## Colin Kapernick Should Be Washington’s Starting QB

After starting quarterback Alex Smith broke his leg in Week 11, the Washington Redskins rode their journeyman backup, Colt McCoy, to two losses and a 7-3 deficit against the Philadelphia Eagles in Week 13 before he also broke his leg. Struck with misfortune at the most important position in professional sports, Washington trotted out Mark Sanchez, a player signed off the street to back up McCoy.

This obviously didn’t work out well. Sanchez had not played an NFL game since 2015, and he went on to record the worst expected points added (EPA) per play (-0.627) of any NFL QB in 2018 with at least 20 pass attempts. This includes Nathan Peterman. Sanchez was promptly benched in a blowout 40-16 loss to the Giants in Week 14. His replacement: Josh Johnson, a 32-year-old journeyman who has played for 12 different NFL teams and who reportedly had to play Madden to learn the names of his new teammates.

Hindsight is 20-20, but it’s worth asking if this skid could have been avoided — or at least somewhat mitigated — had Washington signed free agent Colin Kaepernick instead of Sanchez. It’s even worth wondering if they still should sign him. A playoff berth for the Redskins is highly unlikely, but they are still not mathematically eliminated. Could signing Kaepernick help the team win out, finish 9-7, and give them a shot at the postseason?

Let’s look at this as a purely football decision and put aside any public relations baggage that would come with signing Kaepernick. Let’s also assume that Kaepernick is in decent enough shape to put on a jersey right now and play at the levels we have seen from him in the past. (For what it’s worth, he has said that he’s remained in game shape.)

I looked at standard measures of quarterback performance like yards per attempt along with more advanced stats like EPA per play and success rate, which measures how often a player keeps his team “on schedule” or on track for a first down. The first question — “Should Washington have signed Sanchez or Kaepernick?” — is straightforward to answer.

Using data from Ron Yurko’s EPA model, I analyzed both of the QBs over their careers to see which one has been better at creating expected value per pass. I also broke out the contribution of yards after the catch to help with the comparison. Yards after catch is probably best thought of as the product of scheme and wide receiver skill, but passes that are on time and on target from a QB surely help as well.

##### Kaepernick has easily outperformed Sanchez

Attempts, yards per attempt, expected points added per play, success rate and yards after catch EPA per play for Kaepernick and Sanchez, 2009-18

Passer Attempts Yards/ Attempt EPA/Play Success Rate YAC EPA/Play
Colin Kaepernick 1,941 7.2 +0.17 0.45 +0.67
Mark Sanchez 2,403 6.6 +0.00 0.45 +0.60

Data includes two-point conversions but does not include kneel downs.

Source: Elias Sports Bureau

The contest wasn’t a contest at all. Kaepernick is superior to Sanchez over his career by a large margin and across a wide spectrum of metrics. Kaepernick’s career yards per pass attempt is higher than Sanchez’s by more than half a yard. His career EPA per play is on the order of 40 times better than Sanchez, despite their yards after catch EPA per play being relatively close.

Kaepernick has been far from perfect. His career yards per attempt is no better than league average, and his career completion percentage is low at 59.8 percent. His greatest flaws as a passer show themselves at the intermediate depths, where his completion percentage is well below average. Whether this is because he struggles to make reads or because his decision making on slower developing routes is poor is an open question. What is clear is that neither Kaepernick nor Sanchez is particularly accurate across most depths of target.

Kaepernick, however, has also affected game outcomes with his legs. He is not exactly young anymore, though, at 31 years old; we might expect a decline in rushing effectiveness that typically accompanies NFL QBs as they age. Still, Kaepernick’s legs are fresh, and Sanchez has never shown the ability to add value on the ground.

Career expected points added per rush for Colin Kaepernick and Mark Sanchez, 2009-18

EPA/Rush
Kaepernick +0.21
Sanchez -0.05

Meanwhile, Kaepernick adds roughly equal value to his team whether he runs or passes the football, making him a legitimate dual threat. It was this ability that took the San Francisco 49ers within 5 yards of winning the 2012-13 Super Bowl. What’s more, the league has become more open to the air raid concepts Kaepernick ran at the University of Nevada, as evidenced by the ascendancy of Kansas City’s Patrick Mahomes, who played in an air raid system at Texas Tech. There are legitimate reasons to believe that Kaepernick could still fit in the league.

Kaepernick’s path to snaps in Washington is blocked by current quarterback Johnson, who has just 193 total career pass attempts to his name and, like Sanchez, is a year older than Kaepernick. When we look at his career efficiency numbers compared with Kaepernick’s, we can see why Johnson hasn’t been allowed much opportunity to throw. Plays with Johnson under center have resulted in negative value for his teams.

##### Kaepernick has outperformed Johnson, too

Attempts, yards per attempt, expected points added per play, success rate and yards after catch EPA per play for Kaepernick and Johnson, 20tk-18

Passer Attempts YARDS/ ATTEMPT EPA/PLAY SUCCESS RATE YAC EPA/PLAY
Colin Kaepernick 1,941 7.2 +0.17 0.45 +0.67
Josh Johnson 193 6.1 -0.04 0.46 +0.60

Data includes two-point conversions but does not include kneel downs.

So what about moving forward? Could Kaepernick help Washington win? Our best predictors of future performance at the QB position are career efficiency measures like yards per attempt and EPA per play — far more useful than looking only at Kaepernick’s most recent season.

##### Kaepernick would be in the middle of the pack this year

Every quarterback with a minimum of 20 pass attempts this season in the NFL, compared with the career numbers of Colin Kaepernick

Source: Elias Sports Bureau

Most starting quarterbacks with NFL experience did indeed create value per play above what we might expect from Kaepernick, but Kaepernick’s worst season is still better than 26 percent of the quarterbacks who have attempted a pass in the NFL in 2018. Kaepernick may be a fringe starting NFL talent, but he is likely better than many of the quarterbacks who have seen playing time this season, including even Alex Smith.

It’s probable that Kaepernick could start for Washington and produce enough with his arm and his legs to salvage their playoff hopes. There remains the opportunity for Washington to sign him and find out for certain. Instead he continues to languish in free agency.

Check out our latest NFL predictions.

CORRECTION (Dec. 15, 2018, 11:45 a.m.): A previous headline on this story misspelled Colin Kaepernick’s name.

## Can You Win Tic-Tac-Toe Blindfolded?

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,2 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

Chess fans like to crow that there are more possible games of chess than there are atoms in the universe. Well la di da. What about us tic-tac-toe devotees? How many possible games of tic-tac-toe are there for us?

## Riddler Classic

From Tom Hanrahan, a twist on the classic:

You are about to play a game of tic-tac-toe, with one advantage and one big disadvantage. The advantage is you get to go first. The disadvantage is you are blindfolded and therefore not informed of your opponent’s moves.

It works as follows. The squares of the board are numbered 1 through 9, like so:

\begin{matrix}\nonumber 1&2&3\\4& 5 &6\\7 &8& 9\end{matrix}

You go first, calling out a number corresponding to the square in which you would like your “X” to be placed. Your opponent then chooses a square for her “O,” but you don’t know which. You continue like this, alternating turns. Whenever you choose a square that is already occupied by your opponent, you are informed that the square is occupied, and you must then choose another one until you find an empty square.

Can you devise a strategy where (just like in regular tic-tac-toe!) you are guaranteed never to lose?

## Solution to the previous Riddler Express

Congratulations to Harry Posner of Boston, winner of last week’s Riddler Express!

Last week we met Louie, who lived in a town that had a 50 percent chance of rain each morning and an independent 40 percent chance each evening. Louie walked to and from work each day, bringing an umbrella with him if it was raining and not bringing one if it wasn’t. On Sunday night, two of his three umbrellas were with him at home and one was at his office. What were the chances that he made it through the work week without getting wet?

The chances of Louie staying nice and dry were exactly 69.27 percent.

This puzzle’s submitter, Josh Vandenham, suggested three ways to get to the answer. The first is to proceed by brute force through all of the possible weather patterns, keeping track of Louie’s umbrellas in each case. There are two relevant times of day, for five days, and two things can happen at each of those points (rain or shine), therefore there are $$2^{10}=1,024$$ possible weather patterns. That’s a lot, sure, but not totally impossible.

The second is to pare down the possibilities and just keep track of the different “states” of Louie’s umbrellas. He could have three at home and zero at work, two at home and one at work, one at home and two at work, or zero at home and three at work. Just four states, which isn’t too complicated. We can see the probability of each state in this glimpse of the spreadsheet of solver Nate Langhinrichs.

By the the time Louie arrives home on Friday night, there is a 30.73 percent chance he has gotten caught out in the rain, sans umbrella, or a 69.27 percent he’s stayed dry.

The third way to solve is to generate some computer-simulated meteorology and commutes. Solver Lowell Vaughn, for example, took this approach and was kind enough to share his Python code.

Finally, yet another way to approach this problem would be with something called Markov chains — models of random events, which use some fancy linear algebra stuff like matrices. In this approach, the state of affairs (the umbrellas) depends on the state of affairs that came before. This approach was used to great effect by solver Aaron Cote. The movement through the random states (the work week) is described by a transition matrix, which contains the probabilities of umbrellas moving from one place to another on any given day. In our particular case, the matrix looks like this:

\begin{pmatrix}\nonumber 0.3 &0.2 &0.0 &0.0 &0.5\\
0.3 &0.5 &0.2 &0.0& 0.0\\
0.0 &0.3 &0.5 &0.2& 0.0\\
0.0 &0.0 &0.3 &0.5 &0.2\\
0.0 &0.0 &0.0 &0.0 &1.0\end{pmatrix}

In this solution, there are five states: zero, one, two or three umbrellas at home plus the state in which Louie has already gotten wet. The rows of the matrix are Louie’s current state, and the columns are his destination. For example, he starts in the third row (two umbrellas at home). There is no chance he’ll end up with zero umbrellas at home, there’s a 0.3 chance he’ll end the day with just one at home, a 0.5 chance with two at home, a 0.2 chance with three at home, and no chance he’ll get wet on this first day. To get the probabilities for the entire work week, we simply multiply this matrix by itself five times, representing the meteorological randomness unfolding over the five days, which gives us the following:

\begin{pmatrix}\nonumber 0.04791 &0.07634 &0.04976 &0.01776 &0.80823\\
0.11451 &0.19889 &0.15274 &0.06752 &0.46634\\
0.11196 &0.22911 &0.22553 &0.12610 &0.3073\\
0.05994 &0.15192 &0.18915 &0.12425 &0.47474\\
0 &0 &0 &0 &1\end{pmatrix}

Last, we take a look at the third row (the state in which he began) and the final column: That’s the chance he gets wet during the week. Subtract from 1 to find the chance that he didn’t get wet and you get 69.27 percent.

All in all, given the extremely precipitous climate in which Louie lives, his haphazard umbrella scheme doesn’t work too badly. TGIF.

## Solution to the previous Riddler Classic

Congratulations to Steve Altschuld of New Albany, Ohio, winner of last week’s Riddler Classic!

Last week, seven antisocial settlers were moving to a circular prairie with a radius of 1 mile, where they would temporarily overcome their anxieties to work together to build houses that were far apart from each other. Specifically, they wanted to maximize the average distance between each settler and his or her nearest neighbor. With seven houses to build, this was pretty straightforward: One would build his house in the center of the circle, while the other six would form a regular hexagon along its circumference. Every settler would be exactly 1 mile from his nearest neighbor, so the average distance is 1 mile. But at the last minute, one especially antisocial settler canceled his move to the prairie altogether, leaving just six settlers with houses to build. With fewer people, could they find a better arrangement? Could they increase the average distance to more than 1 mile?

Yes, indeed they could. Specifically, they could increase the average nearest-neighbor distance to about a whopping 1.0023 miles! Ah, wide-open spaces.

Here’s what the optimal antisocial prairie neighborhood looks like, courtesy of this puzzle’s submitters, Randi Goldman and Zach Wissner-Gross.

Notice that the “center” house is just a little bit off-center. That’s the key.

The particular case of six settlers turns out to be an unusually tricky one, as Randi and Zach explained: If there are two settlers, they’ll simply build houses at diametrically opposite points on the circumference. If there are three, four or five settlers, they will arrange their houses as a regular polygon. If there are seven settlers, they’ll form a regular hexagon plus one settler in the center of the circle. But six is different.

Our winner this week, Steve, explained how he got started with his solving: With six settlers, you can place five houses on the circle and one in the middle. (If all six are on the circle, the best you can do is 1 mile apart.) I placed the five outer houses where they would go if I were creating a hexagon without the bottom vertex. I then realized that I could move the center house north and south a bit and slide two pairs of houses — the two pairs opposite each other east-west on the circumference, one pair above the other pair — around the edge of the circle a bit, in tandem. So now I have a formula with three variables: the distance from the center house to the top house, the angle of the top pair from the top vertex, and the angle of the bottom pair from top vertex. This would be a fairly horrendous equation, so I did what many of us do: I spreadsheeted it and toggled until I got my answer.

Solver Laurent Lessard presented his “modeling and optimization” approach, in which he considers various methods for solving such optimization problems, including hill-climbing, interior points, simulated annealing and the very cool-sounding particle swarms. He illustrated the optimal arrangements for this problem not only for six settlers but also for all numbers from two to 21 — from the simple east-west separation all the way to the intricate Ritz cracker.

This excellent solution sparked an interesting discussion on Twitter, in which mathematical collaborations were proposed, additional optimization techniques were suggested, and it was pointed out that a whole field of academic research was devoted to questions like this as they relate to electron crystals. Not only that, I was alerted to what has become my new favorite website: packomania.com. It is what you think it is.

## 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! Consider your holiday shopping done.

## Want to submit a riddle?

Email me at [email protected]

## Zion Williamson Is The Best College Basketball Player In At Least A Decade

Ten games into what will almost certainly be his lone season in Durham, Duke’s Zion Williamson has treated college basketball like a rim on a breakaway. Which is to say, he has left it trembling.

On game days, the anointed freshman effectively has a residency on “SportsCenter,” his highlights the fantasy-come-true of any sports-radio personality or TV show producer. Need to fill time? Just discuss the comical absurdity of an 18-year-old throwing down midgame windmills with ease or opine that he’d be unable to handle the scrutiny if the Cleveland Cavaliers were to select him in the NBA draft.

Duke head coach Mike Krzyzewski shepherded in one of the most heralded recruiting classes of the modern era this summer, an embarrassment of riches featuring the top three prospects in the country. Unsurprisingly, the Blue Devils rank among the top teams in the nation, their lone loss coming against the veteran-laden Gonzaga Bulldogs in Maui. RJ Barrett, the consensus top-ranked player from the 2018 class, leads the Atlantic Coast Conference in scoring. Yet it’s Williamson who most often elicits the shock-and-awe moments that keep Instagram’s highlight-reel accounts fully stocked. It’s Williamson who draws comparisons — again and again and again — to the incomparable LeBron James. It’s Williamson who is appointment television.1

That’s because college basketball has never seen a player like him.

With a 6-foot-7, 285-pound frame, Williamson looks more like a linebacker than he does a forward. The Wall Street Journal, with the help of a university physicist, found that attempting to draw a charge on Williamson is akin to colliding head-on with a Jeep. Among all active players in the NBA, only Boban Marjanovic outweighs him. And at 7-foot-3, Marjanovic is more than half a foot taller than Williamson. The build of the former South Carolina Mr. Basketball is certainly unorthodox.

At Duke’s practice combine, Williamson’s vertical leap exceeded 40 inches. He corrals rebounds and defends the paint with the unadulterated violence of a center, runs the floor with the fluidity of a modern wing, possesses touch with both hands and has a shooting stroke that stretches to the perimeter. Relative to his size, Williamson’s athleticism doesn’t compute. He’s the Refrigerator Perry of the hardwood.

In the one-and-done era of college basketball, Duke is no stranger to dominant freshman — players like Jahlil Okafor, Jabari Parker and Jayson Tatum. But what Williamson is doing in his first year at this level is downright historic for any player, let alone a freshman.

One way we can assess a player’s contributions to his team is Box Plus/Minus, a metric that estimates the number of points per 100 possessions a player contributes above (or below) average using stats found in the box score. BPM has never seen a college player like Williamson. Among players who qualified for the points per game leaderboard at Sports-Reference.com and appeared in at least 10 games since 2010, the first year for which data for all players is available, Williamson’s mark of +20.4 ranks first among 25,793 individual seasons.

Another way to evaluate a player’s contributions is using player efficiency rating. Williamson’s PER of 41.9 is the best mark by any player who saw action in at least 10 games since 2009, the earliest year for the data.

It happens that Williamson is emerging at a moment in which the NBA is putting a premium on positionless players. A decade ago, Williamson might have been relegated to the post, his skill set withering away against taller opponents on the blocks. However, Krzyzewski doesn’t need to shoehorn Williamson in anywhere; ostensibly, he has free reign to roam the backside of the defense like a safety and run the floor in search of rims to pulverize.

On one of the nation’s deadliest offenses, Williamson is likely the team’s most versatile player, dropping in a team-best 1.18 points per possession,2 according to data provided by Synergy Sports. Because of his size and speed, Williamson has been a nightmare to defend in transition, where he contributes a team-best 1.48 points per possession.3 It doesn’t get any easier for the opposition in the half court, where he ranks in the 91st percentile in scoring.

Fronting Williamson in isolation is a fool’s errand. He pours in 1.31 points per possession in those situations, good enough to rank in the 95th percentile nationally, with an adjusted field-goal percentage of 70 percent. Factor in his uncanny court vision and passing abilities, and the equation gets scarier. On isolation plays that include passes, Williamson is scoring 1.37 points per possession, which ranks in the 96th percentile.

Allow him to find a spot on the interior of the defense, and you’re asking for more problems. Williamson scores a team-best 1.14 points per possession on post-ups, which ranks in the 89th percentile. When the opposing defense doesn’t send an additional defender, Williamson scores a robust 1.44 points per possession, which ranks in the 99th percentile.

Williamson is adept at setting a pick in a pick-and-roll set, but he can also run it. On six pick-and-roll possessions as the ball handler, he scored 10 points.

Defensively, Williamson is more than serviceable. As the primary defender, he allows 0.72 points per possession, which ranks in the 73rd percentile. Duke’s defense has improved considerably from a year ago, when Krzyzewski was so fed up with the team’s performance that he instituted a zone defense. This season, the Blue Devils are playing a zone base on just 3 percent of minutes and rank in the 97th percentile in points allowed per possession. Some of that certainly is attributable to the switchable Williamson, who averages two blocks and two steals per contest.

His numbers already stack up well against the last five players to go No. 1 in the draft — and many draft projections indeed suggest he’ll go first overall.

##### Zion sure looks like a No. 1 overall pick

How Williamson’s scoring prowess compares with previous top NBA draft picks based on their national percentile rank in points per possession

Points Per Poss. Percentile
Draft Player School Overall Off. Transition Half-Court
? Z. Williamson Duke 95% 93% 91%
2018 D. Ayton Arizona 98 93 98
2017 M. Fultz Washington 71 52 70
2016 B. Simmons LSU 80 66 74
2015 K. Towns Kentucky 96 100 94
2014 A. Wiggins Kansas 77 85 68
2013 A. Bennett UNLV 97 93 94
2012 A. Davis Kentucky 99 94 99
2011 K. Irving Duke 99 90 98
2010 J. Wall Kentucky 63 56 48
2009 B. Griffin Oklahoma 94 88 92
2008 D. Rose Memphis 76 62 75
2007 G. Oden Ohio State 88 94 87

Source: Synergy Sports

Williamson is averaging 20.4 points and 9.0 rebounds per contest, with a true-shooting percentage of 67.5. Only three other players since 1992 have hit those benchmarks, and each was an upperclassmen. And let’s not forget to factor his defense into the comparisons: No player in the past 25 years has averaged 20 points, eight rebounds, two blocks and two steals per contest. But that’s where Williamson is.

At its roots, basketball is a sport largely defined by the exploitation of mismatches. Williamson is a mismatch for virtually every player tasked with defending him, and he’s putting up numbers that haven’t been seen in at least a quarter-century. Williamson garnered a reputation as a high flyer by punishing rims and opponents at the high school level, but his first — and likely only — season at the college level has revealed a more polished game that extends to every area of the court, not just above the rim.

## California Dominates Among House Democrats. What Does That Mean For The Next Congress?

California is huge — it has 39.5 million residents, making it the largest state in the U.S. by population. As a result, it has by far the most House members — 53 in total. Texas, by comparison, is the second-most-populous state and only has 36 representatives. So it’s not necessarily surprising that California is sending more Democrats to Congress than is any other state — 46 Democratic representatives in the new Congress will be from California. Still, since the end of World War II, the House’s majority party has never had this large a share of its membership come from a single state.

The state that had the most members in a party’s caucus in a given year has always, of course, been one of the more populous states, like New York, Pennsylvania or Texas. But those large states hold a bigger share of the caucus when they’re dominated by a single party, like California is now. For instance, in the 1946 election, Texas elected Democrats to all 21 of its House seats, which amounted to 11 percent of all House Democrats; the party was in the minority that year after a GOP wave. And New York, which had the most representatives before California took over, sometimes had more seats than any other state in both parties’ caucuses, as it did in 1948 and 1960. Back when California was less of a single-party state, it occasionally pulled off the same feat, including as recently as 2006, when it led the Democratic caucus and tied Texas for the lead in the GOP caucus.

Nearly 20 percent of the incoming Democratic caucus will hail from California, and using data primarily from Gary Jacobson’s data set on House elections from 1946 to 2014, I found that no state has ever been responsible for a larger percentage of the majority party’s House caucus during the post-World War II period.14

That said, California’s share of the Democratic caucus has been even larger than it is now — 20.7 percent after 2014 and 20.1 percent after 2016. The catch is that Republicans won the majority in both of those elections, which meant that even though California represented a significant share of the Democratic caucus, the state’s representatives had relatively little power.

In the Republican delegation, Texas has held the most seats since 2004 (counting 2006, when it tied with California at 9.4 percent) — and it leads the party’s caucus again this year with 11.5 percent of the GOP’s House seats.

From 1970 to 2002, California also had — or tied for — the largest share of the GOP caucus. As recently as 1992, California had a larger share of the Republican caucus than the Democratic one, even though Democrats held more seats in the state. But the GOP’s position in California has weakened since the early 1990s, a trend often blamed on Proposition 187, which in 1994 sought to, among other things, eliminate public services to illegal immigrants and require state employees to report illegal immigrants to federal authorities. The theory is that this ballot measure turned California’s sizable Hispanic population away from the Republican Party, which campaigned in support of the proposition, and drove those voters into the arms of the Democratic Party. Now the California GOP seems almost like an endangered species, a development punctuated by the complete wipeout of Republican members from Orange County — a traditional home of California conservatism — in the midterm election.

Given the size of California’s congressional delegation, it will be interesting to see what issues California Democrats pursue — especially as relates to President Trump. Several members of the state’s delegation are in line to take over key leadership positions in the House, which would give them more power to take on the president, if they choose. For example, Rep. Adam Schiff, the incoming chairman of the House Intelligence Committee, will get to determine whether and how the House is involved in investigations related to Russian interference in the 2016 election, and he just raised eyebrows by saying that the president could face jail time. Rep. Maxine Waters will head the Financial Services Committee, where she wants to investigate the Trump Organization’s financing. Many commentators have also suggested that Waters could pursue the president’s still-unreleased tax returns. Additionally, one lower-profile Californian slated to be a committee head — Rep. Zoe Lofgren, who is in line to lead the House Administration Committee — may be thrust into the national spotlight. Uncertainty surrounding the outcome in North Carolina’s 9th District could lead to a congressional investigation, which Lofgren’s committee would spearhead. Rep. Mark Takano is seeking to chair the Committee on Veterans’ Affairs, and if he succeeds, he’d be the fourth potential Democratic committee chair from the state (that we know of).

For Pelosi, the sizable California delegation could boost her bid to become House speaker again — after all, she faces dissent within the Democratic ranks from a faction looking to spoil her efforts to remain head of the party. Matthew Green, a political science professor at Catholic University, told me that in leadership elections, “lawmakers are more likely to vote for candidates who are elected from their state.” So we might expect most California Democrats to back Pelosi. Still, there is a fairly wide ideological range among the returning California Democrats, and most of the incoming freshmen won seats in battleground races. In fact, one freshman, Gil Cisneros, signed a letter opposing Pelosi’s candidacy for House speaker. So if some new members from previously Republican districts break against Pelosi in her bid for speaker, that would eat into her base of home-state support. However, at this stage, only Cisneros has openly demonstrated opposition and most other California representatives have expressed support.

California Democrats could be too politically diverse to agree on many legislative priorities, but the group may be able to generate momentum on a few specific issues. “You might see a little more action on climate change and immigration that specifically have to do with where California has really pushed back against the Trump administration,” said Eric McGhee, a research fellow at the Public Policy Institute of California. Given the federal-state conflict that has defined the relationship between the president and California in recent years, it would make sense that California Democrats would push hard on environmental issues, even if a Republican Senate and president mean that those initiatives have little chance of becoming law.

## A Weird NFL Weekend Leaves Us Even More Confused

gfoster: (Geoff Foster, sports editor): NFL Week 14 was very odd in many respects (and the week isn’t over) with the Raiders, Niners and Giants winning and the Rams, Texans, Steelers and Patriots all losing. It all went a long way to making the playoff picture even murkier. What was your biggest takeaway from the week?

Salfino (Michael Salfino, contributor): How much should we be worried about the Rams? Is every offense entitled to one hiccup like this, or is it part of a pattern that began with the Lions, who did not care about play-action at all and just covered the receivers. The Bears also did not bite. Does Los Angeles have a Plan B?

neil (Neil Paine, senior sports writer): It was definitely startling to see the Rams’ offense be held in check so thoroughly. Jared Goff was terrible. Todd Gurley did next to nothing. The Rams’ offensive expected points added in the game was -23.5. That was 29.6 points worse than their second-worst offensive game of the season … which was Week 13 vs. Detroit. And it was 33.8 points of EPA worse than their low before the Detroit game.

sara.ziegler (Sara Ziegler, assistant sports editor): I know people talk a lot about playing in the cold as a problem, and I usually roll my eyes. But was that a factor here?

neil: The Rams have only played four games where temp was under 50 degrees in the Sean McVay era.

Salfino: I know, that temperature stuff. I just can’t believe these guys from all different parts of the country are suddenly able to only play in warm weather. But that’s going to be the theory of the case now almost certainly.

gfoster: The Rams game at Detroit was definitely curious. They came out of the bye completely flat, Goff played poorly, and most people kinda wrote it off to rust. But now I’m starting to wonder if teams, as Mike alluded to, are starting to figure out this McVay offense.

Salfino: This kind of thing has happened before. The 1994 49ers team that won the Super Bowl and was electrifying on offense laid an egg against the Eagles that year, losing 40-8. They had 189 yards that game.

And on defense, the 1985 Bears famously flubbed a primetime game against the Dolphins late in the year for their only loss that season.

gfoster: That Detroit game was in a dome, Sara.

Salfino: This can’t be Cooper Kupp, can it? My theory of playing the Rams was to just ignore the running game. I figured a team that gave them fits would basically concede Gurley. What really surprised me about the Chicago performance was that Gurley didn’t even get going. They had nothing. The Bears didn’t even accept the slow death of Gurley running.

sara.ziegler: But why didn’t the Rams even try to run Gurley? Only 11 carries?

neil: Good question, Sara. They had been almost exactly balanced (49.7 percent pass/50.3 percent run) on first down, but last night they passed on 73 percent of first downs. Despite averaging 4.6 yards per carry on the first downs where they did run.

Salfino: My feeling watching the game with Gurley is that the Rams wanted to get wide open passes by faking to Gurley like they usually do, and then when that didn’t work, they were behind the down and distance and had to straight-up pass, with typically disastrous results.

neil: Right — Goff had a 23.0 passer rating on 1st down.

Salfino: What happens to a play-action offense when no one buys into the deception? When the defense just ignores it?

sara.ziegler: I guess I would argue that you should just run the ball.

Especially with a guy like Gurley.

Salfino: Exactly right. That’s when they should run. This is probably why McVay was so hard on himself in the post-game.

sara.ziegler: And for good reason! LOL

gfoster: Let’s talk about the ending of the Dolphins-Patriots game, which was probably the highlight of the year. Although, I may be partial to the Chris Carson front flip a couple weeks ago.

neil: Incredible. Just look at the diagram:

Longest game-winning scoring play in NFL history, I believe.

Salfino: Kenyan Drake made the best nonlateral decision ever on a lateral play. Or maybe the worst since anyone other than Gronk easily tackles him.

gfoster: The funniest sequence of that was when Drake was looking to lateral more and then you could see him to say to himself, “Oh wait, I can just run this in from here.”

sara.ziegler: Gronk definitely failing his defensive audition.

Salfino: Why was Gronk even on the field? It was not a Hail Mary situation 69 yards from pay dirt.

neil: Right, clearly Ryan Tannehill doesn’t have the arm for that throw in the air. He’s not Patrick Mahomes.

gfoster: Tannehill can throw 80 yards. You didn’t know that?

sara.ziegler:

Salfino: Did Drake just laugh at the idea of Gronk tackling him?

Gronk looked like I imagine Brady would trying to make that tackle. And ironically, he finally looked like Gronk on offense.

neil: And Bill Belichick left Devin McCourty off the field for that play in favor of Gronkowski. Shades of Malcolm Butler in the Super Bowl. Too cute for his own good.

gfoster:

sara.ziegler: I just need to take a second to thank Drake for giving me 12.2 fantasy points on that play.

Salfino: Fantasy scoring on that play is hilarious. It goes as a Tannehill touchdown pass. There were no screams about that because who’s playing Tannehill?

sara.ziegler: LOL, good point.

Salfino: How dumb are the Dolphins though for not getting a guy as electric as Drake the ball more on offense? But they’re 7-6. Have to be one of the worst winning teams at this juncture of the season in memory, but they do own wins against the Bears and Patriots.

gfoster: Salfino is not a Frank Gore fan.

Salfino: OMG, Frank Gore. The dude is a survivor, I’ll give him that. He’s going to end up in the Hall of Fame, too. But he’s been just a guy for so long now.

Gronk’s “defense” is getting the headlines, but he had a big game offensively Sunday. There’s no doubt the offense is world’s different when he’s healthy — and it’s hard to remember a playoffs when he was remotely healthy.

Salfino: The Patriots’ problem is that they lacked offensive upside. But then Tom Brady really looked like the Brady of old vs. Old Brady. Gronk got rolling. Gordon was hyper-efficient. The running game was trash, but that’s sort of old-school Patriots too. Even the defense struggling seemed normal. But losing that game was not normal at all. If you told me New England was going to lose, I’d figure it was their offense flagging the game.

neil: Although it’s worth noting they forced zero turnovers against a Tannehill Phins offense.

sara.ziegler: That’s sort of the beauty of those lateral plays actually working: It’s a fluke, not a systemic problem for them.

neil: But this is definitely the type of toss-up game they usually find a way to win, not lose.

sara.ziegler: For sure. Which is what made it so fun!

neil: At least for 31 fanbases searching for Patriots schadenfreude.

Salfino: I really thought one of the Patriots and Steelers would emerge in the AFC, and now maybe both of those teams are going to be playing wild-card weekend.

gfoster: There are four AFC teams at 7-6: Ravens, Colts, Dolphins, Titans. Which one of those is going to make the playoffs in your eyes? Or will it be the Browns, Neil?

neil: They’re “in the hunt”!

For the first time in approximately 30 years.

Salfino: I think the sixth team in the AFC will be the Colts. Andrew Luck is totally out of his shoulder issue and throwing the ball downfield. T.Y. Hilton has nearly 600 receiving yards in the past four games. Luck-to-Hilton is maybe the most lethal combination in football right now.

gfoster: Not Luck-to-Ebron?

neil: For what it’s worth, our model thinks the Ravens still have the best chance at 55 percent.

sara.ziegler: I like the Ravens. They were super unlucky to lose to the Chiefs.

I mean, come on.

Salfino: The Ravens did everything right on defense. Tyreek Hill takes standing eight counts with three different injuries. And you look up at the end of the game and Mahomes has nearly four bills and the Hill has 139 receiving yards. Spencer Ware looked very dangerous. How can anyone stop the Chiefs?

neil: The diagram on that one is amazing, too:

(In case you can’t tell, I am addicted to these things.)

Salfino: Only one player could make that throw, and only one receiver could race to make that catch. The probability for Mahomes-to-Hill should have been, like, 50 percent

neil: Maybe Aaron Rodgers could. But certainly only one QB on a playoff-bound team.

Salfino: Yes, maybe Rodgers.

sara.ziegler: (And he probably doesn’t have a receiver this year who could catch it.)

neil: That might not have even been Mahomes’ most jaw dropping pass of the day!

Salfino: The Ravens blitzed the hell out of Mahomes, and it really seemed to give him fits, but then again you look at the stat sheet and are like, “??????”

gfoster: I would normally say here that the Chargers could hang with the Chiefs and look like the AFC’s Super Bowl-bound team. But that was a somewhat lifeless effort by them Sunday. Against Jeff Driskel and probably the worst defense in the NFL.

sara.ziegler: I guess we’ll find that out on Thursday, when the Chiefs and Chargers play.

Salfino: I thought it was going to be typical Chargers. But maybe typical Chargers is having easily the second-best team in the conference and somehow being the fifth seed. As for the Bengals performance, it fits the “letdown game” theory between Pittsburgh and Kansas City.

gfoster: Although, it should be noted that Mike Badgley hit four of four field goals, including a 59 yarder. That actually ties the total of made Chargers field goals for the last two seasons.

sara.ziegler: LOL

Salfino: How is Hill going to play that game on Thursday? He was like Rocky on the stool at the end of that Ravens game.

The thing about the Chargers that’s weird is their pace of play. They were 29th in plays before last week and then put up another relatively low play count.

Could Mike Tomlin get fired if the Steelers miss the playoffs? Should he?

sara.ziegler: Not in light of the Le’Veon Bell mess, I’m guessing.

The Steelers’ running game was nonexistent, with no James Conner even.

Salfino: Has Bell’s absence even hurt the team? Sunday was the first game you could say they lost because of it, arguably. But the defense could not stop Derek Carr. Think about that sentence in the context of this year.

gfoster: I don’t think this Steelers team is very good. They now have the Patriots and then AT the Saints. They could easily be 7-7-1 going into final week.

sara.ziegler: I’ve been amazed all season at how high the Steelers’ Elo was. But they just kept winning — until the past three games.

neil: Looking at our Elo, though, the Steelers usually pick up steam late in seasons. They haven’t had a swoon like this since 2012.

And that year they could pin it on Charlie Batch starting some games.

Salfino: Explain to me how Roethlisberger goes 25-for-29, the Steelers defense is still near the top of the league in yards allowed per play, and they lose to the Raiders. Tomlin totally blows the end of the game by not calling a timeout, he gets his own lateral play to work, and then the kicker falls down.

sara.ziegler: Field goal kicking has been about average this year, at 84.2 percent made. But this week was a bad one for kickers, who made only 42 field goals out of 56 attempts.

Salfino: Steelers vs. Patriots is the game of the week, but not for the reasons we thought going into the season. These are two desperate teams now. The Steelers are teetering on elimination, and New England can’t win the conference without a bye, IMO.

Do you know how hard it is to pass like Roethlisberger has this year and have a top defense in yards per play and still struggle to win?

gfoster: They haven’t beaten a truly good team this season. Especially now that we can safely call the Panthers a bad team.

And the Jags.

And the Falcons.

The Steelers’ best win was arguably over the Browns!

Salfino: They really should have beaten the Chargers, though. But you’re right.

sara.ziegler: And they would have beaten Oakland, if not for their kicker falling down.

neil: … another really bad team.

Salfino: Are we worried about the Saints? They did not really bounce back at all offensively from last week’s loss to the Cowboys. You have had the feeling all year that Sean Payton was worried about the depth of his receiving corps, and they had nothing other than Michael Thomas on Sunday — and Thomas really had to grind it out. Nothing in that game against a terrible Tampa defense was easy, which is shocking.

gfoster: But on Thanksgiving, we were singing the praises of Brees’s ability to throw TD passes to four different guys who walked in off the street and put on Saints jerseys.

Salfino: I think the Saints defense is underrated now and the Saints offense is overrated.

gfoster: Where are Austin Carr, Keith Kirkwood, Tommylee Lewis and Dan Arnold?

Salfino: Arnold was inactive on Sunday. Crippling loss.

That quartet sounds like a country rock band lineup.

neil: Are we rattling off Saints WRs or members of the 1973-74 Cavaliers?

Salfino: Nice pull, Neil!

gfoster: Brees and the Saints are always bad in Tampa, it seems. Kinda like how Brady always seems to struggle in Miami. What is it about Florida?

Salfino: The Saints really pulled that game out of the fire and it was huge. Could give them the No. 1 seed, and I think they really need it.

gfoster: Here’s a question: If we could switch the results of one of the narrow losses in the first eight weeks, are we talking about the Giants as a sleeper playoff team?

neil: People are talking about the Giants as a sleeper playoff team NOW.

(At least on WFAN.)

gfoster: They have two wins more impressive than Pittsburgh: at Texans, Bears.

Salfino: Eli Manning is going to resign the Giants into giving him a lifetime contract. He is sucking all hope out of their prospective QB search.

Eli is the Frank Gore of QBs.

neil: Sara and I theorized that Eli paid Kyle Lauletta to keep screwing up.

“Here’s $50, go commit a traffic violation in New Jersey.” Salfino: Eli’s last four wins were against opposing QBs Mullen, Fitzpatrick, Daniel, Sanchez. sara.ziegler: My favorite thing in football this season is how bad the Giants are at tanking. Salfino: Exactly! It’s not that hard. sara.ziegler: Remember when the Giants basically didn’t play Saquon Barkley in the second half against Philly? And handed the Eagles that game? Salfino: Although the Jets would have the No. 1 pick right now if Sam Darnold didn’t mess it all up by winning. neil: Broadway Sam can’t help himself. gfoster: A lot of teams are struggling to tank. These guys need to watch more NBA. The Niners won’t quit. Salfino: What about Josh Allen’s insane running. This is not a sustainable QB model, or am I wrong? neil: Did I read that Allen broke a Mike Vick rushing record Sunday? Salfino: No QB ever had two consecutive games of 99+ yards rushing (in the modern era anyway), and now he has three. neil: gfoster: He seems like he’s looking to run. You watch a QB like Watson, Rodgers, Mahomes — they are so reluctant to do it. Always have eyes down the field until they physically cross the line of scrimmage. Salfino: My theory with Allen is that his running is so effective and reliable that it’s hurting his development as a passer. gfoster: He also has the worst supporting cast of possibly any QB ever. Salfino: Darnold escapes to throw and not run, too. Especially on his touchdown pass Sunday, which was an incredible play. sara.ziegler: Allen is like Bizarro Mahomes. Salfino: Sara mentioned the Eagles. Is their window closing? They’re going to have to rebuild their defense, which is bereft of impact players. Their skill players are mediocre. Alshon Jeffery is not a No. 1 receiver, remotely. Suddenly their team-building seems suspect. sara.ziegler: They had seemed to be playing better since that walloping by the Saints. But maybe not so much. neil: Will we look back at 2017 as a weird, one-off year in general? Eagles take advantage of a strange hiccup in the general arc of the game? Salfino: Especially winning with Foles. gfoster: One more NFC East thought: The Amari Cooper trade was probably the most derided front office move of the year. I myself openly laughed at it. Now… sara.ziegler: Salfino: The Cooper trade is going to go down in history as the best in-season deal. He was the missing piece. Everyone else is now in the role that they are suited to be in. Dak Prescott was explosive Sunday. I can’t believe I’m saying it. The bug for the Cowboys was supposed to be their decision-making by Jerry Jones and his family, and that’s turned out to be their strength. Seriously, name the team that’s drafted better recently than the Cowboys. Now add Cooper to this. God, I hate myself for saying this. gfoster: The issue with that trade was more relative to the wide receiver market. Golden Tate, Josh Gordon and Demaryius Thomas were all traded for a far smaller return. The difference is that prior to the deal, I would have lumped Cooper in with that tier of receiver, but it’s possible that his problem was even more Derek Carr than I thought. Salfino: My view is that Cooper is an explosive player who can take the top off the defense. Those other guys, including Gordon now, cannot. gfoster: OK, before we go, I want to get in one college football question off the big news of the weekend: Did Heisman voters get this one right? Salfino: Oklahoma somehow pulled a Favre to Rodgers in college football. sara.ziegler: I’m still kinda shocked that Kyler Murray won. It really came down to performances in the conference championships. neil: It’s funny because the Tua-is-unstoppable narrative had been in place for like two months (or more). Yet the signs were there that Kyler was a legitimate threat to him. He had a better NCAA passing efficiency, better QBR. Betting odds even favored Kyler on Saturday AM. Salfino: My take is that Alabama would be great/No. 1 in the country with pretty much a typical college QB, but Oklahoma absolutely must have Murray to rank where they are. So Murray is the MVP of college football for sure. gfoster: Here’s the flip side of that: Tagovailoa barely played in the fourth quarter most of the season, while Murray was needing to score 40 to 50 points every week to beat any team. Salfino: I’ve heard the draft people concede the Murray would be a first-round pick. Now the question I guess is how high? There are no rules anymore after Baker. sara.ziegler: Unless he’s an Oakland A by that point… gfoster: And, likewise, Mahomes coming out of the same Big 12 nonsense football that looks like two 11-year-olds playing Madden. Salfino: If Murray is a top-five pick, the financial calculus changes dramatically. He may never get another MLB contract. Look at ninth-overall picks in history, for example. neil: Yes it does change the formula we looked at here. gfoster: All right, last question: Quickly give me the Week 14 Super Bowl prediction and No. 1 overall pick prediction, since we have a legitimate race this year. neil: I guess I shouldn’t stick with my October pick of the Vikings… sara.ziegler: LOL They’re not out of it… neil: Although who knows! We’ll see tonight. sara.ziegler: I still think it will be the Chiefs out of the AFC, but who knows from the NFC. Even after last night, I just can’t get behind the Bears. gfoster: Sara, just pick the Vikings, it’s fine. We will forget about it. sara.ziegler: I can’t. The moment I do, it’s over for them. Salfino: I think the Raiders are the favorite for the No. 1 pick because San Francisco is going to face backups against the Rams in Week 17. I picked Saints-Steelers in the preseason. I will stick with the Saints — figuring that Payton figures it out. AFC has to be the Chiefs now. They do have a pass rush. They absolutely cannot lose Hill or Kelce though. (And obviously Mahomes.) Betting on Andy Reid in January though and the Chiefs in January at home, yikes. sara.ziegler: I’ll take a long shot for the No. 1 pick with the Jaguars. That’s a team that looks like it does not care. neil: I will speak for the model and pick the Saints coming out of the NFC. We have them at 26 percent to win it all. AFC favorite is Chiefs, though I share Mike’s concerns there, despite my crush on Mahomes. And I’ll go with the Cardinals at No. 1, our model’s pick for the worst record. ##### Forecasting the race to the bottom Fewest projected 2018 wins according to FiveThirtyEight’s NFL Elo model Wins Team Current Projected remaining Total 32 Cardinals 3 0.6 3.6 31 49ers 3 0.7 3.7 30 Raiders 3 0.8 3.8 29 Jets 4 0.9 4.9 28 Bills 4 1.2 5.2 Simulated ties included as half-wins. gfoster: I’m saying Saints over Chargers. Cardinals with the first pick (they have at Seattle and Rams still). And if the Chargers get drilled by the Chiefs on Thursday, I will sneak into WordPress and delete all of this. Check out our latest NFL predictions. ## WordPress 5 Upgrade: Why I Broke My Site With It Gutenberg sounds like the place that a hard fought battle took place in Europe maybe during the “Great Wars” or during the Middle Ages but Gutenberg is not connected to history its the name given to the new WordPress editor that WordPress 5 brings to the blogosphere. I fully expected and was prepared to backup before upgrading, I have multiple sites so I had tested the upgrade on other sites. I figure though the best way to fix something is to break it first so I went ahead with it and upgraded https://matthewleffler.com to the newest and greatest and YES … it broke a lot of stuff. I’m using it now to post, and I can add stuff to the site, I just cant really edit anything like the homepage or any post or page made with the previous editor I used. I suspect Gutenberg will allow you to edit previous classic editor pages and posts with no fuss, but if you use a 3rd party plugin builder I’d recommend caution. Sometimes when I entered a page I made in a third party page builder it would show in classic form as the familar collection of short codes and strings of letters that arent even in html or css or php for that matter. Its not the 11th hour here, I just suspect the association between the 3rd party builder and building pages has been severed. I expect that a reinstall of the builder or an update from the builder will resolve this issue. Now some of you may be in trouble though. What if your builder came with the theme you may have purchased? As in you didnt purchase the builder…if you have been able to update it then I’d hope you’re headed for smooth calm waters, but of the themes I own thats not the case with any one of them. Gutenberg therefore may be headed to breaking all the themes we’ve gone out and bought. Now Gutenberg is associated with a battle. I personally didnt like it in WordPress 4. My reasons are that as they add features in a sandbox play pen I cant seem to break out of the play pen and do the actual coding I know. Its been my main distaste for Divi and any builder. They make it easier by making it less accessible. So backup your site. If you used a third party builder proceed with caution or wait for updates from your builder’s builder. 🙂 And if you knew html and css and built your site in the classic browser you’re good to go! I am going to be able to get out of having to update my homepage for bit. :-). Thanks Gutenberg. I’m not the only one who is a detractor of this editor. Most of you all are too. The WordPress plugin rating is pretty damning. https://www.matthewleffler.com/wordpress-5-upgrade-why-i-broke-my-site-with-it/ ## The Little, Mathematically Determined House On The Prairie 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 Josh Vandenham, precipitation permutations: Louie walks to and from work every day. In his city, there is a 50 percent chance of rain each morning and an independent 40 percent chance each evening. His habit is to bring (and use) an umbrella if it’s raining when he leaves the house or office, but to leave them all behind if not. Louie owns three umbrellas. On Sunday night, two are with him at home and one is at his office. Assuming it never starts raining during his walk to his home or office, what is the probability that he makes it through the work week without getting wet? ## Riddler Classic From Randi Goldman and Zach Wissner-Gross, little misanthropic houses on the prairie: Antisocial settlers are building houses on a prairie that’s a perfect circle with a radius of 1 mile. Each settler wants to live as far apart from his or her nearest neighbor as possible. To accomplish that, the settlers will overcome their antisocial behavior and work together so that the average distance between each settler and his or her nearest neighbor is as large as possible. At first, there were slated to be seven settlers. Arranging that was easy enough: One will build his house in the center of the circle, while the other six will form a regular hexagon along its circumference. Every settler will be exactly 1 mile from his nearest neighbor, so the average distance is 1 mile. However, at the last minute, one settler cancels his move to the prairie altogether (he’s really antisocial). That leaves six settlers. Does that mean the settlers can live further away from each other than they would have if there were seven settlers? Where will the six settlers ultimately build their houses, and what’s the maximum average distance between nearest neighbors? ## Solution to the previous Riddler Express Congratulations to Brenda Holloway of Manchester, Connecticut, winner of last week’s Riddler Express! Last week, Alice and Bob were facing off in a footrace. The route was a straight path out followed by the same straight path back. But Alice literally wanted to face off — she wanted to run faster than Bob such as to maximize the amount of time they spent facing each other after she made the U-turn but before the two passed each other going in opposite directions. Assuming the turnaround time is negligible and the two each commit to running the race at a constant speed, how much faster than Bob should Alice run? If Bob runs at speed $$B$$, Alice should run at speed $$(1+\sqrt{2})B$$, or about 2.4 times his speed. This (obviously) is a maximization problem, meaning we’re trying to find the value of a variable that maximizes some larger expression. That means we need a mathematical expression to maximize. Let’s try to piece that together. Suppose the distance to the U-turn — that is, the halfway point of the race — is $$D$$. (It won’t matter exactly what that distance is.) Suppose Alice’s speed, which we’re trying to calculate, is $$A$$. The time it takes Alice to get there is $$D/A$$. In that amount of time, Bob will have run a distance of $$B\cdot (D/A)$$. So the distance between the two runners at the moment Alice turns around is $$D-B\cdot (D/A)$$. Now the two are running toward each other, so we must combine their speeds. They will, combined, cover that distance and pass each other after a time of $$(D-B\cdot (D/A))/(A+B)$$. That’s the amount of time we want to maximize. A handy mathematical way to maximize things is to take derivatives. Specifically, we want to take the derivative of the expression above with respect to $$A$$, set it equal to zero, and solve that for $$A$$. That will give us a set of extremes, be they maxima or minima. The derivative of the expression that we’ll set to zero looks like: \begin{equation*}\frac{D(-A^2+2AB+B^2)}{A^2(A+B)^2}=0\end{equation*} That equation equals zero for two values of $$A$$: $$(1+\sqrt{2})B$$ and $$(1-\sqrt{2})B$$. The latter of these doesn’t make sense for the case of our footrace (it’s negative), so we know the first must be the value we’re after. If Bob runs at speed $$B$$, Alice should run at speed $$(1+\sqrt{2})B$$, or about 2.4 times his speed. ## Solution to the previous Riddler Classic Congratulations to Peter Ingraham of Brooklyn, New York, winner of last week’s Riddler Classic! Last week, after facing each other down for so long in that footrace, Alice and Bob fell in love, got married and wanted to have kids. Potentially lots of kids. They figured out that the amount of work involved in having a child is equal to 1 divided by the age of that child. So if a child is 0, the work is infinite. If the child is 1, the work is 1; if a child is 2, the work is ½; and so on. They decided that they only wanted to have another kid if and when the total work involved for all of their other kids was equal to 1 or less. Ignoring real-world technicalities such as death, twins and the inability to decide precisely when one has a child: Will Alice and Bob have an infinite number of children? Can we predict, with an equation, when they will have their Nth child? First, yes, Alice and Bob would have infinity children if they could. But they would have them very, very slowly. After about 10,000 kids, they’ll have to wait more than 10 years to have the next one, and the gap between children keeps increasing forever. Solver Scott Wu plotted how long they will wait to have their next child, based on how many children they’ve had so far, for their first 50,000 children. That looks like this: Our winner this week, Peter, provided the following proof-by-contradiction of why the number of children the couple will eventually have is infinite: Suppose for the sake of argument that there was some point where Alice and Bob stopped having more kids, and that at this point they have $$k$$ kids and $$n$$ years have passed. Let’s examine the amount of work required at time $$2n$$. All the kids are now age $$n$$ or more. As an upper bound, each kid is worth at most $$1/n$$ work, the amount required for the youngest child. Therefore the total work is at most $$k\cdot (1/n) = k/n$$. But the number $$k$$ is always less than $$n$$: The gaps start at 1 year and always get longer. So Alice and Bob should have had another kid by this time since their total work $$k/n$$ is less than 1. This is a contradiction. Therefore they never stop having kids. There does not appear to be an exact, elegant formula for when Alice and Bob have their Nth child. But the Nth child does come at approximately N log N, a fact that we could ascertain by generating lots of simulated child data and running a regression. So, for example, the 1,000th child would be born approximately 1,000 log 1,000 — or 6,908 — years after the first child. Solver Laurent Lessard plotted the birthdates by the ordinal childbirths: “Meet my brother, Bob Smith CMXLVII. Yeah, he’s my big brother, can’t you tell? He was born about 5,000 years ago.” ## 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! Consider your holiday shopping done. ## Want to submit a riddle? Email me at [email protected] ## Trump Is Only Popular In Rural Areas Welcome to Pollapalooza, our weekly polling roundup. ## Poll(s) of the week The 2018 midterm election confirmed America’s urban-rural divide; Democrats excelled in cities, Republicans dominated in the country and the suburbs were the tiebreaker that handed Democrats the House. Will the 2020 election play out the same way? This week, we got two polls of President Trump’s approval rating that suggest it might. First, a Selzer & Co. (one of our favorite pollsters) national poll conducted Nov. 24-27 for Grinnell College found that Trump had a 43 percent approval rating and a 45 percent disapproval rating among all adults. However, his support isn’t distributed equally across different types of communities. He’s enormously popular among residents of rural areas, with a 61 percent approval rating and a 26 percent disapproval rating. In small towns, that breakdown is 44 percent approve vs. 42 percent disapprove. But in suburban areas, only 41 percent of residents approve of the job that Trump is doing as president, while 50 percent disapprove. Trump’s approval rating is lowest among urbanites — 31 percent approve of him while 59 percent disapprove. We saw similar geographic trends in an Investor’s Business Daily/TIPP poll that was conducted from Nov. 26 to Dec. 2. Trump again got the highest marks from residents of rural areas — a 62 percent approval rating and a 35 percent disapproval rating. And yet again, his standing took a nosedive among suburbanites and urbanites. In suburban areas, Trump’s approval rating was 32 percent, and his disapproval rating was 60 percent. In urban areas, his approval rating was 27 percent, and his disapproval rating was 67 percent. (The IBD/TIPP poll didn’t include “small town” as an option for respondents.) Overall, Trump’s approval/disapproval spread was much lower in the IBD/TIPP poll (39 percent approve, 55 percent disapprove) than it was in the Selzer poll, which explains why the IBD/TIPP poll is worse for Trump in all three geographic categories as well. Here are the results of the polls side by side: ##### Trump is more popular in rural areas Presidential net approval rating among adults by density type Category Selzer Poll IBD/TIPP Poll Urban -28 -40 Suburban -9 -28 Small town* +2 Rural +35 +27 Overall -2 -16 * The Investor’s Business Daily/TIPP poll did not include a breakdown for “small town.” Sources: Selzer & Co., Grinnell College, Investor’s Business Daily This is perhaps stating the obvious, but Trump would do well to improve his standing among suburban and urban voters before 2020. Less than 20 percent of the U.S. population lives in rural areas. Granted, not all rural voters will cast their ballot for the president, nor will all urban and suburban voters back whoever is the Democratic nominee. But elections are winner-take-all contests waged within discrete geographic areas — states or districts. According to the Congressional Density Index from CityLab, a news website covering urban issues, just 70 congressional districts are “pure rural,” and an additional 114 are a “rural-suburban mix.” CityLab is still in the process of making similar assessments for states, but David Montgomery, a journalist for CityLab, told FiveThirtyEight that 11 states could be classified as mostly rural, while an additional 17 could be classified as a mix of rural areas and suburbs. The former are worth a combined 53 electoral votes, while the latter are worth a combined 138; 270 are needed to win a presidential election. None of this means that Trump lacks a path to electoral victory. It’s still early in the 2020 campaign; approval ratings may change, and a person’s feelings about the president aren’t the only determinant of his or her vote. But those numbers aren’t great for Republicans even if institutions like the Electoral College give disproportionate influence to rural areas. Without urban and suburban areas, they’ll find it difficult to cobble together a sustainable majority. ## Other polling nuggets • A YouGov poll found that only 26 percent of Americans either “strongly” or “somewhat” approve of the way Trump is handling the fallout from the killing of journalist Jamal Khashoggi. There was a sharp party divide in responses: 57 percent of Republicans approved, while only 6 percent of Democrats did. • 59 percent of Americans today either “strongly” or “somewhat” approve of the way George H.W. Bush handled his presidency, from 1989 to 1993, according to YouGov. That includes 53 percent of Democrats and 77 percent of Republicans. You can see for yourself how Bush’s approval rating changed over the course of his presidency using our presidential approval rating tracker. • A Gallup poll taken in France earlier this year, before the riots in December over increased living costs, found that President Emmanuel Macron’s job approval had declined by double digits among the three poorest of France’s five income groups but remained virtually unchanged among the two richest groups. • Americans still prefer to watch the news instead of reading or listening to it, according to a study by the Pew Research Center: 47 percent of respondents said they preferred to watch the news, 34 percent said they preferred to read the news, and 19 percent said they preferred listening to it. These habits remained mostly unchanged from 2016. Among those who would rather watch the news, 75 percent said they preferred doing so on the television, while 20 percent said they preferred to watch online. • A poll conducted by The Research Moms, a group of researchers at Edison Research, found that only 15 percent of moms said they split parenting responsibilities evenly with another parent. Forty-three percent said they handle the majority of the parenting responsibilities, and 41 percent said they handle all the parenting responsibilities. The Research Moms surveyed mothers in the U.S. age 18 to 64. • According to a Quinnipiac poll of New York City voters, 57 percent of New Yorkers approve of Amazon locating one of its new headquarters in Queens, while 26 percent disapprove. But when respondents were asked about the$3 billion in tax breaks that Amazon will get from the city and state government as part of its deal to relocate, support was roughly split, with 10 percent unsure.
• Support for Amazon is even higher in Virginia, where a second headquarters is planned. A poll by Christopher Newport University asked registered voters in the state whether they approve or disapprove of the announcement that Virginia would provide \$573 million in incentives for an Amazon headquarters; 68 percent said they approve of the announcement, while 30 percent said they disapprove.
• The masses have spoken, determining that “Die Hard” is not a Christmas movie. That’s according to a Morning Consult/Hollywood Reporter poll, which found that only a quarter of American adults considered the Bruce Willis vehicle a Christmas movie; 62 percent said it was not, and 13 percent said they didn’t know or had no opinion on this important matter.
• Armenians go to the polls Sunday to participate in snap parliamentary elections, the first since the “non-violent velvet revolution” protests in April and May that resulted in the resignation of Prime Minister Serzh Sargsyan. An in-person survey of 1,100 voters conducted this week by an affiliate of the Gallup International Association in Armenia found that more than 69 percent of Armenians who plan to participate in elections said they would vote for the My Step alliance, led by current acting Prime Minister Nikol Pashinyan, followed by about 6 percent who said they would vote for the Prosperous Armenia Party. The Republican Party of Armenia, which had served as the ruling party, polled at less than 2 percent.

## Trump approval

According to FiveThirtyEight’s presidential approval tracker, 42.1 percent approve of the job Trump is doing as president, while 52.3 percent disapprove (a net approval rating of -10.2 points). At this time last week, 42.4 percent approved and 52.6 percent disapproved (a net approval rating of -10.2 points). One month ago today, Trump had an approval rating of 41.8 percent and a disapproval rating of 52.8 percent, for a net approval rating of -11.0 points.

## Did The Packers Squander Aaron Rodgers?

The dismissal of Green Bay coach Mike McCarthy — who was let go after the Packers’ stunning home loss to the Arizona Cardinals on Sunday — wasn’t exactly a shock. Perennially tabbed as a Super Bowl contender out of the NFC, McCarthy’s team had gone just 11-16-1 over the past two seasons, including a disappointing 8-9-1 in games that featured future Hall of Fame quarterback Aaron Rodgers as Green Bay’s primary passer.1 It was time for a change along the sidelines that Vince Lombardi once roamed.

Things weren’t always so bleak on the frozen tundra. The McCarthy era had its high points, particularly early on — when he and Rodgers appeared to have Green Bay positioned on the cusp of a potential dynasty. But between postseason near-misses, roster changes, injuries and coaching miscues, McCarthy’s Packers never fulfilled that promise. Instead, it’s fair to wonder whether Green Bay squandered the prime of one of the most talented QBs in NFL history.

The Packers team that McCarthy inherited in 2006 from Mike Sherman2 was one in transition — and that meant navigating some heavy-duty Brett Favre melodrama in his first two seasons at Green Bay’s helm. However, McCarthy quickly found that he had an all-time great on his hands in Rodgers, who, when he took over the starting job at age 25, was just entering his best years as a passer. The McCarthy-Rodgers marriage sputtered to a 6-10 finish in its first season but yielded great results shortly thereafter: an 11-5 playoff campaign in Year 2, then a Super Bowl crown in Year 3 and a 15-1 regular season (with Rodgers winning MVP) in Year 4. The sky seemed to be the limit for McCarthy and his star QB.

Since the end of the 2011 regular season, however, the Packers have gone just 5-6 in the playoffs; by comparison, Tom Brady and the postseason Patriots are 13-5 over the same span. Green Bay’s record includes a crushing home defeat against the New York Giants two weeks after that 15-1 season ended and another loss in which they watched helplessly as ex-49er Colin Kaepernick destroyed their defense in 2012 — still one of the greatest individual QB games in playoff history. The Packers’ postseason circumstances have not always been ideal: For instance, that Giants game was actually the only time since 2011 that Green Bay lost in the playoffs while favored — meaning the rest of the losses were as underdogs. But at the same time, the Pack have also had clear chances to return to the Super Bowl, and they came up short in each of them.

All told, it remains mystifying that a quarterback of Rodgers’s stature hasn’t won more frequently. If we run a simple logit regression between a QB’s Yards Above Backup in a season and whether his team made the Super Bowl,3 we’d expect Rodgers to have made 1.86 Super Bowls in his career through 2017 — roughly twice as many as he’s actually been to. (Meanwhile, other contemporary QBs — such as Ben Roethlisberger, Eli Manning and even Brady — have gone to more than twice as many Super Bowls as we’d expect from their individual stats.)

##### Rodgers hasn’t won as much as he should have

Top 10 NFL starting quarterbacks by Yards Above Backup QB, 1990-2017, with their actual and expected Super Bowl appearances

Quarterback Years Starting YARDS Above Backup Actual Expected Diff.
1 Peyton Manning 17 21,585 4 4.15 -0.15
2 Tom Brady 16 19,735 8 3.63 +4.37
3 Drew Brees 16 17,250 1 2.89 -1.89
4 Brett Favre 19 13,047 2 1.86 +0.14
5 Aaron Rodgers 10 10,988 1 1.86 -0.86
6 Ben Roethlisberger 14 10,945 3 1.35 +1.65
7 Philip Rivers 12 10,721 0 1.54 -1.54
8 Steve Young 8 10,022 1 1.65 -0.65
9 Matt Ryan 10 8,251 1 1.14 -0.14
10 Tony Romo 9 8,192 0 1.11 -1.11

1990 was the first season of the NFL’s current playoff format. Expected Super Bowls are based on a season-by-season logit regression between a QB’s Yards Above Backup and whether his team made the Super Bowl.

Source: Pro-Football-Reference.com

Over time, it became more and more difficult for the Packers to come within striking distance of the Super Bowl. In 2015, Rodgers slumped to career-worst numbers without top wideout Jordy Nelson, though the team as a whole was still good enough to get to the divisional playoffs before losing. In 2016, it was more of the same when Rodgers mused that Green Bay could still “run the table” — sparking an eight-game winning streak that saw the QB return to vintage form and left the Packers a win away from the Super Bowl.4 By then Rodgers was 34 years old, so a sense of urgency was setting in when 2017 came and went without a playoff berth — even though that could be written off as the byproduct of Rodgers missing nine starts.

The 2018 season was always going to be the real crossroads for McCarthy. With a healthy Rodgers leading the way, the Pack could always count on contending in the past, so this year’s expectations were no different. But Rodgers’s numbers have been merely good, not great. Brett Hundley isn’t around anymore to take any blame. And unlike in 2015, when Green Bay was talented enough to survive despite a downturn in its QB’s individual stats, there has been no answer from the team’s supporting cast this time around. It all came crashing down around McCarthy in the loss to Arizona as 13½-point favorites, Green Bay’s single most disappointing defeat since the merger according to Pro-Football-Reference’s point-spread data.

We can visualize the Packers’ decline over McCarthy’s final few years at the helm using FiveThirtyEight’s Elo ratings. Specifically, I’ve been tinkering with an experimental version of Elo that keeps a separate adjustment for the primary QB in each game, similar to how we treat starting pitchers in our MLB ratings.5 Using this, we can trace how a team’s performance rises and falls independent of its QB — which is useful in cases like 2017, when Rodgers was hurt and Hundley started nine games. (For instance, by season’s end, the Packers would have projected to be a 1529 Elo team with Rodgers starting — compared to a 1427 team with Hundley. And remember, 1500 is average.)

At the beginning of 2015, the Packers had an effective Elo of 1622, which included a 73-point boost from having Rodgers at QB and a 49-point boost from his teammates. By the end of the year, Green Bay’s effective Elo was still in the same neighborhood (1597), despite Rodgers’s adjustment actually dropping to negative 11, because the rest of the team carried a larger share of the weight (+108). Meanwhile, at the peak of the Packers’ run-the-table surge in 2016, the team’s 1657 effective Elo arose out of a 61-point boost from Rodgers and 97 additional points (relative to league average) from the rest of the team.

But fast-forward to now, and it’s clear how much the Packers have crumbled around Rodgers. His own adjustment is 16 points of Elo above an average QB, the lowest it’s been since Week 10 of the 2016 season. But he’s still expected to be above average; his supporting cast, by contrast, has fallen to a negative-67 score relative to the average team. That’s the worst they have been in Rodgers’s entire NFL career, and it isn’t especially close. Keeping QB play constant, the Packers’ Elo has dropped by a total of 139 points since the end of the 2016 season, which is essentially the difference in current Elo ratings of the 11-1 Los Angeles Rams and the 6-6 Carolina Panthers.

The reasons for the slide are varied, but many can be traced back to a series of poor drafts under former general manager Ted Thompson, who was replaced by current front-office chief Brian Gutekunst in January. As Sports Illustrated’s Kalyn Kahler pointed out last week, only three of Green Bay’s 17 draftees from 2014 and 2015 remain on the current roster. While no team can avoid dry spells in the NFL draft if given enough time, the Packers also — largely by design — did little in the way of enlisting outside help as a backup plan.6 Combine those infrastructural problems with criticisms of McCarthy’s offensive scheme (criticisms of a perceived lack of innovation that Rodgers apparently shared), plus legitimate complaints about Rodgers’s own decline in performance, and a season like this was bound to happen to Green Bay sooner or later.

Even so, it came contrary to preseason predictions. Going into the schedule, you might have penciled in this week’s matchup against the Atlanta Falcons as a marquee game with playoff implications. Instead, it will be the third-worst game of the week, according to our combination of matchup quality (i.e., the harmonic mean of the teams’ Elo ratings in each game) and game importance (how likely it is to swing every team’s odds of making the playoffs):7

##### The best matchups of Week 14

Week 14 games by the highest average Elo rating (using the harmonic mean) plus the total potential swing for all NFL teams’ playoff chances based on the result, according to FiveThirtyEight’s NFL predictions

Playoff % Playoff %
Team A Current Avg. Chg* Team B Current Avg. Chg* Total Change Game Quality
BAL 65.0% +/-15.1 KC 100.0% +/-0.0 31.8 1628
PHI 28.3 24.2 DAL 81.1 19.4 51.0 1578
MIN 59.7 19.9 SEA 87.7 11.8 41.4 1572
CHI 94.4 4.3 LAR 100.0 0.0 10.8 1615
IND 9.8 10.1 HOU 98.2 2.4 23.6 1515
MIA 6.6 7.4 NE 99.7 0.5 16.2 1537
WSH 26.4 11.7 NYG 0.1 0.1 24.9 1435
TB 1.7 2.0 NO 100.0 0.0 6.9 1570
TEN 18.9 10.6 JAX 0.1 0.1 21.9 1478
PIT 83.8 11.0 OAK 0.0 0.0 23.7 1453
CAR 17.8 9.9 CLE 0.3 0.4 22.0 1454
DEN 20.9 11.1 SF 0.0 0.0 24.7 1427
LAC 96.0 3.6 CIN 0.9 1.3 9.1 1504
GB 1.4 1.3 ATL 1.1 1.2 5.5 1469
DET 0.3 0.3 ARI 0.0 0.0 4.2 1412
BUF 0.0 0.0 NYJ 0.0 0.0 2.4 1377

Game quality is the harmonic mean of the Elo ratings for the two teams in a given matchup. Total Change adds up the potential swing in playoff odds for every team in the league (not just the two teams listed).

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

Source: ESPN.com

Although the Packers hadn’t replaced a coach at midseason since 1953, Sunday’s loss forced their hand. Now they’ll need to figure out who’s next, from a candidate list that includes big names among both pro coordinators (Josh McDaniels) and up-and-coming college coaches (Lincoln Riley). They’ll also need to hope Rodgers’s issues were more related to McCarthy’s offense and less to his getting older and less productive — basically, that the next Packer coach will be more Mike Shanahan to Rodgers’s John Elway than Jimmy Johnson to his Dan Marino. So while the Packers may not have much on the line over the rest of their games, this promises to be the most interesting offseason Green Bay has had since Favre was retiring and unretiring more than a decade ago.

Make sure to check out FiveThirtyEight’s Elo ratings using our NFL prediction interactive, which simulates the rest of the season 100,000 times and tracks how often each team should make the playoffs and win the Super Bowl. And did you know you can also pick against the Elo algorithm in our prediction game? Maybe you can also climb up our giant leaderboard (or, if you’re like me, fall down it with each passing week).

Here are the games in which Elo made its best — and worst — predictions against the reader picks last week:

##### Elo’s dumbest (and smartest) picks of Week 13

Average difference between points won by readers and by Elo in Week 13 matchups in FiveThirtyEight’s NFL prediction game

PICK WIN PROB. PICK WIN PROB. Result READERS’ NET PTS
CIN 52% DEN 59% DEN 24, CIN 10 +8.5
PIT 62 PIT 54 LAC 33, PIT 30 +6.7
LAR 68 LAR 79 LAR 30, DET 16 +4.1
ATL 53 ATL 50 BAL 26, ATL 16 +1.5
KC 83 KC 89 KC 40, OAK 33 +0.4
SEA 83 SEA 83 SEA 43, SF 16 -1.5
MIA 58 MIA 57 MIA 21, BUF 17 -2.3
NE 67 NE 65 NE 24, MIN 10 -3.8
PHI 69 PHI 66 PHI 28, WSH 13 -4.1
TEN 78 TEN 72 TEN 26, NYJ 22 -4.4
CHI 69 CHI 72 NYG 30, CHI 27 -6.1
HOU 77 HOU 69 HOU 29, CLE 13 -6.6
CAR 59 CAR 64 TB 24, CAR 17 -7.8
GB 73 GB 79 ARI 20, GB 17 -10.5
IND 51 IND 62 JAX 6, IND 0 -14.0
NO 64 NO 74 DAL 13, NO 10 -15.3

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.

After a series of narrow wins at midseason, the algorithm handed the readers their worst loss (-55.2 points on average) since Week 3. Some of the blame can go to the subject of this column — the Green Bay Packers, whose loss not only cost Mike McCarthy his job but also cost users 10.5 points on average. But readers were also burned by the Jaguars’ win over the Colts and the Cowboys’ upset victory over the Saints. Add it up, and Elo has beaten the average reader 12 times in 13 weeks this season.

But congrats to Mike Edelstein, who led all users in Week 13 with 137.0 points, and to one of my favorite leaderboard names, Greg Chili Van Hollebeke, who maintained his No. 1 ranking on the season with 1,002.1 points. Thanks to everyone who has been playing — and if you haven’t, be sure to get in on the action! 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.