So Your Archipelago Is Exploding. How Doomed Is Your Island?

🚨🚨🚨 “The Riddler” book is out now! It’s chock-full of the best puzzles from this column (and, fret not, their answers) and some riddles that have never been seen before. I hope you enjoy it, and thank you for riddling with us these past three years. 🚨🚨🚨

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-size and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,30 and you may get a shoutout in next week’s column. If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter.

Riddler Express

From Philip Ruo, a puzzle of pondering playing perfection:

The NFL season is in full swing, and only one undefeated team remains — the 6-0 Los Angeles Rams. In theory, though, given the current NFL scheduling scheme — or at least what Wikipedia says it is — what is the largest number of teams that could finish a regular season 16-0?

Submit your answer

Riddler Classic

From Ricky Jacobson and Ben Holtz, geological disaster looms beneath:

You live on the volcanic archipelago of Riddleria. The Riddlerian Islands are a 30-minute boat ride off the shores of the nearby mainland. Your archipelago is connected via a network of bridges, forming one unified community. In an effort to conserve resources, the ancient Riddlerians who built this network opted not to build bridges between any two islands that were already connected to the community otherwise. Hence, there is exactly one path from any one island to any other island.

One day, you feel the ground start to rumble — the islands’ volcanoes are stirring. You’re not sure whether any volcano is going to blow, but you and the rest of the Riddlerians flee the archipelago in rowboats bound for the mainland just to be safe. But as you leave, you look back and wonder what will become of your home.

Each island contains exactly one volcano. You know that if a volcano erupts, the subterranean pressure change will be so great that the volcano will collapse in on itself, causing its island — and any connected bridges — to crumble into the ocean. Remarkably, other islands will be spared unless their own volcanoes erupt. But if enough bridges go down, your once-unified archipelagic community could split into several smaller, disjointed communities.

If there were N islands in the archipelago originally and each volcano erupts independently with probability p, how many disjointed communities can you expect to find when you return? What value of p maximizes this number?

Submit your answer

Solution to last week’s Riddler Express

Congratulations to 👏 Sarry Al-Turk 👏 of Toronto, winner of last week’s Riddler Express!

Last week, you learned about a girl who loves to sing “The Unbirthday Song” to people — as one does. But she can only do that, of course, if it’s not the person’s actual birthday. If she kept singing it to random people until it happened to be someone’s birthday, how long would her singing streak go before it became more likely than not that she would encounter someone whose birthday it is?

Care for those vocal cords, child: It’s 252 people.

The probability that it’s not an individual person’s birthday is 364/365. The probability that you sing to N people in a row without it having been anyone’s birthday is \((364/365)^N\) — since the birthdays are independent events, we can multiply that fraction over and over to match the number of people. We want to find the number N such that that probability is larger than 0.5.

We could just stick that straight into a computer solver, but it’s Friday, so let’s have some fun and do a little algebra.31 First, we can take the logarithm of both sides, to get N out of the exponent, and then we can rearrange things a little bit:

\begin{equation*}(364/365)^N > 0.5\end{equation*}

\begin{equation*}N\log(364/365) > \log(0.5)\end{equation*}

\begin{equation*}N > \log(0.5)/\log(364/365)\end{equation*}

That numerator, log(0.5), equals about -0.3, and that denominator, log(364/365), equals about -0.001. That fraction equals about 253. So the singing streak is expected to go 252 people before it became more likely than not that a birthday boy or girl would be encountered.

And a very merry unbirthday to you, dear reader — unless, of course, it is the big day.

Solution to last week’s Riddler Classic

Congratulations to 👏 Clemens Fiedler 👏 of Krems, Austria, winner of last week’s Riddler Classic!

Last week, a farmer wanted to tether a goat — as one does. Specifically, the farmer wanted to tether the goat to the fence that surrounded his circular field such that the goat could graze on exactly half the field, by area. The field had a radius R. How long should the goat’s tether be?

The tether should be a bit longer than the radius — specifically, it should have a length of about 1.159R.

Solver Russell No-last-name-given showed us what this looks like, pictured below. The field is green with radius R; the goat’s would-be grazing area is gray, with radius r.

The picture is all fine and good, but what about that math? It looks a little nasty. And it is a little nasty, I’m afraid. But, hey, it’s nearly Halloween, so let’s surrender to the nastiness and fear.

The area on the field available to the goat is the intersection between two circles. And there just happens to be a whole body of knowledge about such circle-circle intersections. One way to think about it is to consider the two different shapes that the goat’s tether allows it to graze in. The first is the big “pizza slice”, defined in the image above by the two diagonal green radii and the bottom arc of the gray circle, and the second are the narrower areas between the pizza slice and the fence.

Hector Pefo broke this math down a little bit more for us in his diagram (this time, the goat is on the southern end of the field):

And finally, Laurent Lessard showed us a way to get to this same solution with calculus.

Either way, I hope you enjoy it, goat. Nom nom nom.

Want more riddles?

Well, aren’t you lucky? There’s a whole book full of the best of them and some never seen before, called “The Riddler,” and it’s in stores now!

Want to submit a riddle?

Email me at [email protected]

ZF takes 35 percent stake in autonomous driving specialist ASAP

FRANKFURT (Reuters) – Car parts maker ZF Friedrichshafen said on Friday it acquired a 35 percent stake in ASAP, a Germany-based maker of software and testing systems for autonomous driving applications and electric vehicles.

ASAP specializes in car-to-x communication, human-machine interfaces and electronic architecture and last year generated sales of 84 million euros. It employs 1,100 staff.

ZF’s Chief Executive Officer Wolf-Henning Scheider recently said ZF will invest about 12 billion euros in electromobility and autonomous driving over the next five years.

A purchase price for the ASAP stake was not disclosed.

Reporting by Arno Schuetze, editing by Riham Alkousaa

Comcast says its fastest internet reaches more U.S. homes than any other provider

(Reuters) – Comcast Corp said on Thursday that its fastest-speed gigabit internet service now reaches more homes than any other provider in the United States after it completed rollout to nearly all 58 million homes and businesses it serves.

The milestone widens its greater coverage over telecoms rivals. Competitor Verizon Communications Inc races to deploy its next-generation 5G wireless service on mobile phones and in the home with speeds theoretically rivaling cable company products. Verizon launched its home internet 5G service in October, the first commercial offering of its kind in the United States.

Comcast’s high-speed internet business is one of its biggest contributors to revenue and profit as customers for its video services decline. The segment has helped prop up the media and communications conglomerate’s finances.

So-called cord cutters, many of whom continue to rely on broadband providers such as Comcast for internet services, have started defecting to video-streaming services such as Netflix, Hulu and Youtube TV for television programming.

That trend sparked a wave of media company mergers. Walt Disney Co struck a deal to buy 21st Century Fox for $71.3 billion and AT&T Inc bought Time Warner for $85 billion, and both have vowed to build streaming video services for consumers looking for a lower-cost alternative to traditional pay television services.

Comcast lost to Disney on a bid to buy Fox this year but prevailed against Disney in an auction to buy satellite television broadcaster and media company Sky.

Reporting by Kenneth Li; Editing by Cynthia Osterman

Robot market growth slows as trade war hits industrial spending: robot industry chief

TOKYO (Reuters) – An escalating trade war between the United States and China has dampened manufacturers’ appetite for investment in equipment, causing growth in the industrial robot market to slow, the chief of the global robot industry group said.

Many global manufacturers “are now in a wait-and-see mode, wondering whether to shift production (away from China) to, let’s say, Vietnam or the United States,” said Junji Tsuda, chief of the International Federation of Robotics (IFR), in an interview on Thursday.

IFR, which brings together nearly 60 global robot suppliers and integrators, predicts worldwide industrial robot sales this year to grow 10 percent compared to last year’s 30 percent jump.

China is the world’s largest robots market with a 36 percent global share, with its sales volume exceeding the total of Europe and the Americas combined.

Tsuda, also the chairman of Japan’s Yaskawa Electric Corp, said the manufacturers would move out of the wait-and-see mode by the end of this year.

It will take a while for the direction of the trade war to be clear, Tsuda said. “But global demand for smartphones, semiconductors and autos have been solid, and the time will eventually come that they can wait no longer and will resume investment to meet the demand.”

Yaskawa, one of the world’s top robot manufacturers, last week cut its annual operating profit forecast to 59 billion yen ($524.40 million) from 65.5 billion yen, citing a slowdown in smartphone-related demand in China and growing caution over the trade dispute.

From next year onwards, however, IFR expects the robot market growth to pick up again, forecasting an average 14 percent increase per year through 2021.

($1 = 112.5100 yen)

Reporting by Makiko Yamazaki; Editing by Muralikumar Anantharaman

Philip Rivers Has The Supporting Cast He Deserves Again

Conventional NFL wisdom says teams should do whatever it takes to snag a Franchise Quarterback™ — that from there, the winning just takes care of itself. But for most of Philip Rivers’s career, his Los Angeles (née San Diego) Chargers have been the exception to that rule. Taken fourth overall in the 2004 draft, Rivers has been the elite passer that teams dream about building around. And yet, his team has just four total playoff wins to show for it, including only one this decade.

This year, though, Los Angeles looks poised to reverse that trend and actually capitalize on having a future Hall of Fame QB in its midst, while there’s still time left in Rivers’s career to do it. The Chargers walloped the Browns 38-14 in Cleveland last Sunday, bringing their record to 4-2 on the season — and giving them a 61 percent probability of making their first playoff appearance since 2013. Although L.A.’s postseason bid is far from assured, right now the Chargers have set themselves up with their most promising start to a season in a long time.

This Charger renaissance has been building for a few years, since the team finally began surrounding Rivers again with better playmakers on both sides of the ball. On defense, that goes back to 2012, when former general manager A.J. Smith drafted pass-rusher Melvin Ingram 18th overall. After a slow start to his career, Ingram has blossomed into a Pro Bowler and an annual double-digit sack candidate. Under Smith’s successor, Tom Telesco, the Chargers have also grabbed several defensive contributors through the draft, including sack-machine DE Joey Bosa,17 solid LB Denzel Perryman, up-and-coming CB Desmond King II and rookie S Derwin James (who, in his first season, already ranks as the NFL’s fifth-best safety according to ProFootballFocus’s player grades). Toss in outside pickups such as DT Brandon Mebane and CB Casey Hayward — another Pro Bowler from last season — plus the guidance of proven coordinator Gus Bradley, and the Chargers’ defensive talent base has undeniably made strides over the past handful of seasons.

On offense, Telesco also made key acquisitions that helped pave the way for this year’s hot start when he took WR Keenan Allen in the third round of the 2013 draft and RB Melvin Gordon 15th overall in 2015. Picking first-round running backs is always tricky business, but Gordon has been a good one so far in his career, with a couple of 1,400-yards-from-scrimmage seasons under his belt (in 2016 and 2017) and an excellent start to 2018 as well. Meanwhile, Allen has taken the lead from top San Diego-era targets Malcom Floyd and Antonio Gates and forged his own chemistry with Rivers — only four receivers leaguewide have more yards through the air since 2017 than Allen does. (It also helps that Allen has stayed healthy these past two seasons after missing 23 combined games in 2015-16.) Allen and Gordon aren’t the only teammates making Rivers’s life easier: The offensive line has been much better with free-agent C Mike Pouncey anchoring the middle, while change-of-pace RB Austin Ekeler has proven himself exceptionally tough to bring down — he leads all RBs in yards after first contact per rush. More broadly, in its second year under head coach Anthony Lynn, Los Angeles now has the offensive pieces to beat teams in multiple ways.

Add it all up and it’s clear that Rivers, who turns 37 in December, has a much better group of talent around him to work with than in years past. Here’s a look at the changes in Rivers’s own production over time — as measured by his Yards Above Backup Quarterback (YABQ) — along with how his top skill-position teammates and defense have also evolved:

Philip Rivers is great again — and he has help

Los Angeles Chargers’ production from quarterback Philip Rivers and his supporting cast, 2006-2018

Season Rivers YABQ/G Top RB YdSc/G Top Rec. YdSC/G Team Def. efficiency
2018 99.2 M. Gordon 124.2 K. Allen 80.0 54.9
2017 75.1 M. Gordon 98.8 K. Allen 87.6 63.0
2016 31.8 M. Gordon 88.5 T. Williams 66.2 51.1
2015 48.3 D. Woodhead 68.2 K. Allen 45.3 38.6
2014 45.7 B. Oliver 53.3 M. Floyd 53.5 42.8
2013 79.6 R. Mathews 90.3 K. Allen 65.4 32.2
2012 -3.9 R. Mathews 59.9 M. Floyd 50.9 55.4
2011 48.0 R. Mathews 96.6 V. Jackson 72.3 33.2
2010 77.1 M. Tolbert 59.4 A. Gates 48.9 64.3
2009 97.0 L. Tomlinson 55.3 V. Jackson 73.6 46.4
2008 86.5 L. Tomlinson 96.0 V. Jackson 72.9 38.7
2007 26.4 L. Tomlinson 121.8 A. Gates 61.5 62.6
2006 58.5 L. Tomlinson 145.2 A. Gates 57.8 61.1

Per-game measures are relative to team schedule lengths, not individual games played.

YABQ: Yards Above Backup Quarterback, a measure of QB performance that gives credit for passing and rushing, and adjusts for strength of schedule.

YDSC: yards from scrimmage, or rushing yards plus receiving yards.

Defensive efficiency: ESPN’s measure of a defense’s per-play effectiveness on a 0-100 scale.

Source: ESPN Stats & Information Group, pro-Football-Reference.com

It probably isn’t a coincidence that Rivers is currently enjoying his best statistical performance in years, with Gordon and Allen also contributing more than any Charger rusher and receiver since the days of LaDainian Tomlinson and Vincent Jackson. It’s a little circular, in that sense: Is Rivers making them better, or are they helping Rivers rediscover his form? (Gordon’s ability to run against stacked defenses, for instance, has opened up space for Rivers to throw downfield.) Either way, the ingredients have been in place for a late-career QB rejuvenation. Right now, Rivers is on pace to tie for the ninth-most-efficient post-merger performance for a passer age 35 or older, according to Pro-Football-Reference.com’s advanced passing index. As far as old-man QB seasons go, this is one of the best in history.

Of course, with the Chargers, it’s about more than just improved talent. It’s also about execution, something this team has often been found sorely lacking over the years. As Mike Tanier wrote in his L.A. chapter for Football Outsiders’ 2018 Almanac, you could make a pretty convincing case that the 2017 Chargers missed the playoffs because of two very fundamental football activities: tackling and kicking. Last year, Los Angeles let opponents break tackles at an incredible rate and missed numerous field goals and extra points, helping to turn a team with 10-and-a-half-win point differential into a sad-sack nine-game-winner.

This year’s place-kicking game hasn’t been great (Caleb Sturgis made just 71 percent of his total field goals and extra points before he was sidelined by an injury), but it’s no longer dead-last in football, which I suppose is an accomplishment. Plus, the Chargers rank among the best in the league in terms of kickoffs, a big reason for their fourth-ranked net starting field position. And as for the tackling woes, they appear to be a thing of the past. According to Football Outsiders’ charting data, only 3.9 percent of plays by Charger opponents have seen a broken tackle, good for 10th best in the league this year. Relatedly, the Chargers are also allowing the league’s sixth-lowest rate of yards after first contact per rush this season, another major sign of defensive progress as compared with last season.

The Chargers must have practiced their tackling

Los Angeles Chargers’ defensive performance and league ranking in preventing opponents from breaking tackles or gaining yards after contact

Year Broken tackles/play NFL Rank Opponents’ yards after 1st contact/rush NFL Rank
2018 3.9% 10 1.56 6
2017 13.3 31 2.31 32

Source: Football Outsiders, ESPN Stats & Information Group

Los Angeles will put its improved talent and newfound execution on display in London on Sunday, for a game against the Tennessee Titans that ranks among the best of Week 7 in terms of both matchup quality (i.e., the harmonic mean of the two teams’ Elo ratings in each game) and how much it figures to swing either team’s odds of making the playoffs:

The best matchups of Week 7

Week 7 games by the highest average Elo rating (using the harmonic mean) plus the total potential swing for the two teams’ playoff chances, according to FiveThirtyEight’s NFL predictions

Playoff % Playoff %
Team A Current Avg. Chg* Team B Current Avg. Chg* Total Change Game Quality
CAR 43.4% ±12.8 PHI 64.2% ±12.2 25.0 1586
LAC 60.6 14.6 TEN 41.3 12.6 27.2 1524
WSH 38.8 16.3 DAL 40.2 16.2 32.6 1517
BAL 68.7 11.5 NO 72.2 9.7 21.1 1605
CHI 43.0 12.2 NE 78.4 9.0 21.3 1560
CIN 49.6 11.2 KC 95.8 3.6 14.8 1575
JAX 46.7 13.8 HOU 23.6 12.9 26.7 1470
MIA 42.8 12.6 DET 24.3 9.8 22.4 1496
MIN 57.0 13.4 NYJ 14.7 7.1 20.5 1513
LAR 95.8 3.3 SF 3.1 2.8 6.1 1512
ATL 27.7 6.5 NYG 1.2 1.0 7.5 1454
BUF 10.2 5.7 IND 4.1 2.3 8.0 1417
DEN 3.8 2.6 ARI 1.4 0.8 3.4 1418
TB 20.7 5.6 CLE 1.1 1.0 6.6 1394

Game quality is the harmonic mean of the Elo ratings for the two teams in a given matchup.

*Average change is weighted by the likelihood of a win or loss. (Ties are excluded.)

Source: ESPN.com

For the Chargers, it’s part of a long road trip that will keep them away from Southern California until Nov. 18. The StubHub Center doesn’t exactly offer an intimidating advantage even when they are at home, but it does bear watching how L.A. manages all that travel. Even so, the Chargers’ season will still probably hinge on the final few matchups of the season — their last five games are either against division rivals or the biggest threats to their wild-card chances. If Rivers and his improved supporting cast can continue to thrive up to and including the month of December, we’ll know the Chargers have stamped their ticket back to the postseason and given their star QB at least one more chance to shine on the game’s brightest stage.

FiveThirtyEight vs. the readers

Attention football fans! Be sure to check out our constantly updating NFL prediction interactive, which uses FiveThirtyEight’s Elo ratings to forecast the rest of the season. And if you think you can outsmart Elo, step right up to our prediction game, which lets you pick against our model (and your fellow readers) for bragging rights and a place on our giant leaderboard.

Here are the games where Elo made its best — and worst — predictions against the field of prognosticators last week:

Elo’s dumbest (and smartest) picks of Week 6

Average difference between points won by readers and by Elo in Week 6 matchups in FiveThirtyEight’s NFL prediction game

OUR PREDICTION (ELO) READERS’ PREDICTION
PICK WIN PROB. PICK WIN PROB. Result READERS’ NET PTS
BUF 52% HOU 60% HOU 20, BUF 13 +9.4
TEN 53 BAL 54 BAL 21, TEN 0 +4.8
GB 66 GB 75 GB 33, SF 30 +3.3
LAR 69 LAR 75 LAR 23, DEN 20 +1.2
CIN 54 CIN 51 PIT 28, CIN 21 +1.2
MIN 74 MIN 79 MIN 27, ARI 17 +0.9
ATL 67 ATL 64 ATL 34, TB 29 -3.9
SEA 67 SEA 63 SEA 27, OAK 3 -4.4
CAR 55 CAR 58 WSH 23, CAR 17 -5.3
PHI 71 PHI 66 PHI 34, NYG 13 -5.4
NE 54 NE 50 NE 43, KC 40 -6.2
LAC 69 LAC 60 LAC 38, CLE 14 -9.1
NYJ 67 NYJ 57 NYJ 42, IND 34 -9.9
MIA 54 CHI 59 MIA 31, CHI 28 -15.4
DAL 53 JAX 60 DAL 40, JAX 7 -16.2

Home teams are in bold.

The scoring system is nonlinear, so readers’ average points don’t necessarily match the number of points that would be given to the average reader prediction.

What’s been a great season for Elo kept getting better in Week 6 as the algorithm beat the average reader by 55 points, its second-best showing of the entire year so far. Human predictors really only had one major feather in their cap — Houston’s Nathan Peterman-fueled win over Buffalo (a very bad team whose badness Elo refuses to acknowledge) — but otherwise they saw Elo run roughshod over their picks. Elo correctly called wins for Dallas and Miami when readers picked otherwise, and it had a lot more confidence than readers in the Jets’ and Chargers’ victories as well. All told, the average reader is now down 233 points to Elo for the season to date.

Among the readers who weren’t destroyed by Elo, congrats to John D. Harden, who led all users with 275 points in Week 6, and to Jevon Mallett, who continues to lead all users for the season with 453 points. Thanks to everyone who played last week — and if you didn’t play, get in on the game already! You can make picks now and still try your luck against Elo, even if you haven’t played yet.

Check out our latest NFL predictions.

Will The Midterms Decide Who Runs In 2020?

Welcome to FiveThirtyEight’s weekly politics chat. The transcript below has been lightly edited.


sarahf (Sarah Frostenson, politics editor): It is now 21 DAYS UNTIL THE MIDTERMS!! And while voters will mainly be deciding who controls Congress, they’ll also maybe be deciding what kind of Democrat should run in 2020. For instance, if Democrats don’t take back the House, does that mean a Joe Biden run in the 2020 Democratic primary is more likely? Or if there is a blue wave and Democrats gain 60+ seats, does that make the road easier for a more progressive Democrat like Sen. Kamala Harris?

clare.malone (Clare Malone, senior political writer): Man, if the Democrats lose the House, I think there will be some straight-up PANIC.

natesilver (Nate Silver, editor in chief): There would be, although one could ask whether it was warranted or not.

clare.malone: I don’t think Joe Biden needs them to lose the House to prove he’s a good candidate. He could just point to Democratic Senate losses, maybe?

Assuming that Democrats lose in a couple of red states, a candidate like Biden could say, “Look, I will make inroads in a place like that.”

But I’m interested in Nate’s House take.

natesilver: I mean, to a first approximation I think a lot of this stuff is silly.

Here’s why:

As David says, there isn’t much of a pattern for how midterms affect the next presidential election.

Certainly. it will affect Democrats’ attitude, but how much that attitudinal change affects 2020, and whether that is helpful or hurtful to Democrats, is pretty up in the air, IMO.

clare.malone: Right — I mean was just about to say, proof aside (proof! facts!), I think candidates and party apparatchiks always use a loss to motivate their constituents.

That attitudinal thing can be pretty powerful in a primary campaign. See: Bernie Sanders.

natesilver: I’m skeptical that Biden could use Senate losses to justify the need for more conservative candidates … if Democrats also win the House.

We’ll see, though. There are some pretty wacky scenarios that are within the realm of possibility, like Democrats winning 35 House seats but losing four Senate seats.

clare.malone: I think people’s minds are on the Senate right now, though. And the Republican majority there does lie in smaller states and regions that Democrats have gradually lost over the past couple of decades.

It’s not an absurd argument to make in 2019.

perry (Perry Bacon Jr., senior writer): I think Biden has to decide if he wants to run or not. He was kind of confused about whether to run in 2016. And based on what he’s been saying, he doesn’t seem to know now either. I think a really strong push to draft him might encourage him to get in the running. And I think Democrats not winning the House (assuming that they lose the Senate too) will get more people to encourage him to run. Biden would be an important figure if he got in the race, in large part because others in this more “centrist” lane might not run if he is in.

clare.malone: I don’t think Biden is a Mario Cuomo: I think he’ll get in the race. I’m not sure how much he’ll toy with people up until the very end.

natesilver: Are people’s expectations that Democrats will win the Senate? If so, people aren’t paying much attention (certainly not paying much attention to our forecast).

clare.malone: I don’t know. I don’t think people expect that. I guess you hear “blue wave” bandied about and you could make assumptions.

sarahf: And it wasn’t always so dire in the Senate either — it wasn’t until early October that Democrats’ odds worsened dramatically.

But OK, let’s set aside what could happen in the Senate for a moment and assume that there is a huge blue wave in the House and even in some key gubernatorial races like Stacey Abrams’s, in Georgia, and Andrew Gillum’s, in Florida.

It doesn’t mean Democrats win in 2020, but doesn’t it change the playing field of candidates in the Democratic primary? Or would Sens. Harris, Elizabeth Warren and Cory Booker run no matter what?

clare.malone: I think Gillum or Abrams wins would be huge. It would challenge some norms about what sorts of candidates win in states where you need to win over moderates or Republican-leaning independents.

natesilver: Gov. Scott Walker losing his re-election bid in Wisconsin might have some interesting narrative implications too, although not in the same way that Gillum and Abrams do.

perry: I’m interested in Abrams’s and Gillum’s gubernatorial bids and Rep. Beto O’Rourke’s Texas Senate run because they are all making the case that it is a better strategy to try to amp up the base to get greater minority and youth turnout rather than trying to win over swing voters. If they do significantly better in their states than more moderate candidates from previous years, I think that would buttress Democrats like Warren and Harris, who are more likely to run more decidedly liberal campaigns.

But the Midwest is interesting, as Nate is hinting at. The Democrats are doing well in the Midwest with a bunch of candidates who are kind of bland and fairly centrist-friendly. The South and the Midwest are, of course, very different regions, too.

natesilver: I guess I’ve just never dealt with an election before where you’d get the sort of split verdict like the one we’re predicting, where Democrats win the House and do pretty darn well in gubernatorial races but fall short –– and possibly even lose seats –– in the Senate. And some of the high-profile toss-up races could also go in different directions. Maybe Gillum wins in Florida but Abrams loses in Georgia, for example.

In that case, there would be a sort of battle-of-narrative-interpretations over the midterms.

sarahf: As our colleague Geoffrey Skelley wrote, the last time the Senate and House moved in opposite directions during a midterm was in 1982, during under Ronald Reagan’s presidency.

Part of that was because Reagan had a pretty bad approval rating, in the low 40s … which isn’t too far off from where President Trump’s sits now.

natesilver: And I guess 1982 was interpreted as being pretty bad for Reagan? I was 4 years old then, so I don’t remember. 😉

sarahf: But we could get a really weird coalition of Democrats with competing priorities in 2019 if they do take back the House.

And that could make finding a general-election candidate that appeals to both the more moderate and more progressive wings of the party … challenging.

clare.malone: I guess this is why so many people in the post-2016 party were enamored of the Sanders economic message.

It gets to the progressive heart of things while trying to avoid the touchy culture stuff.

But, of course, Democrats have to figure out the Trump factor. Trump will inevitably drag culture wars stuff into a campaign.

perry: Sens. Tammy Baldwin, Sherrod Brown, Bob Casey and Amy Klobuchar are likely to win in the Midwest, an important region of the country for Democrats electorally — and some of that group could win easily. Post-election, we will be able to see the counties in Minnesota where Trump won in 2016 but that Klobuchar carried in 2018 — and I think there may be a lot of them. Plus, that’s the kind of thing she could talk about if she decides to run for president.

clare.malone: Right. But none of those senators have the buzz factor in this shadow primary that we’re in right now.

Nor the fundraising.

But that could change post-November.

sarahf: Speaking of fundraising …

What do we make of all the 💰💰💰 pouring into O’Rourke’s campaign?

Why aren’t more Democratic supporters funding races where the Democratic candidate actually stands a chance of winning?

natesilver: Oh no, you’re going to trigger me, Sarah.

The O’Rourke fundraising narrative is so fucking dumb.

Democrats are raising huge amounts of money EVERYWHERE.

EVERYWHERE.

clare.malone: We spend a lot of time here on numbers, but I always think of people reacting to politicians they really like in almost pheromone-tinged ways. People are irrational actors when it comes to politics — it’s why they vote by party even when the party positions do a 180 (see, ahem, the post-2016 GOP on trade, Russia, and so on.)

perry: In terms of O’Rourke, I was surprised the majority of the money came from Texas, according to his campaign. So it was not just coastal elites who liked seeing a white man delivering Black Lives Matter talking points. Houston, Austin and Dallas all have plenty of Democrats, but they are not Los Angeles, Washington, D.C., or New York. That also pushes back on the idea that he is somehow taking money away from other close races around the country.

clare.malone: Democrats see inspirational stuff in O’Rourke’s response to the NFL kneeling issue and the incident where a black man was shot and killed in his own home.

They like that he’s saying this stuff in Texas.

They also really dislike Ted Cruz.

perry: I think this kind of small-dollar fundraising is a real talent and shows real political appeal. It is what made Howard Dean, Barack Obama and Bernie Sanders such viable candidates.

clare.malone: O’Rourke’s also gotten a lot of media buzz, so people know his name, unlike, say, Sen. Joe Donnelly (running for re-election in Indiana) or former Gov. Phil Bredesen (running for Senate in Tennessee).

So they send O’Rourke money!

natesilver: Texas is also a big state with a lot of wealth, and Democrats there haven’t had a lot to donate to in a while.

perry: I can’t tell if O’Rourke should run for president if he loses the Senate race. But he should definitely think about it.

Hard.

clare.malone: I mean, the thing about O’Rourke running in 2020 is that he’s proved he can fundraise and he’s still young(-ish), but he’s been in Congress awhile, which is an asset. People can’t call him too inexperienced the way they could with, say, failed Missouri Senate candidate Jason Kander.

perry: But I’m not sure how the midterms affect the political outsiders like lawyer Michael Avenatti, billionaire Tom Steyer and former New York Mayor Michael Bloomberg. That is the one group I’m probably the most curious about. I feel like I know who the main established candidates are — the senator and governor types like Warren, Booker or Montana Gov. Steve Bullock. I suspect the more it seems like Democrats are in crisis, the more these outsiders have a rationale to run.

sarahf: Bloomberg did just re-register as a Democrat.

clare.malone: Real question: Does Avenatti actually want to run or does he just like the attention?

I don’t think he really wants to run.

natesilver: I think Avenatti’s chances are overrated because people are overcompensating for their failure to see Trump last time.

natesilver: He massively, massively, massively fucked up in the Kavanaugh thing.

He’s polling at 1 percent.

I don’t think his chances are zero … I just think he’s one from a long list of long shot possibilities.

clare.malone: POLLS!

Bloomberg’s flirtations feel so off for this political moment with the Democrats.

perry: I think Avenatti, Bloomberg and Steyer would love to be president, so if there is demand for their candidacies, they will be more than eager to jump in. But whether there’s demand for their candidacies is going to depend on whether Democrats need a savior.

sarahf: I guess what I’m trying to wrap my head around is: Under what scenario does it make sense for these outsider candidates to run?

perry: If Democrats lose the House and Senate.

natesilver: Make sense for them or make sense for Democrats?

perry: It makes sense for them.

natesilver: If Avenatti thinks it will help to sell more books and put him on TV even more, he’ll run.

If he thinks it will damage his brand in the long term, maybe not.

perry: Yes, Avenatti may just want the fame.

clare.malone: Right.

Steyer and Bloomberg are more interesting because they actually have $$$$.

perry: Bloomberg endorsed Hillary Clinton in 2016. Maybe he feels like he should just run.

He tried to be a team player, and it didn’t work.

sarahf: No matter the national environment for Democrats?

clare.malone: E G O

perry: I think a lot of these candidates are more responsive to, say, “Morning Joe” than FiveThirtyEight.

I will be watching what “Morning Joe” says the day after the election.

sarahf: OK, so, what happens in 2018 means nothing for 2020 … but in a world where they are related, what are you looking for on election night to give you clues about 2020?

perry: I’m looking for results that will create narratives that make it easier for people to run — or not run. I assume Klobuchar wants to be president. Does she win her Senate election by so much that she convinces herself (and others) that she is the electable candidate Democrats want?

Or do Democrats do poorly enough in swing states that people who are too centrist for the party’s activist crowd (e.g., Biden, Bloomberg or Colorado Gov. John Hickenlooper) convince themselves and others that they are the solution?

Maybe O’Rourke, Abrams and Gillum do so well that it’s clear Democrats should try to grow the base and focus on swing voters less. Or they do terribly — and the message is that Democrats should be thinking about the center more.

natesilver: Again, it depends a lot on what happens (obviously). If Democrats sweep both chambers, or lose both chambers, there are some pretty clear takeaways. Otherwise, I’m not sure that the midterms will affect people’s behavior that much. I do think the Abrams and Gillum gubernatorial races are important, though. Plus, there’s the fact that Democrats have nominated an awful lot of women. And if women do well, it could (perhaps quite correctly!) lead to a narrative that Democratic candidates should look more like the party they’re representing, which is to say diverse and mostly female.

perry: I think I might view the 2018 election results less as telling us important information about 2020 and more as data points that will be spun by self-interested people into rationales for what they already wanted to do anyway.

clare.malone: I guess I’m mostly focusing on what kinds of women turn out to vote for Democrats in this election. I want to see whether there’s elevated turnout in communities we don’t usually see elevated turnout in, particularly with women. There are a huge number of female candidates potentially on the Democratic docket for 2020, and Warren, for example, has already made an interesting ad about running as an angry women in the age of Trump. What I’m saying here is that I’m eager to see what the zeigtgeisty take away from Nov. 6 will be, in addition to what stories “Good Morning America” is running vs. “Morning Joe” (as a proxy for what Americans who aren’t microscopically interested in politics will take away from the election).

sarahf: Indeed. And I’ll be looking for FiveThirtyEight’s 🔥 takes as well.

What Happens When Humans Fall In Love With An Invasive Species

On a rocky strip of Lake Superior beachfront, the rites of spring begin at dusk and involve fish. Lots and lots of fish. Every year, like clockwork, slender, silvery rainbow smelt, each no longer than your hand, return from deeper waters. They arrive just as the crust of winter ice on the water breaks apart, looking to spawn in the frigid creeks that run out of the hills north of Duluth, Minnesota. For three or four nights, maybe a week if you’re lucky, thousands of smelt jostle their way out of the lake.

And that’s where the humans are waiting.

On this night in early May, on the narrow mouth of the Lester River, there are only about a couple dozen people present. They stand around, bundled in hooded sweatshirts layered under thick rubber overalls that cover their bodies from toe to nipple. The smelt have not yet arrived and the beach is quiet. Waves lap the shore. Someone kicks a rock.

But 40 years ago, smelt fishing on the Lester River was something else entirely. “There were people all over the place, bumper to bumper on London Road,” said Don Schreiner, fisheries specialist with the Minnesota Sea Grant. These now-tranquil shores were once home to a circus tent that housed an all-night smelt fry and a party atmosphere so wild that Schreiner’s parents wouldn’t even take him and his siblings down to the beach. In addition to hangovers, the smelt also brought a tourism industry. There were professional fishermen catching and selling smelt. It was a huge cultural event. “And then,” Schreiner said. “It crashed.”

Starting around 1979, smelt numbers in Lake Superior plummeted. In ’78, commercial fishing companies took in nearly 1.5 million pounds of smelt. A decade later, the haul was 182,000 pounds. There is no commercial smelt fishing on Lake Superior today. But because the smelt in Lake Superior are an invasive species, their decline is actually a sign that the lake is becoming healthier, ecologically speaking. From a cultural and economic perspective, though, the North Shore isn’t what it was. So is the decline of smelt something to celebrate? And if so, who should be throwing the party?

Some people miss the glory days of Lester River fishing even when evidence suggests that Lake Superior and the people who rely on it are better off now. Facts, it turns out, can’t always sway emotion or reshape business plans. And these issues are not unique to smelt. All over the world, you’ll find invasive species that are beloved by humans — even as these foreign plants and animals alter or damage the environment. The fight against invasive species is often framed as a technological problemhow do you selectively eliminate a species once it’s made itself at home in an environment? But in reality, it’s also a question of human hearts and minds. And those might be the harder obstacle to clear.


Smelt may not fit into the stereotype that invasive species are all bad, but the sea lamprey does. Snake-like fish that suck the blood of other animals, lamprey were devastating to the Great Lakes, all but wiping out populations of native trout. At the same time, native herring populations were also declining, and lamprey may have had a hand in that, too, Schreiner said. The lamprey’s swath of destruction cleared the way for smelt, whose populations grew as they filled the gaps those native species left behind.

In the world of invasive species, sea lamprey are, arguably, public enemy No. 1 — the toothy alien maw grinning from a wanted poster.

But while the lamprey and smelt are connected, they affect the environment very differently. In the world of invasive species, sea lamprey are, arguably, public enemy No. 1 — the toothy alien maw grinning from a wanted poster. Nobody loves a sea lamprey. They kill native fish. They are neither beautiful nor delicious.9 They put commercial fishermen out of work. The story of the lamprey is the story of a clear villain that the good guys can (at least try to) vanquish. A poison designed to kill lamprey, and only lamprey, has helped drop the population from nearly 800,000 to around 100,000 in Lake Superior.

That’s the narrative about invasive species that you’re most likely to hear. Whether it’s kudzu engulfing Southern forests, emerald ash borers wiping out the tree canopy in whole cities, or the beaver-like nutria devouring Louisiana like a swamp buffet, the prototypical invasive species story doesn’t leave a lot of room for the color gray.

A half-hour of fishing nearly fills a 10-gallon bucket with rainbow smelt. On a few nights in early spring, thousands of these invasive (and delicious) fish swim en masse from the deep waters of Lake Superior and into coastal streams.

But smelt are more complicated — which is to say they have more redeeming characteristics. Take, for instance, their relationship with lake trout. Smelt numbers exploded as wild lake trout declined in the 1950s and ’60s. Around the time Don Schreiner’s parents were refusing to take him to late-night fishing parties, commercial fisheries on Lake Superior were bringing in millions of pounds of smelt a year. For the trout that remained, those smelt became a crucial food source, as other, native food supplies were lost. In 1986, smelt accounted for 80 percent of a Lake Superior trout’s diet. Decades later, smelt are still a major food source for trout, even as the smelt themselves may be partly responsible for the shrinking numbers of the trout’s native food source — herring. Smelt also form the basis of the diet of the Lake Superior salmon, another species that came to the lake from somewhere else. The salmon are a mostly self-sustaining population now, but even though they’re not native to the lake, no state government is making an effort being made to eradicate them, Schreiner said, because, well, many people enjoy fishing for salmon.10

All of this produces a rat’s nest of competing interests and emotions. The people who I met fishing on the Lester River want smelt to stick around so they can share a tradition (and a meal) with their children and grandchildren. Steve Dahl, an independent commercial fisherman I interviewed, wanted the smelt gone because they interfered with his herring business. Schreiner sees smelt as a useful, if maybe not ideal, food source that now plays a role in the ecosystem of the lake. And he remembered that in 2005, as Minnesota’s Department of Natural Resources was making long-term plans for managing wildlife in the lake, some people who like to fish for salmon tried to convince the department to start adding more smelt to the lake in hopes of producing more salmon. Even if some people really did want the smelt gone, pretty much everyone I spoke to agreed there’s no clear means of killing the species off.

Turns out, this kind of nuanced story is the norm in the world of invasive species. It’s the sea lamprey — clear villains — that are the exception. In Lake Superior in 2017, for instance, the National Oceanic and Atmospheric Administration counted 82 non-native species, only about a quarter of which were harmful invasive species that provided no redeeming benefits.

Globally, nobody knows exactly how many invasive species have muscled their way into spaces where nature didn’t intend them to go, or what percentage of those species are smelt-like mixed bags vs. lamprey-like forces of pure destruction. Instead, invasion biologists have synthesized decades of research into a simple rule of thumb. Of all the species introduced to new environments, we can assume that about 10 percent will successfully start breeding and living on their own. Of those, about 10 percent will become truly harmful. In other words, 1 percent of all non-native species will end up seriously harming their new homes. We don’t know everything, said Marc Cadotte, professor of urban forest conservation and biology at the University of Toronto, Scarborough. But “we do know it is a small minority of species that end up becoming serious problems.”


Technically speaking, smelt are not an invasive species. Instead, they are classified as a non-native species, a larger category of which invasive species are just a subset. According to a 1999 executive order that established the National Invasive Species Council, an invasive species is a non-native plant or animal “whose introduction does or is likely to cause … harm.” But what counts as “harm”?

The answer to that question is supposed to show us how to cut through the knots of competing interests and decide how to allocate scarce resources for the management of invasive species. But “harm” is also basically impossible to define objectively. An ecologist might see harm as altering the function of the natural ecosystem or reducing the populations of native species, Cadotte said. While someone else, looking at the same situation but focused on economic impacts and recreation, might not see the harms that worry the ecologist. It’s very common to have a plant or animal seem obviously harmful to one group of people and obviously benign to another. Take cats. “Cats are introduced all over the world. They have massive impacts on native songbird populations. But nobody in their right mind would classify them as invasive and try to control them,” Cadotte said. “I mean, except Australia.”

There are plenty of other examples. Take those salmon introduced to Lake Superior and prized by many sport fishermen. The state of Minnesota regulates the size and quantity of salmon you can catch, which helps keep their numbers stable. The Grand Portage Band of Lake Superior Chippewa, on the other hand, treats salmon as an invasive species that it wants gone. There’s no limit on how many of the fish tribal members can catch. In the past, the tribe has actually killed non-native sport fish in its streams in order to more effectively stock those streams with native trout, said Seth Moore, director of biology and environment for the Grand Portage band.

Another example: The earthworms that live in the soil along the shores of Lake Superior are invaders from Europe, and while they’re great for gardens, they alter soil quality in forests and make those ecosystems less hospitable to native plants, said Stuart Reitz, professor of entomology at Oregon State University. In other parts of the country, beekeepers and ranchers have fought bitterly over whether an invasive flower, called yellow starthistle, should be considered generally beneficial (because it is to bees) or generally harmful (because it is to livestock), said Mark Hoddle, director of the Center for Invasive Species Research at the University of California, Riverside.

This isn’t just trivia. Invasive species control is always expensive, and you only get the resources to launch a full-court press against a plant or animal — like the hundreds of millions of dollars spent in the last six decades to get sea lamprey populations under control — on the rare and shining occasion when everyone in power agrees on what “harm” is. And so the definition of invasive species has also created fights within the biological sciences. In 2011, Mark Davis, a biology professor at Minnesota’s Macalester College, published an essay in Nature in which he and 18 co-authors argued that the field of invasion biology had become too weighted toward viewing all non-native species as bad and worthy of eradication. “Harm,” he argued, had come to mean “change.” “And, boy, this world is a bad place to be if any change is viewed as bad,” Davis told me.

But other biologists have pushed back against Davis. Some, like Daniel Simberloff, professor of environmental science at the University of Tennessee, Knoxville, really are suspicious of the idea that an ecosystem changed by non-native species is something that could be neutral or balanced, let alone good. “A parking lot [still counts as] an ecosystem,” he pointed out. But even if this new ecosystem is healthy in its own way, that doesn’t mean it’s a good replacement for the forest that once occupied that land.

Most of the scientists I spoke to, however, had not drawn such hard lines in their views. Non-native incursions could be neutral — or, at least, not bad enough that they needed to be prioritized for eradication. The basic idea was that we should try to stop new invasive species, and when something is really damaging, we should invest in serious eradication efforts, but some non-native species just aren’t worth spending the energy and cash required to get rid of them. Smelt, in this conception, are a non-native species, not an invasive one. They’re here now, and we have to deal with them. “You have to dance with the one what brung ya,” said Marc Gaden, communications director for the Great Lakes Fisheries Commission. “Manage with the reality that’s out there.”

But that could be changing. In the future, it might be easier to wage a lamprey-esque war against a smelt-esque species.


Invasive species management is a small-government sort of problem. The federal government can contribute in some ways, particularly by seizing unwanted flora and fauna during customs checks, but most choices about which species to accept and which to fight are being made at the level of the states … and counties … and cities … and even on the level of individual private parks and reserves. Eradication campaigns are complex and expensive, so usually a lot of people have to agree about that a species is harmful before it gets marked for death. But technology is changing both the costs and the stakes. In a few years, it could be a lot easier and cheaper to stage a successful eradication campaign, Simberloff said.

“We’re getting to the point with the technology where we need to have these conversations for the first time. Do we want a world of gardens, or something wild and dangerous?”

There are a variety of biological controls that scientists may be able to use in the future to produce animals that can’t effectively maintain their own population, reducing a species’ numbers not by killing off existing members but by blocking the next generation from breeding. For example, researchers are working on mosquitoes that are genetically engineered to die off before maturity. And rats whose genome has been altered so that all their offspring are infertile. And fish bred so that all their offspring are male. Simberloff sees that as mostly a good thing — a way to empower governments and communities to protect native ecosystems at a lower cost. A way, more to the point, of pushing back against the Mark Davises of the world who argue that the expense of eradication is reason enough to give up and let an ecosystem change.

But if and when these techniques are perfected, their use — and the disagreements about them — will be highly decentralized. Right now, when there’s a dispute about whether something causes harm, there’s not a clear framework for how to decide who wins. Peer pressure is a big lever, Moore said. He told me that the Grand Portage tribe and other management agencies responsible for Lake Superior waters have all pushed on each other at various times. If there’s enough peer pressure, he said, it can alter the policies of other agencies, as when the state of Michigan was considering allowing fish farms to operate in the Great Lakes. The Grand Portage Band opposed that decision, he said, and so did a lot of other agencies that manage fish on the lakes. Ultimately, the idea was shot down. Some disputes, though, seem to “persist and persist without really being resolved,” Simberloff said. And Reitz told me that the decisions about which species get tackled and which don’t depend mostly on politics — who can make a case that a problem is big enough to deserve government money.

Even then, a different kind of politics can enter the picture. In the summer of 2016, Florida Keys officials sought, and won, the federal government’s approval to release genetically modified mosquitoes with the goal of eliminating an invasive mosquito population … and with it, the risk of the Zika virus. But local residents didn’t want their island to be a testing ground. The political battle has dragged on in the years since residents voted against the trial — even as a different kind of altered mosquito, this one carrying a bacteria that kills other mosquitoes, were released in another part of the Keys and elsewhere.

The future, experts told me, is likely to be full of scenarios like this, where one group is able to move to eradicate a species, even if other, nearby communities disagree. The shape of the natural world would come down to who has the political power, money, will — and vision.

“It all depends on what we want,” Reitz said. “Is it what people wish and desire [to serve human tastes], or do we want some continuous legacy — some long-term persistence with what nature was in the past? We’re getting to the point with the technology where we need to have these conversations for the first time. Do we want a world of gardens, or something wild and dangerous?”


People gather at the mouth of Minnesota’s Lester River, waiting for schools of rainbow smelt to swim in from Lake Superior. Nobody knows exactly when the fish will arrive, so smelting is a social affair where people share bonfires and beer to pass the time.

For now, the smelt will continue to alter the ecosystem of Lake Superior, and their presence will create something different than what existed in the past. And humans’ reactions will be different too. While many of the folks who gathered to fish on the rocky beach of the Lester River were white men, like the crowds Schreiner remembered from childhood, I did meet one woman, Sam Bo. She was Hmong, a member of an indigenous group from Southeast Asia, many of whom have immigrated to Minnesota.

Bo herself lives in the town of Coon Rapids, a two-and-a-half-hour drive from the Lester River. It was her first time making the excursion, but the smelt, she’d been told, were worth it. Lots of Hmong were smelt fishing now, she said, pointing out several other groups on the beach. The fish are similar to a species native to Southeast Asia, and the Hmong there catch them in much the same way.

Finally, as darkness fell, a man waded chest-deep into the water. Holding a net on a long pole, like a porous frying pan, he swished it back and forth along the bottom of the river and came up with net half full of wriggling, bouncing silver fish. In minutes, all the people on the shore had joined him, waddling into the flow as fast as hip waders and uneven ground would allow. Under the moonlight, with small waves gently nudging both her and the smelt toward shore, Sam Bo pulled up a bounty of fish. And she smiled.

Kangaroo attacks couple in northeastern Australia, injures woman

SYDNEY (Reuters) – Australian wildlife carers Jim and Linda Smith are lucky to be alive, an ambulance official said, after they were attacked by a kangaroo in northeastern Queensland state.

The Smiths were feeding wild kangaroos on their property in the Darling Downs when a grey kangaroo buck struck out at Jim Smith, knocking him to the ground.

The kangaroo attacked his wife, Linda, when she ran to help him, leaving her with a collapsed lung, broken ribs, cuts and scratches.

“It’s scary, it knocked me over once or twice and once they grab you, you can see what they do”, Jim said, showing his injuries.

It was only when their son came out and hit the kangaroo with a piece of wood that the marsupial stopped the attack and returned to nearby bushland, Australian media reported.

Linda Smith was taken to Toowoomba Hospital, where she underwent surgery, media reports said.

“If the kangaroo was able to continue to inflict further injury, her life was, yes, in danger,” Queensland Ambulance Service’s senior operations supervisor Stephen Johns said.

Australia has roughly 45 million kangaroos and it is not unusual for them to come into conflict with people as housing has expanded to areas where the marsupials live.

They are even more likely to be driven into populated areas in search of food and water in drought-stricken areas.

Reporting by Stefica Nicol Bikes; Writing by Karishma Singh

The Bears Don’t Need Blitzes To Destroy Your Quarterback

When Vic Fangio was named defensive coordinator of the Chicago Bears in 2015, he took the helm of a ship that was essentially already at the bottom of the ocean. Not only were the Bears mired in a four-season playoff drought, but Chicago was also coming off consecutive seasons in which it fielded arguably the worst defense in franchise history.

“We obviously aren’t a good team,” defensive end Jared Allen succinctly put it in 2014 after the Bears allowed consecutive opponents to pile up 50-plus points, a feat that had no precedent in modern professional football.

Now, Chicago is under the direction of head coach Matt Nagy, atop the NFC North and in the midst of a three-game winning streak for the first time since the beginning of the 2013 season. But seemingly all anyone can talk about is Fangio’s defense.

In its most recent victory, Chicago dismantled Tampa Bay’s then-league-best offense in a 48-10 bloodletting. Chicago’s front seven had Ryan Fitzpatrick and Jameis Winston, who made his season debut, running toward the nearest airport.

Fitzpatrick and Winston haven’t been Chicago’s only victims, though.

When it comes to getting at the quarterback, the Bears are off to the third-best start in franchise history. Even though the team had a bye in Week 5, its 18 sacks rank second in the league, one shy of the Pittsburgh Steelers’ 19. One-fourth of Chicago’s 16 best single-game sack performances since 2015 came in the first four weeks of this season. At 4.5 sacks per contest so far, Chicago is on pace to tie the NFL single-season sack record of 72, a record the Bears set in 1984.

Chicago’s 11.6 percent sack rate1 is 1.5 percentage points ahead of the next-best team. If the Bears can maintain that pace, they would set the the fifth-best mark since 1980, according to Pro-Football-Reference.com. Chicago’s defense is collapsing the pocket better than perhaps any team.

But here’s the remarkable thing about the Bears: They are racking up the sacks despite hardly blitzing.

The Bears rank last in the league in blitzing, defined as sending five or more pass rushers at a quarterback who’s dropping back to throw, with 5.0 per contest, according to data from ESPN Stats & Information Group. If Chicago maintained its blitz average for the rest of the season, it would be the sixth-lowest rate since 2006, the first year for which data is available.

This is in no small part a function of the Bears’ new $141 million linebacker. Khalil Mack, who became the highest paid defensive player in NFL history after the Bears traded for him last month, is tied for fifth in the NFL in sacks (five) and tied for first in forced fumbles (four). In terms of pressure applied, Mack is ahead of the pace he set in 2016 when he was named defensive player of the year. In Week 3 of this season, during the Bears’ 16-14 win over Arizona, the Cardinals went as far as tasking three men with containing Mack. Late in the second quarter, after Mack beat every last one of those Cardinals, his teammate Akiem Hicks swooped in for the sack.

Mack is not only a transcendent talent capable of getting to the quarterback on seemingly every snap; his play has also raised the performance of his teammates. Mack, Hicks, Danny Trevathan, Aaron Lynch and Roy Robertson-Harris have accounted for at least 1.5 sacks apiece this season. “Those boys inside can raise so much hell, it’s outrageous,” said hell-raiser Richard Dent, a Hall of Fame defensive end and a member of the vaunted 1985-86 Bears defense, in an interview with The Athletic.

Blitzing requires a defensive player to eschew coverage in favor of pressure. Like so many other aspects of football, the blitz is a risk-reward proposition. Get to the quarterback quickly enough, and the play is over — and you may have even created a takeaway. Get to the quarterback a step late, and he will likely find a target in the hole you’ve left.

Leaguewide, blitzing is trending down, largely because the game has gotten faster and offensive efficiency continues to skyrocket. It seems that defensive coordinators are content to send fewer pass rushers at the quarterback and instead rely on their secondary in coverage. In four consecutive seasons, the number of blitzes faced by quarterbacks has dropped, according to data from ESPN Stats & Information. Opposing quarterbacks saw a 17 percent decrease from 2013 to 2017 in total five-man blitzes.

Long a proponent of blitz-scarce schemes, Fangio oversees an optimal situation in Chicago, where the Bears largely abstain from blitzing — yet they still manage to get to the quarterback.

“I think the ideal thing is you’d like to pressure when you want to and not feel like you have to,” Fangio told The Athletic. “If you can get to that point, then you feel pretty good.”

Fangio was well ahead of the trend of blitz-less defenses. He has held an NFL defensive coordinator role each season since 2011, when he took that job with the San Francisco 49ers, and over that stretch, his defenses have always been among the league’s most blitz-reluctant outfits.

Other teams have used this formula before. Most notably, Jacksonville last season was able to get to the AFC championship game and field one of the best defenses in football while ranking second in sacks and last in blitzes. Chicago’s defense is 7.6 points better than average this season, according to Pro-Football-Reference’s Defensive Simple Rating System. That’s the franchise’s best mark since the 1985 and 1986 campaigns, when the Bears went a combined 29-3 and won a Super Bowl.

Blitz-less defenses aren’t always dominant; the 2006 Indianapolis Colts blitzed the least of any team for which data is available and were the fourth-worst defense in the AFC. But Chicago’s defense is dominating, leading the league in Football Outsiders’ Defense-adjusted Value Over Average,2 while ranking no lower than third in pass and rush defense.

This weekend, Chicago travels to Miami to take on a Dolphins outfit missing several offensive linemen, setting the stage for more defensive highlights from the Bears. A franchise long synonymous with hard-nosed defense and strong play from the linebacker corps has re-established its identity under Fangio.

Check out our latest NFL predictions.

So You Want To Tether Your Goat. Now What?

🚨🚨🚨 “The Riddler” book is out now! It’s chock-full of the best puzzles from this column (and, fret not, their answers) and some that have never been seen before. I hope you enjoy it, and thank you for riddling with us these past three years. 🚨🚨🚨

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-size and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,4 and you may get a shoutout in next week’s column. If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter.

Riddler Express

From Luke Robinson, a serenading stumper:

My daughter really likes to hear me sing “The Unbirthday Song” from “Alice in Wonderland” to her. She also likes to sing it to other people. Obviously, the odds of my being able to sing it to her on any random day5 are 364 in 365, because I cannot sing it on her birthday. The question is, though, how many random people would she expect to be able to sing it to on any given day before it became more likely than not that she would encounter someone whose birthday it is? In other words, what is the expected length of her singing streak?

Submit your answer

Riddler Classic

From Moritz Hesse, some grazing geometry:

A farmer owns a circular field with radius R. If he ties up his goat to the fence that runs along the edge of the field, how long does the goat’s tether need to be so that the goat can graze on exactly half of the field, by area?

(The great thing about this puzzle, Moritz notes, is that if you get sick of math, you can find the answer through trial and error with your own circular field and your favorite goat, horse, cow, kangaroo, sheep, unicorn, centaur or sphinx.)

Submit your answer

Solution to last week’s Riddler Express

Congratulations to 👏 Stefan Heidekrüger 👏 of Munich, winner of last week’s Riddler Express!

Last week’s Express brought a fill-in-the-blank challenge: What’s the next number in this series?

9, 10, 19, 24, 31, 40, 51, 64, 79, 90, ?

It’s A9.

A9?! What the … ?

The trick to filling in this blank was recognizing that these numbers aren’t in our usual base-10, or decimal, number system. Rather they are in the base-16, or hexadecimal, system. Hexadecimal is often used by computer programmers. And since we only have 10 digits that go with our usual base-10 system, base-16 uses the letters A through F to represent the values 10 through 15.

OK, back to our series. The pattern is \((N+2)^2\), where \(N\) is the number’s position in the sequence. So the first number is \(3^2\), or 9. The second number is \(4^2\), or 16, which is represented as 10 in hexadecimal. The third number is \(5^2\), or 25, which is 19 in hexadecimal. And so on. Our missing number is \(13^2\), or 169 — or A9 in hexadecimal.

Solution to last week’s Riddler Classic

Congratulations to 👏 Eric Roshan-Eisner 👏 of San Francisco, winner of last week’s Riddler Classic!

Last week you were brought in to solve a serious problem at the Riddler Intelligence Agency, or RIA. Namely, the RIA had been infiltrated by spies, and your job was to root them out. There were N agents total, and K of them were spies. You knew the values of N and K but not, at first, the identities of the spies. You could send any number of agents on a remote island retreat as many times as you wanted. If all of the spies were on the retreat, they would assemble for a secret spy meeting; if any of the spies were not on the retreat, the meeting would not take place. The only thing you learned from each retreat was whether or not this meeting happened.

It cost $1,000 per person to send agents on these retreats. What was the least you could spend while still identifying all of the spies? Assume you knew that N = 1,024 agents and K = 17 spies.

This week’s winner, Eric Roshan-Eisner, explained that it will take at least 122 retreats to identify all the spies: The total number of possible spy configurations within those 1,024 people is N choose K, or about \(4\cdot 10^{36}\). That number is very big — but it doesn’t mean we need that many retreats to suss out our spies.

Think of each retreat as a moment to learn one bit of information about the arrangement of spies (that is, whether or not the spy meeting occurred). I’m using “bit” there intentionally — the key to solving this puzzle is to translate that \(4\cdot 10^{36}\) number into binary, a number that needs 122 “bits” — one digit in a binary number — to be expressed. Every retreat you organize returns to you exactly one piece of yes-or-no, 0-or-1 information — that is, whether or not the spy meeting happened. That’s your bit. Therefore, the minimum number of retreats necessary to differentiate between all four undecillion possibilities is 122. The exact strategy you should use to do this, Eric wrote, is left as an exercise to the reader.

Others picked up the baton there. Tim Black, a grad student at the University of Chicago (Go Maroons!), found a strategy to identify the spies in 131 retreats, and also proved that it is impossible to do so in fewer than 122.

Thomas Swayze also found a 131-retreat strategy, which cost about $93 million. Thomas wrote that his strategy to find the spies was to use a form of binary search to single them out one by one: Start with some subset, S, of the agents that we know contains at least one spy. Then pick a subset, T, of S, and keep the agents in T at home while sending the entire rest of the agency on the retreat. If there’s a meeting, we know that T contains no spy — so leave all the agents in T out of all future retreats. If there is no meeting, there is some spy in T. Either way, we now have a smaller set that we know has a spy. Once we’ve outed one spy, we send him on all future retreats and repeat the process to find all the remaining spies, one by one. The tricky part is deciding how big to make the set T. It depends on the number of agents left, the number of spies we’ve caught, and the size of the set S. Thomas was kind enough to share the Python code he used.

Finally, Laurent Lessard described a strategy that used more retreats (191) but cost less (about $66 million).

But hey, if identifying spies were easy — or cheap — everybody would do it.

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