check our guide to see if it’s available to you.


fivethirthyeight--2020-10-05--How Hatred Came To Dominate American Politics

To anyone following American politics , it ’ s not exactly news that Democrats and Republicans don ’ t like each other .
Take what happened in the presidential debate last week .
President Trump and former Vice President Joe Biden did little to conceal their disdain of one another .
And although the debate marked a low point in our national discourse , it was a crystallization of a long-developing trend : loathing the opposing party .
This is hardly a new trend ; in fact , it ’ s increasingly common among American voters .
However , this @ @ @ @ @ @ @ call “ negative partisanship ” — has reached levels that are not just bad for democracy , but are potentially destructive .
And extreme partisan animosity is a prelude to democratic collapse .
It wasn ’ t always this bad , though .
Forty years ago , when asked to rate how “ favorable and warm ” their opinion of each party was , the average Democrat and Republican said they felt OK-ish about the opposite party .
But for four decades now , partisans have increasingly turned against each other in an @ @ @ @ @ @ @ views of the other party are currently at an all-time low .
So how did we get to this point ?
Broadly speaking , there are three trends that we can point to .
The first is the steady nationalization of American politics .
The second is the sorting of Democrats and Republicans along urban/rural and culturally liberal/culturally conservative lines , and the third is the increasingly narrow margins in national elections .
The combination of these three trends has turned Washington , D.C. , into a high-stakes battle where cross-party compromise is @ @ @ @ @ @ @ holding out for complete control .
Sixty years ago , state and local politics loomed larger than they do now , which meant national parties operated more like loose labels whose main function was to come together every four years to argue over who should run for president under that party .
As President Eisenhower reportedly quipped as late as 1950 , “ There is not one Republican Party , there are 48 state Republican parties.
” The same was true of the Democratic Party at the time .
By the 1970s , @ @ @ @ @ @ @ that partisan politics had reached their end , with split-ticket voting hitting record-high levels as candidates successfully ran on local issues and pledges to better serve their constituents .
But beneath the surface , the parties were realigning .
The civil rights movement of the 1960s and the culture wars of the 1970s and 1980s not only turned conservative Democrats into Republicans and liberal northeastern Republicans into Democrats , it also shifted the focus of politics such that Washington became the arbiter of national values .
National parties began building up major fundraising @ @ @ @ @ @ @ standardize their messaging so that it actually meant something to vote for a Democrat or a Republican .
Coupled with the steady decline of local media , this has resulted in a greater emphasis on national politics and less attention paid to local and state politics .
Practically speaking , elections are increasingly viewed as referendums on the president and the party that controls the White House , leaving little room for individual members of Congress to distinguish themselves from their national parties .
This brings us to the second trend that has @ @ @ @ @ @ @ : sorting .
The ideologies of the party were less hard and fast 40 years ago .
The Republican Party had a significant share of moderates and liberals , the inheritors of a tradition of moderate good-government Yankee republicanism that dated back to President Lincoln , and the Democratic Party once had a significant share of conservative populists from the South and the Great Plains .
In this sense , American politics operated more like a four-party system , with jumbled liberal and conservative coalitions within and across the two parties .
Senators @ @ @ @ @ @ @ more than their parties , with complex coalitions of urban liberals and rural conservatives in both parties .
However , as our politics became increasingly nationalized , the political sorting of the parties accelerated .
The civil rights movement is the most obvious example of this : Many in political science consider it the most significant issue ( though far from the only issue ) driving political sorting , as it changed the center of gravity in both parties .
Today , it ’ s simply harder for voters to hold a viewpoint @ @ @ @ @ @ @ party .
For instance , there are far fewer anti-abortion Democrats or abortion-rights Republicans now than 30 years ago because these kinds of stances are unwelcome in the party .
Some voters changed their party to match their beliefs ; others changed their beliefs to match their party .
But ultimately , both shifts contributed to the parties taking clearer and more distinct stances on a growing number of social issues , which led to more and more voters adjusting their views to match their partisanship .
Political scientists have called this process @ @ @ @ @ @ @ is that as more issues have become nationalized , partisan conflicts have broadened to absorb these issues .
And as the parties have taken clearer national stances , particularly around cultural and identity-based issues , voters sort more clearly into parties based on these stances .
Cultural values are much more connected to geography than economic values .
Both the rich and poor live in cities , suburbs and exurbs .
But those who are socially liberal tend to live in cities , whereas those who are socially conservative tend to inhabit small @ @ @ @ @ @ @ issues has thus generated a significant partisan density divide .
And because geography also corresponds to racial and ethnic diversity ( basically , cities are multicultural and exurbs are mostly white ) , this adds another division onto the partisan divide : race .
With all these identities accumulating on top of each other , partisanship has become a kind of “ mega-identity , ” as political scientist Lilliana Mason argues , with party identification standing for much , much more .
In fact , it ’ s reached the point that when @ @ @ @ @ @ @ size them up as a “ Trump voter ” or a “ Biden voter.
” That kind of easy stereotyping leads us to see the other party as distant and different .
And typically , things that are distant and different are also more threatening .
But neither side has come to dominate .
Instead , America has experienced an extended period of national parity between the two parties .
Elections have swung back and forth in an almost predictable pendulum fashion since 1992 — unified control of one party , divided government @ @ @ @ @ @ @ , and so forth , over and over .
This back and forth has defied predictions of permanent Republican and Democratic majorities , but the closeness of elections has kept such elusive predictions of total domination both tantalizingly within reach ( for one side ) and dangerously close ( for the other side ) .
Simultaneously , the swings in power have imparted the lesson that when you ’ re down , the best thing to do is demonize the other side , refuse to compromise , wait for public opinion to tack @ @ @ @ @ @ @ the pendulum back to a majority .
These contradictory impulses lead to a few big policy swings ( consider the changes on health care and tax policy under the Trump administration ) during periods of unified government , and increasingly , in executive branch activities .
They also create gridlock elsewhere and lead to a politics of zero-sum messaging , in which the party trying to win back the White House never has any incentive to compromise because it just blurs the message and helps the party in power seem more successful and @ @ @ @ @ @ @ the stakes of elections — keep rising .
Yet beneath the surface of hyper-partisan politics , the parties themselves actually have a lot of internal division , which means they share a version of the same dilemma : Republicans and Democrats can ’ t please all the different voters and groups who fall into their party and want their issue to be prioritized .
But in a polarized two-party system , they can make it clear why the other party is bad .
Coming into their convention , for instance , Democrats had @ @ @ @ @ @ @ the moderates that were visible during the presidential primary .
But the convention focused less on policy and more on the existential risk presented by a second Trump term .
The party reminded people that , whatever concerns they have about Biden , a vote for Biden is also a vote against Trump .
Republicans similarly focused on messaging against the Democrats ( even if one of the reasons Trump emerged victorious in the 2016 primary was because the party was so divided that it couldn ’ t decide ) .
Trump has @ @ @ @ @ @ @ but even for the few remaining Trump-skeptic Republicans , nothing unites like a common enemy .
And in a two-party system , being anti-anti-Trump counts the same as being pro-Trump .
If all of this seems unsustainable , it should .
The current levels of hyper-partisanship are clearly dangerous .
It ’ s bad news for a democracy when 60 to 70 percent of people view fellow citizens of the other party as a serious threat .
And the more the parties continue to unify their supporters by casting the other party as @ @ @ @ @ @ @ will rise .
There are two possible ways this ends .
The first is the one we all fear — the unwinding of our democracy , because one or both sides hate each other so much that they are willing to support anti-democratic and authoritarian leadership in order to maintain power .
( This is the threat Democrats have explicitly raised in recent months . )
The other scenario is a major realignment and/or a collapse of one ( or both ) of the two major parties , which could reorient American political @ @ @ @ @ @ @ of an earlier era .
The growing partisan hatreds and the forces driving them have been a long time in the making .
It ’ s possible they are coming to an end .
But more than any other time in the last century and a half , they are testing the very foundations of American democracy .

To anyone following American politics, it’s not exactly news that Democrats and Republicans don’t like each other. Take what happened in the presidential debate last week. President Trump and former Vice President Joe Biden did little to conceal their disdain of one another. And although the debate marked a low point in our national discourse, it was a crystallization of a long-developing trend: loathing the opposing party.
This is hardly a new trend; in fact, it’s increasingly common among American voters. However, this level of hatred — which political scientists call “negative partisanship” — has reached levels that are not just bad for democracy, but are potentially destructive. And extreme partisan animosity is a prelude to democratic collapse.
Polling 101: Should You Trust The Polls In 2020? | FiveThirtyEight
It wasn’t always this bad, though. Forty years ago, when asked to rate how “favorable and warm” their opinion of each party was, the average Democrat and Republican said they felt OK-ish about the opposite party. But for four decades now, partisans have increasingly turned against each other in an escalating cycle of dislike and distrust — views of the other party are currently at an all-time low.
So how did we get to this point?
Broadly speaking, there are three trends that we can point to. The first is the steady nationalization of American politics. The second is the sorting of Democrats and Republicans along urban/rural and culturally liberal/culturally conservative lines, and the third is the increasingly narrow margins in national elections.
[Live Updates: We’re Tracking The Vote And Voting Problems]
The combination of these three trends has turned Washington, D.C., into a high-stakes battle where cross-party compromise is difficult, and both sides are increasingly holding out for complete control.
Sixty years ago, state and local politics loomed larger than they do now, which meant national parties operated more like loose labels whose main function was to come together every four years to argue over who should run for president under that party. As President Eisenhower reportedly quipped as late as 1950, “There is not one Republican Party, there are 48 state Republican parties.” The same was true of the Democratic Party at the time. By the 1970s, in fact, many political observers declared that partisan politics had reached their end, with split-ticket voting hitting record-high levels as candidates successfully ran on local issues and pledges to better serve their constituents.
But beneath the surface, the parties were realigning. The civil rights movement of the 1960s and the culture wars of the 1970s and 1980s not only turned conservative Democrats into Republicans and liberal northeastern Republicans into Democrats, it also shifted the focus of politics such that Washington became the arbiter of national values. National parties began building up major fundraising and campaign consultant-driven operations, helping to standardize their messaging so that it actually meant something to vote for a Democrat or a Republican.
Coupled with the steady decline of local media, this has resulted in a greater emphasis on national politics and less attention paid to local and state politics. Practically speaking, elections are increasingly viewed as referendums on the president and the party that controls the White House, leaving little room for individual members of Congress to distinguish themselves from their national parties.
This brings us to the second trend that has contributed to the rise of negative partisanship: sorting. The ideologies of the party were less hard and fast 40 years ago. The Republican Party had a significant share of moderates and liberals, the inheritors of a tradition of moderate good-government Yankee republicanism that dated back to President Lincoln, and the Democratic Party once had a significant share of conservative populists from the South and the Great Plains.
In this sense, American politics operated more like a four-party system, with jumbled liberal and conservative coalitions within and across the two parties. Senators and representatives’ distinct geographic outlooks mattered more than their parties, with complex coalitions of urban liberals and rural conservatives in both parties. However, as our politics became increasingly nationalized, the political sorting of the parties accelerated. The civil rights movement is the most obvious example of this: Many in political science consider it the most significant issue (though far from the only issue) driving political sorting, as it changed the center of gravity in both parties.
Today, it’s simply harder for voters to hold a viewpoint that doesn’t align with their party. For instance, there are far fewer anti-abortion Democrats or abortion-rights Republicans now than 30 years ago because these kinds of stances are unwelcome in the party. Some voters changed their party to match their beliefs; others changed their beliefs to match their party. But ultimately, both shifts contributed to the parties taking clearer and more distinct stances on a growing number of social issues, which led to more and more voters adjusting their views to match their partisanship.
Political scientists have called this process “conflict extension.” The basic idea is that as more issues have become nationalized, partisan conflicts have broadened to absorb these issues. And as the parties have taken clearer national stances, particularly around cultural and identity-based issues, voters sort more clearly into parties based on these stances.
Cultural values are much more connected to geography than economic values. Both the rich and poor live in cities, suburbs and exurbs. But those who are socially liberal tend to live in cities, whereas those who are socially conservative tend to inhabit small towns. This partisan sorting on cultural issues has thus generated a significant partisan density divide. And because geography also corresponds to racial and ethnic diversity (basically, cities are multicultural and exurbs are mostly white), this adds another division onto the partisan divide: race.
With all these identities accumulating on top of each other, partisanship has become a kind of “mega-identity,” as political scientist Lilliana Mason argues, with party identification standing for much, much more. In fact, it’s reached the point that when you meet somebody, you can immediately size them up as a “Trump voter” or a “Biden voter.” That kind of easy stereotyping leads us to see the other party as distant and different. And typically, things that are distant and different are also more threatening.
But neither side has come to dominate. Instead, America has experienced an extended period of national parity between the two parties. Elections have swung back and forth in an almost predictable pendulum fashion since 1992 — unified control of one party, divided government, unified control of the other party, and so forth, over and over.
This back and forth has defied predictions of permanent Republican and Democratic majorities, but the closeness of elections has kept such elusive predictions of total domination both tantalizingly within reach (for one side) and dangerously close (for the other side). Simultaneously, the swings in power have imparted the lesson that when you’re down, the best thing to do is demonize the other side, refuse to compromise, wait for public opinion to tack against the party in power and ride the pendulum back to a majority.
These contradictory impulses lead to a few big policy swings (consider the changes on health care and tax policy under the Trump administration) during periods of unified government, and increasingly, in executive branch activities. They also create gridlock elsewhere and lead to a politics of zero-sum messaging, in which the party trying to win back the White House never has any incentive to compromise because it just blurs the message and helps the party in power seem more successful and legitimate. Thus, frustration — and the stakes of elections — keep rising.
Yet beneath the surface of hyper-partisan politics, the parties themselves actually have a lot of internal division, which means they share a version of the same dilemma: Republicans and Democrats can’t please all the different voters and groups who fall into their party and want their issue to be prioritized. But in a polarized two-party system, they can make it clear why the other party is bad.
Coming into their convention, for instance, Democrats had to repair splits between the progressives and the moderates that were visible during the presidential primary. But the convention focused less on policy and more on the existential risk presented by a second Trump term. The party reminded people that, whatever concerns they have about Biden, a vote for Biden is also a vote against Trump.
Republicans similarly focused on messaging against the Democrats (even if one of the reasons Trump emerged victorious in the 2016 primary was because the party was so divided that it couldn’t decide). Trump has remade the party in his image, but even for the few remaining Trump-skeptic Republicans, nothing unites like a common enemy. And in a two-party system, being anti-anti-Trump counts the same as being pro-Trump.
If all of this seems unsustainable, it should. The current levels of hyper-partisanship are clearly dangerous. It’s bad news for a democracy when 60 to 70 percent of people view fellow citizens of the other party as a serious threat. And the more the parties continue to unify their supporters by casting the other party as the enemy, the higher this number will rise.
There are two possible ways this ends. The first is the one we all fear — the unwinding of our democracy, because one or both sides hate each other so much that they are willing to support anti-democratic and authoritarian leadership in order to maintain power. (This is the threat Democrats have explicitly raised in recent months.)
The other scenario is a major realignment and/or a collapse of one (or both) of the two major parties, which could reorient American political coalitions and resurrect some of the overlaps of an earlier era. The growing partisan hatreds and the forces driving them have been a long time in the making. It’s possible they are coming to an end. But more than any other time in the last century and a half, they are testing the very foundations of American democracy.


fivethirthyeight--2020-10-05--Trump Is Giving Dangerous Advice. Being Afraid Of COVID-19 Has Helped Us Control COVID-19.

The president announced his own discharge from Walter Reed National Military Medical Center Monday afternoon , tweeting : One phrase stood out : “ Don ’ t be afraid of Covid.
” After announcing that he will be leaving the hospital following treatment for COVID-19 , President Trump said not to fear the disease that has killed more than 209,000 Americans and infected more than 7 million .
There ’ s a long history of the president of the United States imploring his people not to give in to fear .
But in this case , Trump is giving dangerous @ @ @ @ @ @ @ face of the most deadly pandemic in a century .
It ’ s also useful .
Fear has motivated us to understand as much as possible about how the virus spreads , and fear can drive us to take the actions necessary to stop it .
If we don ’ t acknowledge the legitimately frightening reality of this disease , we may not be motivated to act responsibly to reduce transmission .
Willfully ignoring that fear puts everyone at risk .
Early in the pandemic , much of the fear was stoked by @ @ @ @ @ @ @ at our disposal for stopping its spread were limited and blunt .
We knew it was a good idea to wash your hands and not touch your face , but it quickly became apparent that those simple steps weren ’ t enough .
By the time states ’ initial lockdowns measures were starting to ease , researchers had learned a lot more about how COVID-19 spreads .
Thanks to vigorous scientific investigation , we learned that people can shed the virus before they even have symptoms .
We learned that tiny , airborne @ @ @ @ @ @ @ the larger , wet droplets we already knew carry it .
And we discovered that masks can help reduce the number of those virus-laden particles a person expels and inhales .
We also learned the virus wasn ’ t as deadly as initially thought , and some modes of transmission — like surfaces — weren ’ t as big of a threat .
We were getting a handle of what to be afraid of , and what not to be .
Armed with all of this information , public health experts were able @ @ @ @ @ @ @ and individuals can do to avoid getting and spreading the virus .
Keep six feet of distance between yourself and people who don ’ t live in the same house as you .
Wear a mask whenever you ’ re out in public .
Wash your hands ( still a good idea ! )
and try to limit how often you ’ re leaving your home .
These guidelines are recommended by the Centers for Disease Control and Prevention , the World Health Organization , countless local public health organizations and , yes @ @ @ @ @ @ @ And the best evidence we have suggests that these simple actions work .
A June study published in Nature estimated as many as 60 million COVID-19 infections were avoided thanks to social distancing and lockdown efforts .
And disease modelling projects that tens of thousands of lives could be spared with widespread adoption of social distancing and mask-wearing .
The president ’ s message not to be afraid of the virus is dangerous if it encourages Americans to reject the things they do because they ’ re afraid of the virus .
And @ @ @ @ @ @ @ .
Think of the grocery store worker who has to stock shelves while dozens of strangers brush past them , or the nurse who has to come in close proximity with patients daily , many of whom may have active COVID-19 infections .
Without the fear of what this disease can do to you , there ’ s little motivation to protect them .
It ’ s easier to feel secure when you ’ re the president of the United States , of course .
But that ’ s not a reality the @ @ @ @ @ @ @ .
In our reality , fear is rational , and it ’ s what pushes us to act .
By telling us there ’ s nothing to fear , Trump is both ignoring the experience of millions of Americans , and giving further fuel to those whose response to fear is denial .
Fear on its own isn ’ t useful .
But neither is a dismissal of reality .

The president announced his own discharge from Walter Reed National Military Medical Center Monday afternoon, tweeting:
https://twitter.com/realDonaldTrump/status/1313186529058136070
One phrase stood out: “Don’t be afraid of Covid.” After announcing that he will be leaving the hospital following treatment for COVID-19, President Trump said not to fear the disease that has killed more than 209,000 Americans and infected more than 7 million.
There’s a long history of the president of the United States imploring his people not to give in to fear. But in this case, Trump is giving dangerous advice.
Fear is natural in the face of the most deadly pandemic in a century. It’s also useful. Fear has motivated us to understand as much as possible about how the virus spreads, and fear can drive us to take the actions necessary to stop it. If we don’t acknowledge the legitimately frightening reality of this disease, we may not be motivated to act responsibly to reduce transmission. Willfully ignoring that fear puts everyone at risk.
Early in the pandemic, much of the fear was stoked by how little we knew. The tools at our disposal for stopping its spread were limited and blunt. We knew it was a good idea to wash your hands and not touch your face, but it quickly became apparent that those simple steps weren’t enough.
By the time states’ initial lockdowns measures were starting to ease, researchers had learned a lot more about how COVID-19 spreads. Thanks to vigorous scientific investigation, we learned that people can shed the virus before they even have symptoms. We learned that tiny, airborne particles can spread the virus just like the larger, wet droplets we already knew carry it. And we discovered that masks can help reduce the number of those virus-laden particles a person expels and inhales. We also learned the virus wasn’t as deadly as initially thought, and some modes of transmission — like surfaces — weren’t as big of a threat. We were getting a handle of what to be afraid of, and what not to be.
Armed with all of this information, public health experts were able to develop recommendations for exactly what communities and individuals can do to avoid getting and spreading the virus. Keep six feet of distance between yourself and people who don’t live in the same house as you. Wear a mask whenever you’re out in public. Wash your hands (still a good idea!) and try to limit how often you’re leaving your home. These guidelines are recommended by the Centers for Disease Control and Prevention, the World Health Organization, countless local public health organizations and, yes, the White House, too.
And the best evidence we have suggests that these simple actions work. A June study published in Nature estimated as many as 60 million COVID-19 infections were avoided thanks to social distancing and lockdown efforts. And disease modelling projects that tens of thousands of lives could be spared with widespread adoption of social distancing and mask-wearing.
The president’s message not to be afraid of the virus is dangerous if it encourages Americans to reject the things they do because they’re afraid of the virus. And that has implications for all of us. Think of the grocery store worker who has to stock shelves while dozens of strangers brush past them, or the nurse who has to come in close proximity with patients daily, many of whom may have active COVID-19 infections. Without the fear of what this disease can do to you, there’s little motivation to protect them.
It’s easier to feel secure when you’re the president of the United States, of course. But that’s not a reality the rest of us live day to day. In our reality, fear is rational, and it’s what pushes us to act. By telling us there’s nothing to fear, Trump is both ignoring the experience of millions of Americans, and giving further fuel to those whose response to fear is denial. Fear on its own isn’t useful. But neither is a dismissal of reality.


fivethirthyeight--2020-10-05--What We Actually Know About The President’s Health

In this episode of the FiveThirtyEight Politics podcast , the crew discusses the president ’ s COVID-19 prognosis with two @ @ @ @ @ speak with Dr. Craig Spencer of Columbia University about President Trump ’ s current health @ @ @ @ @ to work and campaigning .
The crew also speaks with Lara Brown , a professor @ @ @ @ @ Washington University , about how past administrations have addressed presidential illnesses .

In this episode of the FiveThirtyEight Politics podcast, the crew discusses the president’s COVID-19 prognosis with two guests. First, they speak with Dr. Craig Spencer of Columbia University about President Trump’s current health and ability to get back to work and campaigning. The crew also speaks with Lara Brown, a professor of political science at George Washington University, about how past administrations have addressed presidential illnesses.


fivethirthyeight--2020-10-05--Politics Podcast: How The President’s Health Could Shape The Rest Of The Campaign

In the four days since President Trump was diagnosed with COVID-19 , the public has received limited and conflicting information @ @ @ @ @ make sense of the patchy details we do have , the FiveThirtyEight Politics podcast crew @ @ @ @ @ Craig Spencer about Trump ’ s prognosis and ability to get back to work and @ @ @ @ @ to presidential scholar Lara Brown about past presidents and how their illnesses have been addressed @ @ @ @ @ 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 is recorded Mondays and Thursdays .
Help new listeners @ @ @ @ @ us a rating and review on iTunes .
Have a comment , question or suggestion @ @ @ @ @ bad polling ” ?
Get in touch by email , on Twitter or in the @ @

In the four days since President Trump was diagnosed with COVID-19, the public has received limited and conflicting information about his health. To make sense of the patchy details we do have, the FiveThirtyEight Politics podcast crew spoke with emergency room doctor Craig Spencer about Trump’s prognosis and ability to get back to work and campaigning. They also talked to presidential scholar Lara Brown about past presidents and how their illnesses have been addressed.
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 is recorded 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--2020-10-05--Biden Has Made Some Modest Gains After The Debate

There ’ s been so much news going on that I nearly forgot about the existence of a Supreme Court vacancy when participating in a virtual conference this morning .
And in some ways , the news makes life hard for us polling analysts .
We have had , in rapid succession : the death of Justice Ruth Bader Ginsburg , a series of threats by President Trump in which he refused to commit to a peaceful transition of power , the announcement of Trump ’ s intention to nominate Amy Coney Barrett to replace Ginsburg , the release of @ @ @ @ @ @ @ tax returns by the New York Times , the first presidential debate , the news of Trump ’ s COVID-19 diagnosis and subsequent hospitalization — along with a cluster of other cases at the White House — and now his plans to leave Walter Reed Medical Center later today .
With that said , the debate provides a clear enough line in the sand — with many pollsters planning releases just prior to or just after the debate — that it ’ s worth doing a before-and-after comparison of the polls .
One @ @ @ @ @ @ @ national polling average , where Biden ’ s lead has inched up to 8.1 points from 7.1 points before the debate : Another way to see this is by comparing post-debate polls to the last , pre-debate version of both national polls and polls of the same states by the same polling firms .
That ’ s what I ’ ve done in the table below , covering the 11 national polls and 11 state polls that have been released since the debate .
And on average , Biden gained 1.5 percentage points @ @ @ @ @ @ @ of these polls .
In some cases , the pre-debate poll was conducted months before the debate .
But even if we only focus on the polls that released results at some point in September , the top line is similar : Biden ’ s gain is 1.4 percentage points , on average .
And for what it ’ s worth , a swing of 1 or 2 points toward Biden is consistent with the effects that first debates have had for challengers in the past — although we should note that sometimes @ @ @ @ @ @ @ of weeks .
These averages , of course , conceal a lot of variation within individual polls ; depending on which poll you look at , Biden ’ s national lead is as large as 14 points ( in the most recent NBC News/Wall Street Journal poll ) or as small as 2 points ( in a John Zogby Strategies poll ) .
I ’ ll admit to finding the NBC/WSJ poll intriguing , as it ’ s the only live-caller national poll we have since the debate , and NBC/WSJ polls tend @ @ @ @ @ @ @ averages .
Still , averaging the polls is the right strategy in the long run .
Because so many polls have recently been released , you ’ re going to have a few eccentricities .
Remember , an 800-person poll nominally has a 3.5-point margin of error .
However , that margin pertains only to one candidate ’ s vote share ; in a two-candidate race , the margin of error on the difference between the candidates will be roughly twice that then , or 7 points in this case .
That means @ @ @ @ @ @ @ 8 points , it should be fairly routine to get everything from a 15-point Biden lead to a 1-point lead .
And keep in mind that with a confidence interval of 95 percent , the margin of error only covers 95 percent of polls ; 1 in 20 polls should fall outside that range .
( At least in theory ; in practice , pollsters are often reluctant to publish polls that appear to be large outliers . )
It ’ s harder to tell , though , what effect the president ’ @ @ @ @ @ @ @ the race .
YouGov conducted polls right before and after the news and found Biden ahead by 8 points in both .
Morning Consult shows Biden having gained 1 point over the past few days .
And Ipsos had Biden ahead by 10 points in a poll conducted after the news of Trump ’ s diagnosis broke , compared to Biden ’ s 9-point advantage in a poll conducted after the debate but before the president ’ s diagnosis .
The John Zogby Strategies poll that showed Biden ahead by only 2 points @ @ @ @ @ @ @ news , although that ’ s not a pollster I ’ d give a lot of credence to .
The series of state polls by the New York Times and Siena College are also worth mentioning here , since they ’ re the only live-caller polls in the mix apart from the NBC/WSJ one — and since they were conducted partly after Trump ’ s COVID-19 diagnosis .
And these contain strong results for Biden , showing him with leads of 8 points in Arizona , 7 points in Pennsylvania and 5 points @ @ @ @ @ @ @ each state .
However , they ’ re still smaller leads than what previous NYT/Siena polls of those states found — Biden led by 9 points in their Arizona poll in September , for instance .
This raises an interesting question : Should you focus more on how a poll compares to a pollster ’ s previous poll or how it compares to other polls in that state ?
There isn ’ t really a right answer here , it ’ s a mix of both .
But to explain how our model @ @ @ @ @ @ @ the September Arizona poll , a 9-point lead had been a particularly strong result for Biden to the point of being a mild outlier .
So the most recent NYT/Siena poll counted as a good result for him on balance , as it confirmed he has a clear lead there now , and he gained ground in our Arizona polling average .
Finally , keep in mind that the reason it ’ s still so hard to understand the effects of the president ’ s COVID-19 diagnosis is because it is an evolving @ @ @ @ @ @ @ his prognosis , which can vary from day to day under the coronavirus , but also the news about the cluster of cases at the White House and the lack of reliable information about his condition .
So if the public wasn ’ t initially sympathetic to Trump — and they mostly weren ’ t , in part because a large majority of the public thinks Trump didn ’ t take appropriate precautions — everything we ’ ve learned since then probably isn ’ t going to make public sentiment better for him @ @ @ @ @ @ @ situation remains unpredictable .
This year , of course , unpredictable news events haven ’ t always had a large effect on the polls .

There’s been so much news going on that I nearly forgot about the existence of a Supreme Court vacancy when participating in a virtual conference this morning. And in some ways, the news makes life hard for us polling analysts. We have had, in rapid succession: the death of Justice Ruth Bader Ginsburg, a series of threats by President Trump in which he refused to commit to a peaceful transition of power, the announcement of Trump’s intention to nominate Amy Coney Barrett to replace Ginsburg, the release of substantial information about the president’s tax returns by the New York Times, the first presidential debate, the news of Trump’s COVID-19 diagnosis and subsequent hospitalization — along with a cluster of other cases at the White House — and now his plans to leave Walter Reed Medical Center later today.
With that said, the debate provides a clear enough line in the sand — with many pollsters planning releases just prior to or just after the debate — that it’s worth doing a before-and-after comparison of the polls. One way to discern this is via our national polling average, where Biden’s lead has inched up to 8.1 points from 7.1 points before the debate:
Another way to see this is by comparing post-debate polls to the last, pre-debate version of both national polls and polls of the same states by the same polling firms. That’s what I’ve done in the table below, covering the 11 national polls and 11 state polls that have been released since the debate. And on average, Biden gained 1.5 percentage points from the pre-debate to the post-debate versions of these polls.
Biden’s gained some ground since the debate Change in Joe Biden’s margin in each pollster’s post-debate poll compared to their latest, pre-debate version, at the state and national level Pre-debate poll Post-debate poll Pollster End date Biden lead or deficit end date Biden lead or deficit Diff. AZ NYT/Siena 9/15 +9.0 10/3 +8.0 -1.0 FL NYT/Siena 6/18 +6.0 10/1 +5.0 -1.0 GA Landmark Communications 8/31 -7.0 9/30 +2.0 +9.0 MI Public Policy Polling 8/29 +4.0 10/1 +6.0 +2.0 MO Remington 9/17 -8.0 10/1 -5.0 +3.0 NH Emerson College 11/26/19 +4.0 10/2 +8.0 +4.0 OH Trafalgar Group 10/3 -4.0 OH YouGov 7/24 -1.0 10/2 +0.0 +1.0 PA YouGov 9/21 +4.0 10/2 +7.0 +3.0 PA NYT/Siena 9/27 +9.0 10/2 +7.0 -2.0 US YouGov 9/23 +5.0 10/3 +8.0 +3.0 US YouGov 9/23 +5.0 10/2 +8.0 +3.0 US NBC/WSJ 9/16 +8.0 10/1 +14.0 +6.0 US John Zogby Strategies 8/29 +4.5 10/2 +2.0 -2.5 US IBD/TIPP 9/19 +6.0 10/1 +3.0 -3.0 US HarrisX 9/25 +5.0 10/1 +7.0 +2.0 US Data for Progress 9/15 +11.0 10/1 +10.0 -1.0 US Ipsos 9/29 +9.0 10/1 +9.0 +0.0 US Ipsos 9/29 +9.0 10/3 +10.0 +1.0 US Change Research 9/20 +9.0 9/30 +13.0 +4.0 US Morning Consult 9/29 +8.0 10/4 +9.0 +1.0 Trafalgar Group has not previously polled Ohio, so no comparison is available. For the John Zogby Strategies polls, versions with and without third-party candidates are averaged together. The previous NYT/Siena poll in Florida and the Emerson College poll in New Hampshire was conducted among registered voters, while the post-debate polls were conducted among likely voters.
In some cases, the pre-debate poll was conducted months before the debate. But even if we only focus on the polls that released results at some point in September, the top line is similar: Biden’s gain is 1.4 percentage points, on average. And for what it’s worth, a swing of 1 or 2 points toward Biden is consistent with the effects that first debates have had for challengers in the past — although we should note that sometimes a debate bounce fades after a couple of weeks.
These averages, of course, conceal a lot of variation within individual polls; depending on which poll you look at, Biden’s national lead is as large as 14 points (in the most recent NBC News/Wall Street Journal poll) or as small as 2 points (in a John Zogby Strategies poll). I’ll admit to finding the NBC/WSJ poll intriguing, as it’s the only live-caller national poll we have since the debate, and NBC/WSJ polls tend to stick pretty close to our polling averages. Still, averaging the polls is the right strategy in the long run.
Because so many polls have recently been released, you’re going to have a few eccentricities. Remember, an 800-person poll nominally has a 3.5-point margin of error. However, that margin pertains only to one candidate’s vote share; in a two-candidate race, the margin of error on the difference between the candidates will be roughly twice that then, or 7 points in this case. That means, if Biden is truly ahead by 8 points, it should be fairly routine to get everything from a 15-point Biden lead to a 1-point lead. And keep in mind that with a confidence interval of 95 percent, the margin of error only covers 95 percent of polls; 1 in 20 polls should fall outside that range. (At least in theory; in practice, pollsters are often reluctant to publish polls that appear to be large outliers.)
It’s harder to tell, though, what effect the president’s COVID-19 diagnosis may have had on the race. YouGov conducted polls right before and after the news and found Biden ahead by 8 points in both. Morning Consult shows Biden having gained 1 point over the past few days. And Ipsos had Biden ahead by 10 points in a poll conducted after the news of Trump’s diagnosis broke, compared to Biden’s 9-point advantage in a poll conducted after the debate but before the president’s diagnosis. The John Zogby Strategies poll that showed Biden ahead by only 2 points nationally was also conducted after the COVID-19 news, although that’s not a pollster I’d give a lot of credence to.
The series of state polls by the New York Times and Siena College are also worth mentioning here, since they’re the only live-caller polls in the mix apart from the NBC/WSJ one — and since they were conducted partly after Trump’s COVID-19 diagnosis. And these contain strong results for Biden, showing him with leads of 8 points in Arizona, 7 points in Pennsylvania and 5 points in Florida– above his polling averages in each state. However, they’re still smaller leads than what previous NYT/Siena polls of those states found — Biden led by 9 points in their Arizona poll in September, for instance.
This raises an interesting question: Should you focus more on how a poll compares to a pollster’s previous poll or how it compares to other polls in that state? There isn’t really a right answer here, it’s a mix of both. But to explain how our model views this, in the case of the September Arizona poll, a 9-point lead had been a particularly strong result for Biden to the point of being a mild outlier. So the most recent NYT/Siena poll counted as a good result for him on balance, as it confirmed he has a clear lead there now, and he gained ground in our Arizona polling average.
Finally, keep in mind that the reason it’s still so hard to understand the effects of the president’s COVID-19 diagnosis is because it is an evolving story. It’s not just his prognosis, which can vary from day to day under the coronavirus, but also the news about the cluster of cases at the White House and the lack of reliable information about his condition. So if the public wasn’t initially sympathetic to Trump — and they mostly weren’t, in part because a large majority of the public thinks Trump didn’t take appropriate precautions — everything we’ve learned since then probably isn’t going to make public sentiment better for him.
With all that said, the situation remains unpredictable. This year, of course, unpredictable news events haven’t always had a large effect on the polls.