fivethirthyeight--2020-07-24--What To Watch For On The English Premier League’s Final Match Day

cwick ( Chadwick Matlin , deputy editor ) : Tony , Grace , Ryan — we ’ ve gathered again to talk about English soccer , which is really to say , we ’ ve gathered again to talk about just how bad Kepa Arrizabalaga is at his job .
And I guess we can also talk about the EPL on the eve of the season ’ s final matches , as three teams compete for just two Champions League spots and three teams compete to keep their head above two relegation spots .
Let ’ s start with the @ @ @ @ @ @ @ an 89 percent chance to make it into the Top 4 , according to FiveThirtyEight ’ s model .
Manchester United has a 76 percent chance , and Leicester has just a 35 percent chance .
How do those numbers sit with you all ?
Seem about right ?
ryan ( Ryan O ’ Hanlon , FiveThirtyEight contributor and author of the No Grass in the Clouds newsletter ) : I wouldn ’ t take any of those numbers as an accurate assessment of how confident I am in any of those teams @ @ @ @ @ @ @ of the table , it makes sense .
Chelsea can still finish Top 4 if they lose and Sunday ’ s Manchester United-Leicester game doesn ’ t end in a draw .
And since Leicester and United are playing each other , they can only both get in if they draw with each other AND Chelsea loses .
Frankly , though , no outcome would surprise me at this point .
grace ( Grace Robertson , FiveThirtyEight contributor and author of the Grace on Football newsletter ) : It feels right to me @ @ @ @ @ @ @ big and loud , but they didn ’ t play too badly against last week ’ s 3-0 loss to the Spurs and could certainly lay a glove on Man United .
But just looking at the table , it ’ s clear what the most likely outcome is .
At this point in the season , one point is a lot of points !
I do think the wild card is that the Wolves , who play Chelsea Sunday , are the kind of side who could cause Chelsea problems .
They @ @ @ @ @ @ @ on the counter .
Lampard hasn ’ t developed a clear strategy for breaking down deep defending sides , so Chelsea will have to rely more on individual quality for that game .
tchow ( Tony Chow , video producer ) : Worth pointing out that Man United are currently favorites according to FiveThirtyEight to win THIS year ’ s Europa league ( at 35 ) .
So even if they fail to make Top 4 in the league , there ’ s always that route for them .
ryan : Should United @ @ @ @ @ @ @ get five teams into the Champions League ?
tchow : Yes .
I am 100 percent here for this .
cwick : Ole Gunnar Solskjaer does not strike me as a galaxy-brain type .
tchow : If Chelsea fail to make Top 4 , they too could also make it if they win the Champions League this year .
Our model gives them a … [ checks predictions ] … less than 1 percent chance of that .
ryan : If Wolves are blowing Chelsea out — not impossible !
— maybe we @ @ @ @ @ @ @ between Brendan Rodgers and OGS .
There ’ s a precedent for this !
tchow : The Disgrace of Old Trafford has a nice ring to it .
grace : My memory is always the Euro 2004 game where Denmark and Sweden somehow managed to draw 2-2 , guaranteeing both to qualify for the next round even though Italy won their game in the same group .
Italy ’ s Antonio Cassano running for a huge celebration before the guys on the bench tell him the other game ’ s score will stay @ @ @ @ @ @ @ Lampard is developing some huge “ I want to speak to the manager ” energy .
tchow : I have always thought that Frank was a great name for the male counterpart of Karen .
ryan : Sir , you ARE the manager .
cwick : Uh , the Europa League is AFTER this weekend ’ s games , right ?
So you want Manchester United to throw it on a 35 percent chance ?
?
?
cwick : Meanwhile , what happened to Leicester ?
They had a 95 percent chance to @ @ @ @ @ @ @ the league restarted !
grace : The performances haven ’ t even been that poor .
SPI went from giving Leicester a rating of 81.6 before the restart to a lowly 81.3 today .
ryan : Leicester ’ s expected goal differential actually improved after the break , too !
cwick : So it ’ s nothing more than an unlucky run ?
I have enough to blame on the unrelenting chaos of the universe .
I need more than just randomness to explain the world around me !
grace : This is @ @ @ @ @ @ @ the extent that Leicester has a problem , it ’ s that Brendan Rodgers likes to constantly improvise and introduce new tactical ideas to shake things up , but his bag of tricks eventually runs dry .
ryan : United also got a lot better all of a sudden , thanks to the signing of Bruno Fernandes and the reintegration of Paul Pogba .
grace : It ’ s wild how players who can pass the ball forward seem to be important in this sport about getting the ball forward into the opposition @ @ @ @ @ @ @ of the season , if you told Leicester that all they ’ d have to do to qualify for the Champions League was to win the final game of the season at home , they absolutely would ’ ve taken that , right ?
grace : No doubt about it .
cwick : The FiveThirtyEight model gives United a 44 percent chance of winning , Leicester a 30 percent chance of winning , and a 26 percent chance of a draw .
tchow : Is the King Power really the King Power when @ @ @ @ @ @ @ “ At home ” doesn ’ t mean the same thing now , does it ?
cwick : Have there been analyses on whether home field advantage has been sapped since the restart in multiple leagues ?
tchow : Shhh , don ’ t scoop our own stories , Chad !
I think we ’ re working on something like this accounting for all the other European leagues .
grace : There was a lot of noise about the Bundesliga having fewer home wins , but I ’ m not sure anyone has @ @ @ @ @ @ @ bold claims .
ryan : The Financial Times found that not much has changed , except for one thing : Refs are awarding fewer cards to away teams now .
tchow : All the games on Sunday are at 11 a.m. EDT .
How many screens is too many this Sunday ?
If you had to choose only three games to pay attention to , there ’ s Man United vs. Leicester .
What are your other two ?
ryan : Wolves-Chelsea , and then Watford-Arsenal .
Remember : Watford outshot Arsenal , @ @ @ @ @ @ @ season in September .
cwick : Arsenal vs. Watford should be total chaos .
Chelsea vs. Wolves is a glimpse into the future of the EPL .
grace : I would go for both of those two also .
ryan : Although I would hate to pass up an opportunity to watch West Ham ’ s Michail Antonio , who is now the best player in the world .
cwick : Ryan , you ’ re like a hermit crab .
Every week you outgrow your old best player in the world , @ @ @ @ @ @ @ another .
ryan : That ’ s … the nicest thing anyone ’ s ever said to me ?
grace : “ The new greatest player in the world is … oh , let ’ s go with… James Ward-Prowse.
” ryan : I think you guys at FiveThirtyEight would call me a “ Bayesian.
” I ’ m just “ updating my priors , ” people !
cwick : What has you crushing on Antonio ?
ryan : He ’ s leading the league in both shots and expected goals since the @ @ @ @ @ @ @ ball upfield — and he ’ s built like a running back .
grace : He is very good .
I think there was always a desire to play him wide or even at wingback due to his defensive solidity and stamina , but he seems to have adapted to playing upfront without any difficulty at all .
Maybe this is just where he should ’ ve been playing the whole time .
It almost feels like Leicester signing striker after striker before realizing Jamie Vardy could play upfront and just score lots @ @ @ @ @ @ @ will win the league next year , is what we ’ re saying .
tchow : And England could ’ ve won a World Cup if Antonio was striker .
Too far ?
cwick : OK , back to the relegation race .
At the bottom of the table , the FiveThirtyEight model gives Bournemouth a 5 percent chance of avoiding relegation , Watford only a 34 percent chance and Aston Villa a 62 percent chance .
Watford has crashed and burned since the restart .
They had a 75 percent chance of @ @ @ @ @ @ @ ryan : They also fired their third manager of the season less than a week ago .
tchow : The win over Arsenal REALLY helped Aston Villa .
grace : A final-day relegation dogfight like this is always extremely difficult to call .
tchow : I was trying to figure out why Bournemouth had only a 5 percent chance to not get relegated .
They are 3 points behind Watford , and the two teams have the same goal differential .
So , on Sunday , Bournemouth will have to 1 ) beat @ @ @ @ @ @ @ loses badly against West Ham and 3 ) hope they beat Everton by more goals than Watford beats their opponent , who is … Arsenal .
Ohhhhh , now the 5 percent makes total sense .
ryan : Watford have definitely been a much better team than Villa over the course of the season , but they also are relying on an interim-manager game to win one of the most important games in the history of the club .
grace : I ’ m sure former West Ham midfielder Hayden Mullins and former @ @ @ @ @ @ @ very clear tactical idea that they ’ ve had enough time to get across to the Watford players .
The Pozzo family , who owns Watford , has a very … liberal sense of when to change managers .
If they pull this off , the Pozzos should build a statue outside the stadium of themselves .
ryan : If you hire four new managers in a season , do you get four “ new manager bounces ” ?
tchow : Y ’ all stop .
This chat is just setting up perfectly @ @ @ @ @ @ @ .
And that can ’ t happen .
ryan : They were also pretty good under Nigel Pearson !
They took the 13th-most points in the league over the stretch while he was managing .
grace : It was very up and down , in fairness .
Pearson got a string of good early results but only two wins since the restart .
ryan : Villa , meanwhile , have been weirdly competent since then .
They have the worst defense in the league , by xG allowed , but they ’ ve @ @ @ @ @ @ @ .
Villa ’ s leading scorer is Jack Grealish .
He has seven goals !
Add that to an awful defense , and somehow they ’ re not favorites to get relegated .
grace : Close followers of Aston Villa coach Dean Smith ’ s seemed to insist that his Brentford sides always ran very hot and cold .
He seems to have transferred that to the Premier League .
tchow : Finish this sentence : If Villa get relegated , Grealish goes to _________ .
ryan : Manchester United were once the @ @ @ @ @ @ @ I don ’ t really get that .
grace : I think he ’ d be a good get for a lot of teams , but the price is probably going to be inflated due to his nationality .
tchow : I think a lot of teams could use him .
Actually , I ’ m not sure why I even caveated that question with “ if Villa get relegated.
” There ’ s a high chance he ’ s gone regardless .
cwick : OK , we can ’ t end the @ @ @ @ @ @ @ real entity most likely to be relegated after this season .
Chelsea ’ s defense was run off the pitch on Wednesday , letting in five goals to Liverpool .
Kepa ’ s own defenders were screaming at him , Though I guess screaming at Kepa isn ’ t so new .
tchow : Trust , if Chelsea end up in fifth , it ’ ll most likely be because of Kepa .
cwick : What should Chelsea do ?
?
grace : StatsBomb ’ s data on Football Reference estimates Kepa has @ @ @ @ @ @ @ Second-worst is Everton ’ s Jordan Pickford at just 4.1. ryan : The back-of-the-napkin math is that one goal of goal differential is roughly equal to one point in the table .
Give Chelsea 10 more points , and they qualified for Europe a long time ago .
grace : Liverpool had five shots on target against Chelsea , and Kepa conceded them all .
He ’ s long been bad but seems to be in particularly poor form .
tchow : I ’ ve gotten in trouble , both in our work @ @ @ @ @ @ @ for continuing to make fun of Kepa .
He makes it hard not to , but I think I have to refrain .
cwick : Wow , Tony , so mature .
Think of what could have been for you and Arsenal .
tchow : I mean , in a lot of ways , he would be the “ perfect ” keeper for Arsenal .
Misery loves company .
cwick : I love soccer because you can basically search for any player name and a team name and get some random link to @ @ @ @ @ @ @ .
tchow : You say that , Chad , but I ’ m searching “ Messi to Arsenal ” and I ’ m getting zero results .
grace : I mean , Messi has been to Arsenal .
And scored lots of goals there in the process .

What To Watch For On The English Premier League’s Final Match Day
cwick (Chadwick Matlin, deputy editor): Tony, Grace, Ryan — we’ve gathered again to talk about English soccer, which is really to say, we’ve gathered again to talk about just how bad Kepa Arrizabalaga is at his job. And I guess we can also talk about the EPL on the eve of the season’s final matches, as three teams compete for just two Champions League spots and three teams compete to keep their head above two relegation spots.
Let’s start with the Champions League race, where Chelsea has an 89 percent chance to make it into the Top 4, according to FiveThirtyEight’s model. Manchester United has a 76 percent chance, and Leicester has just a 35 percent chance. How do those numbers sit with you all? Seem about right?
ryan (Ryan O’Hanlon, FiveThirtyEight contributor and author of the No Grass in the Clouds newsletter): I wouldn’t take any of those numbers as an accurate assessment of how confident I am in any of those teams. But, just given the shape of the table, it makes sense. Chelsea can still finish Top 4 if they lose and Sunday’s Manchester United-Leicester game doesn’t end in a draw. And since Leicester and United are playing each other, they can only both get in if they draw with each other AND Chelsea loses. Frankly, though, no outcome would surprise me at this point.
grace (Grace Robertson, FiveThirtyEight contributor and author of the Grace on Football newsletter): It feels right to me. Leicester’s collapse has been big and loud, but they didn’t play too badly against last week’s 3-0 loss to the Spurs and could certainly lay a glove on Man United. But just looking at the table, it’s clear what the most likely outcome is. At this point in the season, one point is a lot of points!
I do think the wild card is that the Wolves, who play Chelsea Sunday, are the kind of side who could cause Chelsea problems. They have a compact defense and primarily attack on the counter. Lampard hasn’t developed a clear strategy for breaking down deep defending sides, so Chelsea will have to rely more on individual quality for that game.
tchow (Tony Chow, video producer): Worth pointing out that Man United are currently favorites according to FiveThirtyEight to win THIS year’s Europa league (at 35). So even if they fail to make Top 4 in the league, there’s always that route for them.
ryan: Should United throw the game so the EPL can get five teams into the Champions League?
tchow: Yes. I am 100 percent here for this.
cwick: Ole Gunnar Solskjaer does not strike me as a galaxy-brain type.
tchow: If Chelsea fail to make Top 4, they too could also make it if they win the Champions League this year. Our model gives them a … [checks predictions] … less than 1 percent chance of that.
ryan: If Wolves are blowing Chelsea out — not impossible! — maybe we’ll get some midgame handshake deal between Brendan Rodgers and OGS. There’s a precedent for this!
tchow: The Disgrace of Old Trafford has a nice ring to it.
grace: My memory is always the Euro 2004 game where Denmark and Sweden somehow managed to draw 2-2, guaranteeing both to qualify for the next round even though Italy won their game in the same group. Italy’s Antonio Cassano running for a huge celebration before the guys on the bench tell him the other game’s score will stay with me forever.
ryan: Just imagine Frank Lampard’s post-game reaction.
grace: Frank Lampard is developing some huge “I want to speak to the manager” energy.
tchow: I have always thought that Frank was a great name for the male counterpart of Karen.
ryan: Sir, you ARE the manager.
cwick: Uh, the Europa League is AFTER this weekend’s games, right? So you want Manchester United to throw it on a 35 percent chance???
ryan: C’mon, you’re Manchester United! Have some self-confidence!
cwick: Meanwhile, what happened to Leicester? They had a 95 percent chance to qualify as of June 8, before the league restarted!
tchow: Brendan Rodgers should deliver a mea culpa.
grace: The performances haven’t even been that poor. SPI went from giving Leicester a rating of 81.6 before the restart to a lowly 81.3 today.
ryan: Leicester’s expected goal differential actually improved after the break, too!
cwick: So it’s nothing more than an unlucky run? I have enough to blame on the unrelenting chaos of the universe. I need more than just randomness to explain the world around me!
grace: This is still a very good season. To the extent that Leicester has a problem, it’s that Brendan Rodgers likes to constantly improvise and introduce new tactical ideas to shake things up, but his bag of tricks eventually runs dry.
ryan: United also got a lot better all of a sudden, thanks to the signing of Bruno Fernandes and the reintegration of Paul Pogba.
grace: It’s wild how players who can pass the ball forward seem to be important in this sport about getting the ball forward into the opposition goal.
ryan: At the beginning of the season, if you told Leicester that all they’d have to do to qualify for the Champions League was to win the final game of the season at home, they absolutely would’ve taken that, right?
grace: No doubt about it.
cwick: The FiveThirtyEight model gives United a 44 percent chance of winning, Leicester a 30 percent chance of winning, and a 26 percent chance of a draw.
tchow: Is the King Power really the King Power when there are no fans, though? “At home” doesn’t mean the same thing now, does it?
grace: The King Powerless.
tchow: Perfect.
cwick: Have there been analyses on whether home field advantage has been sapped since the restart in multiple leagues?
tchow: Shhh, don’t scoop our own stories, Chad! I think we’re working on something like this accounting for all the other European leagues.
grace: There was a lot of noise about the Bundesliga having fewer home wins, but I’m not sure anyone has a large enough sample size to make bold claims.
ryan: The Financial Times found that not much has changed, except for one thing: Refs are awarding fewer cards to away teams now.
tchow: All the games on Sunday are at 11 a.m. EDT. How many screens is too many this Sunday? If you had to choose only three games to pay attention to, there’s Man United vs. Leicester. What are your other two?
ryan: Wolves-Chelsea, and then Watford-Arsenal. Remember: Watford outshot Arsenal, 30-7, when they played earlier this season in September.
cwick: Arsenal vs. Watford should be total chaos. Chelsea vs. Wolves is a glimpse into the future of the EPL.
grace: I would go for both of those two also.
ryan: Although I would hate to pass up an opportunity to watch West Ham’s Michail Antonio, who is now the best player in the world.
cwick: Ryan, you’re like a hermit crab. Every week you outgrow your old best player in the world, shed him, and nestle up inside another.
ryan: That’s … the nicest thing anyone’s ever said to me?
grace: “The new greatest player in the world is … oh, let’s go with… James Ward-Prowse.”
ryan: I think you guys at FiveThirtyEight would call me a “Bayesian.” I’m just “updating my priors,” people!
cwick: What has you crushing on Antonio?
ryan: He’s leading the league in both shots and expected goals since the restart. Also, he carries the ball upfield — and he’s built like a running back.
grace: He is very good. I think there was always a desire to play him wide or even at wingback due to his defensive solidity and stamina, but he seems to have adapted to playing upfront without any difficulty at all. Maybe this is just where he should’ve been playing the whole time.
It almost feels like Leicester signing striker after striker before realizing Jamie Vardy could play upfront and just score lots of goals.
ryan: West Ham will win the league next year, is what we’re saying.
tchow: And England could’ve won a World Cup if Antonio was striker. Too far?
grace: I can dream.
cwick: OK, back to the relegation race. At the bottom of the table, the FiveThirtyEight model gives Bournemouth a 5 percent chance of avoiding relegation, Watford only a 34 percent chance and Aston Villa a 62 percent chance. Watford has crashed and burned since the restart. They had a 75 percent chance of staying in the league on June 8.
ryan: They also fired their third manager of the season less than a week ago.
tchow: The win over Arsenal REALLY helped Aston Villa.
grace: A final-day relegation dogfight like this is always extremely difficult to call.
tchow: I was trying to figure out why Bournemouth had only a 5 percent chance to not get relegated. They are 3 points behind Watford, and the two teams have the same goal differential. So, on Sunday, Bournemouth will have to 1) beat Everton 2) hope that Aston Villa loses badly against West Ham and 3) hope they beat Everton by more goals than Watford beats their opponent, who is … Arsenal. Ohhhhh, now the 5 percent makes total sense.
ryan: Watford have definitely been a much better team than Villa over the course of the season, but they also are relying on an interim-manager game to win one of the most important games in the history of the club.
grace: I’m sure former West Ham midfielder Hayden Mullins and former Arsenal backup goalkeeper Graham Stack have a very clear tactical idea that they’ve had enough time to get across to the Watford players.
The Pozzo family, who owns Watford, has a very … liberal sense of when to change managers. If they pull this off, the Pozzos should build a statue outside the stadium of themselves.
ryan: If you hire four new managers in a season, do you get four “new manager bounces”?
tchow: Y’all stop. This chat is just setting up perfectly for a 5-0 Watford win on Sunday. And that can’t happen.
ryan: They were also pretty good under Nigel Pearson! They took the 13th-most points in the league over the stretch while he was managing.
grace: It was very up and down, in fairness. Pearson got a string of good early results but only two wins since the restart.
ryan: Villa, meanwhile, have been weirdly competent since then. They have the worst defense in the league, by xG allowed, but they’ve allowed the third-fewest xG since play resumed.
Villa’s leading scorer is Jack Grealish. He has seven goals! Add that to an awful defense, and somehow they’re not favorites to get relegated.
grace: Close followers of Aston Villa coach Dean Smith’s seemed to insist that his Brentford sides always ran very hot and cold. He seems to have transferred that to the Premier League.
tchow: Finish this sentence: If Villa get relegated, Grealish goes to _________.
cwick: Everton.
ryan: Manchester United were once the betting favorites to sign him, but I don’t really get that.
grace: I think he’d be a good get for a lot of teams, but the price is probably going to be inflated due to his nationality.
tchow: I think a lot of teams could use him. Actually, I’m not sure why I even caveated that question with “if Villa get relegated.” There’s a high chance he’s gone regardless.
cwick: OK, we can’t end the chat without talking about Kepa, the real entity most likely to be relegated after this season. Chelsea’s defense was run off the pitch on Wednesday, letting in five goals to Liverpool. Kepa’s own defenders were screaming at him, Though I guess screaming at Kepa isn’t so new.
tchow: Trust, if Chelsea end up in fifth, it’ll most likely be because of Kepa.
cwick: What should Chelsea do??
grace: StatsBomb’s data on Football Reference estimates Kepa has cost Chelsea 9.8 goals this season. Second-worst is Everton’s Jordan Pickford at just 4.1.
ryan: The back-of-the-napkin math is that one goal of goal differential is roughly equal to one point in the table. Give Chelsea 10 more points, and they qualified for Europe a long time ago.
grace: Liverpool had five shots on target against Chelsea, and Kepa conceded them all. He’s long been bad but seems to be in particularly poor form.
tchow: I’ve gotten in trouble, both in our work texts and in personal soccer-group texts, for continuing to make fun of Kepa. He makes it hard not to, but I think I have to refrain.
cwick: Wow, Tony, so mature. Think of what could have been for you and Arsenal.
tchow: I mean, in a lot of ways, he would be the “perfect” keeper for Arsenal. Misery loves company.
cwick: I love soccer because you can basically search for any player name and a team name and get some random link to pop up with some rumor or take.
tchow: You say that, Chad, but I’m searching “Messi to Arsenal” and I’m getting zero results.
grace: I mean, Messi has been to Arsenal. And scored lots of goals there in the process.
tchow: Club legend, really.
Check out our latest soccer predictions.


fivethirthyeight--2020-07-24--The NWSL Is About To Crown A Brand-New Champion

In 22 games over the past month , the NWSL Challenge Cup saw breakout performances from the league ’ s goalkeepers , three playoff games decided on penalties , quarterfinal upsets of the top two seeds , and , after teams had combined for just one goal in four quarterfinal matches , a five-goal game in the semifinals .
On Sunday afternoon , the tournament will end with the Houston Dash or Chicago Red Stars holding up their first NWSL trophy .
The final match of the tournament will be held at Rio Tinto Stadium in the suburbs of Salt @ @ @ @ @ @ @ on CBS at 12:30 p.m. Eastern , and FiveThirtyEight ’ s Club Soccer Predictions give the Red Stars a 59 percent chance to win .
Here ’ s what to watch for .
Even when no one else had confidence in them , the Houston Dash believed they could win .
With their 1-0 semifinal victory over the Portland Thorns , the Dash reached their first final in club history .
Before this tournament , they hadn ’ t even qualified for the playoffs .
Forward Rachel Daly said the semifinal win was @ @ @ @ @ @ @ in itself , including the starters , bench and staff .
She said the team showed grit .
“ The city of Houston ’ s behind us , ” Daly said .
“ I think a lot of people have doubted us in the past .
Again , I always harp on that .
The respect we have for each other and the belief we have in this locker room is phenomenal , and I think we have to take that into the next match in order to win.
” So far , @ @ @ @ @ @ @ Challenge Cup , tied for the league lead with Lynn Williams of the North Carolina Courage and up one on Dash teammate Shea Groom .
If Daly scores again , she ’ ll surpass Williams and be in position to win the golden boot for the tournament .
Despite the wear and tear of the tournament , Houston has suffered few injuries .
The Dash missed Christine Nairn and Megan Oyster against Portland , but overall , the team seemed to benefit from the longer break between group play and the knockouts .
@ @ @ @ @ @ @ can create consistent chances , along with Kristie Mewis and Bri Visalli .
The Dash are up for the challenge .
Before the semifinal , Daly talked about controlling their emotions , and they ’ ll have to continue to keep those feelings in check to win it all against an experienced Chicago team .
Chicago has been here before .
The Red Stars have playoff experience , including the 2019 NWSL championship game .
That history likely helped against an inexperienced Sky Blue squad in the semifinal ; Chicago won 3-2 to @ @ @ @ @ @ @ But the Red Stars also looked worn down after Wednesday ’ s match , a visible reminder of the fact that these teams have played six games since June 27 .
Though Chicago rotated its lineup , it still had to face the Spirit , Thorns and Courage to start group play .
The Red Stars also lost a number of players during the tournament ; some are questionable going into Sunday .
Against Houston , players to watch include Bianca St. Georges , who scored and notched an assist against Sky Blue @ @ @ @ @ @ @ This will also mark Kealia Watt ’ s first game against her former team .
Watt didn ’ t score in the semifinal but contributed in a massive way on the defensive end .
She ’ ll be important on both sides of the ball on Sunday .
Red Stars coach Rory Dames complimented Savannah McCaskill , Katie Johnson and other young players after the semifinal .
He ’ s willing to give them the chance to play in the big game , which can benefit them both now and in the future @ @ @ @ @ @ @ get players experience , ” Dames said .
“ We ’ ll continue to give players opportunities in these kinds of situations , and that ’ s the only way that they can grow , because you can ’ t replicate it .
”

The NWSL Is About To Crown A Brand-New Champion What to watch for in Sunday’s Challenge Cup final.
In 22 games over the past month, the NWSL Challenge Cup saw breakout performances from the league’s goalkeepers, three playoff games decided on penalties, quarterfinal upsets of the top two seeds, and, after teams had combined for just one goal in four quarterfinal matches, a five-goal game in the semifinals.
On Sunday afternoon, the tournament will end with the Houston Dash or Chicago Red Stars holding up their first NWSL trophy.
The final match of the tournament will be held at Rio Tinto Stadium in the suburbs of Salt Lake City. The broadcast kicks off on CBS at 12:30 p.m. Eastern, and FiveThirtyEight’s Club Soccer Predictions give the Red Stars a 59 percent chance to win. Here’s what to watch for.
Houston Dash
1-2-1
Even when no one else had confidence in them, the Houston Dash believed they could win. With their 1-0 semifinal victory over the Portland Thorns, the Dash reached their first final in club history. Before this tournament, they hadn’t even qualified for the playoffs.
Forward Rachel Daly said the semifinal win was proof of how much the team believes in itself, including the starters, bench and staff. She said the team showed grit.
“The city of Houston’s behind us,” Daly said. “I think a lot of people have doubted us in the past. Again, I always harp on that. The respect we have for each other and the belief we have in this locker room is phenomenal, and I think we have to take that into the next match in order to win.”
So far, Daly has scored three goals in the Challenge Cup, tied for the league lead with Lynn Williams of the North Carolina Courage and up one on Dash teammate Shea Groom. If Daly scores again, she’ll surpass Williams and be in position to win the golden boot for the tournament.
Despite the wear and tear of the tournament, Houston has suffered few injuries. The Dash missed Christine Nairn and Megan Oyster against Portland, but overall, the team seemed to benefit from the longer break between group play and the knockouts. Houston is also better if Nichelle Prince can create consistent chances, along with Kristie Mewis and Bri Visalli.
The Dash are up for the challenge. Before the semifinal, Daly talked about controlling their emotions, and they’ll have to continue to keep those feelings in check to win it all against an experienced Chicago team.
Chicago Red Stars
1-2-1
Chicago has been here before.
The Red Stars have playoff experience, including the 2019 NWSL championship game. That history likely helped against an inexperienced Sky Blue squad in the semifinal; Chicago won 3-2 to advance to its second consecutive final.
But the Red Stars also looked worn down after Wednesday’s match, a visible reminder of the fact that these teams have played six games since June 27. Though Chicago rotated its lineup, it still had to face the Spirit, Thorns and Courage to start group play. The Red Stars also lost a number of players during the tournament; some are questionable going into Sunday.
Against Houston, players to watch include Bianca St. Georges, who scored and notched an assist against Sky Blue and had an overall outstanding tournament. This will also mark Kealia Watt’s first game against her former team. Watt didn’t score in the semifinal but contributed in a massive way on the defensive end. She’ll be important on both sides of the ball on Sunday.
Red Stars coach Rory Dames complimented Savannah McCaskill, Katie Johnson and other young players after the semifinal. He’s willing to give them the chance to play in the big game, which can benefit them both now and in the future.
“We’ll continue to get players experience,” Dames said. “We’ll continue to give players opportunities in these kinds of situations, and that’s the only way that they can grow, because you can’t replicate it.”


fivethirthyeight--2020-07-24--Confidence Interval: Democrats Could Win 60 Seats In The Senate

Welcome to another episode of Confidence Interval , where we make a persuasive case for a hot take … and @ @ @ @ @ really feel about the idea .
This time , elections analyst Nathaniel Rakich ponders whether @ @ @ @ @ 13 seats in the U.S. Senate this November to have a 60-seat filibuster-proof majority .

Welcome to another episode of Confidence Interval, where we make a persuasive case for a hot take … and then reveal how confident we really feel about the idea. This time, elections analyst Nathaniel Rakich ponders whether the Democrats can pick up 13 seats in the U.S. Senate this November to have a 60-seat filibuster-proof majority.


fivethirthyeight--2020-07-24--Politics Podcast: The U.S. Isn’t Prepared For A Pandemic Election

The clock is ticking for states to make sure they can safely and effectively administer this November ’ s general election .
In March , it became clear that states needed to reconfigure in-person voting and significantly scale up mail voting so that Americans could cast their ballots during the coronavirus pandemic .
During the primaries , voters experienced postponed elections , consolidated polling places , long lines , mail ballots that never reached them and long delays in counting those ballots .
In this installment of the FiveThirtyEight Politics podcast , election attorney Myrna Pérez of the Brennan Center @ @ @ @ @ @ @ Rakich to discuss how prepared states are for the general election , with only 100 days remaining .
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 @ @ @ @ @ @ @ polling vs. bad polling ” ?
Get in touch by email , on Twitter or in the comments .

The clock is ticking for states to make sure they can safely and effectively administer this November’s general election. In March, it became clear that states needed to reconfigure in-person voting and significantly scale up mail voting so that Americans could cast their ballots during the coronavirus pandemic. During the primaries, voters experienced postponed elections, consolidated polling places, long lines, mail ballots that never reached them and long delays in counting those ballots.
In this installment of the FiveThirtyEight Politics podcast, election attorney Myrna Pérez of the Brennan Center for Justice joins Galen Druke and Nathaniel Rakich to discuss how prepared states are for the general election, with only 100 days remaining.
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--2020-07-24--The Winners And Losers In MLB’s New Playoff Format

Earlier this week , we released our MLB predictions to reflect each team ’ s chances during this year ’ s shortened , 60-game schedule .
But it wouldn ’ t be baseball in 2020 without one last curveball before first pitch .
In an eleventh-hour amendment to the 2020 season ’ s structure , the owners and players union agreed on Thursday to expand the postseason from the usual 10 teams to 16 .
The playoffs will include every division ’ s first- and second-place teams , along with two extra wild cards from each league .
My colleague @ @ @ @ @ @ @ and we ’ ve updated our MLB predictions interactive to reflect baseball ’ s new postseason reality .
So whose odds changed the most ?
Well , the expanded playoff system has altered the overall World Series picture some : The Dodgers — aka the best team in baseball — were the biggest movers , losing almost 3 percentage points of championship probability ( still leaving them at an MLB-best 19 percent going into the season ) .
The Astros and Yankees each lost nearly 1 percentage point , and everyone else gained @ @ @ @ @ @ @ percentage point apiece : These swings boil down to the extra postseason series that top teams will have to play , even if they win their divisions .
Nearly as important , the new system also reduces the odds that any reasonably talented team will miss the playoffs — meaning the playoffs will include more teams that are legitimate threats to pull off upsets .
Among teams that gained the most postseason probability , the biggest beneficiaries weren ’ t the top teams — L.A. ’ s playoff odds went up by only @ @ @ @ @ @ @ club .
Rather , the big winners were the good-but-not-great teams that could still make noise if they get in the field .
The Boston Red Sox , for all their problems , picked up 30 points of playoff probability under the new system .
The Chicago White Sox went from just a 27 percent playoff probability under the old system to over 57 percent now , another increase of around 30 points .
The Athletics , Angels , Rays , Diamondbacks , Indians and Braves all got boosts of at least 25 @ @ @ @ @ @ @ The teams helped the most were those that looked pretty solid on paper but weren ’ t especially likely to win their divisions or even take one of the old wild-card slots .
The expanded postseason has given them another path to make the playoffs — and a chance to create havoc once there .
The change in format also filters into the odds of making subsequent rounds : The Red Sox , D-backs and Angels are also the teams whose odds of making the division series ( the “ Elite Eight ” @ @ @ @ @ @ @ most ; the Dodgers , Yankees , Astros and Twins all saw their division series odds go down by at least 8 percentage points apiece .
A similar story goes for making the league championship series and even the World Series — MLB ’ s middle class got a boost , while the elite teams took a hit .
The old theory that a team ’ s primary job is to simply make the playoffs — and ride the wave of randomness after they arrive — might be truer now than ever before @ @ @ @ @ @ @ will now punch a postseason ticket .
Our model thinks the new format will have a leveling effect , pulling the top teams slightly down and giving a bonus to those clubs who would have been at the fringe of the playoff picture under the old system but still have enough talent to make things interesting in a postseason series .
Although the overall effect wasn ’ t enough to keep the Dodgers , Yankees and Astros from staying World Series favorites , their odds have dropped by a not-insignificant amount .
That @ @ @ @ @ @ @ to the 2020 season .
Because , hey , apparently we didn ’ t already have enough chaos in this strange , short , pandemic-marred campaign .

The Winners And Losers In MLB’s New Playoff Format The change was good news for baseball’s middle class. Not so much for the Dodgers.
Earlier this week, we released our MLB predictions to reflect each team’s chances during this year’s shortened, 60-game schedule. But it wouldn’t be baseball in 2020 without one last curveball before first pitch. In an eleventh-hour amendment to the 2020 season’s structure, the owners and players union agreed on Thursday to expand the postseason from the usual 10 teams to 16. The playoffs will include every division’s first- and second-place teams, along with two extra wild cards from each league.
My colleague Jay Boice has crunched the numbers, and we’ve updated our MLB predictions interactive to reflect baseball’s new postseason reality. So whose odds changed the most? Well, the expanded playoff system has altered the overall World Series picture some: The Dodgers — aka the best team in baseball — were the biggest movers, losing almost 3 percentage points of championship probability (still leaving them at an MLB-best 19 percent going into the season). The Astros and Yankees each lost nearly 1 percentage point, and everyone else gained or lost less than two-thirds of a percentage point apiece:
Which teams gained or lost the most title probability? Largest gains or losses in 2020 championship probability — according to the FiveThirtyEight model — for teams whose odds moved by at least +/-0.2 percentage points under MLB’s new postseason format Moving up Championship Probability Team Division Before After Diff. Red Sox AL East 1.5% 2.0% +0.6 Diamondbacks NL West 1.5 2.0 +0.5 Athletics AL West 3.0 3.4 +0.4 Cubs NL Central 2.9 3.2 +0.3 Cardinals NL Central 2.0 2.3 +0.3 Angels AL West 1.0 1.3 +0.3 Rockies NL West 0.5 0.7 +0.3 Rays AL East 4.9 5.2 +0.3 Braves NL East 3.0 3.3 +0.3 Mets NL East 3.4 3.6 +0.3 Brewers NL Central 2.6 2.9 +0.2 White Sox AL Central 1.0 1.2 +0.2 Rangers AL West 0.4 0.6 +0.2 Phillies NL East 1.1 1.3 +0.2 Blue Jays AL East 0.3 0.5 +0.2 Padres NL West 1.2 1.4 +0.2 Moving down Championship Probability Team Division Before After Diff. Nationals NL East 6.5% 6.4% -0.2 Twins AL Central 6.6 6.4 -0.2 Yankees AL East 14.4 13.6 -0.8 Astros AL West 13.4 12.5 -0.9 Dodgers NL West 21.7 18.9 -2.8 Predictions as of July 24, 2020.
These swings boil down to the extra postseason series that top teams will have to play, even if they win their divisions. Nearly as important, the new system also reduces the odds that any reasonably talented team will miss the playoffs — meaning the playoffs will include more teams that are legitimate threats to pull off upsets.
Among teams that gained the most postseason probability, the biggest beneficiaries weren’t the top teams — L.A.’s playoff odds went up by only 9 percentage points, second-fewest of any club. Rather, the big winners were the good-but-not-great teams that could still make noise if they get in the field. The Boston Red Sox, for all their problems, picked up 30 points of playoff probability under the new system. The Chicago White Sox went from just a 27 percent playoff probability under the old system to over 57 percent now, another increase of around 30 points. The Athletics, Angels, Rays, Diamondbacks, Indians and Braves all got boosts of at least 25 percentage points.
The common theme: The teams helped the most were those that looked pretty solid on paper but weren’t especially likely to win their divisions or even take one of the old wild-card slots. The expanded postseason has given them another path to make the playoffs — and a chance to create havoc once there.
Whose playoff outlook got brighter? Largest gains in 2020 playoff probability — according to the FiveThirtyEight model — under MLB’s new postseason format, for teams with a current playoff probability of at least 25 percent Playoff Probability Team Division Before After Diff. Red Sox AL East 29.9% 60.2% +30.4 White Sox AL Central 27.4 57.6 +30.2 Athletics AL West 45.3 73.6 +28.4 Angels AL West 22.7 50.7 +28.0 Rays AL East 54.6 81.3 +26.7 Diamondbacks NL West 28.9 55.3 +26.3 Indians AL Central 54.6 80.8 +26.2 Braves NL East 39.5 64.9 +25.4 Padres NL West 25.6 50.3 +24.7 Mets NL East 42.3 66.5 +24.2 Reds NL Central 42.6 66.7 +24.2 Cubs NL Central 43.1 66.8 +23.7 Brewers NL Central 39.6 63.3 +23.6 Cardinals NL Central 38.6 62.2 +23.6 Rangers AL West 14.8 37.3 +22.6 Phillies NL East 22.8 45.2 +22.3 Nationals NL East 57.3 78.9 +21.5 Blue Jays AL East 13.0 34.2 +21.3 Twins AL Central 66.9 87.9 +21.0 Rockies NL West 15.6 36.3 +20.7 Astros AL West 76.5 92.5 +16.0 Yankees AL East 81.6 94.5 +12.9 Dodgers NL West 87.4 96.0 +8.6 Predictions as of July 24, 2020.
The change in format also filters into the odds of making subsequent rounds: The Red Sox, D-backs and Angels are also the teams whose odds of making the division series (the “Elite Eight” of this bracket) went up the most; the Dodgers, Yankees, Astros and Twins all saw their division series odds go down by at least 8 percentage points apiece. A similar story goes for making the league championship series and even the World Series — MLB’s middle class got a boost, while the elite teams took a hit.
The old theory that a team’s primary job is to simply make the playoffs — and ride the wave of randomness after they arrive — might be truer now than ever before, even as 53 percent of teams will now punch a postseason ticket. Our model thinks the new format will have a leveling effect, pulling the top teams slightly down and giving a bonus to those clubs who would have been at the fringe of the playoff picture under the old system but still have enough talent to make things interesting in a postseason series.
Although the overall effect wasn’t enough to keep the Dodgers, Yankees and Astros from staying World Series favorites, their odds have dropped by a not-insignificant amount. That should add an extra element of uncertainty to the 2020 season. Because, hey, apparently we didn’t already have enough chaos in this strange, short, pandemic-marred campaign.
Jay Boice contributed research.


fivethirthyeight--2020-07-24--Are You A Pinball Wizard?

Are You A Pinball Wizard?

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 Peter Mowrey comes an elegant electoral enigma : Riddler Township is having its quadrennial presidential election .
Each of the town ’ s 10 “ shires ” is allotted a certain number of electoral votes : two , plus one additional vote for every 10 citizens ( rounded to the nearest 10 ) .
The names and populations of the 10 shires are summarized in the table below .
As you may know , under this sort of electoral system , it is quite possible for a presidential candidate @ @ @ @ @ @ @ win the election .
If there are two candidates running for president of Riddler Township , and every single citizen votes for one or the other , then what is the lowest percentage of the popular vote that a candidate can get while still winning the election ?
Riddler Pinball is a game with an infinitely long wall and a circle whose radius is 1 inch and whose center is 2 inches from the wall .
The wall and the circle are both fixed and never move .
A single pinball starts 2 @ @ @ @ @ @ @ from the center of the circle .
To play , you flick the pinball toward a spot of your choosing along the wall , specified by its distance x from the point on the wall that ’ s closest to the circle , as shown in the diagram below .
The goal of the game is simple : Get the ball to bounce as many times as possible .
Let ’ s take a look at some games to see how they play out .
If you aim too far to the right @ @ @ @ @ @ @ is too small ) , the pinball will quickly bounce its way through the gap between the circle and the wall .
That ’ s what happened in the game below , when x was 0.75 inches , resulting in a rather pedestrian four bounces .
But if you aim too far to the left ( i.e.
, your value of x is too big ) , the pinball will quickly come back out the same side it went in .
That ’ s what happened in the next game , when x @ @ @ @ @ @ @ four bounces .
As you can see , Riddler Pinball is an unforgiving game — the slightest error can tank your chances of victory .
But if you strategize just right , it ’ s possible to do quite well .
What ’ s the greatest number of bounces you can achieve ?
And , more importantly , what value of x gets you the most bounces ?
Congratulations to 👏 Rick Schubert 👏 of San Diego , California , winner of last week ’ s Riddler Express .
Last week , you @ @ @ @ @ @ @ , albeit in a shortened season .
Your true batting average was .350 , meaning you had a 35 percent chance of getting a hit with every at-bat .
If you had four at-bats per game , what were your chances of batting at least .400 over the course of the 60-game season ?
In a 60-game season , with four at-bats per game , there were 240 total at-bats .
Forty percent of 240 was 96 , so to bat at least .400 you needed at least 96 hits .
Since each @ @ @ @ @ @ @ the binomial distribution to determine the probability of each number of hits .
For example , the probability of getting exactly 96 hits in 240 at-bats was equal to 0.3596 ( i.e.
, getting a hit in 96 at-bats ) times 0.65144 ( i.e.
, not getting a hit in the remaining 144 at-bats ) , times the number of ways you can order 96 hits among 240 at-bats ( 240 choose 96 ) .
Again , that was just the probability of getting exactly 96 hits .
To find the probability of @ @ @ @ @ @ @ to add up the probabilities of getting 96 hits , 97 hits , 98 hits , and so on , up to ( the very unlikely ) case of 240 hits .
Alternatively , you could have added up the probabilities of getting between zero and 95 hits , and then subtracted this from 1 .
Whether you did this by hand , by spreadsheet or by computer code , the correct answer was 6.1 percent .
It turned out that it was 16 times easier to bat .400 over 60 games than @ @ @ @ @ @ @ 162 games , where the probability was just 0.38 percent .
The puzzle ’ s submitter , Taylor Firman , extended this further , looking at the probability of anyone in the league batting .400 , based on each player ’ s own career batting average .
For a 60-game season , Taylor found that this probability was about 3.4 percent , while it was just 0.002 percent for a 162-game season .
So if no one catches Ted Williams this year , forget about it .
For extra credit , you were @ @ @ @ @ @ @ a hit in at least 56 consecutive games within the 60-game season , tying or breaking Joe DiMaggio ’ s record .
It was helpful to first calculate the probability of keeping the streak alive — that is , getting at least one hit in a game .
Again using the binomial distribution , this probability was 82.15 percent .
But while it was likely you ’ d get a hit in any given game , pulling that off 56 times in a row was another story .
As Mark Girard explained , @ @ @ @ @ @ @ a streak of at least 56 games : • Getting a hit in games 1 to 56 • Not getting a hit in game 1 and getting a hit in games 2 to 57 • Not getting a hit in game 2 and getting a hit in games 3 to 58 • Not getting a hit in game 3 and getting a hit in games 4 to 59 • Not getting a hit in game 4 and getting a hit in games 5 to 60 Each of these five cases was very unlikely @ @ @ @ @ @ @ very unlikely .
Overall , your chances of having a 56-game hitting streak in a 60-game season stood at just 0.0028 percent .
And remember , that was assuming you were a lifetime .350 hitter !
Over a 162-game season , these chances improved by about tenfold , to 0.033 percent .
It would appear that Joe DiMaggio ’ s record is quite safe .
Finally , for extra extra credit , you had to find your chances of both batting at least .400 and getting a hit in at least 56 games @ @ @ @ @ @ @ these events were not independent .
In other words , if you hit .400 , you were more likely to have a very long hitting streak , and vice versa .
Paul Wright worked it out analytically , starting with streaks of 56 , 57 , 58 , 59 or 60 games , each of which had their own corresponding probabilities of occurring .
Then , for each streak , you knew that the games within the streak had one , two , three or four hits , while the remaining handful of @ @ @ @ @ @ @ Putting the streak and non-streak games together , the probability of batting at least .400 and having a hitting streak of at least 56 games was about 0.0027 percent .
This was very close to the answer for the extra credit , meaning If you tied or broke Joe DiMaggio ’ s record in 60 games , then it was very likely that you ’ d also bat at least .400 .
Finally , Angela Zhou calculated your chances of reaching both milestones over a 162-game season .
It wasn ’ t likely @ @ @ @ @ @ @ of Kensington , Connecticut , winner of last week ’ s Riddler Classic .
Last week , the tortoise and the hare were about to begin a 10-mile race along a “ stretch ” of road .
The tortoise was driving a car that traveled 60 miles per hour , while the hare was driving a car that traveled 75 miles per hour .
( For the purposes of this problem , you were asked to assume that both cars accelerated from 0 miles per hour to their cruising speed instantaneously . )
@ @ @ @ @ @ @ and realized if it waited until two minutes had passed , they would cross the finish line at the exact same moment .
And so , when the race began , the tortoise drove off while the hare patiently waited .
But one minute into the race , after the tortoise had driven 1 mile , something extraordinary happened .
The road turned out to be magical and instantaneously stretched by 10 miles !
As a result of this stretching , the tortoise was now 2 miles ahead of the hare , who @ @ @ @ @ @ @ the end of every subsequent minute , the road stretched by 10 miles .
With this in mind , the hare did some more mental math .
How long after the race began should the hare have waited so that both the tortoise and the hare crossed the finish line at the same exact moment ?
At first , it might have seemed like neither the tortoise nor the hare would ever finish the race .
How could they , when they drove a mile or so per minute , while the road @ @ @ @ @ @ @ key was to realize that the road stretched uniformly , which meant it could carry each car along as it stretched .
To better understand this , let ’ s take a closer look at the tortoise over time .
After one minute , it traveled 1 mile , or 10 percent of the total distance .
Then , the road stretched to a length of 20 miles .
But because the stretching was uniform , the tortoise was still 10 percent of the way across , meaning it was 2 miles down @ @ @ @ @ @ @ it was 3 miles down the road .
Then , after the road stretched to a length of 30 miles , the tortoise was 4.5 miles down the road .
But rather than focusing on the distance the tortoise traveled , you should have zeroed in on the fraction of the total distance it covered each minute .
In the first minute , the tortoise drove 1/10 of the total distance .
In the second minute , it drove 1/20 .
In the third minute , it drove 1/30 , In the fourth @ @ @ @ @ @ @ N minutes , it drove 1/10 · ( 1/1 + 1/2 + 1/3 + 1/4 + … + 1/N ) .
As many solvers noticed , that sum inside the parentheses is none other than the Nth harmonic number !
Once this sum exceeded 10 , the tortoise was guaranteed to have finished the race .
This happened 12,367 minutes — more than eight days — into the competition .
Calculating this was no small feat .
But alas , much like the idling hare , you still had your work cut out @ @ @ @ @ @ @ t finish exactly 12,367 minutes into the race — the sum of the first 12,367 terms of the harmonic series is in fact greater than 10 .
The precise time turned out to be approximately 12,366.47 minutes .
But as solvers Hector Pefo and Josh Silverman cleverly observed , you didn ’ t need to calculate this exact time .
As long as the hare started running the moment the tortoise completed 20 percent of the race , they ’ d finish together .
That ’ s because the hare would then travel @ @ @ @ @ @ @ over the same amount of time , perfectly balancing the fact that the hare traveled 25 percent faster .
At this point , you just needed to determine when the tortoise had finished 20 percent of the race .
After just four minutes , when the race was 40 miles long , the tortoise had traveled about 8.33 miles — just a shade over 20 percent of the way .
Since the tortoise drove 1 mile per minute , it must have passed the 20 percent mark a third of a minute ( @ @ @ @ @ @ @ And so the hare took off exactly 3 minutes and 40 seconds into the race .
You can see this epic tie in all its glory , courtesy of Allen Gu : Solver Hypergeometricx extended the puzzle further , looking at what would happen if the road stretched continuously over time , rather than discretely every minute , finding that the hare would then wait e2−1 minutes ( about 6 minutes and 23 seconds ) into the race .
And the moral of all this ?
Slow and stretchy wins the race .
@ @ @ @ @ @ @ ?
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 Peter Mowrey comes an elegant electoral enigma:
Riddler Township is having its quadrennial presidential election. Each of the town’s 10 “shires” is allotted a certain number of electoral votes: two, plus one additional vote for every 10 citizens (rounded to the nearest 10).
The names and populations of the 10 shires are summarized in the table below.
Which way will Riddler Township swing? Shire Population Electoral votes Oneshire 11 3 Twoshire 21 4 Threeshire 31 5 Fourshire 41 6 Fiveshire 51 7 Sixshire 61 8 Sevenshire 71 9 Eightshire 81 10 Nineshire 91 11 Tenshire 101 12
As you may know, under this sort of electoral system, it is quite possible for a presidential candidate to lose the popular vote and still win the election.
If there are two candidates running for president of Riddler Township, and every single citizen votes for one or the other, then what is the lowest percentage of the popular vote that a candidate can get while still winning the election?
Submit your answer
Riddler Classic
Riddler Pinball is a game with an infinitely long wall and a circle whose radius is 1 inch and whose center is 2 inches from the wall. The wall and the circle are both fixed and never move. A single pinball starts 2 inches from the wall and 2 inches from the center of the circle.
To play, you flick the pinball toward a spot of your choosing along the wall, specified by its distance x from the point on the wall that’s closest to the circle, as shown in the diagram below.
The goal of the game is simple: Get the ball to bounce as many times as possible.
(Note: This is a geometry problem, not a physics problem. In other words, assume the system is frictionless and that all collisions are perfectly elastic.)
Let’s take a look at some games to see how they play out.
If you aim too far to the right (i.e., your value of x is too small), the pinball will quickly bounce its way through the gap between the circle and the wall. That’s what happened in the game below, when x was 0.75 inches, resulting in a rather pedestrian four bounces.
But if you aim too far to the left (i.e., your value of x is too big), the pinball will quickly come back out the same side it went in. That’s what happened in the next game, when x was 0.9 inches, again yielding just four bounces.
As you can see, Riddler Pinball is an unforgiving game — the slightest error can tank your chances of victory. But if you strategize just right, it’s possible to do quite well.
What’s the greatest number of bounces you can achieve? And, more importantly, what value of x gets you the most bounces?
Submit your answer
Solution to last week’s Riddler Express
Congratulations to 👏 Rick Schubert 👏 of San Diego, California, winner of last week’s Riddler Express.
Last week, you set your sights on breaking baseball records, albeit in a shortened season. Your true batting average was .350, meaning you had a 35 percent chance of getting a hit with every at-bat. If you had four at-bats per game, what were your chances of batting at least .400 over the course of the 60-game season?
In a 60-game season, with four at-bats per game, there were 240 total at-bats. Forty percent of 240 was 96, so to bat at least .400 you needed at least 96 hits. Since each at-bat was independent, you could use the binomial distribution to determine the probability of each number of hits.
For example, the probability of getting exactly 96 hits in 240 at-bats was equal to 0.3596 (i.e., getting a hit in 96 at-bats) times 0.65144 (i.e., not getting a hit in the remaining 144 at-bats), times the number of ways you can order 96 hits among 240 at-bats (240 choose 96).
Again, that was just the probability of getting exactly 96 hits. To find the probability of at least 96 hits, you had to add up the probabilities of getting 96 hits, 97 hits, 98 hits, and so on, up to (the very unlikely) case of 240 hits. Alternatively, you could have added up the probabilities of getting between zero and 95 hits, and then subtracted this from 1. Whether you did this by hand, by spreadsheet or by computer code, the correct answer was 6.1 percent.
It turned out that it was 16 times easier to bat .400 over 60 games than it was over a full slate of 162 games, where the probability was just 0.38 percent.
The puzzle’s submitter, Taylor Firman, extended this further, looking at the probability of anyone in the league batting .400, based on each player’s own career batting average. For a 60-game season, Taylor found that this probability was about 3.4 percent, while it was just 0.002 percent for a 162-game season. So if no one catches Ted Williams this year, forget about it.
For extra credit, you were asked to find your chances of getting a hit in at least 56 consecutive games within the 60-game season, tying or breaking Joe DiMaggio’s record. It was helpful to first calculate the probability of keeping the streak alive — that is, getting at least one hit in a game. Again using the binomial distribution, this probability was 82.15 percent. But while it was likely you’d get a hit in any given game, pulling that off 56 times in a row was another story.
As Mark Girard explained, there were several distinct ways to achieve a streak of at least 56 games:
Getting a hit in games 1 to 56
Not getting a hit in game 1 and getting a hit in games 2 to 57
Not getting a hit in game 2 and getting a hit in games 3 to 58
Not getting a hit in game 3 and getting a hit in games 4 to 59
Not getting a hit in game 4 and getting a hit in games 5 to 60
Each of these five cases was very unlikely. And together, they were still very unlikely. Overall, your chances of having a 56-game hitting streak in a 60-game season stood at just 0.0028 percent. And remember, that was assuming you were a lifetime .350 hitter! Over a 162-game season, these chances improved by about tenfold, to 0.033 percent. It would appear that Joe DiMaggio’s record is quite safe.
Finally, for extra extra credit, you had to find your chances of both batting at least .400 and getting a hit in at least 56 games. This was especially tricky, since these events were not independent. In other words, if you hit .400, you were more likely to have a very long hitting streak, and vice versa.
Paul Wright worked it out analytically, starting with streaks of 56, 57, 58, 59 or 60 games, each of which had their own corresponding probabilities of occurring. Then, for each streak, you knew that the games within the streak had one, two, three or four hits, while the remaining handful of games could also have zero hits. Putting the streak and non-streak games together, the probability of batting at least .400 and having a hitting streak of at least 56 games was about 0.0027 percent. This was very close to the answer for the extra credit, meaning If you tied or broke Joe DiMaggio’s record in 60 games, then it was very likely that you’d also bat at least .400.
Finally, Angela Zhou calculated your chances of reaching both milestones over a 162-game season. It wasn’t likely.
Solution to last week’s Riddler Classic
Congratulations to 👏 Jim Boyce 👏 of Kensington, Connecticut, winner of last week’s Riddler Classic.
Last week, the tortoise and the hare were about to begin a 10-mile race along a “stretch” of road. The tortoise was driving a car that traveled 60 miles per hour, while the hare was driving a car that traveled 75 miles per hour. (For the purposes of this problem, you were asked to assume that both cars accelerated from 0 miles per hour to their cruising speed instantaneously.)
The hare did a quick mental calculation and realized if it waited until two minutes had passed, they would cross the finish line at the exact same moment. And so, when the race began, the tortoise drove off while the hare patiently waited.
But one minute into the race, after the tortoise had driven 1 mile, something extraordinary happened. The road turned out to be magical and instantaneously stretched by 10 miles! As a result of this stretching, the tortoise was now 2 miles ahead of the hare, who remained at the starting line.
At the end of every subsequent minute, the road stretched by 10 miles. With this in mind, the hare did some more mental math.
How long after the race began should the hare have waited so that both the tortoise and the hare crossed the finish line at the same exact moment?
At first, it might have seemed like neither the tortoise nor the hare would ever finish the race. How could they, when they drove a mile or so per minute, while the road stretched 10 miles per minute? The key was to realize that the road stretched uniformly, which meant it could carry each car along as it stretched.
To better understand this, let’s take a closer look at the tortoise over time. After one minute, it traveled 1 mile, or 10 percent of the total distance. Then, the road stretched to a length of 20 miles. But because the stretching was uniform, the tortoise was still 10 percent of the way across, meaning it was 2 miles down the road. After another minute, it was 3 miles down the road. Then, after the road stretched to a length of 30 miles, the tortoise was 4.5 miles down the road.
But rather than focusing on the distance the tortoise traveled, you should have zeroed in on the fraction of the total distance it covered each minute. In the first minute, the tortoise drove 1/10 of the total distance. In the second minute, it drove 1/20. In the third minute, it drove 1/30, In the fourth minute, it was 1/40. After N minutes, it drove 1/10 · (1/1 + 1/2 + 1/3 + 1/4 + … + 1/N). As many solvers noticed, that sum inside the parentheses is none other than the Nth harmonic number! Once this sum exceeded 10, the tortoise was guaranteed to have finished the race. This happened 12,367 minutes — more than eight days — into the competition.
Calculating this was no small feat. But alas, much like the idling hare, you still had your work cut out for you.
The tortoise didn’t finish exactly 12,367 minutes into the race — the sum of the first 12,367 terms of the harmonic series is in fact greater than 10. The precise time turned out to be approximately 12,366.47 minutes.
But as solvers Hector Pefo and Josh Silverman cleverly observed, you didn’t need to calculate this exact time. As long as the hare started running the moment the tortoise completed 20 percent of the race, they’d finish together. That’s because the hare would then travel a distance that was 25 percent longer over the same amount of time, perfectly balancing the fact that the hare traveled 25 percent faster.
At this point, you just needed to determine when the tortoise had finished 20 percent of the race. After just four minutes, when the race was 40 miles long, the tortoise had traveled about 8.33 miles — just a shade over 20 percent of the way. Since the tortoise drove 1 mile per minute, it must have passed the 20 percent mark a third of a minute (i.e., 20 seconds) prior. And so the hare took off exactly 3 minutes and 40 seconds into the race.
You can see this epic tie in all its glory, courtesy of Allen Gu:
Solver Hypergeometricx extended the puzzle further, looking at what would happen if the road stretched continuously over time, rather than discretely every minute, finding that the hare would then wait e2−1 minutes (about 6 minutes and 23 seconds) into the race.
And the moral of all this? Slow and stretchy wins the race.
Want more riddles?
Well, aren’t you lucky? There’s a whole book full of the best puzzles from this column and some never-before-seen head-scratchers. It’s called “The Riddler,” and it’s in stores now!
Want to submit a riddle?
Email Zach Wissner-Gross at riddlercolumn@gmail.com.


fivethirthyeight--2020-07-24--Americans Mostly Support Voting By Mail

Americans Mostly Support Voting By Mail

Welcome to Pollapalooza , our weekly polling roundup .
How do you hold an election during a pandemic ?
Most states are encouraging voters to cast their ballots by mail this November to avoid spreading the coronavirus , and some of them are revising their election laws to make that easier .
Under normal circumstances , 34 states ( plus Washington , D.C. ) have allowed people to vote absentee for any reason , including five that conduct vote-by-mail elections by default ( i.e.
, every voter is automatically mailed a ballot ) .
But as of Thursday , at @ @ @ @ @ @ @ vote absentee this fall , including seven states and Washington , D.C. , that will mail voters ballots by default .
That leaves approximately 54 million eligible voters across nine states who must provide an excuse to vote absentee this fall ( though some of those states may still change their laws before Election Day ) .
And a new poll out this week found the American people largely supportive of efforts to expand absentee voting .
According to the Pew Research Center , 65 percent of adults said that any voter should @ @ @ @ @ @ @ without an excuse .
Furthermore , an additional 14 percent thought a documented reason should be required , but that COVID-19 should count as one of the reasons .
As a result , only 19 percent of Americans believed that voters should need an excuse other than the pandemic to vote absentee .
However , as on so many other issues , Republicans and Democrats don ’ t agree on this .
While a whopping 83 percent of Democrats supported no-excuse absentee voting ( and another 11 percent thought COVID-19 should be a @ @ @ @ @ @ @ of Republicans thought so .
Another 17 percent thought COVID-19 should be an acceptable excuse , but that still left 37 percent of Republicans believing voters must provide a non-pandemic-related excuse to vote absentee .
You might be tempted to chalk up this divide to President Trump ’ s recent rants against voting by mail .
And according to another poll released this week , from ABC News/The Washington Post , 78 percent of Trump supporters do see mail-in voting as “ vulnerable to significant levels of fraud.
” ( It ’ s @ @ @ @ @ @ @ actually long been a partisan issue : The party splits in the Pew poll were similar in October 2018 .
( That said , Republican opposition to no-excuse absentee voting has grown a bit since then . )
However , just because voters want the option to vote absentee doesn ’ t mean they ’ ll actually do it .
The ABC News/Washington Post poll also found that 59 percent of Americans would prefer to vote in person in this year ’ s election , while 38 percent would prefer to vote by @ @ @ @ @ @ @ along demographic lines , which could put heightened stress on our democracy this November .
For instance , Republican respondents told ABC News/The Washington Post that they preferred to vote in person , 79 percent to 20 percent .
But Democratic respondents preferred to vote by mail , 51 percent to 46 percent .
That could mean that votes cast in person will skew toward Republicans this fall , while mail-in votes skew toward Democrats .
And since in-person votes are typically reported first on election night , that could mean that initial @ @ @ @ @ @ @ favorable to Trump — perhaps causing him to claim victory prematurely .
But Biden could actually turn out to be the winner days after Election Day in this scenario , as mailed ballots are counted and Democratic votes are added to the till .
This could cause a national crisis if Trump decries those late-counted ballots as fraudulent or if he refuses to concede .
In addition , the poll found that college-educated and wealthier voters were more comfortable voting by mail .
Specifically , respondents with postgraduate degrees said they preferred voting @ @ @ @ @ @ @ ; those with just a four-year college degree were split 49 percent to 49 percent .
Respondents with less than four years of college said they preferred to vote in person , 59 percent to 37 percent , and respondents with a high school diploma or less opted for in-person voting 68 percent to 29 percent .
As a result , underprivileged voters could be disproportionately affected if the pandemic forces the closure or consolidation of polling places this November , either putting them at heightened risk of contracting COVID-19 while waiting in @ @ @ @ @ @ @ According to the Kaiser Family Foundation , 60 percent of parents with schoolchildren wanted schools to wait to restart in-person classes , while only 34 percent wanted schools to reopen sooner .
This preference was largely driven by parents of color , 91 percent of whom were worried that their child will catch COVID-19 if schools reopen .
Only 55 percent of white parents shared that concern .
• A Morning Consult poll found that the vast majority of Americans — 72 percent — supported mandating face masks in public spaces in their @ @ @ @ @ @ @ who refused to do so ) .
Despite perceptions that wearing a mask has become a partisan issue , even Republicans supported the policy , 58 percent to 35 percent .
• According to another part of the ABC News/Washington Post poll , a record 69 percent of Americans said that they think white and nonwhite people do not receive equal treatment in the criminal justice system ; only 26 percent said they do receive equal treatment .
Black respondents have long held this view in ABC News/Washington Post polling , but for @ @ @ @ @ @ @ majority of white people .
• As evidenced by the fact that Opening Day was yesterday ( four months late ) , this year ’ s Major League Baseball season will look a little different from usual .
Most obviously , the season will only have 60 games — down from the standard 162 — but it will still crown a World Series champion .
According to Morning Consult , though , a plurality of fans think the 2020 champion deserves an asterisk .
Forty-four percent of baseball fans said that winning the @ @ @ @ @ @ @ be less meaningful than winning after a full regular season , while 35 percent believed it would be just as meaningful .
( In reality , a 60-game season isn ’ t that much worse at assessing a team ’ s true talent than a 162-game season — but neither is perfect . )
According to FiveThirtyEight ’ s presidential approval tracker , 40.3 percent of Americans approve of the job Trump is doing as president , while 55.6 percent disapprove ( a net approval rating of -15.3 points ) .
At this @ @ @ @ @ @ @ and 55.6 percent disapproved ( a net approval rating of -15.2 points ) .
One month ago , Trump had an approval rating of 41.0 percent and a disapproval rating of 55.3 percent , for a net approval rating of -14.3 points .
In our average of polls of the generic congressional ballot , Democrats currently lead by 8.2 percentage points ( 49.4 percent to 41.2 percent ) .
A week ago , Democrats led Republicans by 8.3 points ( 49.0 percent to 40.7 percent ) .
At this time last month , @ @ @ @ @ @ @ 48.7 percent to 40.5 percent ) .
Check out all the polls we ’ ve been collecting ahead of the 2020 elections .

Welcome to Pollapalooza, our weekly polling roundup.
Poll(s) of the week
How do you hold an election during a pandemic? Most states are encouraging voters to cast their ballots by mail this November to avoid spreading the coronavirus, and some of them are revising their election laws to make that easier.
Under normal circumstances, 34 states (plus Washington, D.C.) have allowed people to vote absentee for any reason, including five that conduct vote-by-mail elections by default (i.e., every voter is automatically mailed a ballot). But as of Thursday, at least 41 states are allowing anyone to vote absentee this fall, including seven states and Washington, D.C., that will mail voters ballots by default. That leaves approximately 54 million eligible voters across nine states who must provide an excuse to vote absentee this fall (though some of those states may still change their laws before Election Day).
And a new poll out this week found the American people largely supportive of efforts to expand absentee voting. According to the Pew Research Center, 65 percent of adults said that any voter should be able to vote early or absentee without an excuse. Furthermore, an additional 14 percent thought a documented reason should be required, but that COVID-19 should count as one of the reasons. As a result, only 19 percent of Americans believed that voters should need an excuse other than the pandemic to vote absentee.
However, as on so many other issues, Republicans and Democrats don’t agree on this. While a whopping 83 percent of Democrats supported no-excuse absentee voting (and another 11 percent thought COVID-19 should be a valid excuse), only 44 percent of Republicans thought so. Another 17 percent thought COVID-19 should be an acceptable excuse, but that still left 37 percent of Republicans believing voters must provide a non-pandemic-related excuse to vote absentee.
You might be tempted to chalk up this divide to President Trump’s recent rants against voting by mail. And according to another poll released this week, from ABC News/The Washington Post, 78 percent of Trump supporters do see mail-in voting as “vulnerable to significant levels of fraud.” (It’s not.) But absentee-voting access has actually long been a partisan issue: The party splits in the Pew poll were similar in October 2018. (That said, Republican opposition to no-excuse absentee voting has grown a bit since then.)
However, just because voters want the option to vote absentee doesn’t mean they’ll actually do it. The ABC News/Washington Post poll also found that 59 percent of Americans would prefer to vote in person in this year’s election, while 38 percent would prefer to vote by mail. And there were stark differences along demographic lines, which could put heightened stress on our democracy this November.
For instance, Republican respondents told ABC News/The Washington Post that they preferred to vote in person, 79 percent to 20 percent. But Democratic respondents preferred to vote by mail, 51 percent to 46 percent. That could mean that votes cast in person will skew toward Republicans this fall, while mail-in votes skew toward Democrats. And since in-person votes are typically reported first on election night, that could mean that initial results on Nov. 3 will be overly favorable to Trump — perhaps causing him to claim victory prematurely. But Biden could actually turn out to be the winner days after Election Day in this scenario, as mailed ballots are counted and Democratic votes are added to the till. This could cause a national crisis if Trump decries those late-counted ballots as fraudulent or if he refuses to concede.
In addition, the poll found that college-educated and wealthier voters were more comfortable voting by mail. Specifically, respondents with postgraduate degrees said they preferred voting by mail 54 percent to 44 percent; those with just a four-year college degree were split 49 percent to 49 percent. Respondents with less than four years of college said they preferred to vote in person, 59 percent to 37 percent, and respondents with a high school diploma or less opted for in-person voting 68 percent to 29 percent. As a result, underprivileged voters could be disproportionately affected if the pandemic forces the closure or consolidation of polling places this November, either putting them at heightened risk of contracting COVID-19 while waiting in line or disenfranchising them altogether.
Other polling bites
According to the Kaiser Family Foundation, 60 percent of parents with schoolchildren wanted schools to wait to restart in-person classes, while only 34 percent wanted schools to reopen sooner. This preference was largely driven by parents of color, 91 percent of whom were worried that their child will catch COVID-19 if schools reopen. Only 55 percent of white parents shared that concern.
A Morning Consult poll found that the vast majority of Americans — 72 percent — supported mandating face masks in public spaces in their state (and imposing penalties for those who refused to do so). Despite perceptions that wearing a mask has become a partisan issue, even Republicans supported the policy, 58 percent to 35 percent.
According to another part of the ABC News/Washington Post poll, a record 69 percent of Americans said that they think white and nonwhite people do not receive equal treatment in the criminal justice system; only 26 percent said they do receive equal treatment. Black respondents have long held this view in ABC News/Washington Post polling, but for the first time, so did a majority of white people.
As evidenced by the fact that Opening Day was yesterday (four months late), this year’s Major League Baseball season will look a little different from usual. Most obviously, the season will only have 60 games — down from the standard 162 — but it will still crown a World Series champion. According to Morning Consult, though, a plurality of fans think the 2020 champion deserves an asterisk. Forty-four percent of baseball fans said that winning the World Series in a shortened season will be less meaningful than winning after a full regular season, while 35 percent believed it would be just as meaningful. (In reality, a 60-game season isn’t that much worse at assessing a team’s true talent than a 162-game season — but neither is perfect.)
Trump approval
According to FiveThirtyEight’s presidential approval tracker, 40.3 percent of Americans approve of the job Trump is doing as president, while 55.6 percent disapprove (a net approval rating of -15.3 points). At this time last week, 40.3 percent approved and 55.6 percent disapproved (a net approval rating of -15.2 points). One month ago, Trump had an approval rating of 41.0 percent and a disapproval rating of 55.3 percent, for a net approval rating of -14.3 points.
Generic ballot
In our average of polls of the generic congressional ballot, Democrats currently lead by 8.2 percentage points (49.4 percent to 41.2 percent). A week ago, Democrats led Republicans by 8.3 points (49.0 percent to 40.7 percent). At this time last month, voters preferred Democrats by 8.2 points (48.7 percent to 40.5 percent).
Check out all the polls we’ve been collecting ahead of the 2020 elections.