fivethirthyeight--2020-08-07--The Best Players Opting Out Of The NFL, NBA, WNBA, NHL And MLB In 2020

Facing the uncertainty of playing sports in a pandemic , which can mean risking one ’ s health or being sealed off in a bubble away from home and family , every pro athlete has had to make a difficult choice : return to the game or opt to sit out part or all of a season ?
Among the pro leagues that have restarted , most players have chosen to play — but not all .
According to a running count maintained by ESPN ’ s Stats & Information Group , 128 players in five leagues had opted out @ @ @ @ @ @ @ And among those in the NFL , NBA , WNBA , NHL and MLB , a surprising number are stars — or at least they have been productive players in recent seasons .
To get a sense of just how much talent each league is or will be missing , I calculated the leaguewide percentile rank for every opt-out player according to our value metric of choice in each sport .
I did this across two windows of time : the most recent season and over the past three seasons .
Overall , @ @ @ @ @ @ @ 10th of players in their respective sports ( over the past three seasons ) — and 55 overall who ranked among the top third — have opted out , which underscores just how many good players are watching from the metaphorical sidelines during the pandemic .
The NFL has had a lot of opt-outs — 66 in total — in part because the league ’ s player pool is so large .
But that list also includes plenty of big names by Approximate Value .
New York Jets linebacker C.J .
Mosley was @ @ @ @ @ @ @ 2 AV ) last season because of a groin injury , but he was a four-time Pro Bowler before that , and he tied for 50th in total AV among NFL players over the last three seasons .
Mosley said he opted out to keep from putting his family at risk .
Also among top NFL opt-outs were guard Larry Warford , who ’ s been named to the Pro Bowl three years running , and Nate Solder , one of the best offensive tackles of the past decade .
And the most @ @ @ @ @ @ @ out in 2020 is Pro Bowl linebacker Dont ’ a Hightower , who leads a group of eight New England Patriots that have opted out of the season .
Aside from the Patriots , no other team in the five leagues we looked at had more than five players opt out of playing in 2020 .
Fewer NBA opt-outs have been high-impact producers over the past few seasons , but the headliners above do have star power .
Washington Wizards swingman Bradley Beal was tied as the 40th best player in the league @ @ @ @ @ @ @ 15th over the past three seasons .
Beal ’ s decision was about more than COVID-19 ; he was also recovering from a rotator cuff injury that had hampered him all season .
“ This was a difficult decision and one that I did not take lightly as the leader of this team , ” Beal said .
“ I wanted to help my teammates compete for a playoff spot in Orlando , but also understand that this will be best for all of us in the long term.
” Spencer Dinwiddie of @ @ @ @ @ @ @ the Wizards ranked as the second- and third-best players to opt out , regardless of the time frame .
Dinwiddie tested positive for the coronavirus in June and was held out for precautionary reasons ; Bertāns opted out to avoid injury heading into free agency .
The WNBA is the league with the most talent withdrawn from the 2020 season , by far .
If we compare across sports , no other league comes close to matching the 26 percent share of opt-outs among players who ranked in the top 10th of the @ @ @ @ @ @ @ seasons : The biggest name in any sport to opt out is Delle Donne , who was the best player in the WNBA last season .
( She ’ s one of four Washington Mystics to miss the season , along with Tina Charles , LaToya Sanders and Natasha Cloud — all of whom ranked among the league ’ s Top 50 players over the previous three seasons . )
But Jonquel Jones of the Connecticut Sun was the second-most valuable player in the WNBA last season , and she also decided to @ @ @ @ @ @ @ .
“ After careful thought and consideration , I ’ ve decided to forgo the upcoming WNBA season and use this time to focus on personal , social and familial growth , ” Jones said .
In terms of the player pool , the WNBA is a much smaller league than the other pro sports , so the fact that 11 players are sitting out after ranking among the top third of the WNBA over the past three seasons is striking .
At the other end of the spectrum from the WNBA , @ @ @ @ @ @ @ barely seen any moderate-profile players opt out , much less high-profile ones .
The best player by goals above replacement this season who chose not to return to hockey ’ s bubble was defenseman Travis Hamonic of the Calgary Flames , who didn ’ t even rank among the top 400 players in the league this year .
Chicago Blackhawks forward Andrew Shaw and Edmonton Oilers blueliner Mike Green fared better when ranked over the previous three seasons , but neither cracked the top 300 .
And overall , only these eight NHL @ @ @ @ @ @ @ out , period .
( Perhaps contributing to the decision for most to play were the league ’ s protocols and location in Canada ; there have been no positive tests recorded in the NHL ’ s two bubbles in Toronto and Edmonton , Alberta . )
In baseball , the best player to opt out ( whether looking at last season or a three-year window ) is center fielder Lorenzo Cain of the Milwaukee Brewers , who ranked 178th in wins above replacement last year and 34th from 2017 through 2019 .
@ @ @ @ @ @ @ unknowns surrounding our game at this time , I feel that this is the best decision for me , my wife and our three kids , ” Cain said in a statement last week .
David Price , who was set to begin his first year with the Dodgers after being acquired from the Boston Red Sox , is the second-best MLB player from last season to sit out for 2020 .
No .
2 over the past three seasons is Buster Posey of the San Francisco Giants , the future Hall of @ @ @ @ @ @ @ July after he and his wife adopted premature twin girls .
Also among the Top 10 in MLB : Atlanta ’ s Nick Markakis , who subsequently opted back in , and New York Mets designated hitter Yoenis Céspedes , whose departure caused drama last week when he didn ’ t tell the team about his decision and failed to show up for a game .
All in all , it ’ s been a blessing for fans to be able to see sports come back over the past few weeks and to @ @ @ @ @ @ @ the world perform yet again .
But the level of play has been poorer for the lack of these stars , most of whom chose to sit out the return over concerns for their health or that of their families .
Fans shouldn ’ t fault them for that , and they should wish them the best when they do come back to play again .
Until then , their absences will be yet another factor that feels “ off ” about sports as leagues try to play on through the pandemic .

Facing the uncertainty of playing sports in a pandemic, which can mean risking one’s health or being sealed off in a bubble away from home and family, every pro athlete has had to make a difficult choice: return to the game or opt to sit out part or all of a season? Among the pro leagues that have restarted, most players have chosen to play — but not all.
According to a running count maintained by ESPN’s Stats & Information Group, 128 players in five leagues had opted out by Thursday’s NFL deadline. And among those in the NFL, NBA, WNBA, NHL and MLB, a surprising number are stars — or at least they have been productive players in recent seasons.
To get a sense of just how much talent each league is or will be missing, I calculated the leaguewide percentile rank for every opt-out player according to our value metric of choice in each sport. I did this across two windows of time: the most recent season and over the past three seasons. Overall, 20 athletes who ranked among the top 10th of players in their respective sports (over the past three seasons) — and 55 overall who ranked among the top third — have opted out, which underscores just how many good players are watching from the metaphorical sidelines during the pandemic.
Which NFL stars have opted out? Best NFL players to opt out of the 2020 season due to COVID-19 concerns, based on Approximate Value (AV) over the past three seasons (2017-19) Most Recent Season Last 3 Seasons Name Team AV Percentile AV Percentile C.J. Mosley Jets 2 43 32 98 Larry Warford Free agent 9 92 30 98 Nate Solder Giants 9 92 30 98 Dont’a Hightower Patriots 17 100 28 97 Eddie Goldman Bears 7 83 24 95 Star Lotulelei Bills 10 94 23 94 Marcus Cannon Patriots 7 83 20 91 Michael Pierce Vikings 8 88 19 89 L. Duvernay-Tardif Chiefs 7 83 16 86 Patrick Chung Patriots 5 70 15 84 Sources: ESPN Stats & Information Group, Pro-Football-Reference.com
The NFL has had a lot of opt-outs — 66 in total — in part because the league’s player pool is so large. But that list also includes plenty of big names by Approximate Value. New York Jets linebacker C.J. Mosley was limited to just two games (and 2 AV) last season because of a groin injury, but he was a four-time Pro Bowler before that, and he tied for 50th in total AV among NFL players over the last three seasons. Mosley said he opted out to keep from putting his family at risk. Also among top NFL opt-outs were guard Larry Warford, who’s been named to the Pro Bowl three years running, and Nate Solder, one of the best offensive tackles of the past decade. And the most valuable player from last season to sit out in 2020 is Pro Bowl linebacker Dont’a Hightower, who leads a group of eight New England Patriots that have opted out of the season. Aside from the Patriots, no other team in the five leagues we looked at had more than five players opt out of playing in 2020.
Which NBA stars have opted out? Best NBA players to opt out of the 2020 restart due to COVID-19 concerns, based on RAPTOR wins above replacement (WAR) over the past three seasons (2017-18 through 2019-20) Most Recent Season Last 3 Seasons Name Team WAR Percentile WAR Percentile Bradley Beal Wizards 4.6 93 23.6 98 Spencer Dinwiddie Nets 4.2 90 14.2 94 Dāvis Bertāns Wizards 4.2 90 12.4 92 Trevor Ariza Trail Blazers 2.1 74 5.3 79 Willie Cauley-Stein Mavericks 1.9 72 5.2 79 Thabo Sefolosha Rockets 0.4 48 4.4 76 DeAndre Jordan Nets 1.8 70 4.2 75 Wilson Chandler Nets 0.4 49 3.3 72 Avery Bradley Lakers 1.1 61 2.3 67 Taurean Prince Nets 0.8 56 1.1 60 Sources: ESPN Stats & Information Group, Basketball-Reference.com, NBA Advanced Stats
Fewer NBA opt-outs have been high-impact producers over the past few seasons, but the headliners above do have star power. Washington Wizards swingman Bradley Beal was tied as the 40th best player in the league by RAPTOR WAR this season and ranks 15th over the past three seasons. Beal’s decision was about more than COVID-19; he was also recovering from a rotator cuff injury that had hampered him all season. “This was a difficult decision and one that I did not take lightly as the leader of this team,” Beal said. “I wanted to help my teammates compete for a playoff spot in Orlando, but also understand that this will be best for all of us in the long term.” Spencer Dinwiddie of the Brooklyn Nets and Dāvis Bertāns of the Wizards ranked as the second- and third-best players to opt out, regardless of the time frame. Dinwiddie tested positive for the coronavirus in June and was held out for precautionary reasons; Bertāns opted out to avoid injury heading into free agency.
Which WNBA stars have opted out? Best WNBA players to opt out of the 2020 season due to COVID-19 concerns, based on consensus wins generated (CWG) over the past three seasons (2017-19) Most Recent Season Last 3 Seasons Name Team CWG Percentile CWG Percentile Elena Delle Donne* Mystics 6.6 100 16.5 100 Jonquel Jones Sun 5.0 99 14.7 99 Liz Cambage Aces 4.0 95 9.6 96 Tiffany Hayes Dream 1.5 64 8.8 94 Kristi Toliver Sparks 3.1 88 8.4 93 Tina Charles Mystics 1.0 56 7.9 91 Chiney Ogwumike Sparks 2.7 83 7.1 88 LaToya Sanders Mystics 3.1 87 6.6 87 Renee Montgomery Dream 1.2 61 6.6 87 Natasha Cloud Mystics 2.7 82 4.8 81 *Delle Donne did not officially opt out with the WNBA, which did not grant her a medical exemption, but she is not expected to play this season. CWG is based on a combination of win shares and player efficiency rating. Sources: ESPN Stats & Information Group, Basketball-Reference.com
The WNBA is the league with the most talent withdrawn from the 2020 season, by far. If we compare across sports, no other league comes close to matching the 26 percent share of opt-outs among players who ranked in the top 10th of the WNBA in value over the past three seasons:
Which sport is missing the most star power? Share of opt-outs by leaguewide percentile rank in value over the previous three seasons for major American pro sports leagues Share of opt-outs among players in league’s… Sport Top 10% Top 25% Top 33% Top 50% WNBA 26% 17% 14% 11% NBA 4 4 4 3 NFL 2 2 2 2 MLB 2 2 2 1 NHL 0 0 1 1 Sources: ESPN Stats & Information Group, Sports-Reference.com, FanGraphs
The biggest name in any sport to opt out is Delle Donne, who was the best player in the WNBA last season. (She’s one of four Washington Mystics to miss the season, along with Tina Charles, LaToya Sanders and Natasha Cloud — all of whom ranked among the league’s Top 50 players over the previous three seasons.) But Jonquel Jones of the Connecticut Sun was the second-most valuable player in the WNBA last season, and she also decided to sit out the season over COVID-19 concerns. “After careful thought and consideration, I’ve decided to forgo the upcoming WNBA season and use this time to focus on personal, social and familial growth,” Jones said. In terms of the player pool, the WNBA is a much smaller league than the other pro sports, so the fact that 11 players are sitting out after ranking among the top third of the WNBA over the past three seasons is striking.
Which NHL stars have opted out? NHL players to opt out of the 2020 restart due to COVID-19 concerns, based on goals above replacement (GAR) over the past three seasons (2017-18 through 2019-20) Most Recent Season Last 3 seasons Name Team GAR Percentile GAR Percentile Andrew Shaw Blackhawks 0.6 36 12.6 75 Mike Green Oilers -0.9 5 12.1 74 Travis Hamonic Flames 2.3 56 8.7 68 Sven Bärtschi Canucks -0.1 17 8.1 66 Roman Polák Stars 0.2 26 5.9 61 Karl Alzner Canadiens -0.3 12 0.7 36 Steven Kampfer Bruins 0.4 34 0.3 30 Zach Trotman Penguins -0.1 17 -0.1 19 Sources: ESPN Stats & Information Group, Hockey-Reference.com
At the other end of the spectrum from the WNBA, we have the NHL, which has barely seen any moderate-profile players opt out, much less high-profile ones. The best player by goals above replacement this season who chose not to return to hockey’s bubble was defenseman Travis Hamonic of the Calgary Flames, who didn’t even rank among the top 400 players in the league this year. Chicago Blackhawks forward Andrew Shaw and Edmonton Oilers blueliner Mike Green fared better when ranked over the previous three seasons, but neither cracked the top 300. And overall, only these eight NHL players in ESPN’s data opted out, period. (Perhaps contributing to the decision for most to play were the league’s protocols and location in Canada; there have been no positive tests recorded in the NHL’s two bubbles in Toronto and Edmonton, Alberta.)
Which MLB stars have opted out? Best MLB players to opt out of the 2020 season because of COVID-19 concerns, based on wins above replacement (WAR) over the past three seasons (2017-19) Most Recent Season Last 3 Seasons Name Team WAR Percentile WAR Percentile Lorenzo Cain Brewers 2.2 87 13.2 98 Buster Posey Giants 1.4 79 8.4 95 David Price Dodgers 2.1 86 7.0 94 Mike Leake Diamondbacks 1.1 73 5.6 91 Ryan Zimmerman Nationals 0.2 50 4.5 87 Nick Markakis* Braves 0.7 66 4.1 86 Collin McHugh Red Sox 0.4 59 3.3 83 Yoenis Céspedes Mets — — 2.6 79 Joe Smith Astros 0.5 62 2.3 77 Welington Castillo Nationals -0.6 7 1.8 74 *Opted out before the season but decided to return during the season. Sources: ESPN Stats & Information Group, Baseball-Reference.com, FanGraphs
In baseball, the best player to opt out (whether looking at last season or a three-year window) is center fielder Lorenzo Cain of the Milwaukee Brewers, who ranked 178th in wins above replacement last year and 34th from 2017 through 2019. “With all of the uncertainty and unknowns surrounding our game at this time, I feel that this is the best decision for me, my wife and our three kids,” Cain said in a statement last week. David Price, who was set to begin his first year with the Dodgers after being acquired from the Boston Red Sox, is the second-best MLB player from last season to sit out for 2020. No. 2 over the past three seasons is Buster Posey of the San Francisco Giants, the future Hall of Fame catcher who opted out in early July after he and his wife adopted premature twin girls. Also among the Top 10 in MLB: Atlanta’s Nick Markakis, who subsequently opted back in, and New York Mets designated hitter Yoenis Céspedes, whose departure caused drama last week when he didn’t tell the team about his decision and failed to show up for a game.
All in all, it’s been a blessing for fans to be able to see sports come back over the past few weeks and to watch some of the greatest athletes in the world perform yet again. But the level of play has been poorer for the lack of these stars, most of whom chose to sit out the return over concerns for their health or that of their families. Fans shouldn’t fault them for that, and they should wish them the best when they do come back to play again. Until then, their absences will be yet another factor that feels “off” about sports as leagues try to play on through the pandemic.


fivethirthyeight--2020-08-07--Can You Reach The Beach?

Can You Reach The Beach?

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 .
The Riddler Isles are a chain of small islands on the Constant Sea .
One of them , Euclid Island , is perfectly rectangular and measures 3 miles long by 2 miles wide .
While walking across the island on a recent vacation , I was often interested in locating the point on the shore that was nearest to my current position .
One morning , I realized that from where I was standing there were two distinct points on the shore that were both the closest such points .
@ @ @ @ @ @ @ only to realize it had been made years earlier .
It turned out I was on a hiking trail that connected all such locations on the island — those with multiple nearest points on the shore .
What is the total length of this trail on Euclid Island ?
Extra credit : Al-Battani Island is another of the Riddler Isles , but it ’ s elliptical rather than rectangular .
Al-Battani Island ’ s major axis is 3 miles long , while its minor axis is 2 miles long .
Like Euclid Island @ @ @ @ @ @ @ that connects all locations with multiple nearest points on the shore .
What is the total length of this trail on Al-Battani Island ?
This week ’ s Riddler Classic is inspired by Kareem Carr : We usually think of addition as an operation applied to a field like the rational numbers or the real numbers .
And there is good reason for that — as Kareem says , “ Mathematicians have done all the hard work of figuring out how to make calculations track with reality .
They kept modifying and refining @ @ @ @ @ @ @ .
It took centuries of brilliant minds to do this !
” Now suppose we defined addition another ( admittedly less useful ) way , using a classic model organism : the nematode .
To compute the sum of x and y , you combine groups of x and y nematodes and leave them for 24 hours .
When you come back , you count up how many you have — and that ’ s the sum !
It turns out that , over the course of 24 hours , the nematodes pair @ @ @ @ @ @ @ offspring 50 percent of the time .
( If you have an odd number of nematodes , they will still pair up , but one will be left out . )
So if you want to compute 1+1 , half the time you ’ ll get 2 and half the time you ’ ll get 3 .
If you compute 2+2 , 25 percent of the time you get 4 , 50 percent of the time you ’ ll get 5 , and 25 percent of the time you ’ ll get 6 @ @ @ @ @ @ @ , let ’ s define exponentiation for sums of nematodes .
Raising a sum to a power means leaving that sum of nematodes for the number of days specified by the exponent .
With this number system , what is the expected value of ( 1+1 ) 4 ?
Extra credit : As N gets larger and larger , what does the expected value of ( 1+1 ) N approach ?
Congratulations to 👏 David Daly 👏 of Glendale , Arizona , winner of last week ’ s Riddler Express .
Last week @ @ @ @ @ @ @ round of the Riddler Rock , Paper , Scissors tournament .
The rules were simple : Rock beat scissors , scissors beat paper , and paper beat rock .
Moreover , the game was “ sudden death , ” so the first person to win a single round was immediately declared the grand champion .
( If both players chose the same object , then you simply played another round . )
Fortunately , your opponent was someone you had studied well .
Based on the motion of their arm , you could @ @ @ @ @ @ @ play rock or paper with equal probability , ( 2 ) play paper or scissors with equal probability or ( 3 ) play rock or scissors with equal probability .
( Every round fell into one of these three categories . )
If you strategized correctly , what were your chances of winning the tournament ?
Well , if you strategized like solver Carenne Ludeña , you won the tournament a whopping 100 percent of the time .
When your opponent played rock or paper with equal probability , you knew with certainty @ @ @ @ @ @ @ and that meant if you played paper you couldn ’ t lose .
You also had a 50 percent chance of winning the round , i.e.
, whenever your opponent played rock .
Each of the three scenarios listed in the problem had a corresponding response .
As we just said , when your opponent played rock or paper , you should play paper .
When your opponent played paper or scissors , you should play scissors .
And when your opponent played rock or scissors , you should play rock .
With @ @ @ @ @ @ @ the time , draw half the time , and lose … never .
At this point , many solvers recognized this meant you were guaranteed to win the tournament eventually , as the probability of drawing infinitely many games was vanishingly small .
Solver Stephen Paisley formally demonstrated this with the geometric series 1/2 + 1/4 + 1/8 + 1/16 + … ( your chances of having won in each successive round ) , which indeed sums to 1 , or 100 percent .
Finally , as some readers observed , the original @ @ @ @ @ @ @ When you were told that your opponent would “ play rock or paper with equal probability , ” most solvers assumed that meant both probabilities were 50 percent , rather than being equal but less than 50 percent .
While that was the intent of the puzzle , it wasn ’ t explicitly stated .
If these equal probabilities were close to 50 percent , then your strategy wouldn ’ t change ( although your chances of winning the tournament would go down ) .
For example , if you knew there was @ @ @ @ @ @ @ play rock , a 40 percent chance they ’ d play paper and a 20 percent chance they ’ d play scissors , then your best bet would still be to play paper .
But instead of always winning the tournament , your chances of victory would be 0.4 + 0.42 + 0.43 + … , or 2/3 .
But once the equal probabilities dipped below one-third , you needed to adjust your strategy .
Suppose you knew there was a 10 percent chance your opponent would play rock , a 10 percent @ @ @ @ @ @ @ an 80 percent chance they ’ d play scissors .
Now your best bet was to play rock , and your chances were 0.8 + 0.8 ( 0.1 ) + 0.8 ( 0.1 ) 2 + 0.8 ( 0.1 ) 3 + … , or 8/9 .
Any which way , it seems like you ’ re pretty good at rock , paper , scissors .
My winning move against you would be not to play .
Congratulations to 👏 Rick 👏 of Cloverdale , California , winner of last week ’ s @ @ @ @ @ @ @ inaugural graduating class of Riddler High School , more than 100 students strong , received their diplomas .
They were lined up along the circumference of the giant circular mosaic on the plaza in front of the school , while their principal , Dr. Olivia Rhodes , stood atop a tall stepladder in the middle .
Dr. Rhodes observed that every one of the N graduates — all except Val , the valedictorian — was standing in the wrong place .
Moreover , Dr. Rhodes said that no two graduates were in the @ @ @ @ @ @ @ ( Two graduates would be in the correct position relative to each other if , for example , graduate A was supposed to be 17 positions counterclockwise of graduate B and was indeed 17 positions counterclockwise of graduate B — even if both graduates were in the wrong positions . )
But Val corrected Dr. Rhodes .
Given the fact that there were N students , there must have been at least two who were in the correct position relative to each other .
Given that there were more than 100 graduates , @ @ @ @ @ @ @ who were posing for the class photo ?
That was a lot of information to take in .
To summarize , there were N students arranged in a circle .
Exactly one of them was in the correct position , while N−1 were not .
Furthermore , this value of N guaranteed that at least two students were in the correct position relative to each other .
The puzzle ’ s submitter , Dave Moran , solved this by looking at how far apart each student was from their correct position ( say @ @ @ @ @ @ @ a function of their correct position , x.
Let ’ s call this function E ( x ) .
So because Val was correctly in the first position , E ( 1 ) = 0 , meaning she was zero spots away from her correct position .
But E ( 2 ) , E ( 3 ) , and so on , all the way to E ( N ) , were nonzero , since all the other students were in the wrong position .
But what if no students had been in @ @ @ @ @ @ @ ?
Well , imagine if there had been two students with correct positions a and b , such that E ( a ) = E ( b ) .
That would have meant they were shifted the same number of spots clockwise from their correct positions , and so they would have been in the correct position relative to each other !
To avoid this situation , no two students could have had the same value of E ( x ) .
Now recall that there were N students .
That meant E @ @ @ @ @ @ @ N distinct values , from 0 to N−1 .
And because no two students could have the same value of E ( x ) , every value from 0 to N−1 had to be taken by one and only one student .
We ’ re getting there — but first , a slight detour .
Solver Eric Dallal looked at the sum of all the errors , E ( 1 ) + E ( 2 ) + E ( 3 ) + … + E ( N ) .
If you started with @ @ @ @ @ @ @ , this sum would be zero .
You could also swap different pairs of students over and over again to get any desired overall arrangement of the class .
But every time you swapped two students , the sum either didn ’ t change , or it increased or decreased by N. And that meant this sum had to be a multiple of N. Okay , we ’ re in the home stretch .
For there to have been no students who were in the correct position relative to each other , we @ @ @ @ @ @ @ that is , the sum of the numbers from 0 to N−1 , or N ( N−1 ) /2 — to be a multiple of N. This was true whenever N was odd .
To summarize , it was only possible to arrange students so that no two were in the correct position relative to each other when N was odd .
Want an example of such an arrangement ?
Well , you ’ re in luck , thanks to solver Inga .
Consider a class with 101 students — an odd number @ @ @ @ @ @ @ , but suppose everyone else was reflected across the line connecting Val and Dr. Rhodes .
If the salutatorian was supposed to be directly clockwise from Val , they now found themselves in position 101 , meaning E ( 2 ) was 101−2 , or 99 .
Working your way around the circle , you ’ d see that each student indeed had a unique value of E ( x ) .
At last , we return to the original question that was posed .
What was the smallest class size such that @ @ @ @ @ @ @ been in the correct relative position ?
That would be the smallest even number greater than 100 , and so the answer was 102 .
In addition to this week ’ s winner , Val from the inaugural graduating class really knew her number theory .
The other seniors , including Zach , need to step up their game .
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 @ @ @ @ @ @ @ 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
The Riddler Isles are a chain of small islands on the Constant Sea. One of them, Euclid Island, is perfectly rectangular and measures 3 miles long by 2 miles wide. While walking across the island on a recent vacation, I was often interested in locating the point on the shore that was nearest to my current position.
One morning, I realized that from where I was standing there were two distinct points on the shore that were both the closest such points. I was excited by my discovery, only to realize it had been made years earlier. It turned out I was on a hiking trail that connected all such locations on the island — those with multiple nearest points on the shore.
What is the total length of this trail on Euclid Island?
Extra credit: Al-Battani Island is another of the Riddler Isles, but it’s elliptical rather than rectangular. Al-Battani Island’s major axis is 3 miles long, while its minor axis is 2 miles long. Like Euclid Island, Al-Battani Island has a hiking trail that connects all locations with multiple nearest points on the shore. What is the total length of this trail on Al-Battani Island?
The solution to this Riddler Express can be found in the following week’s column.
Riddler Classic
This week’s Riddler Classic is inspired by Kareem Carr:
We usually think of addition as an operation applied to a field like the rational numbers or the real numbers. And there is good reason for that — as Kareem says, “Mathematicians have done all the hard work of figuring out how to make calculations track with reality. They kept modifying and refining the number system until everything worked out. It took centuries of brilliant minds to do this!”
Now suppose we defined addition another (admittedly less useful) way, using a classic model organism: the nematode. To compute the sum of x and y, you combine groups of x and y nematodes and leave them for 24 hours. When you come back, you count up how many you have — and that’s the sum!
It turns out that, over the course of 24 hours, the nematodes pair up, and each pair has one offspring 50 percent of the time. (If you have an odd number of nematodes, they will still pair up, but one will be left out.) So if you want to compute 1+1, half the time you’ll get 2 and half the time you’ll get 3. If you compute 2+2, 25 percent of the time you get 4, 50 percent of the time you’ll get 5, and 25 percent of the time you’ll get 6.
While we’re at it, let’s define exponentiation for sums of nematodes. Raising a sum to a power means leaving that sum of nematodes for the number of days specified by the exponent.
With this number system, what is the expected value of (1+1)4?
Extra credit: As N gets larger and larger, what does the expected value of (1+1)N approach?
The solution to this Riddler Classic can be found in the following week’s column.
Solution to last week’s Riddler Express
Congratulations to 👏 David Daly 👏 of Glendale, Arizona, winner of last week’s Riddler Express.
Last week, you made it to the final round of the Riddler Rock, Paper, Scissors tournament.
The rules were simple: Rock beat scissors, scissors beat paper, and paper beat rock. Moreover, the game was “sudden death,” so the first person to win a single round was immediately declared the grand champion. (If both players chose the same object, then you simply played another round.)
Fortunately, your opponent was someone you had studied well. Based on the motion of their arm, you could tell whether they would (1) play rock or paper with equal probability, (2) play paper or scissors with equal probability or (3) play rock or scissors with equal probability. (Every round fell into one of these three categories.)
If you strategized correctly, what were your chances of winning the tournament?
Well, if you strategized like solver Carenne Ludeña, you won the tournament a whopping 100 percent of the time. When your opponent played rock or paper with equal probability, you knew with certainty they wouldn’t play scissors, and that meant if you played paper you couldn’t lose. You also had a 50 percent chance of winning the round, i.e., whenever your opponent played rock.
Each of the three scenarios listed in the problem had a corresponding response. As we just said, when your opponent played rock or paper, you should play paper. When your opponent played paper or scissors, you should play scissors. And when your opponent played rock or scissors, you should play rock. With this strategy, you would win half the time, draw half the time, and lose … never.
At this point, many solvers recognized this meant you were guaranteed to win the tournament eventually, as the probability of drawing infinitely many games was vanishingly small. Solver Stephen Paisley formally demonstrated this with the geometric series 1/2 + 1/4 + 1/8 + 1/16 + … (your chances of having won in each successive round), which indeed sums to 1, or 100 percent.
Finally, as some readers observed, the original puzzle was slightly ambiguous as written. When you were told that your opponent would “play rock or paper with equal probability,” most solvers assumed that meant both probabilities were 50 percent, rather than being equal but less than 50 percent. While that was the intent of the puzzle, it wasn’t explicitly stated.
If these equal probabilities were close to 50 percent, then your strategy wouldn’t change (although your chances of winning the tournament would go down). For example, if you knew there was a 40 percent chance your opponent would play rock, a 40 percent chance they’d play paper and a 20 percent chance they’d play scissors, then your best bet would still be to play paper. But instead of always winning the tournament, your chances of victory would be 0.4 + 0.42 + 0.43 + …, or 2/3.
But once the equal probabilities dipped below one-third, you needed to adjust your strategy. Suppose you knew there was a 10 percent chance your opponent would play rock, a 10 percent chance they’d play paper and an 80 percent chance they’d play scissors. Now your best bet was to play rock, and your chances were 0.8 + 0.8(0.1) + 0.8(0.1)2 + 0.8(0.1)3 + …, or 8/9.
Any which way, it seems like you’re pretty good at rock, paper, scissors. My winning move against you would be not to play.
Solution to last week’s Riddler Classic
Congratulations to 👏 Rick 👏 of Cloverdale, California, winner of last week’s Riddler Classic.
Last week, the inaugural graduating class of Riddler High School, more than 100 students strong, received their diplomas. They were lined up along the circumference of the giant circular mosaic on the plaza in front of the school, while their principal, Dr. Olivia Rhodes, stood atop a tall stepladder in the middle.
Dr. Rhodes observed that every one of the N graduates — all except Val, the valedictorian — was standing in the wrong place. Moreover, Dr. Rhodes said that no two graduates were in the correct position relative to each other. (Two graduates would be in the correct position relative to each other if, for example, graduate A was supposed to be 17 positions counterclockwise of graduate B and was indeed 17 positions counterclockwise of graduate B — even if both graduates were in the wrong positions.)
But Val corrected Dr. Rhodes. Given the fact that there were N students, there must have been at least two who were in the correct position relative to each other.
Given that there were more than 100 graduates, what was the minimum number of graduates who were posing for the class photo?
That was a lot of information to take in. To summarize, there were N students arranged in a circle. Exactly one of them was in the correct position, while N−1 were not. Furthermore, this value of N guaranteed that at least two students were in the correct position relative to each other.
The puzzle’s submitter, Dave Moran, solved this by looking at how far apart each student was from their correct position (say, in the clockwise direction) as a function of their correct position, x. Let’s call this function E(x). So because Val was correctly in the first position, E(1) = 0, meaning she was zero spots away from her correct position. But E(2), E(3), and so on, all the way to E(N), were nonzero, since all the other students were in the wrong position.
But what if no students had been in the correct position relative to each other? Well, imagine if there had been two students with correct positions a and b, such that E(a) = E(b). That would have meant they were shifted the same number of spots clockwise from their correct positions, and so they would have been in the correct position relative to each other! To avoid this situation, no two students could have had the same value of E(x).
Now recall that there were N students. That meant E(x) could take on exactly N distinct values, from 0 to N−1. And because no two students could have the same value of E(x), every value from 0 to N−1 had to be taken by one and only one student.
We’re getting there — but first, a slight detour. Solver Eric Dallal looked at the sum of all the errors, E(1) + E(2) + E(3) + … + E(N). If you started with a correct arrangement of the entire class, this sum would be zero. You could also swap different pairs of students over and over again to get any desired overall arrangement of the class. But every time you swapped two students, the sum either didn’t change, or it increased or decreased by N. And that meant this sum had to be a multiple of N.
Okay, we’re in the home stretch. For there to have been no students who were in the correct position relative to each other, we needed the sum of the errors — that is, the sum of the numbers from 0 to N−1, or N(N−1)/2 — to be a multiple of N. This was true whenever N was odd.
To summarize, it was only possible to arrange students so that no two were in the correct position relative to each other when N was odd.
Want an example of such an arrangement? Well, you’re in luck, thanks to solver Inga. Consider a class with 101 students — an odd number. Val was in the correct position, but suppose everyone else was reflected across the line connecting Val and Dr. Rhodes. If the salutatorian was supposed to be directly clockwise from Val, they now found themselves in position 101, meaning E(2) was 101−2, or 99. Working your way around the circle, you’d see that each student indeed had a unique value of E(x).
At last, we return to the original question that was posed. What was the smallest class size such that at least two students had to have been in the correct relative position? That would be the smallest even number greater than 100, and so the answer was 102.
In addition to this week’s winner, Val from the inaugural graduating class really knew her number theory. The other seniors, including Zach, need to step up their game.
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--2020-08-10--Why GOP Senators Are Sticking With Trump — Even Though It Might Hurt Them In November

Arizona Sen. Martha McSally handily defeated her primary challenger Tuesday , with the help of an endorsement from President Trump .
Her chances of winning the general election are even more closely tied to Trump ’ s — and she ’ s embracing that connection .
She has attacked the “ liberal hack media ” for criticizing the president , predicted he will win Arizona in November and repeatedly appeared with him in his visits to the state , following her advisors ’ plan to stay close to Trump , even if that means going down with a sinking ship @ @ @ @ @ @ @ sinking feeling .
The U.S. Senate race in Arizona is rated as “ lean Democrat ” by most analysts .
And a recent Marist poll showed her doing even worse than Trump in the state , trailing Democrat Mark Kelly by 12 percentage points .
The same survey showed Trump trailing Democratic presidential candidate Joe Biden by 5 points .
Now that McSally has made it past a primary challenge , though , she might benefit from shifting gears .
Research suggests Republicans running for the House and Senate this year would benefit @ @ @ @ @ @ @ national Republican Party .
The problem is … that ’ s a lot harder than it used to be .
A little independence goes a long way Even in an age of nationalized politics , it still helps to have an independent identity from your party .
Voters tend to not like blind loyalty , and prefer representatives who are willing to compromise with the opposition party .
In 2018 , Republicans who were endorsed by Trump actually did worse in their general election races than Republicans the president ignored or disparaged , @ @ @ @ @ @ @ who opposed their party ’ s major legislative initiative , repealing Obamacare , did better than those who supported it .
One study even found that Trump rallies raised more money for Democrats than they did for Republicans .
The reason GOP senators could benefit from some independence from the White House is that drawing attention to a candidate ’ s ties to Trump helps polarize a race along the same lines of presidential job approval .
And that is a particularly troubling trend for a president with poor approval ratings .
For @ @ @ @ @ @ @ had more disapprovers than approvers in Arizona and other states with competitive Senate races , including Colorado and Maine .
Linked to Trump , the Republican senators in those states are now getting the same treatment ; McSally , Cory Gardner in Colorado and Susan Collins in Maine all have negative net approval ratings .
As political scientist ( and co-author of the study finding negative effects of Trump endorsements ) Andrew Ballard told me , “ Unpopular presidents probably need to be very strategic and judicious with their usage of their platform @ @ @ @ @ @ @ situations it can do more harm than good.
” Trump failed to follow this advice in 2018 and doesn ’ t seem to be paying it any more heed this year .
And most GOP senators are not effectively keeping their distance from Trump .
Senators up for reelection are siding with Trump Trump may not be able to resist intervening in Senate and House races , given his desire for being the center of attention .
But Republican legislators have choices about how to present themselves .
So far , they are @ @ @ @ @ @ @ Obamacare , opposed the president ’ s impeachment and has rarely publicly criticized the Trump administration .
That is a big shift from 2016 , when she chose not to endorse Trump and bashed his behavior .
Moreover , McSally has voted with Trump ’ s position 95 percent of the time over the last two congressional sessions — far more often than you ’ d expect based on Arizona ’ s politics .
In fact , in the Senate , McSally has the fourth highest “ Trump Plus-Minus ” score , which @ @ @ @ @ @ @ votes in line with the president ’ s position relative to what you would expect from that member based on the partisanship of their state or district .
Other Republican senators up for reelection this year have also remained loyal to Trump ’ s positions .
Gardner has voted with Trump 89 percent of the time during the 115th and 116th Congresses ( he has the second highest “ Trump Plus-Minus ” ) , Thom Tillis ( North Carolina ) with Trump 93 percent of the time , David Perdue ( Georgia ) @ @ @ @ @ @ @ ) 91 percent and Steve Daines ( Montana ) 86 percent .
The one partial exception is Collins , who has sided with Trump two-thirds of the time over the last two Congresses ( though that is still far more than expected based on Trump ’ s losing margin in Maine ) .
Collins has clearly tried to put some distance between herself and Trump as her reelection race draws nearer — but not too much .
She did not support Obamacare repeal , though she voted to acquit the president in his @ @ @ @ @ @ @ Supreme Court nominees .
She went from voting with Trump 77 percent of the time in the 115th Congress ( 2017-18 ) to only 46 percent in the 116th ( 2019-20 ) .
It ’ s been a tough balancing act that may end up pleasing no one .
Indeed , Collins has become the poster child for Republicans ’ unwillingness to seriously break with Trump .
She has been “ disappointed ” in Trump without taking action to restrain him so often that “ Saturday Night Live ” did a skit about @ @ @ @ @ @ @ have a chance to retain an independent reputation , something she ’ s cultivated for years by necessity in blue-ish Maine .
The problem is … that ’ s harder to do these days .
Why it ’ s become more difficult to break with the national party Many members of Congress used to have local reputations independent of their parties , presenting themselves as fighters for local interests and dollars in Washington .
Even if most voters hated Congress , they still liked their own representatives and senators .
But the long-term @ @ @ @ @ @ @ representatives through the lens of national and presidential politics ) and polarization ( voters see the parties as distinct and agree more with one side ) .
Voters learn less about their own legislators and more about the president , in part due to decreasing reliance on local news .
As a result , fewer voters split their tickets , voting for one party ’ s candidate for president and the other ’ s for Senate or the House .
Democrats have faced the same problem in trying to distinguish themselves from their @ @ @ @ @ @ @ of West Virginia ’ s Joe Manchin and Montana ’ s Jon Tester in the 2018 midterms , but Missouri ’ s Claire McCaskill , North Dakota ’ s Heidi Heitkamp and Indiana ’ s Joe Donnelly weren ’ t able to overcome the Republican lean of their states .
Manchin went so far as to appear in ads showing him shooting at policies he disliked and proclaiming “ for me , it ’ s all about West Virginia.
” He won a state that Hillary Clinton lost by more than 42 points @ @ @ @ @ @ @ senators to be seen as separated from their party ’ s president and his priorities .
So even if Republican senators do break with Trump , fewer voters now learn about it because they no longer see state-specific news .
Since voters tend to assume that partisans vote like their parties , voters are often unable to perceive moderate senators ’ divergent policy positions .
And legislators who do break with their party now face a risk of a primary challenger .
McSally won her 2018 Republican primary facing two candidates closely tied @ @ @ @ @ @ @ Ward .
In this year ’ s race to defend the seat she was appointed to , McSally this week fended off a primary challenge from Daniel McCarthy , who tried to build support from local pro-Trump groups .
“ More [ congressional ] members are running scared in the primaries , ” political scientist Sarah Treul told me .
“ Even if they ’ re actually not having quality challengers emerging , they ’ re afraid of it happening .
And I think a lot of them are spending time trying to @ @ @ @ @ @ @ ward off one of those challengers from even coming to the table.
” That usually means doing little to upset the party ’ s base by breaking with the president .
Now that primary season is coming to an end , will Republicans start separating themselves from Trump ?
Some probably don ’ t need to do so to win reelection .
Despite his national unpopularity , senators in more Trump-leaning states , such as Ernst in Iowa and Daines in Montana , may be able to survive with a standard partisan vote @ @ @ @ @ @ @ in Colorado and Tillis in North Carolina likely need to earn a substantial number of votes from Biden supporters to survive .
It ’ s just not clear whether they will break with Trump in public ways or whether late breaks would be enough to help them win .
That said , they may have one option to rally both the Republican faithful and a few swing voters .
It turns out some voters fear giving unified government to the president ’ s party and desire some balance .
If voters expect a @ @ @ @ @ @ @ likely to support Republicans in Congress , which could perhaps keep the Senate in GOP hands .
So terrible Trump polls could be turned into something useful by Republican senators .
They might eventually need to argue that , if Trump is going to lose , voters should trust them to serve as a check on the Democratic agenda .

Arizona Sen. Martha McSally handily defeated her primary challenger Tuesday, with the help of an endorsement from President Trump. Her chances of winning the general election are even more closely tied to Trump’s — and she’s embracing that connection. She has attacked the “liberal hack media” for criticizing the president, predicted he will win Arizona in November and repeatedly appeared with him in his visits to the state, following her advisors’ plan to stay close to Trump, even if that means going down with a sinking ship.
She may already be getting a sinking feeling. The U.S. Senate race in Arizona is rated as “lean Democrat” by most analysts. And a recent Marist poll showed her doing even worse than Trump in the state, trailing Democrat Mark Kelly by 12 percentage points. The same survey showed Trump trailing Democratic presidential candidate Joe Biden by 5 points.
Now that McSally has made it past a primary challenge, though, she might benefit from shifting gears. Research suggests Republicans running for the House and Senate this year would benefit from distancing themselves from Trump and the national Republican Party. The problem is … that’s a lot harder than it used to be.
A little independence goes a long way
Even in an age of nationalized politics, it still helps to have an independent identity from your party. Voters tend to not like blind loyalty, and prefer representatives who are willing to compromise with the opposition party. In 2018, Republicans who were endorsed by Trump actually did worse in their general election races than Republicans the president ignored or disparaged, all else being equal. And Republicans who opposed their party’s major legislative initiative, repealing Obamacare, did better than those who supported it. One study even found that Trump rallies raised more money for Democrats than they did for Republicans.
The reason GOP senators could benefit from some independence from the White House is that drawing attention to a candidate’s ties to Trump helps polarize a race along the same lines of presidential job approval. And that is a particularly troubling trend for a president with poor approval ratings. For most of his presidency, Trump has had more disapprovers than approvers in Arizona and other states with competitive Senate races, including Colorado and Maine. Linked to Trump, the Republican senators in those states are now getting the same treatment; McSally, Cory Gardner in Colorado and Susan Collins in Maine all have negative net approval ratings.
As political scientist (and co-author of the study finding negative effects of Trump endorsements) Andrew Ballard told me, “Unpopular presidents probably need to be very strategic and judicious with their usage of their platform to endorse candidates, because in certain situations it can do more harm than good.” Trump failed to follow this advice in 2018 and doesn’t seem to be paying it any more heed this year. And most GOP senators are not effectively keeping their distance from Trump.
Senators up for reelection are siding with Trump
Trump may not be able to resist intervening in Senate and House races, given his desire for being the center of attention. But Republican legislators have choices about how to present themselves. So far, they are sticking with Trump.
McSally supported repealing Obamacare, opposed the president’s impeachment and has rarely publicly criticized the Trump administration. That is a big shift from 2016, when she chose not to endorse Trump and bashed his behavior. Moreover, McSally has voted with Trump’s position 95 percent of the time over the last two congressional sessions — far more often than you’d expect based on Arizona’s politics. In fact, in the Senate, McSally has the fourth highest “Trump Plus-Minus” score, which measures how often a member of Congress votes in line with the president’s position relative to what you would expect from that member based on the partisanship of their state or district.
Other Republican senators up for reelection this year have also remained loyal to Trump’s positions. Gardner has voted with Trump 89 percent of the time during the 115th and 116th Congresses (he has the second highest “Trump Plus-Minus”), Thom Tillis (North Carolina) with Trump 93 percent of the time, David Perdue (Georgia) 95 percent, Joni Ernst (Iowa) 91 percent and Steve Daines (Montana) 86 percent.
The one partial exception is Collins, who has sided with Trump two-thirds of the time over the last two Congresses (though that is still far more than expected based on Trump’s losing margin in Maine). Collins has clearly tried to put some distance between herself and Trump as her reelection race draws nearer — but not too much. She did not support Obamacare repeal, though she voted to acquit the president in his Senate trial and voted to confirm his Supreme Court nominees. She went from voting with Trump 77 percent of the time in the 115th Congress (2017-18) to only 46 percent in the 116th (2019-20).
It’s been a tough balancing act that may end up pleasing no one. Indeed, Collins has become the poster child for Republicans’ unwillingness to seriously break with Trump. She has been “disappointed” in Trump without taking action to restrain him so often that “Saturday Night Live” did a skit about it.
Still, Collins may still have a chance to retain an independent reputation, something she’s cultivated for years by necessity in blue-ish Maine. The problem is … that’s harder to do these days.
Why it’s become more difficult to break with the national party
Many members of Congress used to have local reputations independent of their parties, presenting themselves as fighters for local interests and dollars in Washington. Even if most voters hated Congress, they still liked their own representatives and senators.
But the long-term trends are nationalization (voters perceive their representatives through the lens of national and presidential politics) and polarization (voters see the parties as distinct and agree more with one side). Voters learn less about their own legislators and more about the president, in part due to decreasing reliance on local news. As a result, fewer voters split their tickets, voting for one party’s candidate for president and the other’s for Senate or the House.
Democrats have faced the same problem in trying to distinguish themselves from their party. Voters recognized the independent streak of West Virginia’s Joe Manchin and Montana’s Jon Tester in the 2018 midterms, but Missouri’s Claire McCaskill, North Dakota’s Heidi Heitkamp and Indiana’s Joe Donnelly weren’t able to overcome the Republican lean of their states. Manchin went so far as to appear in ads showing him shooting at policies he disliked and proclaiming “for me, it’s all about West Virginia.” He won a state that Hillary Clinton lost by more than 42 points.
Nationalization makes it more difficult for senators to be seen as separated from their party’s president and his priorities. So even if Republican senators do break with Trump, fewer voters now learn about it because they no longer see state-specific news. Since voters tend to assume that partisans vote like their parties, voters are often unable to perceive moderate senators’ divergent policy positions.
And legislators who do break with their party now face a risk of a primary challenger. McSally won her 2018 Republican primary facing two candidates closely tied to Trump: Joe Arpaio and Kelli Ward. In this year’s race to defend the seat she was appointed to, McSally this week fended off a primary challenge from Daniel McCarthy, who tried to build support from local pro-Trump groups.
“More [congressional] members are running scared in the primaries,” political scientist Sarah Treul told me. “Even if they’re actually not having quality challengers emerging, they’re afraid of it happening. And I think a lot of them are spending time trying to figure out how [they] can ward off one of those challengers from even coming to the table.”
That usually means doing little to upset the party’s base by breaking with the president.
Can Republicans still jump ship?
Now that primary season is coming to an end, will Republicans start separating themselves from Trump? Some probably don’t need to do so to win reelection. Despite his national unpopularity, senators in more Trump-leaning states, such as Ernst in Iowa and Daines in Montana, may be able to survive with a standard partisan vote.
But McSally, Collins, Gardner in Colorado and Tillis in North Carolina likely need to earn a substantial number of votes from Biden supporters to survive. It’s just not clear whether they will break with Trump in public ways or whether late breaks would be enough to help them win.
That said, they may have one option to rally both the Republican faithful and a few swing voters. It turns out some voters fear giving unified government to the president’s party and desire some balance. If voters expect a Democratic president, they are slightly more likely to support Republicans in Congress, which could perhaps keep the Senate in GOP hands.
So terrible Trump polls could be turned into something useful by Republican senators. They might eventually need to argue that, if Trump is going to lose, voters should trust them to serve as a check on the Democratic agenda.


fivethirthyeight--2020-08-10--Politics Podcast: The Veepstakes Are Almost Over

After missing multiple self-imposed deadlines , presumptive Democratic nominee Joe Biden is expected to announce his running mate this week @ @ @ @ @ the FiveThirtyEight Politics podcast , the crew discusses the conflict within the Democratic Party over @ @ @ @ @ and why the campaign has floated disparate and little-known contenders .
They also compare Biden @ @ @ @ @ polls with Hillary Clinton ’ s standing at this point in 2016 , her peak @ @ @ @ @ can listen to the episode by clicking the “ play ” button in the audio @ @ @ @ @ it in iTunes , the ESPN App or your favorite podcast platform .
If you @ @ @ @ @ learn how to listen .
The FiveThirtyEight Politics podcast is recorded Mondays and Thursdays .
@ @ @ @ @ show by leaving us a rating and review on iTunes .
Have a comment , @ @ @ @ @ good polling vs. bad polling ” ?
Get in touch by email , on Twitter @ @ @ @ @

After missing multiple self-imposed deadlines, presumptive Democratic nominee Joe Biden is expected to announce his running mate this week. In this installment of the FiveThirtyEight Politics podcast, the crew discusses the conflict within the Democratic Party over who that pick should be and why the campaign has floated disparate and little-known contenders. They also compare Biden’s standing in the polls with Hillary Clinton’s standing at this point in 2016, her peak during that cycle.
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--2020-08-10--Our New Metric Shows How Good NFL Receivers Are At Creating Separation

Is Michael Thomas elite ?
On its face , that seems like an outrageous question .
Michael Thomas , the New Orleans wide receiver who led the NFL in receiving yards and set an NFL record for receptions in 2019 on the way to winning Offensive Player of the Year — that Mike Thomas might not be an elite receiver ?
Yet throughout the offseason , NFL analysts have debated whether Thomas ’ s production is best explained by his skill and talent , or if instead he ’ s merely a good receiver who runs a lot of slants @ @ @ @ @ @ @ offense .
Playing with Drew Brees — a former Super Bowl MVP who holds the NFL record for highest career completion percentage , most career passing yards and most career passing touchdowns — certainly doesn ’ t hurt .
And running routes in schemes designed by Sean Payton , a coach with a .630 career win percentage ( 208-131 , third among active NFL coaches ) , probably also has a strong positive effect on his production .
But Thomas ’ s numbers are still eye-popping , and his peers in the NFL @ @ @ @ @ @ @ receivers ( and fifth overall ) in the NFL 100 .
So which is it : elite talent , or elite situation ?
One way to try to answer the question is to look at how well a receiver creates and maintains separation from a defender .
Being quick and fast isn ’ t enough for NFL success ; just ask Yamon Figurs or Darrius Heyward-Bey , both of whom ran a 4.3 40-yard dash at the NFL combine .
The elements of savvy route running — footwork , head and body fakes @ @ @ @ @ @ @ , changing direction sharply without losing speed — all appear to be more reliable indicators of NFL skill and talent than speed .
And the ultimate goal of every route is to create enough separation from a defender to earn a target and make a catch .
To try to capture the results of this game of cat and mouse between receiver and defender , we used NFL Next Gen Stats data that measures the distance between a receiver and the nearest defender at key moments in each play .
Perhaps it ’ @ @ @ @ @ @ @ team sport , assigning credit for something even as seemingly straightforward as separation is complicated .
For instance , short passes are , on average , associated with more separation than deeper passes because a defender ’ s top priority is to avoid getting beat deep .
So we need to account for depth of target and how far the QB had to throw the ball when we apportion credit for the separation a receiver got on a given play .
The type of play call matters , too .
Play-action passes create @ @ @ @ @ @ @ every depth of target on average , so we need to contextualize players who are targeted more often on play-action as well .
We also needed to decide when to measure receiver separation .
Since the most interesting routes to analyze are those that earned a target , there are two obvious points in a play to focus on : the moment the ball leaves the QB ’ s hand and the moment the ball arrives at the receiver ’ s location .
But there again we ’ re confronted with confounders that @ @ @ @ @ @ @ For example , some QBs throw with more anticipation than others , releasing the ball before a receiver has made his break and created the separation necessary for a successful completion .
Measuring separation at the time of the throw punishes teammates with great chemistry .
So we decided to focus on separation at the moment the ball arrives , on the theory that scheme and QB play have the least influence at this crucial moment in a pass play .
Ultimately , our separation model ending up including features that account for @ @ @ @ @ @ @ s separation at the time the QB targeted them , the horizontal and vertical position of the receiver on the field at the time of the throw , where the receiver lined up pre-snap , the distance to the goal line , the amount of break in the receiver ’ s route during the football ’ s journey through the air after it was released , the depth of the QB ’ s drop , the number of other routes that were being run on the play , if the play was a @ @ @ @ @ @ @ the number of deep safeties .
The final model does a decent job of predicting separation at the catch point on a given play .
We used its predictions as a baseline for performance and compared each receiver ’ s actual separation on a given play to what the model expected an average player ’ s separation would have been , given similar circumstances .
This result is a context-adjusted “ separation over expected ” ( SOE ) metric that we can calculate for each NFL receiver .
Since depth of target is @ @ @ @ @ @ @ grouped plays into buckets — depending on whether a pass attempt was short , intermediate or deep — and created an SOE leaderboard for each .
The resulting lists have reasonably strong face validity — players at the top of the leaderboards tend to be widely regarded as good route runners — suggesting SOE could be useful as a descriptive metric .
Two tight ends — Evan Engram of the New York Giants and Zach Ertz of the Philadelphia Eagles — top the list of receiver seasons with the highest separation over expected @ @ @ @ @ @ @ or less ) .
Ertz ’ s targets especially were high value .
While averaging more than a half-yard over expected in separation , his per-play expected points added ( EPA ) was worth more than 0.4 points in 2019 .
As a general rule , however , separation and value are decoupled on short passes .
The defense is typically willing to allow an offense to throw to wide-open players short , then rally to make a tackle for a short gain .
Another interesting feature of short-target SOE is that a @ @ @ @ @ @ @ open on short throws appears to be mostly nonexistent .
Having a high SOE in one season says very little about whether you will have a high SOE in the next .
Short targets are also the only leaderboard where running backs make an appearance , owing to the dearth of targets they get deeper downfield .
These short passes , however , are where Michael Thomas frequently shines .
Forty-eight percent of Thomas ’ s 185 targets came on passes 5 yards or less downfield in 2019 .
In the three seasons @ @ @ @ @ @ @ , Thomas has regularly posted high EPA per play values on these short targets and has been above average in creating separation at the catch point in two of the past three seasons .
Other players appear able to consistently create separation on short targets — Jarvis Landry is one example — but the value of Landry ’ s targets as measured by EPA are much lower than those directed at Thomas .
In fact , on an EPA-per-play basis , throwing short to Landry has a worse point expectation than running the @ @ @ @ @ @ @ — and perhaps it explains why the number of Landry ’ s short targets dropped by nearly half after he moved to the analytics-friendly Cleveland Browns .
Wide receivers make the bulk of their high-value receptions on passes at intermediate depths ( between 5 and 15 air yards ) .
The intermediate SOE leaderboard includes seasons from receivers like Davante Adams , Keenan Allen , Danny Amendola , Cooper Kupp and Adam Humphries , all of whom are generally regarded as skilled route runners .
Interestingly , among the three target depths , @ @ @ @ @ @ @ the most stable year to year .
So while we ’ d like more data , we should probably expect players who show the ability to separate above expectation on routes at these depths to continue to do so .
Thomas isn ’ t in the same class as Adams and Allen when it comes to creating separation — Adams has averaged over a half-yard of SOE the past two years on intermediates routes — but despite the tighter windows , the expected value Thomas created on these targets ranks him among the @ @ @ @ @ @ @ basis .
Perhaps because of his success , Thomas has seen a steady increase in the number of targets at those depths .
And compared to Atlanta ’ s Julio Jones — a receiver whose natural talent and skill set are rarely questioned — Thomas comes out ahead on both our separation and value metrics .
Timo Riske of Pro Football Focus has shown that the best receivers in the league earn their targets all over the field , so it ’ s no surprise to see familiar names in the deep-target SOE @ @ @ @ @ @ @ ball specialists like D.J .
Chark and Kenny Stills at the top of the list — the “ stretch X ” receivers whose job is to take the top off a defense .
And at the bottom of the list we find names like Robby Anderson , a free agent this offseason who reportedly drew few offers from teams ; an aging Larry Fitzgerald ; and the unsigned Kelvin Benjamin .
Finally , we see the continued effect of depth of target on separation .
Deep targets ( at least 15 air yards @ @ @ @ @ @ @ on a per-play basis , but they ’ re also the throws with the tightest windows .
Again it seems instructive to compare Thomas to Jones .
Jones was targeted deep more frequently , suggesting that his skillset is better suited to the demands of beating fast humans in a footrace , but he ’ s also not as successful at creating separation from defenders as Thomas is .
And Julio ’ s targets have , on average , been worth less than Thomas ’ s in the previous three years .
( @ @ @ @ @ @ @ s talent or skills , and both he and Thomas are consistently in the conversation for best receiver in the league . )
When we account for the most impactful context that affects a receiver ’ s most important job — getting open — Thomas is routinely above average in creating that separation .
And targets to him are among the most valuable plays in football across all depths .
There isn ’ t much evidence to support the idea that Mike Thomas is anything but an elite football talent .

Is Michael Thomas elite? On its face, that seems like an outrageous question. Michael Thomas, the New Orleans wide receiver who led the NFL in receiving yards and set an NFL record for receptions in 2019 on the way to winning Offensive Player of the Year — that Mike Thomas might not be an elite receiver? Yet throughout the offseason, NFL analysts have debated whether Thomas’s production is best explained by his skill and talent, or if instead he’s merely a good receiver who runs a lot of slants and benefits from being in an elite offense.
Playing with Drew Brees — a former Super Bowl MVP who holds the NFL record for highest career completion percentage, most career passing yards and most career passing touchdowns — certainly doesn’t hurt. And running routes in schemes designed by Sean Payton, a coach with a .630 career win percentage (208-131, third among active NFL coaches), probably also has a strong positive effect on his production. But Thomas’s numbers are still eye-popping, and his peers in the NFL recently ranked him first among all wide receivers (and fifth overall) in the NFL 100. So which is it: elite talent, or elite situation?
One way to try to answer the question is to look at how well a receiver creates and maintains separation from a defender. Being quick and fast isn’t enough for NFL success; just ask Yamon Figurs or Darrius Heyward-Bey, both of whom ran a 4.3 40-yard dash at the NFL combine. The elements of savvy route running — footwork, head and body fakes, disguising the intent of the route, changing direction sharply without losing speed — all appear to be more reliable indicators of NFL skill and talent than speed. And the ultimate goal of every route is to create enough separation from a defender to earn a target and make a catch.
To try to capture the results of this game of cat and mouse between receiver and defender, we used NFL Next Gen Stats data that measures the distance between a receiver and the nearest defender at key moments in each play. Perhaps it’s no surprise that in the ultimate team sport, assigning credit for something even as seemingly straightforward as separation is complicated. For instance, short passes are, on average, associated with more separation than deeper passes because a defender’s top priority is to avoid getting beat deep. So we need to account for depth of target and how far the QB had to throw the ball when we apportion credit for the separation a receiver got on a given play. The type of play call matters, too. Play-action passes create more separation than non-play-action passes at nearly every depth of target on average, so we need to contextualize players who are targeted more often on play-action as well.
We also needed to decide when to measure receiver separation. Since the most interesting routes to analyze are those that earned a target, there are two obvious points in a play to focus on: the moment the ball leaves the QB’s hand and the moment the ball arrives at the receiver’s location.
But there again we’re confronted with confounders that make apportioning credit and blame difficult. For example, some QBs throw with more anticipation than others, releasing the ball before a receiver has made his break and created the separation necessary for a successful completion. Measuring separation at the time of the throw punishes teammates with great chemistry.
So we decided to focus on separation at the moment the ball arrives, on the theory that scheme and QB play have the least influence at this crucial moment in a pass play. Ultimately, our separation model ending up including features that account for quarterback arm strength, the receiver’s separation at the time the QB targeted them, the horizontal and vertical position of the receiver on the field at the time of the throw, where the receiver lined up pre-snap, the distance to the goal line, the amount of break in the receiver’s route during the football’s journey through the air after it was released, the depth of the QB’s drop, the number of other routes that were being run on the play, if the play was a play-action pass or a screen, and the number of deep safeties.
The final model does a decent job of predicting separation at the catch point on a given play. We used its predictions as a baseline for performance and compared each receiver’s actual separation on a given play to what the model expected an average player’s separation would have been, given similar circumstances. This result is a context-adjusted “separation over expected” (SOE) metric that we can calculate for each NFL receiver.
Since depth of target is so important in determining separation, we grouped plays into buckets — depending on whether a pass attempt was short, intermediate or deep — and created an SOE leaderboard for each. The resulting lists have reasonably strong face validity — players at the top of the leaderboards tend to be widely regarded as good route runners — suggesting SOE could be useful as a descriptive metric.
Separation is highest on short passes, but their value is low Best and worst receiver seasons on short passes as measured by separation over expected (SOE) per play, 2017-19 Top 15 Receivers season targets aDOT epa/play soe/play Evan Engram 2018 40 1.7 0.07 0.98 Zach Ertz 2019 45 2.3 0.43 0.59 Cole Beasley 2019 43 2.8 0.04 0.57 Diontae Johnson 2019 43 0.7 0.15 0.40 Nelson Agholor 2018 51 0.7 0.14 0.38 James Conner 2018 67 -0.9 0.19 0.36 Chris Carson 2019 43 -1.7 0.21 0.35 T.J. Yeldon 2018 71 0.2 -0.09 0.35 Duke Johnson 2018 48 -0.6 0.16 0.33 Jarvis Landry 2018 46 1.4 -0.10 0.33 Davante Adams 2017 48 2.3 0.31 0.30 Dede Westbrook 2019 52 1.1 -0.21 0.29 DeMarco Murray 2017 41 -0.6 0.00 0.29 Jaylen Samuels 2019 53 -1.5 -0.02 0.28 Keenan Allen 2018 64 2.9 0.14 0.28 Bottom 15 Receivers season targets aDOT epa/play soe/play Latavius Murray 2019 41 -1.4 0.17 -0.28 Chris Thompson 2017 43 0.2 0.49 -0.30 Chris Thompson 2018 49 0.8 0.03 -0.31 Larry Fitzgerald 2018 42 2.4 -0.08 -0.32 Adam Humphries 2018 54 1.9 0.23 -0.33 Royce Freeman 2019 45 -0.3 -0.11 -0.34 Phillip Lindsay 2019 44 -1.8 -0.01 -0.34 Larry Fitzgerald 2019 59 1.3 -0.02 -0.35 Nick Chubb 2019 45 -1.0 0.02 -0.36 Le’Veon Bell 2019 71 -0.5 0.00 -0.39 Javorius Allen 2017 56 0.4 -0.12 -0.40 Giovani Bernard 2019 41 -0.8 -0.34 -0.42 David Johnson 2018 66 -1.2 -0.26 -0.44 Robert Woods 2019 48 -0.1 -0.08 -0.45 Todd Gurley 2019 45 0.5 -0.07 -0.49 Regular-season passes of 5 air yards or shorter, minimum of 40 targets. Sources: NFL Next Gen Stats, ESPN Stats & Information Group
Two tight ends — Evan Engram of the New York Giants and Zach Ertz of the Philadelphia Eagles — top the list of receiver seasons with the highest separation over expected on short throws (5 air yards or less). Ertz’s targets especially were high value. While averaging more than a half-yard over expected in separation, his per-play expected points added (EPA) was worth more than 0.4 points in 2019. As a general rule, however, separation and value are decoupled on short passes. The defense is typically willing to allow an offense to throw to wide-open players short, then rally to make a tackle for a short gain.
Another interesting feature of short-target SOE is that a player’s ability to consistently get open on short throws appears to be mostly nonexistent. Having a high SOE in one season says very little about whether you will have a high SOE in the next. Short targets are also the only leaderboard where running backs make an appearance, owing to the dearth of targets they get deeper downfield.
These short passes, however, are where Michael Thomas frequently shines. Forty-eight percent of Thomas’s 185 targets came on passes 5 yards or less downfield in 2019. In the three seasons for which we have Next Gen data, Thomas has regularly posted high EPA per play values on these short targets and has been above average in creating separation at the catch point in two of the past three seasons.
Short, open targets to Mike Thomas are high value … Receiving stats on short passes for Michael Thomas, including separation over expected (SOE) and expected points added (EPA) per play season targets Avg. Depth of Target SOE/PLAY epa/PLAY 2019 88 3.2 0.05 0.25 2018 73 2.9 0.06 0.31 2017 57 2.5 -0.05 0.43 Regular-season passes of 5 air yards or less. Sources: NFL Next Gen Stats, ESPN Stats & Information Group
Other players appear able to consistently create separation on short targets — Jarvis Landry is one example — but the value of Landry’s targets as measured by EPA are much lower than those directed at Thomas. In fact, on an EPA-per-play basis, throwing short to Landry has a worse point expectation than running the ball. That’s somewhat shocking — and perhaps it explains why the number of Landry’s short targets dropped by nearly half after he moved to the analytics-friendly Cleveland Browns.
… while short, open targets to Jarvis Landry are not Receiving stats on short passes for Jarvis Landry, including separation over expected (SOE) and expected points added (EPA) per play season targets Avg. Depth of Target soe/play epa/play 2019 49 1.2 0.23 -0.19 2018 46 1.4 0.33 -0.10 2017 89 1.3 0.23 -0.11 Regular-season passes of 5 air yards or less. Sources: NFL Next Gen Stats, ESPN Stats & Information Group
Wide receivers make the bulk of their high-value receptions on passes at intermediate depths (between 5 and 15 air yards). The intermediate SOE leaderboard includes seasons from receivers like Davante Adams, Keenan Allen, Danny Amendola, Cooper Kupp and Adam Humphries, all of whom are generally regarded as skilled route runners. Interestingly, among the three target depths, SOE on intermediate passes appears to be the most stable year to year. So while we’d like more data, we should probably expect players who show the ability to separate above expectation on routes at these depths to continue to do so.
Davante Adams and Keenan Allen are technicians Best and worst receiver seasons on intermediate passes as measured by separation over expected (SOE) per play, 2017-19 top 15 Receivers season targets aDOT epa/play soe/play Davante Adams 2018 67 9.5 0.53 0.65 Keenan Allen 2017 69 10.3 0.58 0.58 Davante Adams 2019 44 9.1 0.29 0.52 John Brown 2018 42 10.6 0.32 0.46 Danny Amendola 2019 47 8.9 0.25 0.43 Cooper Kupp 2019 50 10.7 1.12 0.40 Adam Humphries 2018 43 9.4 0.53 0.40 Courtland Sutton 2019 49 10.2 0.39 0.39 John Brown 2019 54 10.2 0.18 0.32 Jared Cook 2017 41 9.7 0.54 0.30 Keenan Allen 2019 56 10.1 0.65 0.30 Robert Woods 2019 50 10.5 0.40 0.30 Odell Beckham Jr. 2019 44 9.7 0.29 0.29 Adam Thielen 2018 56 10.1 0.44 0.28 Zach Ertz 2018 79 9.7 0.20 0.25 Michael Thomas 2018 54 10.1 0.59 0.25 BOTTOM 15 RECEIVERS SEASON TARGETS ADOT EPA/PLAY SOE/PLAY DeAndre Hopkins 2019 49 9.7 0.12 -0.23 D.J. Chark 2019 47 10.0 0.27 -0.26 DeAndre Hopkins 2018 80 9.9 0.50 -0.27 Alshon Jeffery 2017 52 10.4 0.33 -0.27 Eric Decker 2017 40 9.5 0.54 -0.28 T.Y. Hilton 2018 52 9.0 0.29 -0.30 Julio Jones 2019 58 10.8 0.42 -0.31 Allen Robinson 2018 47 9.2 0.21 -0.31 Kenny Golladay 2018 51 10.9 0.16 -0.31 Allen Robinson 2019 68 9.9 0.10 -0.32 Terry McLaurin 2019 43 9.9 0.57 -0.36 Devin Funchess 2017 47 10.7 0.35 -0.36 Jared Cook 2018 41 8.7 0.67 -0.38 Cameron Brate 2017 41 11.1 0.23 -0.53 Kenny Golladay 2019 42 9.8 0.31 -0.54 Regular-season passes of between 5 and 15 air yards, minimum of 40 targets. Sources: NFL Next Gen Stats, ESPN Stats & Information Group
Thomas isn’t in the same class as Adams and Allen when it comes to creating separation — Adams has averaged over a half-yard of SOE the past two years on intermediates routes — but despite the tighter windows, the expected value Thomas created on these targets ranks him among the best in the league on a per-play basis. Perhaps because of his success, Thomas has seen a steady increase in the number of targets at those depths. And compared to Atlanta’s Julio Jones — a receiver whose natural talent and skill set are rarely questioned — Thomas comes out ahead on both our separation and value metrics.
Thomas did more on midrange targets than Jones Receiving stats on intermediate passes for Michael Thomas and Julio Jones, including separation over expected (SOE) and expected points added (EPA) per play PLAYER season targets Avg. Depth of Target soe/play epa/play Michael Thomas 2019 71 10.6 0.08 0.72 Michael Thomas 2018 54 10.1 0.25 0.59 Michael Thomas 2017 48 9.4 0.01 0.39 Julio Jones 2019 58 10.8 -0.31 0.42 Julio Jones 2018 65 9.8 -0.07 0.36 Julio Jones 2017 44 10.3 0.03 0.29 Regular-season passes of between 5 and 15 air yards. Source: NFL Next Gen Stats, ESPN Stats & Information Group
Timo Riske of Pro Football Focus has shown that the best receivers in the league earn their targets all over the field, so it’s no surprise to see familiar names in the deep-target SOE ranks. But we also see deep ball specialists like D.J. Chark and Kenny Stills at the top of the list — the “stretch X” receivers whose job is to take the top off a defense. And at the bottom of the list we find names like Robby Anderson, a free agent this offseason who reportedly drew few offers from teams; an aging Larry Fitzgerald; and the unsigned Kelvin Benjamin. Finally, we see the continued effect of depth of target on separation. Deep targets (at least 15 air yards) are the most valuable in football on a per-play basis, but they’re also the throws with the tightest windows.
D.J. Chark was open deep a lot in 2019 Best and worst receiver seasons on deep passes as measured by separation over expected (SOE) per play, 2017-19 TOP 15 Receivers season targets aDOT epa/play soe/play D.J. Chark 2019 30 27.1 0.96 0.41 Kenny Stills 2017 36 25.4 0.46 0.40 Amari Cooper 2019 37 23.3 0.90 0.39 Odell Beckham Jr. 2018 33 24.7 0.72 0.36 Adam Thielen 2017 38 22.0 0.78 0.34 Travis Kelce 2017 31 22.2 1.08 0.33 Jaron Brown 2017 30 24.0 0.52 0.29 Robert Woods 2018 32 23.4 0.29 0.25 Tyreek Hill 2018 48 31.4 0.78 0.25 Curtis Samuel 2019 41 25.7 -0.26 0.24 Brandin Cooks 2017 41 29.2 0.65 0.23 Calvin Ridley 2019 30 25.2 0.68 0.22 Jarvis Landry 2018 39 23.2 0.05 0.19 JuJu Smith-Schuster 2018 33 23.8 0.68 0.17 Brandin Cooks 2018 37 26.9 0.65 0.17 Chris Godwin 2019 30 21.9 1.29 0.13 BOTTOM 15 RECEIVERS SEASON TARGETS ADOT EPA/PLAY SOE/PLAY Odell Beckham Jr. 2019 42 26.6 0.09 -0.18 Dez Bryant 2017 37 23.7 -0.26 -0.20 Marquise Goodwin 2017 35 28.1 0.41 -0.20 Doug Baldwin 2017 36 27.2 0.85 -0.24 DeVante Parker 2019 38 25.2 1.10 -0.25 Alshon Jeffery 2017 41 24.3 0.06 -0.26 Mike Evans 2017 44 23.7 0.20 -0.29 Kelvin Benjamin 2018 30 24.7 -0.47 -0.31 Robby Anderson 2019 42 24.9 0.18 -0.32 Tyler Lockett 2019 31 27.1 0.69 -0.34 Larry Fitzgerald 2017 32 20.1 0.41 -0.34 Marvin Jones 2019 30 23.7 0.48 -0.35 Jarvis Landry 2019 33 22.1 0.89 -0.36 Allen Robinson 2019 37 23.1 0.63 -0.36 Robby Anderson 2018 31 30.7 0.04 -0.42 Regular-season passes greater than 15 air yards, minimum of 30 targets. Sources: NFL Next Gen Stats, ESPN Stats & Information Group
Again it seems instructive to compare Thomas to Jones. Jones was targeted deep more frequently, suggesting that his skillset is better suited to the demands of beating fast humans in a footrace, but he’s also not as successful at creating separation from defenders as Thomas is. And Julio’s targets have, on average, been worth less than Thomas’s in the previous three years. (Again, no one doubts Jones’s talent or skills, and both he and Thomas are consistently in the conversation for best receiver in the league.)
When we account for the most impactful context that affects a receiver’s most important job — getting open — Thomas is routinely above average in creating that separation. And targets to him are among the most valuable plays in football across all depths. There isn’t much evidence to support the idea that Mike Thomas is anything but an elite football talent.


fivethirthyeight--2020-08-10--Notre Dame Didn’t Want To Join A Conference. But The ACC Could Have Helped It Win.

The 2020 college football season is looking less and less likely , with Power Five conferences reportedly on the cusp of calling off or at least postponing fall sports .
Cancellation has seemed inevitable as players across the country have tested positive for COVID-19 , though the move would deal a crushing financial blow to athletic departments , costing athletes a season of their careers and schools a shot at glory .
One of those schools might have more to lose if play is halted because of changes the coronavirus already forced .
Late last month , the sport ’ @ @ @ @ @ @ @ For one year and one year only , Notre Dame was to have dropped its independence and played in a conference .
The school ’ s temporary admittance into the ACC — which Notre Dame confirmed in a terse , two-sentence statement — became a necessity when major conferences began canceling nonconference games .
But after more than a century of Notre Dame remaining unwaveringly independent , this move might have also been the extra boost it needed to get back to the College Football Playoff .
The instances of perhaps college football @ @ @ @ @ @ @ to join a conference are far too many to name here .
In the early 1900s , Notre Dame was shut out of the original Big Ten ( then the Western Conference ) , reportedly because of anti-Catholic sentiment from Michigan coach Fielding Yost .
Ever since then , Notre Dame has turned down overtures to join a conference in football , making statements like this from school president Edward Malloy in 1999 : “ Notre Dame has a core identity , and at that core are these characteristics : Catholic , private @ @ @ @ @ @ @ with a national constituency , we believe independence continues to be our best way forward.
” In 2012 , Notre Dame agreed to join the ACC in every sport but football and hockey , and though it started playing five football games each year against ACC teams , it maintained its football independence .
The pandemic forced the school ’ s hand like nothing else could .
Traditionalists in South Bend might have resented many aspects of their new reality , including the canceled rivalry games against Southern California , Stanford and Navy @ @ @ @ @ @ @ with ACC foes and the path to the playoff through a potential conference championship game .
But for the first time in years , playing in the ACC was unquestionably Notre Dame ’ s best option .
Notre Dame has played a national schedule since the early 20th century .
The school has played 91 times against Navy , 89 against USC and 70 against Pittsburgh , in addition to on-and-off rivalries with Michigan , Michigan State and Purdue .
While this approach has its perks , it almost always results in one @ @ @ @ @ @ @ .
By joining a Power Five league and scheduling only ACC teams for a year , Notre Dame actually made its schedule easier .
By their own doing , in 14 of the past 16 seasons , the Fighting Irish have played at least one team that finished in the top 10 of the AP poll .
They ’ re 2-17 in 19 opportunities against those top 10 teams , and they ’ ve played for a national championship only once .
Ambitious scheduling has derailed a few Irish teams that might otherwise @ @ @ @ @ @ @ team lost only at No .
3 Georgia and at No .
19 Michigan ; the 2017 team slipped up against No .
15 Georgia , No .
7 Miami and No .
20 Stanford ; and the 2015 team fell short on the road at No .
12 Clemson and No .
13 Stanford by 2 points each .
With a softer schedule in place , any of those seasons could have ended on bigger stages .
The only year Notre Dame made the College Football Playoff ( 2018 ) was also @ @ @ @ @ @ @ that the Irish didn ’ t play a regular-season opponent that finished in the top 10 .
And in 2012 , when they made the BCS national championship game , they played only one , a home game against Stanford that Notre Dame won in overtime .
For the moment , Notre Dame ’ s 2020 schedule ranks 53rd among FBS schools — its easiest since 2008 , when it finished the season also ranked 53rd according to ESPN ’ s Football Power Index .
Notre Dame had an elite opponent on its @ @ @ @ @ @ @ Clemson , currently set for Nov. 7 .
But outside of the Tigers , the ACC ’ s struggles are well-documented .
Notre Dame isn ’ t scheduled to play another team ranked in the top 15 of Bill Connelly ’ s SP+ rankings , and only North Carolina ( No .
17 ) and Florida State ( No .
26 ) are in the top 40 .
The average SP+ ranking in the ACC is 5.9 , just ahead of the Pac-12 ( 5.3 ) , the worst of the Power Five @ @ @ @ @ @ @ could have stumbled into a BCS or New Year ’ s Six bowl with two losses , this one had championship potential .
The pandemic may now put an end to the tradition-busting experiment it had forced on Notre Dame .
But maybe the idea of an easier path to the playoff will be enough to entice the Irish to end its independence and join a conference for good .
If that conference is the ACC , all of the pieces could fall into place for Notre Dame ’ s return to national @ @ @

The 2020 college football season is looking less and less likely, with Power Five conferences reportedly on the cusp of calling off or at least postponing fall sports. Cancellation has seemed inevitable as players across the country have tested positive for COVID-19, though the move would deal a crushing financial blow to athletic departments, costing athletes a season of their careers and schools a shot at glory.
One of those schools might have more to lose if play is halted because of changes the coronavirus already forced. Late last month, the sport’s most rigid tradition was toppled: For one year and one year only, Notre Dame was to have dropped its independence and played in a conference. The school’s temporary admittance into the ACC — which Notre Dame confirmed in a terse, two-sentence statement — became a necessity when major conferences began canceling nonconference games. But after more than a century of Notre Dame remaining unwaveringly independent, this move might have also been the extra boost it needed to get back to the College Football Playoff.
The instances of perhaps college football’s most prestigious program resisting temptations to join a conference are far too many to name here. In the early 1900s, Notre Dame was shut out of the original Big Ten (then the Western Conference), reportedly because of anti-Catholic sentiment from Michigan coach Fielding Yost. Ever since then, Notre Dame has turned down overtures to join a conference in football, making statements like this from school president Edward Malloy in 1999: “Notre Dame has a core identity, and at that core are these characteristics: Catholic, private, independent. As a Catholic university with a national constituency, we believe independence continues to be our best way forward.” In 2012, Notre Dame agreed to join the ACC in every sport but football and hockey, and though it started playing five football games each year against ACC teams, it maintained its football independence. The pandemic forced the school’s hand like nothing else could.
Traditionalists in South Bend might have resented many aspects of their new reality, including the canceled rivalry games against Southern California, Stanford and Navy, the need to share TV revenue with ACC foes and the path to the playoff through a potential conference championship game. But for the first time in years, playing in the ACC was unquestionably Notre Dame’s best option.
Notre Dame has played a national schedule since the early 20th century. The school has played 91 times against Navy, 89 against USC and 70 against Pittsburgh, in addition to on-and-off rivalries with Michigan, Michigan State and Purdue. While this approach has its perks, it almost always results in one of the toughest schedules in the country. By joining a Power Five league and scheduling only ACC teams for a year, Notre Dame actually made its schedule easier.
By their own doing, in 14 of the past 16 seasons, the Fighting Irish have played at least one team that finished in the top 10 of the AP poll. They’re 2-17 in 19 opportunities against those top 10 teams, and they’ve played for a national championship only once. Ambitious scheduling has derailed a few Irish teams that might otherwise have had an opportunity. The 2019 team lost only at No. 3 Georgia and at No. 19 Michigan; the 2017 team slipped up against No. 15 Georgia, No. 7 Miami and No. 20 Stanford; and the 2015 team fell short on the road at No. 12 Clemson and No. 13 Stanford by 2 points each. With a softer schedule in place, any of those seasons could have ended on bigger stages.
The only year Notre Dame made the College Football Playoff (2018) was also the only year since that playoff began that the Irish didn’t play a regular-season opponent that finished in the top 10. And in 2012, when they made the BCS national championship game, they played only one, a home game against Stanford that Notre Dame won in overtime. For the moment, Notre Dame’s 2020 schedule ranks 53rd among FBS schools — its easiest since 2008, when it finished the season also ranked 53rd according to ESPN’s Football Power Index.
Notre Dame had an elite opponent on its schedule again with a home game against Clemson, currently set for Nov. 7. But outside of the Tigers, the ACC’s struggles are well-documented. Notre Dame isn’t scheduled to play another team ranked in the top 15 of Bill Connelly’s SP+ rankings, and only North Carolina (No. 17) and Florida State (No. 26) are in the top 40. The average SP+ ranking in the ACC is 5.9, just ahead of the Pac-12 (5.3), the worst of the Power Five conferences. While a previous Irish team could have stumbled into a BCS or New Year’s Six bowl with two losses, this one had championship potential.
The pandemic may now put an end to the tradition-busting experiment it had forced on Notre Dame. But maybe the idea of an easier path to the playoff will be enough to entice the Irish to end its independence and join a conference for good. If that conference is the ACC, all of the pieces could fall into place for Notre Dame’s return to national championship contention.


fivethirthyeight--2020-08-10--Do You Buy That … Kamala Harris Is Most Likely To Become Biden’s Running Mate?

Do You Buy That … Kamala Harris Is Most Likely To Become Biden ’ s Running Mate ?