What We Learned From The First House Vote On Impeachment

Today’s House vote to formalize the impeachment process, spelling out its rules and procedures, isn’t the impeachment vote. That vote — on whether to make Donald Trump only the third-ever president2 to be impeached — will likely come later, after the House holds public hearings. But Thursday’s vote still told us a lot about how the House impeachment is likely to play out.

Simply put, it’s a good bet that not much will change no matter what happens in the hearings. That’s both because Americans’ views on the president are very partisan (basically Republicans almost universally support him but a majority of country does not), and because many of the most damning details about President Trump and his administration’s dealings with Ukraine have probably already come out in the last month. The resolution on Thursday passed 232-196, with two Democrats and no Republicans breaking ranks, and it’s just hard to imagine many members switching sides.

So House Democrats didn’t just ramp up the impeachment process on Thursday. They put themselves on a course that almost certainly ends with a vote impeaching the president and imploring the Senate to remove him from office. With the major implications of this first step in mind, here’s what we learned from today’s vote:

Republicans are already unified behind Trump — unlike in past impeachment processes

In 1974, basically the entire House voted in favor of starting the impeachment process against President Richard Nixon. Literally. It was a 410-4 vote. The vote to start an inquiry against President Bill Clinton in 1998 wasn’t quite as bipartisan, but Clinton still saw 31 Democrats break with him and support an impeachment investigation.3

But none of the 194 House Republicans who voted on Thursday’s resolution to formalize the impeachment investigation of Trump cast a “yes” vote. This was not at all surprising. There’s that entrenched partisanship I mentioned earlier, and Trump’s popularity with the GOP base (and the fear that he’ll support a primary challenger against Republicans who break with him, as he’s done in the past). But additionally, many more moderate Republicans and those in closely contested districts lost reelection last year, so there aren’t a lot of Republicans left in the House who are ideologically opposed to the president or might feel electoral pressure to break with him. Only three remain in districts Hillary Clinton won in 2016: Brian Fitzpatrick of Pennsylvania, Will Hurd of Texas and John Katko of New York. All three voted against the inquiry:

I thought that perhaps one of the 19 House Republicans who are retiring after 2020 might support the impeachment investigation, since they don’t have to worry about a primary challenge or reelection. But those members still might want to run for another office as Republicans or join GOP-connected lobbying shops or conservative organizations, so they could still have reasons to maintain a reputation as Trump loyalists. There also just weren’t a lot of political incentives for House Republicans to vote “yes.” (And electoral considerations aside, surely some of the 197 House Republicans either don’t think Trump did anything wrong or don’t think it’s worthy of impeachment.) The fact that Rep. Justin Amash of Michigan, who left the GOP in July to become an independent, voted for the resolution illustrates, I think, that no one who aspires to remain in GOP politics could vote in favor of it.

For those who want to see Trump leave office, this unified Republican support of the president is another sign that he probably isn’t going anywhere — at least until the 2020 elections. It’s doubtful that Trump’s removal from office (supported by nearly half the country) will become more broadly popular as long as Republican elected officials are opposed to it and keep telling GOP-leaning voters that the president is being unfairly investigated. And a unified Republican vote against even having an investigation is likely to lead to a unified vote against impeachment itself. (Although I don’t want to rule out completely a handful of members voting for impeachment if some even worse evidence against Trump comes out.) With that kind of ironclad support for the president, how could even one Republican senator vote for his removal, never mind the 20 that would be required for the motion to pass?

Democrats are ready to spend 2020 as the pro-impeachment party, even in pro-Trump areas

Of the 31 Democrats who represent House districts that Trump won in 2016, all but two — Collin Peterson of Minnesota and Jeff Van Drew of New Jersey — voted in favor of the impeachment investigation. So did all the other House Democrats who participated in the vote. This wasn’t surprising either — I don’t think House Speaker Nancy Pelosi would have scheduled this vote unless most swing district members were on board. She is deeply concerned about boosting their reelection prospects.

I would expect nearly all these members to follow through and vote in favor of impeachment itself; just as with Republicans, the electoral incentives for Democrats are pretty clear-cut. First, support for impeachment is above 80 percent among Democrats. Thus, even in a Trump-leaning district, it’s very likely that the majority of Democrats there favor impeachment. So a Democratic House member voting against impeachment would risk irritating the core activists, donors, volunteers and liberal voters that she needs to win reelection. Secondly, no matter how strong an argument she makes, a member who votes for an impeachment investigation but against impeaching Trump runs the risks of annoying both Democrats and Republicans in her district, satisfying no one.

Leaning into impeachment is a risk for House Democrats. There’s a scenario — unlikely but possible — in which the Democratic presidential nominee loses key states in the Midwest and is defeated while the party keeps control of the House by winning suburban districts in blue states like California. This scenario, pre-impeachment, could have involved some House Democrats distancing themselves from the party’s nominee and casting themselves as able to work with Trump. But you probably can’t run on being able to work with Trump after you’ve voted to impeach him.

In 2018, the House Democrats campaigned against Republicans’ unpopular Obamacare repeal bill more than against Trump himself. But impeachment puts Trump, the person, even more at the forefront of the 2020 campaign — even for House Democrats not technically running against him.


All in all, I think Thursday’s vote is a pretty good representation of what we can expect from the House impeachment process: Party unity on both sides resulting in Trump’s impeachment. But just because the outcome seems clear doesn’t mean the process can’t be surprising. Remember the hearings on Brett Kavanaugh’s nomination to the Supreme Court ? Remember a group of House Republicans last week forcing themselves into a closed-door hearing being held by the House Intelligence Committee, bringing their cell phones into an area where phones are banned for security reasons? I think we are going to see even more over-the-top shenanigans in the next few months, particularly from House Republicans, who know they don’t have the votes to win this political fight.

Now that everyone knows that the impeachment process in the House is likely to end with a party-line vote that the Democrats win, the hearings aren’t really designed to affect the votes of members. They are really a performance for the press and the public. So I would not expect a sober, somber process.

It’s Early … But There Have Been A Lot Of NBA Foul Outs

In the first Thursday night TNT game of the 2019-20 NBA season, the Milwaukee Bucks picked up a road victory over the Houston Rockets, outscoring the home team 39-24 in the fourth quarter and 26-16 over the final seven-plus minutes of the game. That the Bucks pulled out a close win down the stretch was not unusual in and of itself: On their way to 60 regular-season wins last year, the Bucks were one of the best clutch-time teams in the NBA, going 22-14 in games that were within 5 points at any time in the last five minutes, according to NBA.com. What is unusual about this particular win was that all of clutch time was played without the services of reigning MVP Giannis Antetokounmpo, who fouled out with 5:18 remaining in the game.

The Bucks’ second game of the season also entered clutch time, with their contest against the Miami Heat going to overtime after Antetokounmpo tied the game at the buzzer by tipping a Khris Middleton airball into the hoop. Two minutes and 29 seconds into overtime, though, Antetokounmpo fouled out again. And he wasn’t the only one. Three other players1 fouled out of that game as well.

Foul outs are generally pretty rare, and games with multiple players fouling out are even more so. But that Bucks-Heat matchup was not even the first game this season in which multiple players were disqualified because of fouls, and it almost certainly won’t be the last.2 Foul outs have absolutely skyrocketed early this season.

Through the 51 games played as of Monday night, there had been 21 foul outs. Given that there are 1,230 games played in an NBA season, this puts us on a full-season pace of 506 foul outs this season. How does that compare to previous seasons?3

If this full-season pace holds, the 2019-20 season would see a 60 percent increase in foul outs over the number of foul outs last season, which itself was over a 40 percent increase in foul outs from the year before. The league has not seen even 400 foul outs since the 2006-07 campaign — and prior to last year had not seen 300-plus foul outs since the 2010-11 season.

Some of this year’s incredible foul-out pace is obviously due to a small sample size. There aren’t many games in which four players foul out, and in a sample of just 51 games, having just one will affect the full-season pace quite a bit. But even if you remove that game, the league would still be on pace for 418 foul outs this season, an increase of nearly 32 percent from a year ago.4

What’s behind this early-season phenomenon? There appear to be a few contributing factors. The first is an overall spike in foul calls. Last season, the league averaged 41.6 total foul calls per game, according to data from PBP Stats. This year, that number has shot up to 48.1 per game. Much of that spike can be explained by an increase in the rate of offensive foul calls.

The league identified “Illegal Contact Initiated by Offensive Players” as its first officiating point of education for the 2019-20 season. “The officiating staff will maintain heightened focus on these types of plays moving forward this season,” said Monty McCutchen, Vice President of referee development and training, in a video offering guidance about these types of fouls. But there’s emphasizing a point of education, and then there’s what’s happening this season.

From the 2003-04 to 2018-19 seasons, offensive fouls accounted for 8.8 percent of total fouls. The NBA has broken out offensive fouls by type (i.e., charge vs. non-charge) going back to the 2010-11 season, and in that time, charge calls have ranged between 0.96 and 1.40 per game, and non-charge offensive fouls, such as illegal screens, checked in between 2.05 and 2.68 per game. Overall, offensive fouls per game peaked in 2006-07, at 4.39 per game. That is, until this season.

So far in the 2019-20 campaign, referees are whistling 6.39 offensive fouls per game, nearly 75 percent more than the 3.66 they called a year ago. Charges have spiked from 1.11 per game last season to 1.84 this year. Illegal screens and other offensive fouls have jumped as well, shooting up from 2.55 per game to 4.55 per game. Offensive fouls account for 13.4 percent of all foul calls so far this season and have contributed to 12 of the 21 foul outs leaguewide.

But if offensive fouls are up so dramatically over a year ago, why did the foul-out spike begin last season? And how does that relate to what looks like a second spike this year? The increase in offensive fouls doesn’t seem to be the culprit for the overall movement — the 3.66 offensive foul calls per game last season were just 0.39 more than the year before and lie firmly in the middle of the average number of total offensive foul calls over the previous 15 years. It also doesn’t seem to be due to an increase in pace,5 an increase in overtime games,6 an increase in clutch-time games7 or even an increase in the share of clutch-time games that entered overtime.8

Instead, we may be able to blame a specific group of players: the youngest in the league. Players between 18 and 22 years old are being given more responsibility and a greater share of minutes than ever in our time frame. From 2004 to 2018, these players accounted for between 13.1 percent and 17.9 percent of all leaguewide minutes played. During the 2018-19 season, that number spiked to 20 percent.9

A typical player in that youngest age range averaged 4.4 fouls per 48 minutes, nearly 10 percent greater than a player aged 23 and older, and that’s in line with figures from prior seasons. The 18- to 22-year-olds accounted for 75 of the 317 foul outs the league saw last season, the greatest number of foul outs that group of players had had since the 2008-09 campaign. Perhaps not coincidentally, foul outs began dropping off after that season.

It’s worth noting that the youngins have accounted for five of the 21 foul outs so far this season, which puts them on pace for 121 on the year — or nearly as many as the past two seasons combined. With teams increasingly asking younger players to handle larger and larger minute burdens, and with the league once again looking to crack down on certain types of foul calls, it’s entirely possible we could be in for a season full of players exiting the game early.

Check out our latest NBA predictions.

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Ohio State’s Chase Young Is Playing Like A Heisman Contender

The most dominant college football player on one of the nation’s best teams is a 6-foot-5, 265-pound defensive end. Although the Heisman Trophy is typically reserved for players who score touchdowns, rather than those who prevent them,1 Ohio State’s Chase Young has made a strong case for front-runner status.

“In a day and age when people get caught up in what’s next, he really wants to leave a legacy here,” Ohio State coach Ryan Day told Yahoo’s Pete Thamel. “That makes him special.”

That legacy will no doubt include last weekend, when Young turned a rain-soaked Saturday afternoon into his masterpiece. In the Buckeyes’s 38–7 dismantling of a Wisconsin program that has become Offensive Line U in recent years, Young tied a program record with four sacks,2 five tackles for loss and two forced fumbles. His position coach, Larry Johnson, told ESPN afterwards that it was the best single-game performance he’s ever seen. LeBron James — no stranger to being more physically imposing than his peers — called Young an “absolute monster.”

Young has 13.5 sacks on the season, 3.5 clear of anyone else in the country. The next time he registers one, it will set a new school record. He is second in the nation in forced fumbles with five. Among Power Five defenders, he’s tied for the national lead in tackles for loss (15.5), tied for second in disrupted dropbacks (14.5) and tied for third in defensive pressures (34).3 .

And while these box score metrics are noteworthy, they fail to encapsulate or appropriately contextualize his influence on a game, which is reminiscent of South Carolina’s Jadeveon Clowney and Nebraska’s Ndamukong Suh. Young’s versatility is critical to Ohio State’s success: Against Wisconsin, he lined up at linebacker, defended tight ends in coverage and was moved around on the line. He’s so fast that the Buckeyes don’t even need to blitz to turn a quarterback inside out: Only 11 Power Five teams have blitzed less than the Buckeyes, yet just Pittsburgh has accounted for more total sacks.

Armed with a freakish get-off that Day has called the best he’s ever seen and a mastery of Johnson’s “side-scissors” technique, Young is nearly impossible to block one-on-one. That frequently forces opposing coaches to dial up seven-man pass protections, which in turn has the Buckeyes secondary defending only three receivers. In a pass-heavy economy, that’s no small feat. “A complete game-changer,” is how co-defensive coordinator Jeff Hafley put it to The Athletic’s Bill Landis. “He allows us to do more in coverage.”

Ohio State is bludgeoning its opponents. The margin of victory in each of the team’s eight wins has been no smaller than 24 points, meaning that Young — perhaps in the interest of opposing quarterback safety — is removed from the field of play well before the score goes final. Among defensive linemen, Young is tied for 290th in defensive snaps, playing 261 total snaps this season. Just 17 of those snaps have come in the fourth quarter. His workload consists of little more than half of Ohio State’s total defensive snaps and just 15.5 percent of the Buckeyes’ fourth-quarter defensive snaps.

Heisman voters are mere human beings, biased by factors ranging from region to conference to position to race. Production is rarely contextualized,4 and the data with which these votes are cast is limited when it comes to defensive players. Sacks, tackles for loss and pressures — all of which Young has going for his candidacy — are only a fraction of on-field production and value.

But while imperfect, parsing Ohio State’s defensive splits with and without Young is instructive in identifying his value. While Ohio State allows a best-in-country 3.6 yards per play, with Young on the field, the Buckeyes allow 3.0 (the best mark through eight games since at least 2004), according to ESPN Stats & Information Group. Nearly half of all opponent plays gain zero or negative yardage when Young is on the field, a rate that drops 10.1 percentage points when he sits. Moreover, when Young is removed from the field, the Buckeyes pressure rate drops nearly 12 percentage points.

It is not enough to say Young is an unstoppable force. Mike Renner wrote recently that he’s doing things Pro Football Focus has never seen in its six years of tracking players. To watch Young bull-rush a quarterback is to watch an offensive line collectively drown. He’s too fast. He’s too strong. He’s too intelligent. His is the kind of impact that causes opposing QBs to, as Day put it, “start to feel ghosts and see ghosts.” Young was asked to replace Nick Bosa, the No. 2 pick in last year’s NFL draft. He responded by becoming the linchpin of a potent Ohio State defense and putting together perhaps the best Heisman candidacy by a defensive player we’ve seen in years.

Check out our latest college football predictions.

The Media Frenzy Around Biden Is Fading

When news about President Trump’s call to Ukraine first broke in late September, it seemed like former Vice President Joe Biden would be inextricably linked to the story. Biden was mentioned in more cable news clips and online news stories that week than every other 2020 Democratic candidate combined, according to data from the TV News Archive, which chops up cable news across the three networks we monitor — CNN, MSNBC and Fox News — into 15-second clips1 and Media Cloud, a database of online news.2. That week, Biden was mentioned in 74 percent of cable news clips, while Sen. Elizabeth Warren, the next most-mentioned candidate, was only in 16 percent of clips.

In the past two weeks, however, as the initial flood of impeachment coverage has ebbed, so has the extra attention for Biden.

Last week, almost all candidates were mentioned in a smaller share of cable news clips and online news stories, per a query run early Monday afternoon. That’s likely because of the Oct. 15 primary debate — we’ve noticed that the share of coverage for candidates who participated in debates in the past seemed to go up on debate week and down the week after, just as we see in the table below.

Tulsi Gabbard was mentioned more on cable last week

Share of 15-second cable news clips mentioning each candidate vs. share of online stories mentioning each candidate in a Media Cloud search

Cable TV clips the week of … online stories the week of …
Candidate 10/13/19 10/20/19 diff 10/13/19 10/20/19 diff
Joe Biden 44.1% 39.7% -4.4 59.2% 59.0% -0.2
Elizabeth Warren 26.3 23.0 -3.3 42.1 38.0 -4.1
Bernie Sanders 16.5 17.0 +0.5 34.9 30.0 -4.9
Pete Buttigieg 5.9 6.0 +0.1 19.9 18.2 -1.8
Tulsi Gabbard 7.6 15.4 +7.7 12.9 13.0 +0.1
Kamala Harris 3.8 3.8 +0.0 15.6 12.5 -3.1
Amy Klobuchar 3.8 3.3 -0.6 13.7 8.8 -4.9
Cory Booker 2.3 1.5 -0.8 11.4 7.6 -3.9
Andrew Yang 1.4 0.5 -0.9 9.9 6.0 -3.9
Beto O’Rourke 3.6 2.0 -1.7 5.6 4.0 -1.6
Tom Steyer 2.4 1.8 -0.6 9.6 3.4 -6.3
Tim Ryan 0.0 1.1 +1.1 0.9 2.4 +1.4
Michael Bennet 0.0 0.1 +0.1 1.5 2.1 +0.6
Julián Castro 0.7 0.9 +0.2 3.2 1.9 -1.3
Marianne Williamson 0.2 0.2 +0.0 2.0 1.6 -0.4
John Delaney 0.1 0.2 +0.1 1.2 1.2 -0.1
Steve Bullock 0.1 0.1 +0.0 1.1 0.9 -0.2
Joe Sestak 0.0 0.0 +0.0 0.8 0.3 -0.5

Includes all candidates that qualify as “major” in FiveThirtyEight’s rubric. Each network’s daily news coverage is chopped up into 15-second clips, and each clip that includes a candidate’s name is counted as one mention. For both cable and online news, our search queries look for an exact match for each candidate’s name, except for Julián Castro, for whom our search query is “Julian Castro” OR “Julián Castro.” Media Cloud searches use two of the database’s publication lists: “top online news” and “digital native” publications. Percentages are calculated as the number of stories or clips mentioning each candidate divided by the number of stories or clips mentioning any of the 2020 Democratic contenders for that week.

Sources: Internet Archive’s Television News Archive via the GDELT Project, Media Cloud

While most candidates who participated in the October debate got fewer mentions last week compared to the prior week (the week of the debate), there was one notable exception. Hawaii Rep. Tulsi Gabbard was mentioned in almost twice as many cable news clips this week compared to last. Much of the cable news attention came when former Democratic presidential nominee Hillary Clinton suggested that Gabbard was being groomed by the Russians for a third-party run to undermine Democrats’ chances in 2020. In fact, the most common words mentioned in 15-second clips mentioning Gabbard were “Hillary,” “Clinton,” “Russian” and “asset.”

But Gabbard didn’t get the same amount of attention across networks last week. She was mentioned in 66 clips on CNN and 71 clips on MSNBC, but 339 clips (almost five times as many) on Fox News.

Check out the data behind this series and check back each week for an update on which candidates are getting the most coverage on cable news.

Vegas Thinks The NBA Title Race Is As Wide Open As It’s Been In A Long Time

When the Westgate Las Vegas SuperBook’s 2019-20 NBA championship odds first opened back in May, the Golden State Warriors were the early favorites to win this season’s title. At +175,1 the Warriors’ odds implied a 36 percent chance2 to win the championship — pretty high in absolute terms, but low relative to recent Warriors odds, as it priced in some uncertainty around whether Kevin Durant would re-sign with the team. That same uncertainty had the New York Knicks optimistically tied for the sixth-best title odds in the league (+1600), as the Knicks harbored hopes of drafting Zion Williamson and signing Durant and Kyrie Irving.

A lot has changed in the NBA since then. The Warriors lost Klay Thompson to a torn ACL and Durant to an Achilles injury before Durant signed with the Brooklyn Nets. Finals MVP Kawhi Leonard and Paul George became Los Angeles Clippers; Anthony Davis became a Los Angeles Laker; Russell Westbrook became a Houston Rocket; and LeBron James crept closer to age 35.3 And true to form, the Knicks missed out on the top pick in the NBA draft, whiffed on marquee player acquisitions and saw their title odds fall to +100,000, tied for worst in the league.

When the NBA’s star carousel finally slowed, the top of the league felt about as balanced as it had in recent years. Heading into Tuesday night’s season openers, the Clippers were favored to win it all (+350, good for an implied probability of 22 percent), followed by the Lakers (+400, 20 percent), Milwaukee Bucks (+600, 14 percent), Rockets and Philadelphia 76ers (+800, 11 percent), Warriors (+1200, 8 percent), Utah Jazz and Denver Nuggets (+1600, 6 percent) and Boston Celtics (+2500, 4 percent).4

So how balanced are these teams’ odds in the context of recent NBA history? For starters, the Kawhi-led Clippers are, in odds terms, the NBA’s weakest preseason favorite since the waning months of the George W. Bush administration, or late 2008. In basketball parlance, by then LeBron had already started four All-Star Games; Zion had just started third grade. In any case, Tuesday’s tipoff marked the first time since the start of the 2008-09 season that the NBA’s preseason favorite had championship odds worse than +300.5 Put another way, this is the first time in 11 years in which no NBA team entered the season with an odds-implied probability of at least 25 percent to win it all.

As Vegas odds go, only three of the past 35 NBA seasons6 have featured a weaker preseason favorite than this year’s Clippers: 2007-08 (Dallas Mavericks and San Antonio Spurs, +450), 2006-07 (Mavericks, +400) and 2004-05 (Spurs, +400). All three of those seasons happened to come in the four-year period between the end of the Shaquille O’Neal-Kobe Bryant era and the beginning of the Pau Gasol-Bryant pairing in L.A.7 The Spurs won two titles in that span (and three in five years), but Vegas frequently underestimated them along the way, and San Antonio never owned the top of the odds board as other dynasties have.

The Clippers are the weakest favorite in over a decade

Preseason odds to win the NBA Finals and season results, since 1984-85

Exact odds vary by date and sportsbook. The 1998-99 and 2011-12 seasons were shortened by lockouts.

*Seasons with co-favorites

Sources: Basketball-Reference.com, Sports Odds History, Westgate Las Vegas SuperBook

Despite the team’s low-for-a-favorite odds, Clippers fans would be happy to learn that in the 35 NBA seasons since 1984-85, the preseason favorite or co-favorite made the NBA Finals 27 times and won 18 championships. During the same 35-season period in the NFL, by contrast, only seven preseason favorites or co-favorites won the Super Bowl. The NBA’s +350 favorites don’t win the Finals with the same frequency as NBA favorites in general — only three of seven have made the Finals, and only two have won — but thanks to a handful of somewhat unexpected NBA champions,8 +350 actually represents the median preseason title odds for all NBA champions since 1984-85.9

Beyond the Clippers, the preseason parity of 2019-20 also harkens back to the mid-to-late 2000s. Five of this year’s NBA teams — the Clippers, Lakers, Bucks, Rockets and Sixers — came into the season with odds-implied probabilities to win the NBA championship between 10 percent and 24.99 percent, the most such teams since 2006-07. Eight teams — the five mentioned plus the Warriors, Jazz and Nuggets — carried odds-implied probabilities of 5 percent to 24.99 percent, the most since 2008-09. This stands in contrast to the past 10 years, when championship odds were concentrated in one or two teams per season — usually the Warriors, Cavaliers, Heat or Lakers — and then dwindled from there.

Whether you think there’s value in this year’s NBA odds ultimately comes down to whether you believe any teams have a greater probability to win the championship than the betting markets imply. These perceptions naturally vary between fans, pundits and computer models. FiveThirtyEight’s predictions, powered by the new RAPTOR player ratings, agree with Vegas about which nine teams had the highest preseason probability of winning the NBA Finals. But relative to the oddsmakers, RAPTOR is more bullish on the Rockets and bearish on the Lakers.

FiveThirtyEight’s model estimated that the Rockets entered the season with a 28 percent chance to win it all — best in the league and considerably higher than the 11 percent chance implied by their +800 Vegas odds. By that logic, the Rockets should have priced closer to +255 or +260. Meanwhile, our final preseason forecast gave the Lakers just a 3 percent chance of winning the Finals, seventh-best in the league and a fraction of the 20 percent probability implied by LeBron and Co.’s +400 odds. A 3 percent chance at the Larry O’Brien Trophy suggests that the Lakers’ odds should have been more like +3200.

In the end, this new era of NBA player movement makes the already difficult exercise of basketball prognostication even more challenging. Oddsmakers, computer models and casual bettors need to consider not only the teams today but also potential in-season trades — and which teams have the gumption and chips to pull them off. Here’s to an exciting 2019-20 NBA season, both on and off the floor.

Check out our latest NBA predictions.

Can You Carve The Perfect Pumpkin?

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. Two puzzles are presented each week: the Riddler Express for those of you who want something bite-size and the Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,7 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

This week, Eli Luberoff presents a puzzle in which artistry meets geometry. While at the San Francisco Museum of Modern Art, Eli snapped the following picture from an exhibit by Sol LeWitt:

Darkened 3D solid inside a unit cube

What’s the volume of the darkened solid?

(Assume the outer cube is a unit cube, and that the faces of the solid meet the edges of the unit cube halfway and a fourth of the way along its edges. In other words, the drawing is to scale!)

Submit your answer

Riddler Classic

I want to carve the perfect eye for my pumpkin this Halloween, but I can’t seem to make it the right size. Since symmetry is the key to beauty, the triangular eye should be equilateral and equiangular, which is easier said than done on the surface of a spherical pumpkin!

To be a proper triangle, the three corners should be connected by arcs that are “straight,” meaning they go directly from one corner to the next via the shortest possible path. (Think about air travel: When you flying from the West Coast of the U.S. to Europe, you’ll fly north of the Arctic Circle along the way, since that’s the shortest path over the Earth’s curved surface.)

Anyway, the triangular eye that I made is way too big. Its sides all meet at right angles, and the resulting eye takes up a whole eighth of the pumpkin’s surface, as seen in the animation below.

Triangular

Instead, I want an eye that’s precisely half that size, or one-sixteenth of the pumpkin’s surface. For such an ideal pumpkin eye, at what angle should each of the sides meet?

Submit your answer

Solution to last week’s Riddler Express

Congratulations to 👏James Sears 👏 of Saint John, New Brunswick, Canada, winner of last week’s Riddler Express.

Last week, you had to navigate your way through the number maze below. The number in each box told you how many spaces up, down, left or right you must move to get to the next box. You started at the yellow 6 in the bottom left corner, and you were challenged to make your way to the asterisk.

Number maze. Start from the yellow six in the bottom left corner and finish at the asterisk.

James found his solution by working backwards. First, he tried to find a square from which you could get to the asterisk. Such a square would have to be in the same row or column as the asterisk. The only square that works is the 2 that’s two squares left of the asterisk — no other square in the asterisk’s row or column has a number that equals how many squares away from the asterisk it is. Next, from which squares could you get to that 2? The only such square is a 6 that’s six rows up. Continuing in this fashion, James found a nine-step path that works:

Nine-step solution to the number maze.

Much of Riddler Nation took this puzzle one step further, trying to find the shortest path to the asterisk. David Schwab of Ottawa, Ontario, Canada (man, the Canadians crushed it this week!) performed a breadth-first search, starting with the 6 in the lower left and finding all the squares you could move to, and labeled them as reachable within one step. Then, he found all the squares you could get to from those squares and labeled them as reachable within two steps. He continued this process until all the squares were reached, resulting in the following guide through the maze:

Original maze, where each cell also includes a number in the top-left corner indicating the minimum number of steps it takes to reach that cell if starting from the 6 in the bottom left.

The number in the top left corner of each square indicates how many moves are required to reach that square, starting from the 6 in the lower left corner. It turns out that the asterisk can be reached in eight moves. Meanwhile, that 7 in the top right is the toughest to reach, requiring a whopping 16 moves. Who knew?

Solution to last week’s Riddler Classic

Congratulations to 👏Kyle Tripp 👏 of Concord, California, winner of last week’s Riddler Classic.

Last week you converted dollars into the currency of Riddler Nation: the Dio, worth $538, and the Phantus, worth $19. For example, if you wanted to convert $614, you’d get one Dio and four Phanti, since 614 = 1×538 + 4×19. But if you tried to exchange one dollar more (i.e., $615), then alas, no combination of Dios and Phanti would work. What was the largest number of dollars that could not be converted into Dios and Phanti?

The name of the currency was a clue. Diophantus was a Greek mathematician and the namesake of Diophantine equations, which are polynomial equations that only seek integer solutions. For this particular riddle, the Diophantine equation of interest was 538x + 19y = z, where x represents the number of Dios, y is the number of Phanti, and z is the number of dollars.

Solver Guy Moore solved the problem by looking at increments of 538. For dollar amounts less than 538, only multiples of 19 are exchangeable, all the way up to 19×28 = 532.

Beyond 538, you have more possibilities because we’re working with a second denomination. You can now exchange dollar amounts that are multiples of 19 (in other words, that have a remainder of 0 when divided by 19), as well as dollar amounts that can be exchanged for exactly one Dio and any number of Phanti, such as 538, 557 (538 + 19), 576 (538 + 19 + 19) and so on. You’ll notice that all those numbers share something in common: When divided by 19, they have a remainder of six. That’s because when the number 538 is divided by 19, it leaves a remainder of six.

All this talk of remainders might seem superfluous, but they’re important for understanding how to get to a solution.

When you reach 1,076 (538×2), you can exchange dollar amounts that are multiples of 19, dollar amounts that have a remainder of six when divided by 19 and dollar amounts that have a remainder of 12 when divided by 19. (That’s because when the number 1,076 is divided by 19, it leaves a remainder of 12.)

If you keep going, numbers with different remainders (when divided by 19) become exchangeable every time you hit another multiple of 538. All the numbers become exchangeable when, at last, you reach the 18th (i.e., one less than 19) multiple of 538 — 9,684 — which happens to have a remainder of 13 when divided by 19. Beyond 9,684, every single dollar amount — no matter its remainder when divided by 19 — is exchangeable. For example, what about a large number like 100,000? That equals 538×10 + 4,980×19. That’s a lot of Phanti!

But we still have to find an answer! Let’s return to our discovery of 9,684, which was the first multiple of 538 with a remainder of 13 when divided by 19. (The 13 isn’t very important here — it just happens to be the last of the 19 possible remainders to become exchangeable.) That means numbers less than 9,684 with the same remainder of 13 are not exchangeable. The largest of these is 9,684 – 19 = 9,665, the correct answer.

Many solvers were also quick to point out that this riddle was essentially asking for the Frobenius number, which is the largest value that a set of numbers cannot generate when multiplied by whole numbers and then added together. The Frobenius number for two numbers whose greatest common factor is one can be found by subtracting one from each number, multiplying those values and then subtracting one from that product. In this case, that’s (538 – 1)(19 – 1) – 1, which indeed equals 9,665.

For extra credit, you were asked how your answer would change upon the inclusion of a third currency, worth $101. Guy observed that the Dio would then be equivalent to 23 Phanti plus this new $101 denomination. That means that any time you exchange dollars for a Dio, you could have similarly exchanged it for Phanti and $101s. In other words, the Dio just became obsolete in our calculations! Therefore, the solution to the extra credit was simply the Frobenius number for 101 and 19, which is 1,799.

So when you travel to Riddler Nation, be sure to try to exchange exactly $9,665. They might throw you out of the country, but they’d just as likely applaud your mastery of number theory.

Want more riddles?

Well, aren’t you lucky? There’s a whole book full of the best puzzles from this column and some never-before-seen head-scratchers. It’s called “The Riddler,” and it’s in stores now!

Want to submit a riddle?

Email Zach Wissner-Gross at [email protected].

Where The Public Stands On Impeachment One Month In

Welcome to Pollapalooza, our weekly polling roundup.

Poll(s) of the week

About two weeks ago, we wrote that impeaching President Trump had near-majority support from the American public. This was notable because, at the beginning of October, Americans were about evenly divided on impeachment with just over 45 percent on each side, so there was some question whether this was a new normal or if the numbers would revert to the mean. But so far, support for impeachment hasn’t decreased. According to our impeachment polling tracker, if we look at all the polls, 49.1 percent of Americans support impeachment and 43.5 percent oppose it.

We can also drill down into the different types of questions asked about impeachment. For example, one of the views in our tracker only averages polls that ask Americans if they support beginning the impeachment process, while a separate view averages polls that ask if Americans support Trump’s impeachment and/or removal from office. And right now, there is more support for opening an inquiry than for full-blown impeachment. Currently, 53.1 percent of Americans support beginning the process, while 48.1 percent support impeachment and possible removal.

Support for beginning the impeachment process has been pretty stable, too, since it first shot up to 52.9 percent on Oct. 7. Support has hovered at 52-53 percent, though some of that stability is probably because fewer polls are asking about opening the inquiry. (And I would expect them to eventually taper off completely as the decision to open the inquiry becomes older and older news.)

And a new Quinnipiac poll illustrates some of this. It was the fourth time that Quinnipiac had asked whether Americans supported the impeachment inquiry (it first asked in late September), and it found that a majority of Americans — 55 percent — approve of the inquiry. This result was essentially the same as the previous times they asked: Approval of the inquiry has fluctuated slightly between 51 and 55 percent, while disapproval has remained stuck between 43 and 45 percent.

Support for impeaching and removing the president from office has also been relatively stable in Quinnipiac’s polling. The most recent poll found the country essentially evenly divided on whether Trump should be “impeached and removed from office” — 48 percent said he should be while 46 percent said he shouldn’t be, a gap that’s within the poll’s margin of error. Those numbers have only moved a couple points in either direction since the end of September. That said, our polling average suggests that support for impeachment may still be ticking upward. The increase since the beginning of the month has been slow but steady. As of Thursday night, 48.1 percent of Americans support impeachment and potential removal in our tracker’s average, while 43.7 percent oppose it.

Indeed, net support for impeachment and potential removal is higher in our average than in Quinnipiac’s polling. Our average is more in line with a CNN/SSRS poll released this week that found a full 50 percent of Americans said they believed Trump should be impeached and removed from office, while 43 percent didn’t feel that way.

But arguably the more important measurement to look at is Trump’s approval rating. And at the beginning of October, Trump’s approval rating appeared to sharply decline as the Ukraine scandal unfolded. But his rating has not continued to plummet. Instead, it remains within the same narrow range that it has occupied for most of the year. However, it has slumped to the very bottom edge of that range. Currently, 40.6 percent of Americans approve of Trump and 54.6 percent disapprove — his worst numbers since February. So even if the bottom hasn’t dropped out, it’s possible that current events are keeping his popularity depressed.

Mind you, those events aren’t just limited to impeachment. Over the past two weeks, Trump has ordered the withdrawal of U.S. troops from their position defending Kurdish forces in Syria, and he proposed (then backtracked on) holding the next G-7 summit at his own resort in Florida. These actions drew rare rebukes from members of Trump’s own party, perhaps anticipating that Americans would find them especially serious (or signaling to the public that Trump had crossed a line).

But we’ve seen this movie enough times before to know that Trump’s approval rating might just as quickly perk back up next week. The current drop in Trump’s popularity may or may not be meaningful, but for now, recent events certainly aren’t doing him any favors politically. Indeed, if impeachment support continues to rise, it could be a rough winter for President Trump.

Other polling bites

  • Interestingly, even though the CNN/SSRS poll shows that Americans support impeaching Trump, that doesn’t mean they approve of how Congress is going about it. Only 43 percent approve of the way Democrats in Congress are handling the impeachment inquiry, while 49 percent disapprove. However, the numbers are much worse for Republicans in Congress: just 30 percent approve of the way they’re handling the inquiry and 57 percent disapprove. And Americans say, 50 percent to 40 percent, that Republicans oppose impeachment because they are out to protect Trump at all costs, not because they believe he did not commit impeachable offenses.
  • A final tidbit from that very meaty CNN/SSRS poll: House Speaker Nancy Pelosi’s net favorability rating (favorable rating minus unfavorable rating) is just -2, which is a big improvement from her typical standing in recent years (for example, in September 2017, it was -21). In fact, Pelosi’s net favorability rating is the highest it’s been in CNN/SSRS’s polling since January 2009, which certainly suggests coming out for impeachment hasn’t hurt her.
  • This week, we got our first nonpartisan poll of the Mississippi governor’s race since July. According to Mason-Dixon Polling, Republican Lt. Gov. Tate Reeves leads Democratic Attorney General Jim Hood just 46 percent to 43 percent. The election is on Nov. 5.
  • While national polls indicate that granting statehood to Washington, D.C., is unpopular with the public, a Washington Post/University of Maryland poll finds that Maryland residents support it, 51 percent to 40 percent. What they don’t want is retrocession, an alternative proposal to enfranchise Washingtonians by re-combining the District with Maryland. Marylanders oppose that idea 57 percent to 36 percent.
  • According to a survey by the Public Religion Research Institute, 55 percent of Republicans whose primary news source is Fox News say there is nothing that Trump could do to lose their approval. Only 29 percent of Republicans whose primary news source is not Fox News say that. PRRI also told The Washington Post that 71 percent of Fox-favoring Republicans strongly approve of Trump’s job performance, while only 39 percent of non-Fox-favoring Republicans do.
  • The World Series started on Tuesday, and according to an Ipsos poll conducted before Game 1, 46 percent of Americans planned to follow along. Of them, 37 percent were root, root, rooting for the Washington Nationals,17 while 33 percent wanted the Houston Astros to win18 (28 percent have no preference). However, Series watchers thought the Astros would win, 55 percent to 23 percent — although that was before the Nationals won the first two games of the seven-game series.
  • You may be too old to go trick-or-treating, but there’s another way to get your hands on those sweet, sweet Reese’s Peanut Butter Cups. According to a YouGov poll, 74 percent of parents of children under 18 say they steal at least a few pieces of candy from their kids’ Halloween hauls. Four percent even say they eat all of it — now that’s scary.

Trump approval

According to FiveThirtyEight’s presidential approval tracker, 40.6 percent of Americans approve of the job Trump is doing as president, while 54.6 percent disapprove (a net approval rating of -14 points). At this time last week, 41.6 percent approved and 54.0 percent disapproved (for a net approval rating of -12.4 points). One month ago, Trump had an approval rating of 43.1 percent and a disapproval rating of 53.0 percent, for a net approval rating of -9.9 points.

Generic ballot

In our average of polls of the generic congressional ballot, Democrats currently lead by 6.3 percentage points (46.6 percent to 40.3 percent). Those numbers are unchanged from a week ago. At this time last month, voters preferred Democrats by 6.8 points (46.8 percent to 40.0 percent).

Check out all the polls we’ve been collecting ahead of the 2020 elections.

How Much Do Iowa And New Hampshire Really Matter For 2020?

Joe Biden’s campaign has claimed he doesn’t need to win Iowa and New Hampshire to become the Democratic presidential nominee. Instead, the former vice president has his eyes on states No. 3 and 4 on the primary calendar — Nevada and South Carolina — plus the 14 states that will vote on Super Tuesday, just three days after the South Carolina primary.

The logic makes a certain amount of sense, too. Biden polls better than other candidates among black and Hispanic voters, so the states after nearly-all-white Iowa and New Hampshire definitely play to his strengths, as they’re far more diverse and representative of the Democratic Party. There’s just one problem: Since 1976, when the Iowa caucuses first became an influential part of the nomination process, the eventual Democratic nominee has almost always won either Iowa or New Hampshire (or both). In fact, there’s only one time this didn’t happen — Bill Clinton in 1992, and the circumstances were unusual.9

But maybe there’s a case to be made that Iowa and New Hampshire don’t matter as much for the Democrats as they once did. The states have never offered that many delegates, and their electorates don’t look much like the modern Democratic Party. Arguably, winning South Carolina’s black voters or clinching California on Super Tuesday could matter a lot more. Of course, it’s hard to argue that losing the first two states in the primary is a good strategy — and to be clear, the Biden campaign hasn’t argued they don’t want to win Iowa and New Hampshire, just that it’s not essential. So does the Biden camp have a point? Let’s go over the case for Iowa and New Hampshire mattering as much as they always have in the Democratic primary — and the case for their declining importance.

Case 1: Iowa and New Hampshire are as important as ever

Following reforms to the primary system in the 1970s and Jimmy Carter’s surprise victory in the 1976 Iowa caucuses, both Iowa and New Hampshire have become highly influential primary states, as they are the first two to vote (although there have been several unsuccessful efforts to change that).

Democratic nominees usually get a win in the first two states

Results of the Iowa caucus and New Hampshire primary in competitive Democratic presidential primaries, 1976 to 2016

Candidate who Won …
Cycle Iowa New Hampshire nominee Nominee won Iowa or N.H.
1976 Jimmy Carter* Jimmy Carter Jimmy Carter
1980 Jimmy Carter Jimmy Carter Jimmy Carter
1984 Walter Mondale Gary Hart Walter Mondale
1988 Dick Gephardt Michael Dukakis Michael Dukakis
1992 Tom Harkin† Paul Tsongas Bill Clinton
2000 Al Gore Al Gore Al Gore
2004 John Kerry John Kerry John Kerry
2008 Barack Obama Hillary Clinton Barack Obama
2016 Hillary Clinton Bernie Sanders Hillary Clinton

*Technically “Uncommitted” won the 1976 Iowa caucuses, but Carter finished first among the named candidates.

†Harkin was a U.S. senator from Iowa and a heavy favorite there, so the caucuses were not seriously contested by other candidates.

Sources: News Sources

Winning Iowa or New Hampshire will likely be critical for someone in the 2020 Democratic primary, too, especially if the same candidate wins both states. Sen. Elizabeth Warren is currently in the lead in both places, according to a FiveThirtyEight average of polls in Iowa and New Hampshire since the third Democratic debate in September — although she barely leads in Iowa. She has a narrow 1-point lead over Biden in Iowa and a 4-point edge in New Hampshire, according to our analysis. (RealClearPolitics’s average puts Warren roughly 3 points ahead of Biden in New Hampshire and less than a point behind Biden in Iowa.) But in both states, we’re only talking about a few points separating the top two candidates, so to be clear, the race is still incredibly tight.

And that’s important, because the margin by which a candidate wins Iowa or New Hampshire can have big consequences for the primary. A narrow defeat, for instance, wouldn’t necessarily spell doom for Biden’s campaign. Instead, it could give them an opportunity to spin the loss and talk about the relative lack of diversity in the first two states, said Josh Putnam, a political scientist and FiveThirtyEight contributor who tracks the nomination process. Putnam argued that a defeat by a wide margin would be harder to sell, and Caitlin Jewitt, a political scientist at Virginia Tech who studies presidential primaries, agreed. Jewitt stressed, however, that even a loss could be considered a good showing if the candidate lost by less than predicted. “It’s important to win in Iowa and New Hampshire,” said Jewitt. “But it’s almost more important to do better than you were expected to do.”

Winning or exceeding expectations in Iowa or New Hampshire seems to have a real effect on Democratic primaries, too — especially as it pertains to a candidate’s ability to attract national support. Take John Kerry in 2004. He was polling at about 8 percent nationally before Iowa, but after he won both Iowa and New Hampshire, his numbers went through the roof — a 37-point gain in the polls in a couple weeks — as he steamrolled to victory at the expense of opponents like Howard Dean. Similarly, in 2008, Barack Obama trailed the favorite, Hillary Clinton, by double digits in national polls, but after he won Iowa, he gained nearly 10 points in national support, even though Clinton recovered to win New Hampshire. Eventually, Obama won the lengthy nomination battle. And while Bernie Sanders didn’t win the Democratic nomination in 2016, his strong start in Iowa and New Hampshire helped force Clinton, once again the favorite, into a drawn-out race.

Good early results can boost a campaign

Results in Iowa and New Hampshire and change in national polls for competitive Democratic contests, 2004-16

primary/caucus results Average* in national polls
Year Candidate Iowa margin N.H. Margin Before Iowa After N.H. Change
2004 John Kerry +4.5 +12.1 8.4% 45.3% +36.9
2004 John Edwards -4.5 -26.3 5.4 11.3 +5.9
2004 Howard Dean -19.7 -12.1 23.9 13.0 -10.9
2004 Wesley Clark -37.0 -26.0 14.9 8.0 -6.9
2008 Barack Obama +3.7 -2.6 24.4 33.5 +9.0
2008 John Edwards -3.7 -22.2 14.9 12.8 -2.1
2008 Hillary Clinton -4.5 +2.6 42.0 41.8 -0.2
2016 Hillary Clinton +0.3 -22.5 57.4 52.9 -4.5
2016 Bernie Sanders -0.3 +22.5 34.1 38.7 +4.6

*An average of the national polls in the three weeks before the Iowa caucus and an average of the national polls in the week after the New Hampshire primary in a given election year. There were at least three polls during each period for each cycle.

The eventual nominee in each election cycle is bolded.

Sources: Polls, Dave Leip’s Atlas of U.S. Elections

The bottom line is: Winning or at least outperforming expectations in Iowa and New Hampshire will likely still matter a lot in the Democratic race this year. As Jewitt told me, “If you do well [in Iowa or New Hampshire] … you get more media attention,” and this often means “a rise in the polls, and you get more fundraising.” And as we’ve seen in recent primaries, strong performances in these states can set a candidate up for success.

Case 2: Iowa and New Hampshire matter less and less

There is an argument to be made, however, that while they’re still pivotal for winnowing the field, neither Iowa nor New Hampshire is as critical as they have been historically for securing the Democratic nomination. The main reason being that Iowa and New Hampshire don’t look like the national Democratic Party and, therefore, might not be the best indicators of what the party wants. In 2016, the primary electorate in those two states was 91 percent white and 3 percent black while the national Democratic primary electorate was 66 percent white and 20 percent black.10 Whereas the 14 states that vote on Super Tuesday (March 3) look much more like the Democratic Party — 62 percent of these voters were white in 2016 while 18 percent were black.11 Many of these states also offer far more delegates than either Iowa or New Hampshire — California has the most Democratic delegates and will be voting on Super Tuesday next year, as will Texas, which has the second-most delegates.

And as we saw in the 2016 Democratic primary, Clinton was able to fight on despite underwhelming results in Iowa (where she narrowly won) and New Hampshire (where she lost). Granted, she had overwhelming support from the party establishment that Biden can’t currently match, but her position as the likely nominee was never really in doubt despite a poor showing in Iowa and New Hampshire. What 2016 suggests, then, is that as long as expectations aren’t set too high, somewhat underwhelming results in Iowa and New Hampshire are survivable. Putnam described the Biden campaign’s efforts to discount the importance of Iowa and New Hampshire as “a gamble,” but “one that might pay off” if the results are relatively close and South Carolina still looks favorable for him.

The media might also be more receptive to the idea that Iowa and New Hampshire aren’t representative of the Democratic Party, which may make them less important this year. Already there have been a number of stories about how the primary calendar — especially the Super Tuesday states — may shake up which states matter most to candidates. And as CNN analyst Ronald Brownstein wrote in February, the 14 states voting on March 3 “could advantage the candidates best positioned to appeal to minority voters, particularly African Americans.” So if Biden retains his solid support among African American voters and his campaign’s effort to lower expectations in Iowa and New Hampshire works, Biden might get what he wants — South Carolina and Super Tuesday as his real campaign tests.


Having now looked at the cases for and against Iowa and New Hampshire’s continued importance in the Democratic presidential primary, I do think it’s possible that these two states won’t matter as much. But I can’t help but suspect they’ll be as influential as ever. And that’s because even if the media is warier of the unrepresentative demographics of the first two states, it would still be tough for Biden to recover from dual losses at the beginning of the primary calendar. Remember, Bill Clinton is the only Democratic nominee since 1976 who lost both Iowa and New Hampshire. The winner(s) would likely get glowing coverage, too, while Biden would face more scrutiny. Defeat could also raise doubts among his supporters, given that “electability” is a central selling point of his campaign. And donors, with whom Biden is already struggling, might lose faith in him as well. So as long as Iowa and New Hampshire still get to go first, they’ll probably continue to have an outsized influence on the nomination process.