Over the past few weeks, FiveThirtyEight has explored who led in early primary polls of presidential cycles from 1972to 2016 and who went on to win the nomination. And what we’ve seen is that national surveys conducted in the year before a presidential primary are relatively good indicators of which candidates will advance to the general election, especially when polling averages are adjusted to reflect how well known each candidate was. Now, in the third and final part of our series, we are going to analyze 40-plus years of polls to better understand their predictive power.
There are a number of ways to tackle this question, but one relatively easy way to see how predictive early polls are is to compare a candidate’s polling average1 to their eventual share of the national primary vote. And we found that as a candidate’s polling average increased, their vote share in the primaries also tended to increase. In the chart below, for the calendar year before the primaries began, we averaged each candidate’s polls in the first half of the year (January through June) and in the second half of the year (July through December), and then plotted those two averages against the share of votes each person won in the next year’s primaries, for every competitive nomination process from 1972 to 2016. The correlation is pretty strong for both halves of the year,2 though polls from the second half of the year matched the outcomes a little better, which is not surprising — after all, those polls were conducted closer to the start of primary season.
But it’s easier to see trends if we group some candidates together rather than looking at them all individually, so let’s sort candidates into six big buckets based on their polling average. That clearly shows us that candidates with higher polling averages were also more likely to win higher shares of the primary vote and, therefore, the nomination. Those polling at 35 percent or higher rarely lost the nomination, regardless of whether they attained those heights in the first or second half of the year. They also, on average, won more than half the national primary vote. But those polling below 20 percent in either the first half or second half of the year had at best a 1-in-10 chance of clinching the nomination, and they rarely won a sizable chunk of the popular vote.
High polling averages foreshadowed lots of primary votes
Candidates’ share of the national primary vote by average polling level in the first half of the year before the presidential primaries and polling average in the second half of that year, 1972-2016
Share who became nominee
Avg. Primary Vote share
Share who became nominee
Avg. Primary Vote share
We can also take these polling averages and estimate the probability of a candidate winning a party’s nomination using a logistic regression. And as you can see, candidates polling above 20 percent — whether it’s in the first half of the year (the orange line) or the second half (purple line) — have a higher probability of winning the nomination. In fact, the results for the first and second half of the year are nearly identical — in the second half of the year, candidates with the same polling average had a slightly lower win probability, but we’re talking about a maximum difference of less than 4 percentage points.3 There are certainly more sophisticated ways one could look at this data, but even these simple methods can show that polls conducted this far out in the primary season still have a reasonable amount of predictive power.
We can go a step further and improve our analysis by accounting for a candidate’s level of name recognition.4 In previous installments of this series, we rated candidates’ fame on a five-tier scale,5 and this time we’re using those previous rankings to split up our polling data into two roughly equal groups — candidates with high name recognition6 and those with low name recognition.7 This gives us a broader understanding of whether being well known influenced a candidate’s chances of winning the nomination. (We also limited this part of our analysis to just the first half of the year to see what role name recognition played very early in the cycle.)
And as you can see, well-known candidates who polled in the double digits tended to win a higher share of the primary vote. But candidates who had high name recognition while only polling in the single digits were generally in trouble. Of the 84 highly recognized candidates who polled below 10 percent in surveys from the first half of the year before the primaries, only President Trump went on to win his party’s nomination. And Trump was an unusual case — Republicans started out with strongly negative views of him but quickly changed their tune even though they were already familiar with him. Meanwhile, candidates with lower name recognition in the first half of the year only occasionally advanced to the general election, and in each case, it was on the Democratic side — George McGovern in 1972, Jimmy Carter in 1976, Michael Dukakis in 1988 and Bill Clinton in 1992.
Name recognition makes a big difference
Candidates’ share of the national primary vote by average polling level in the first half of the year before the presidential primaries and whether they had high or low name recognition, 1972-2016
High name recognition
Low name recognition
Share who became nominee
Avg. Primary Vote share
Share who became nominee
Avg. Primary Vote share
In fact, we can use a logistic regression to estimate a high- and low-name-recognition candidate’s chance of winning the nomination based on their polling average (much like we did above, but last time we didn’t sort candidates into categories based on name recognition). And as you can see in the chart below, a low-name-recognition candidate didn’t stand much of a chance of winning unless they were able to climb past 10 percent in the polls in the first half of the year before the primaries. If they were able to hit that mark, then their odds of winning were slightly less than 1 in 4, which put them ahead of a high-name-recognition candidate polling at the same level.
Intuitively, this makes sense — relatively few unknown candidates could poll as high as 10 percent this far out in the election cycle. But for those who could get that much support even though only a small share of people knew about them, their polling numbers signaled a great deal of potential. Take Dukakis in the 1988 cycle: His polling average was about 8 percent in the first half of 1987, and we estimated that his average name recognition was somewhere around 20 percent. Not a bad polling average when you consider that most respondents didn’t know who he was.
In other words, a candidate’s adjusted polling average — polling average divided by name recognition, which we delved into at length in the first two parts of this series — is a decent proxy for teasing out the strength of a candidate, especially early in the election cycle. By accounting for how well known a candidate is, we can get a better read on the field in front of us, including here in the 2020 election cycle. As primary season draws nearer, we’ll be keeping an eye on any candidates with low name recognition who still manage to win a significant chunk of support in the polls.
Fox News loves talking about Bernie Sanders. Every week since the Vermont senator launched his 2020 campaign, Fox News has outstripped MSNBC and CNN in terms of how much coverage each network dedicated to Sanders. Last week, viewers got a chance to hear directly from the candidate at a Fox News town hall in Bethlehem, Pennsylvania. “Your network does not necessarily have a great deal of respect in my world,” Sanders said, “but I thought it was important for me to be here and have a serious discussion about serious issues.”
The town hall meeting was a ratingssuccess for Fox News and seems to have been a boon for the Sanders campaign as well. It led to the highest Google search interest in Sanders since he announced his candidacy and helped Sanders remain the most talked-about candidate on cable news for the third consecutive week, with 969 mentions1 across the three networks last week according to data from the TV News Archive.2
While Sanders and Buttigieg have been getting the most cable news coverage this month, that could change if former Vice President Joe Biden officially jumps in the race this week, as he is expected to do. Biden, who is leading in many early polls of the Democratic primary, managed to get 486 mentions on the three networks this week, which means that even though he’s not officially in the race, he got more cable news coverage than every declared candidate except Sanders and Buttigieg.
sara.ziegler (Sara Ziegler, assistant sports editor): We’ve had almost one full week of games in the NBA playoffs, and trends are emerging. Golden State took a 31-point third-quarter lead over the Clippers on Thursday night … and didn’t lose! So after a few early surprises, things seem to be getting back to what we expected.
One series not playing out according to seeding is San Antonio-Denver. The No. 7 Spurs beat the No. 2 Nuggets 118-108 on Thursday to take a 2-1 lead in the series. This comes as a surprise to the FiveThirtyEight NBA Predictions model, which had Denver as an 88 percent favorite to move on. The Nuggets are still favored, but just 60-40. Are you guys surprised by how this series is going?
chris.herring (Chris Herring, senior staff writer): Not all that much, no. I think I picked Denver out of respect for the season it had. But this was the one team basically everybody had questions about coming in.
I had the series going seven games, with Denver winning. It could easily be 3-0 Spurs right now.
tchow (Tony Chow, video producer): I am surprised, but I don’t think we really should be. It’s the Spurs being the Spurs again.
natesilver (Nate Silver, editor in chief): Our model doesn’t like San Antonio very much, so given their regular-season performance and home-court advantage — and Denver has a big home-court advantage — the Nuggets were pretty clear favorites. But it didn’t really like the Nuggets all that much either. They aren’t a great playoff team because their depth doesn’t really help them in the playoffs, the topline talent is not all that good, and they don’t have much playoff experience.
So I’m surprised that we had them as high as 88 percent, frankly! But not surprised that the Spurs are ahead in the series.
chris.herring: On Denver’s home-court advantage: The Nuggets haven’t beaten the Spurs in San Antonio in 14 tries now.
tchow: I am surprised because at one point in the season, our model gave the Spurs just a 4 percent chance of even making the postseason. We had a story a while back that talked about how they started turning it around (better defense, better bench production), but they were still underdogs going into this series, in my opinion.
sara.ziegler: Yeah, I had sort of counted the Spurs out a long time ago.
Let that be a lesson to me: Never count out Pop.
The experience factor really seems to be hurting the Nuggets so far. (And our model took 3 points away from them for their lack of playoff experience.)
chris.herring: Nuggets coach Mike Malone has talked about the experience factor a pretty decent amount in the past week
His young starting point guard, Jamal Murray, began Game 2 going 0-for-8. Malone was asked if he gave thought to pulling him because of Murray’s performance. He said no, in part because he needed to show his young players that he believed in them, and that he’s with them, win or lose. Murray responded by hitting 8-of-9 in the final quarter to bring the Nuggets all the way back for a dramatic win.
The win probably saved their season for the time being. But it speaks to the volatility of having such a young/young-minded club.
tchow: Murray wasn’t much better in Game 3 — just 6 points and two assists. I’m not trying to pin Denver’s failing’s this postseason all on Murray, though. All the Nuggets starters were pretty terrible in Game 3.
chris.herring: It’s a pretty big contrast between the teams.
While we’re talking about the growing pains for a young team, it’s worth pointing out that the Spurs are being led in part by youngster Derrick White, whose defense is his calling card. I think this is his first real exposure to a national audience, but he’s been playing really well for months.
tchow: White’s Game 3 performance was kind of a reminder for a lot of people who don’t watch the Spurs that he existed.
chris.herring: White’s experience has been different because of all the injuries they’ve had. But White and Dejounte Murray are going to be an annoyingly good backcourt once the team is healthy again next season. AND there’s Bryn Forbes, too.
natesilver: The whole Nuggets backcourt feels like it’s way short of championship caliber. It needs an anchor. There are lots of useful pieces you could rotate around that anchor, like Murray and Gary Harris, but without that anchor, it doesn’t quite come together.
chris.herring: It’s tough: They have a fantastic, sure-handed backup in Monte Morris, who led the NBA in assist/turnover ratio.
chris.herring: He may not win a game for you. But he’s extremely unlikely to ever lose one for you, which you could argue Murray either occasionally does, or comes close to doing. Again: These are the growing pains for a young team sometimes.
sara.ziegler: On to another team that has seemed shaky at times this postseason: the Philadelphia 76ers. But they seem to have recovered from their upset in Game 1 — they’ve beaten the Nets convincingly twice in a row now. What looked different for them in Games 2 and 3?
tchow: Ben. Simmons.
natesilver: Sen. Bimmons.
chris.herring: Yeah, that sounds about right. Whether it was Jared Dudley that got in his head, or just him recognizing that he had to be more aggressive, Simmons has been a completely different player since Game 1.
chris.herring: I hate to say this, because maybe it’s premature, but I was beginning to think that the Nets could steal this series if things broke right for them.
tchow: I think a lot of people thought that, Chris. The Nets are legit and play really hard.
chris.herring: The Nets stole home-court advantage in Game 1. Were basically even at halftime of Game 2. And then get a gift rolled out on a platter for them, with Joel Embiid sitting out of a Game 3 played in their home arena, in front of a fan base that hasn’t hosted a playoff game in four years.
Thursday was their chance. And I think with the loss now, that might be about it.
natesilver: I’m in the Ben-Simmons-is-underrated camp. Yeah, he doesn’t really have a jumpshot. But he does pretty much everything else well. And there have been a lot of players throughout NBA history who have survived or even thrived without jump shots — Giannis Antetokounmpo basically does that now. The advanced stats like Simmons.
tchow: I think it’s very different for a player like Giannis to not have a jump shot than Simmons.
chris.herring: While we’re on the issue of Simmons, I think we learned that Embiid not being there might have been a help for him
For all the wonderful things Embiid does, he plays at a plodding pace.
Someone like Simmons thrives in an up-tempo environment because of his inability to shoot.
tchow: Sara, I found the hot take for next week’s Hot Takedown episode: FiveThirtyEight’s Chris Herring says Sixers are better without Joel Embiid.
chris.herring: They might be in this series! Well, probably not: Greg Monroe was rough.
If they had more depth, they might be.
natesilver: That’s the thing about Philly. Look how bad their bench is:
Everyone’s like, “Why are these four stars such awkward fits together” — and I’ll admit that they’re a little awkward, but with a half-decent bench, it’s an entirely different team.
chris.herring: I don’t think it’s a terrible bench. And the truth is, you can stagger when you have that many stars.
But the spots in which it’s terrible … yeah.
tchow: Sixers’ bench: Who? Who? Who? The big guy. Who? and Who?
chris.herring: That’s their issue, I think. I’m not sure Boban Marjanovic would work against every team. But he’s their backup big.
natesilver: I saw Boban at the United Airlines lounge at Newark Airport one time. He was very big and tall and sitting in a giant lounge chair and still looked very big and tall.
chris.herring: I tweeted last night that I’m pretty sure he dunked last night with one foot still on the ground.
Anyway: I want to talk more about how disappointed I am in Brooklyn
tchow: Are you just disappointed in their central A/C system at Barclays, Chris?
I promise it's no warmer than 8 degrees in Barclays Center right now. Cold as hell in here.
sara.ziegler: Are you disappointed that their slogan is “We go hard,” and then they didn’t?
chris.herring: They did go hard!
It’s not a question of effort with them. It never is. But I think what Nate alluded to is exactly the issue here. The Sixers’ bench isn’t great/may be bad. And the Nets’ second-best player is their bench.
natesilver: Yeah, Brooklyn’s not totally unlike Denver. Excellent depth, no playoff experience, frontline talent is meh.
tchow: Nate, they’re both small-market teams. I get it. (Queens represent!)
Tony trying to start a borough war here.
chris.herring: You generally see Brooklyn go on these massive runs in the second quarter of these games. But then after halftime, the game gets broken open, and Kenny Atkinson — who I really, really like — waits too long to call a timeout!
The Sixers went on a 21-2 (!!!!) run in Game 2 before Atkinson called for timeout. It took a 1-point deficit and expanded it to a 20-point lead for the Sixers. And then the game was over.
tchow: Maybe Atkinson is from the Phil Jackson school of letting the players figure it out on their own.
natesilver: What was the atmosphere like at Barclay’s, Chris? I think it’s one of the coolest venues in sports from an architectural/amenities standpoint, but every time I’ve gone, the fans are sort of half-hearted.
chris.herring: Last night was amazing to start the game. But I think they were sort of stunned to see the team run out of steam.
And as Tony said: I was freezing.
sara.ziegler: Well, it is a hockey rink, too.
chris.herring: So maybe the have to have the ice ready? But good lord.
My phone turned off at one point because of how cold it was.
chris.herring: The atmosphere was really great. It’s good to have the playoffs in Brooklyn again. And hopefully Manhattan at some point in the next couple years. (side-eyes Knicks)
natesilver: Knicks fans should be rooting against Boston and against Golden State, right?
natesilver: I think KD could leave either after a championship or a flameout. But Kyrie — yeah, he’s already flip-flopped enough that I think Knicks fans want the Celtics out by Round 2.
chris.herring: I think I’m just too conditioned to believe that nothing overwhelmingly good can happen for/with the Knicks unless there’s an enormous downside that comes with it.
natesilver: My current scenario is that they get Kyrie and also draft Ja Morant and somehow that turns into a disaster.
sara.ziegler: Speaking of Kyrie, the Celtics are making quick work of the Pacers. Indiana doesn’t seem to have quite enough offense so far to hang with Boston.
tchow: I’m actually interesting to read Chris’s thoughts on this series. I remember A LOT of people were down on Boston going into the playoffs.
chris.herring: Yeah. I had some hope that this could be an interesting series.
But I also was tasked with writing an Indiana-based primer for the ESPN side ahead of this series. When I got to the “Why Indiana can win section,” I sat and stared at my screen for like an hour.
So this actually doesn’t surprise me all that much.
They simply don’t have enough offense. Or ingenuity.
natesilver: I haven’t watched much of that series; pretty much my only recollection was seeing a score that was like 76-59 in the fourth quarter of Game 1 and thinking I needed to update my contact lens prescription, but nope, that was the actual score.
chris.herring: They basically hand the ball off to Bojan Bogdanovic and say, “Do something.” Kind of like a kid who does a magic trick, but is still holding the quarter in his hand, in plain sight, for everyone to see.
tchow: Has Boston done anything to change people’s minds about their chances though?
chris.herring: No. They’re merely beating a flawed, weakened team, IMO.
tchow: That’s what I figured about Boston. The real test, if they do end up beating the Pacers, will probably come against Milwaukee.
chris.herring: In fairness to Nate McMillan and the Pacers, this was always going to be an uphill battle, because they’re playing without Victor Oladipo. It was a great accomplishment to go 21-21 this season without their star player after going 0-7 without him last season.
sara.ziegler: Yeah, they don’t really have anything to feel embarrassed about.
chris.herring: I really like Indiana, and have a soft spot for Little-Engine-That-Could sort of teams. But they need some reinvention.
They could use more firepower. But they need better schemes.
natesilver: I feel like the whole first round could use more firepower. Between inexperienced teams, teams with injury problems, teams without any star talent … it feels a little bit like spring training or something.
tchow: I agree, but it has been more interesting than I imagined.
chris.herring: A little.
sara.ziegler: Let’s talk about the other interesting series in the East: No. 2 Toronto has had its hands full with No. 7 Orlando. The Magic took the first game, but the Raptors stormed back in Game 2. The teams will face off Friday night in Orlando. Do we think the Magic have a realistic shot in this series?
chris.herring: It depends on what you define as “a shot.” I think they can get another game, potentially. I don’t think they will win the series. The Raptors responded in Game 2 the way you hoped a top-flight team would.
sara.ziegler: But the Magic are underrated, Chris!
chris.herring: If and when the NBA move the first round back to a best-of-five, they’re going to use this series as evidence as why. (edited)
natesilver: I think there needs to be a mercy rule where you can concede your playoff series and get like three Lottery Balls or whatever.
sara.ziegler: OK, let’s move back to the West. The Trail Blazers are off to a great start, up 2-0 against the Thunder. Our model is surprised at this series — it had given the Thunder a 77-23 edge. Are you guys surprised?
Which, while God awful, is only a slight regression for them!
natesilver: That whole quadrant of the bracket — OKC, Portland, San Antonio, Denver — seems incredibly weak to me.
chris.herring: If OKC had a team full of sharpshooters, I could understand having more confidence.
But Russ still defends Damian Lillard as if he’s surprised that Dame can/will pull up from 35 feet.
The guy needs to be treated as if he’s Steph at this point
tchow: I don’t want to take anything away from Portland. Yes, they lost Jusuf Nurkic, but CJ and Dame have been awesome this series.
chris.herring: I came in thinking that this might be a sweep or a 4-1 series in favor of OKC. Simply thought that not having Nurkic would hurt against someone like Steven Adams. I thought CJ McCollum would struggle to find a rhythm (he’s coming off an injury and wasn’t good vs. OKC during the season). We watched Dame log 35 a night against the Thunder during the season and still get swept 4-0 during the regular season.
tchow: CJ has been
chris.herring: I didn’t think they had a great chance in this series. They had lost 10 playoff games in a row. With the exception of perimeter shooting, I thought just about everything else would be in OKC’s favor. Wrong, wrong, wrong.
tchow: If Dame wasn’t in Portland, would he still be this underrated? It feels like this is a storyline every season.
sara.ziegler: That’s a good question.
How many people regularly see him play?
tchow: Basketball nerds: “Look at Damian Lillard!”
Basketball fans: “Who this?”
chris.herring: I guess we have to define underrated.
natesilver: He was All-NBA First Team last season, no?
But, yeah, Portland has to be one of the least-watched teams in the league, or at least by people not in the Pacific Time Zone.
chris.herring: Even if you know who he is, and how great he is, I think you could objectively look at this series — and what the Blazers have done the last two years in the playoffs (0-8) — and say OKC should have been favored.
tchow: For OKC to take Game 3, they need to ____________.
And don’t say something like “play better” (looks at Nate).
sara.ziegler: SHOOT BETTER
chris.herring: … shoot better than my 4-year-old nephew does from outside of 23 feet.
natesilver: I’d say they need to play better basketball.
sara.ziegler: In the other non-Warriors series out West, the Rockets are handling the Jazz easily so far, setting up a showdown with Golden State in the second round. This has played out about as expected, right?
chris.herring: I had higher hopes for Jazz-Rockets. Am impressed with how dominant Houston has looked, but thought Utah would play better than this. Their defensive scheme has looked downright nonsensical to me
tchow: If Chris has a soft spot for Indiana, I think I have a soft spot for Utah. I love this team and wanted more out of them this series.
sara.ziegler: Utah is a very likable team.
natesilver: I didn’t expect Houston to dismantle Utah quite so thoroughly.
In fact, I think that’s the story of the first round so far. It’s a highly consequential story because the Rockets are absolutely good enough to give the Warriors a series.
chris.herring: The disappointment I feel with Utah is equivalent to how excited I am for the second round, with Warriors-Rockets.
That will seemingly be the Western Conference finals, just a round early.
natesilver: It would be quite something if the Rockets actually need fewer games to dispatch Utah than Golden State needs with the Clippers.
tchow: The Jazz just seem like a team that’s so close to figuring it out. Maybe not to a point where you think they can beat Golden State, but they’re so good in the regular season. I don’t know what happens to them in the playoffs.
chris.herring: Yeah, I sort of agree in theory, Tony.
But I think what I’ve learned is that I have to be leery of a team that relies on such a young player to be its leading scorer.
natesilver: Maybe you just need more isolation scoring in the playoffs? Or more scoring, period?
chris.herring: I remember a stat from last year: Donovan Mitchell was the first rookie to lead a playoff team in regular-season scoring since Carmelo Anthony.
I think there’s a reason we don’t see it happen much. And I think it’s even more problematic for a team built like that to have all sorts of horrible defensive breakdowns, because at that point, you know they have no shot at keeping up in a shootout against one of the best scorers in modern history.
If Quin Snyder rolls out the exact same defensive scheme that he did in Games 1 and 2, this series will end in a sweep.
natesilver: Is Mitchell … a little bit like Carmelo Anthony in that he’s taking too many shots? I mean, I guess he has to take a lot of shots with that lineup. But Utah really needs another player who can create his own shot.
tchow: What if you played a player like Royce O’Neale more? He’s +1.8 on defense (according to our model), and it looks like they do a bit better defensively with him on the floor.
chris.herring: He’s another example of what Nate is talking about, though: A guy that isn’t likely to create his own shot.
This is a team that will need to take a long, hard look at itself this summer despite how well it’s played during the second half of these last two seasons.
tchow: One obvious fix would be to get rid of Grayson Allen.
natesilver: I also think Utah benefits from being a bit unorthodox. Rubio is an unorthodox point guard. They’re defense-first. They can play at a slow pace, although they picked up their pace a lot this year. They’re well-coached. So there’s an advantage from game-planning in the regular season. But Daryl Morey and the Rockets are going to study the hell out of the Jazz and know how to counter.
chris.herring: Some of these teams are built to play really, really well in the regular season. And there’s incredible value in that, for seeding purposes, etc.
But the inability to change your playing style when you’re forced to is often fatal this time of year.
natesilver: It’s not that they’re going to lose to the Clippers, but I do just have to wonder about a team’s mentality when they can blow a 30-point lead.
chris.herring: NBC analyst Tom Haberstroh pointed out that Steph was only averaging 19.9 points per 36 minutes this season with Boogie on the court, and that he essentially morphed into Malcolm Brogdon.
Averaged 31.4 points per 36 minutes without DeMarcus on the floor.
natesilver: I mean, part of that might be that Steph was being deferential in an effort to get Cousins feeling like himself again.
Which … there isn’t time to do that in the playoffs.
tchow: Definitely. I think Steph went through a similar dip when KD joined too.
chris.herring: The last thing you want is Steph playing nice when you need him to be Steph.
natesilver: It does just seem kind of impossible when you have to shut down Steph AND KD and Klay. Even if the rest of the team kind of sucks.
chris.herring: I tend to think this helps them for now, but the Rockets series was one of the overarching reasons they signed Cousins — to make it so Houston couldn’t switch as much as they did on them last year
natesilver: Yeah. So in some ways, we’re back to last year’s series, which was as even as it gets. The Rockets lately are playing as well as last year. And the Warriors without Cousins are basically last year’s team.
sara.ziegler: After this matchup, will we even want to finish out the playoffs??
natesilver: Well, the Western Conference finals are likely to be an anti-climax.
tchow: LOL. Yes! I for one am very interested to see who comes out of the East to play against Warriors/Rockets.
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.
From Guy Moore, a puzzling progression:
What is the sequence below, and what are its next elements? (The numbers in parentheses provide a helpful hint.)
If N points are generated at random places on the perimeter of a circle, what is the probability that you can pick a diameter such that all of those points are on only one side of the newly halved circle?
Last week, you bought a new clock, only to be dismayed when you got home to discover that its two hands were identical — the hour hand and the minute hand looked exactly the same. How would you ever know what time it was? You soon realized, however, that this wouldn’t always be a problem. For example, when it’s 12:30, the minute hand is exactly on the 6 and the hour hand is halfway between the 12 and the 1. It can’t be the other way around because if the hour hand were exactly on 6, the minute hand would have to be exactly on 12, which it’s not. So in that case, you know what time it is. But how many times during the day are you not able to tell the time?
The clock’s hands will be indistinguishable 286 times a day. At 264 of those, you will truly not be able to tell the time — and even then only for a split second (and if your eyesight is good enough). Not bad, really, considering such a seemingly defective design.
I received many widely varying approaches to this problem that led to correct solutions. Let’s start with the tidy approach of solver Doug DeMoss:
Every hour, the true minute hand will sweep around the whole clock and the true hour hand will sweep across a one-twelfth segment of the clock. Twelve times during that hour — once per one-twelfth segment — there will come a time where the hour hand and the minute hand could be reasonably mistaken for one another. That is, where they could be reversed and still display a reasonable time of day. For example, at about 10 minutes and 4 seconds past 12, it would be impossible to tell whether the clock is reading that time or about 50 seconds past 2. One of those 12 times, however, is when the hands are perfectly aligned, and in that case, we do know what time it is. So there are 11 times an hour when we can’t tell the time, and there are 24 hours in a day, so the answer is 24×11, or 264.
And here’s an arithmetic submission from solver Michael Branicky:
If the hour hand has moved a fraction of the circle h from midnight, then the minute hand has moved m = h/12. Thus, h = 12m. We are searching for times that are also valid the other way around, or m = 12h. Combining those equations, this occurs when h = 144h, or 143h = 0, where both equations are mod 1. This happens 143 times every 12 hours, when h = k /143 for integer k = 0, 1, …, 142. In a full day, this happens 286 times. However, we must also remove the cases — such as midnight — when the minute and hour hands overlap. These happen when h = m, or when h = 12h (again, mod 1), or whenever 11h is an integer. This happens 11 times every 12 hours, or 22 times every full day. Therefore, if you carefully measure the hands, you cannot tell the time at just 286-22 = 264 times during the day.
Solver Mike Seifert took a graphical approach. He plotted the position of the big hand and the little hand, with the big hand’s position as the x-coordinate and the little hand’s position in the y-coordinate. He then flipped the x and y coordinates. Anywhere the two paths coincide is an ambiguous time:
Finally, a few intrepid solvers explained that this clock question could be solved using topology, by thinking about the positions of the hands as a torus and by appealing to the Poincaré duality.
The Virginia Cavaliers and the Baylor Lady Bears cut down the nets in the men’s and women’s NCAA basketball tournaments this month. But what about the unsung transitive champions — the teams that beat those teams during the season, and the teams that beat those teams, and the teams that beat those teams, and so on? Enter last week’s challenge: How many transitive champions were there this past season in the men’s and women’s games? I provided links to the men’s and women’s season results.
There were 359 transitive national champions on the men’s side, including every single Division I school. We’re gonna need a lot more scissors and nets.
Unless you had a lot of time on your hands — and a lot of paper — this problem was an exercise in data analysis and programming. Many solvers were kind enough to share their code, including Benjamin Phillabaum, Colin W., David Fried and Kyle Tripp. Mathematically, this basketball problem is really an exercise in graph theory — the teams are the graph’s vertices and the games are the graph’s directed edges, pointing from the winning team to the losing team. The challenge, therefore, is to see which vertices ultimately connect to the real NCAA champion. And most, as it turns out, did connect.
Luke Benz plotted the men’s Division I transitive champions by degrees of separation and by conference. Teams in the ACC, for example — Virginia’s conference — tended to have tighter claims to the transitive championship, while teams in a conference such as the Patriot League could lay only more distant claims.
The team with the longest path to a coveted transitive national championship were the Division II Fayetteville State Broncos, who can smile upon a chain of eight games. They beat UNC-Asheville who beat USC Upstate who beat Longwood who beat Southern Miss who beat Old Dominion who beat Syracuse who beat Duke who beat Virginia. Congratulations, Broncos!
There were a whopping 1,775 transitive national champions on the women’s side even though true champion Baylor lost only one game all season. (The women’s results to which I linked included many more teams, for one thing, including Division III teams and teams in Canada.) Every Division I women’s team was a transitive national champ — except for the Eastern Kentucky Colonels, who went 2-27 and were winless against other D-I teams.
Eight different teams on the women’s side tied for the longest path, claiming their transitive title thanks to chains of 25 games! One example: the St. Mary’s Lightning (in Alberta) beat Briercrest who beat Okanagan who beat Capilano who beat Vancouver Island who beat Bellevue College who beat Umpqua who beat North Idaho who beat Chandler-Gilbert who beat Anoka-Ramsey who beat Hibbing who beat Bay College who beat Silver Lake who beat Concordia who beat Rochester College who beat Spring Arbor — deep breath — who beat Keiser who beat Florida Memorial who beat Xavier University of Louisiana who beat Southeastern Louisiana who beat SMU who beat South Florida who beat UCLA who beat Cal who beat Stanford who beat Baylor. Phew. Congratulations, Lightning!
Michael Branicky shared his code and plotted the distribution of all the transitive national champions by their shortest distance from beating the actual champion:
Anyway, great season, everybody.
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!
You’re reading Significant Digits, a daily digest of the numbers tucked inside the news. For even more facts, figures and discussion, check out our live FiveThirtyEight Politics podcasts in Texas in May.
In case you were busy circumnavigating the world in a hot air balloon or something, a redacted version of the full 448-page Mueller report was released to the public yesterday. Among many, manyotherthings, the report describes President Trump’s reaction upon first learning that a special counsel had been appointed: “Oh my God. This is terrible. This is the end of my presidency. I’m fucked.” [ABC News]
7 of 18 Democrats
The New York Times sent a climate policy survey to 18 Democratic presidential candidates. Their responses were not monolithic. They all supported remaining in the Paris Agreement, for example. But seven favored a carbon tax, while five others were only willing to consider it. And only seven were “unequivocally in favor of new nuclear energy development.” [The New York Times]
380,000 years after the Big Bang
Long, long ago, a mere 380,000 years after the Big Bang, helium hydride was formed — the first molecule ever to form in the universe. The molecule has since been produced in labs but had been hard to find in space. But now, billions of years after the Big Bang, scientists have discovered helium hydride in a planetary nebula in the constellation of Cygnus, confirming astronomical theories about the “dawn of chemistry.” [The Guardian]
Lowest since 1969
Fewer Americans are filing for unemployment benefits than at any time since 1969, according to the Labor Department. Claims for jobless aid — a proxy measure for layoffs — fell by 5,000 last week to 192,000, the lowest since September 1969. [Associated Press]
27th in WAR
You know what’s also experienced a remarkable fall: the Boston Red Sox. They’re off to a 6-13 start this season and may already be in real trouble, my colleague Neil Paine writes. According to wins above replacement, the Sox have gone from the third-best team in Major League Baseball last season to the 27th-best so far this year. [FiveThirtyEight]
The National Enquirer, the supermarket tabloid, is being sold by American Media Inc. to the CEO of Hudson News, aka that place you buy magazines and Skittles in the airport. The Enquirer had been overseen for many years by David Pecker, a longtime Trump loyalist. [The Washington Post]
From ABC News:
Love digits? Find even more in FiveThirtyEight’s book of math and logic puzzles, “The Riddler.”
If you see a significant digit in the wild, please send it to @ollie.
Welcome to a special, extra edition of FiveThirtyEight’s weekly politics chat. The transcript below has been lightly edited.
sarahf (Sarah Frostenson, politics editor): At long last, we have special counsel Robert Mueller’s report into Russian interference in the 2016 election. And compared with Attorney General William Barr’s summary of the report, which he sent to Congress last month, it paints a murkier picture of whether President Trump might have obstructed justice; for example, the report includes details of the president attempting to fire the special counsel.
Ultimately, though, Mueller’s team wrote that it did not have the confidence to clearly state that the president either did or did not obstruct justice and that “while this report does not conclude that the president committed a crime, it also does not exonerate him.”
So, tell me … now that we have the report, is it a BFD?
ameliatd (Amelia Thomson-DeVeaux, senior writer): The obstruction findings were a BFD, to me, because I was surprised by how clear Mueller was in suggesting that Trump had corrupt intent when he took various actions around the Russia investigation (such as firing FBI Director James Comey). That was a big deal, for Mueller to paint such a dark picture of Trump and his White House.
Mueller essentially told the story of a president who’s willing to intervene in ongoing criminal investigations to serve his own ends, and I wasn’t expecting Mueller to do that so directly.
Whether anything will come of that is another question, though, since Mueller himself didn’t actually come to a conclusion on obstruction.
clare.malone (Clare Malone, senior political writer): “Our analysis led us to conclude that the obstruction-of-justice statutes can validly prohibit a president’s corrupt efforts to use his official powers to curtail, end, or interfere with an investigation.”
That line from the report really stood out to me in contrast to what we’d been hearing from Barr over the past few weeks.
ameliatd: There were a lot of things that were pretty different from what we heard from Barr, both in his summary and in his press conference today — it will be interesting to see what happens if Mueller does testify before Congress. I will be curious to hear what he thinks about how Barr handled this.
clare.malone: I agree, Amelia. I sort of wonder if he’ll unburden himself in a lawyerly way.
ameliatd: I am sure that he’ll do some expert hair-splitting. But still. It will have to be hair-splitting to explain some of the discrepancies between how Barr characterized the report/Mueller’s analysis and what we can read in the actual report.
sarahf: Let’s dive into those discrepancies a bit.
What do we think are the key ways in which Barr’s summary and comments in the press conference on Thursday differed from Mueller’s team’s conclusions?
ameliatd: Well, Barr said on Thursday that Mueller’s decision not to come down on obstruction was not driven by an opinion from the Justice Department saying that a sitting president can’t be indicted. And that was important in the wake of the Barr summary because it raised the question — OK, so is Mueller not coming down on this because there just isn’t enough evidence to support obstruction charges?.
Reading Mueller’s report, it is very clear that he started from the position that he couldn’t indict the president and then charted his path from there.
perry: Barr, to me, implied that Mueller couldn’t reach a conclusion on obstruction, like it was a 50-50 call or something, based on the evidence. It looks like Mueller saw obstruction and the question was should he indict based on that or defer to Congress.
clare.malone: I was going to say what Amelia and Perry said. Barr really seemed to have been misleading.
natesilver (Nate Silver, editor in chief): I’ve mostly read Volume 1 so far — i.e., the collusion/conspiracy part — and there are some discrepancies there as well. Namely, Barr downplays the extent to which people in the Trump campaign were sometimes receptive to efforts to coordinate with Russia. (Although they rebuffed them at other times.)
From the report:
And from Barr’s letter:
perry: Also, Barr in his press conference today implied that Trump was annoyed by the investigation because it was hurting his presidency and the media coverage was bothering him. The report suggests that Trump was worried where the investigation might lead and wanted to stop it by any means necessary.
sarahf: Right. That’s the part of the report that hasn’t gotten as much attention — Mueller’s team wrote that “while the investigation identified numerous links between individuals with ties to the Russian government and individuals associated with the Trump Campaign, the evidence was not sufficient to support criminal charges.”
ameliatd: Barr’s summary also seemed to imply that the fact that there wasn’t an underlying crime (i.e., nobody within the Trump campaign was ultimately charged with coordinating with Russia) had an impact on whether Trump could have obstructed justice. Mueller said very pointedly that you can charge obstruction without an underlying crime.
perry: Mueller’s team also notes that the collusion/conspiracy/coordination investigation was hampered by Trump allies lying about what happened.
clare.malone: More to the Russia side of things, not obstruction?
I think there’s still the question of why Trump was so into being pro-Russia or accepting help. You could maybe extrapolate that he had business interests …
natesilver: But “evidence not sufficient to support criminal charges” is a lot different than “no evidence” or “no effort to coordinate.” For instance, the stuff about former Trump campaign Chairman Paul Manafort sharing internal polling data with Konstantin Kilimnik (a Russian political operative with suspected ties to Russian intelligence) — including the emphasis the Trump campaign would go on to place on Michigan, Wisconsin and Pennsylvania! — isn’t great for Trump. And Mueller isn’t sure what happened to that data, in part because Manafort isn’t a reliable witness so everything about what he did is murky.
perry: Right, there is “no evidence to support criminal charges” on the collusion part is just way different than nothing happened.
clare.malone: Yeah, especially given the narrow definition that Mueller gave to “collusion.” And we should note that there are a lot of other criminal referrals that came from this investigation, so there’s still some story left to tell.
ameliatd: Clare, to your point, it’s also relevant that Mueller focused very narrowly on 2016 election interference. We don’t know what he found and turned over to other investigators.
One other big unanswered question on the Russia side: Why were all of these people making false statements about their ties to Russia?
natesilver: Maybe because (i) there’s a lot of “smoke,” enough for them to be paranoid even if it all doesn’t amount to a criminal conspiracy to interfere with 2016; and/or (ii) nobody actually is quite sure what happened or what didn’t because the campaign was such a shitshow; and/or (iii) they’re people who lie habitually?
And for the most part, the report confirms media reporting, as well as material uncovered in earlier indictments that Mueller issued.
ameliatd: I genuinely don’t know, Nate. I think the explanation could be any of the above, all of the above or none of the above. It’s just so puzzling. It’s also puzzling that Trump saw the Russia investigation as such a serious threat, and ultimately we’re left with something that’s not so dramatic.
natesilver: The one thing Mueller really seems to go out of his way to bat down is the idea that Russia interfered to change the GOP platform on Ukraine — he seems pretty confident that there’s an innocent-enough explanation for that, which is that Trump had already taken a position on Ukraine on the campaign trail and the campaign/Republicans didn’t want the GOP platform to contradict it.
perry: And he also downplays the idea that former Attorney General Jeff Sessions was involved in much of anything during the campaign.
natesilver: Yeah, he bats down the Sessions stuff too.
clare.malone: One thing that does come across in the report is that a lot of this obstruction stuff was self-inflicted. So, it could be just the idea of Trump being habituated to the “deny, deny, deny” theory of PR. Which, when you’re president, leads you down a pretty dangerous road.
perry: I think I get why he wants to end the investigation. Volume 1 documents:
Trump going around telling former national security advisor Michael Flynn to get Hillary Clinton’s emails.
Donald Trump Jr. and Jared Kushner meeting with Russians to get dirt on Clinton.
The various things Manafort was doing that would all look bad for Trump.
So all of that stuff in total looks pretty bad.
natesilver: For the most part, though, if you were one ofthose people who, from the Barr memo, characterized the media’s entire Trump-Russia coverage as a gigantic fail … well, the Mueller report itself makes you look pretty dumb. All of the stuff that people were expecting to be in there is pretty much in there. And some of it is reasonably serious! But does it amount to a criminal conspiracy? Mueller thinks not.
perry: Like Volume 2 (obstruction) is worse for Trump than Volume 1 (collusion), but if Trump knew most of what is detailed in Volume 1, I can see why he wanted to stop the investigation.
clare.malone: Volume 2 just lays out a lot of Keystone Kops scenarios: Trump giving different orders to different people, mismanaged responses to media stories dropping, etc.
natesilver: And also, to the extent that his efforts to obstruct the probe were pretty serious, maybe Mueller didn’t find out everything he could have in Volume 1.
The report actually says that at some point, and it seems particularly relevant for the Manafort-related stuff.
I'm not an expert on this stuff, but this seems like an interesting part on page 18 of the PDF that I haven't seen other people point out, where Mueller says his conclusions could conceivably be different if not for witnesses lying, invoking privilege, etc. pic.twitter.com/nRm85Ec4zj
ameliatd: It does seem pretty clear that Mueller was frustrated with his inability to get reliable information out of Manafort. I wonder now that the report is out whether we’ll actually see any pardons.
That’s been hanging over the investigation this whole time, and it would actually be unusual, from a historical perspective, if no one implicated in the Mueller investigation ended up being pardoned.
natesilver: I mean, that would be a very risky move for the White House politically.
ameliatd: Right. There’s a reason why presidents wait until they’re on their way out the door to pardon people.
clare.malone: Who do we think the most likely candidates for a pardon are?
natesilver: But maybe Trump would do it. You sometimes get the sense that the whole way the White House played it was more to soothe Trump’s ego than to necessarily win the battle of public opinion. The press conference this morning didn’t help the White House at all, I don’t think.
perry: Well, the report suggests that Manafort stayed loyal to Trump. But the report also says he was involved in some of the stuff that looks most collusion-like (meeting with Russian officials and discussing poll numbers).
Pardoning Manafort would be a really stupid political move.
But he might do it anyway.
ameliatd: If this report has taught me anything it is that Trump does not think about risk in a way that I understand.
clare.malone: I feel like Trump definitely misses the forest for the trees. ALL THE TIME.
sarahf: OK, on the question of obstruction of justice, though, what did we learn that was particularly damning or mischaracterized by Barr’s interpretation that made it a big deal?
After all, there were some examples in which Mueller’s team said that the president had the prerogative to, say, fire Comey because it didn’t prevent the FBI from continuing its investigation.
But in other instances, Trump was arguably saved from complicated legal issues only because someone in his administration intervened.
ameliatd: It would have been huge if Trump had actually managed to fire Mueller.
clare.malone: Well, the Comey thing is more complicated, though. It’s within Trump’s power to fire the FBI director, but the way he went about it and the reasons given could tilt it more toward obstruction.
perry: The actual activities had been reported — trying to get Mueller fired, firing Comey. But Mueller provided new details that suggest Trump really was behaving in nefarious ways — like deciding to fire Comey but then trying to get Deputy Attorney General Rod Rosenstein to say he came up with the idea is pretty bold. And trying to get former Trump campaign manager Corey Lewandowki to tell Sessions to basically un-recuse himself from the Russia probe and stop parts of the investigation.
ameliatd: And Barr was making it seem like maybe the evidence wasn’t there, when in fact Mueller said he couldn’t charge Trump but he could, in theory, clear him of wrongdoing. Then Mueller explicitly said he could not exonerate Trump, which suggests Mueller does think the evidence was at least somewhat compelling.
perry: The report shows Trump being deeply involved in the details of trying to stop the investigation and obscure his role in stopping the investigation.
ameliatd: Which makes it pretty clear that Mueller found this evidence at the very least compelling, in terms of obstruction. And he didn’t buy arguments from the president’s defenders that Trump couldn’t obstruct justice by firing Comey because it’s one of his constitutional powers, regardless of his motivation.
ameliatd: I also just want to note that Mueller said explicitly that a president could be charged with obstruction after leaving office. And Barr just closed that door!
natesilver: Are y’all surprised at how wantonly Barr was willing to spin?
clare.malone: No, Nate — I guess not?
natesilver: I mean, I guess I thought that, say, if the actual report were a 5 out of 10 for Trump (on a scale where 0 is terrible and 10 is great), he’d be willing to spin it to a 6 or a 6.5. Instead he tried to spin it to an 8.
ameliatd: I am surprised, if only because it seemed so ill-advised. Eventually, much of the report was going to go to Congress and the public, right? So why be so misleading?
clare.malone: To play to Trump?
perry: I think Nate suggested this in the podcast, but the report would have basically met my expectations if it came out pre-Barr’s summary. But the White House took the Barr letter and framed it as an exoneration. So that made the report even more damning — I expected it to be not that bad, and it was, on the merits, really bad for Trump.
sarahf: So to that point about expectations — how much of the Mueller report did we already have?
ameliatd: I don’t think there’s much of the report that is genuinely new, but there’s a lot we hadn’t heard from Mueller before.
natesilver: Let’s keep in mind: If you’re willing to work for Trump — at, frankly, a lot of risk to your reputation and maybe also some legal risk — then maybe you’re a True Believer after all.
sarahf: But do we really think this is bad for Trump? For example, what do we think Congress actually does next? Or will it be advantageous for Democrats to use this in 2020?
natesilver: It’s not that bad for Trump. It’s a 5 out of 10, relative to pre-Barr letter expectations. But it feels a lot worse because of Barr’s clumsy attempts at spin.
And fundraise off making the full Mueller report available!
perry: The report portrays Trump very negatively. And a report can be bad in a legal sense that is separate from its electoral impact.
ameliatd: One of the main takeaways for me is that the report has given Democrats ammunition to drag this fight out without necessarily calling for impeachment. Instead, they can call Mueller to testify, call Barr to testify, and use what’s in the report to support more investigations.
clare.malone: We’re already seeing Trump campaign emails and videos out today pushing the line that the tables need to be turned and the investigators investigated. We’re already seeing the playbook for how the Mueller report will play out in the campaign: Trump running with the idea that he was persecuted, and Democrats running with the whole “can you believe this guy?” line.
natesilver: The report is bad, but it’s roughly in line with what people would have expected, as Amelia and Perry said. Keep in mind that only 42 percent of the public approves of Trump, and that’s in a really good economy! They don’t think he’s honest about Russia or other things. They also didn’t necessarily expect there to be a smoking gun about collusion/conspiracy. The public was way smarter than the media on this stuff, I think.
ameliatd: Barr’s little intro to obstruction of justice in the press conference, saying that Trump was facing all of these investigations and scrutiny and there was ultimately no collusion, seems like it will be very useful for Trump and his defenders.
perry: So earlier today, House Majority Leader Steny Hoyer made this “no impeachment” statement. And as you can see the tweet referring to it was ratioed:
“Based on what we have seen to date, going forward on impeachment is not worthwhile at this point. Very frankly, there is an election in 18 months and the American people will make a judgement,” House Majority Leader Steny Hoyer told @DanaBashCNN .
natesilver: But Hoyer is right on the politics of this. Impeachment is not a popular option. As Amelia said, call Mueller to testify. Call Barr to testify. Call other people to testify. So you can have a drip, drip, drip against Trump, mostly to satisfy partisans and keep him off balance. But impeachment? Not popular.
natesilver: It’s also Trump’s first term. The Nixon/Clinton impeachment efforts both came in the second term, when those presidents were lame ducks and there wasn’t any recourse from the public.
ameliatd: I’m not sure this gives Democrats much fodder for more investigations because the obstruction stuff was so clear and there don’t seem to be many more avenues to explore the 2016 election. Maybe it helps them get momentum to look into Trump’s finances for ties to Russia?
natesilver: Also, if Trump were unpopular enough that he could be not only impeached but also removed by the Senate — which would mean that his approval rating with Republicans would have to be way down — wouldn’t you rather run against him anyway?
That would probably imply he had like a 29 percent approval rating or something, in which case the Democratic nominee in 2020 would be on track to win in an epic landslide and maybe pick up some huge congressional majorities too.
clare.malone: But what does it take for him to slide to that point? And is that a realistic expectation given our political environment, Nate? That just seems to be a pretty unlikely thing to happen.
natesilver: No, I’m not saying that at all.
I’m saying that impeachment won’t actually result in his removal from office unless he’s fallen to like 30 percent.
But if he’s fallen to 30 percent, Democrats don’t want to impeach him because then they’re basically guaranteed a landslide victory in 2020!
ameliatd: And if they impeach him, they risk turning him into a martyr.
sarahf: OK, to wrap … We have the report. And the evidence that Mueller had on the question of obstruction justice was a bigger deal than Barr indicated in his initial summary. But what does the report’s release actually change? Is it a question of who wins the political narrative?
ameliatd: This is the tricky thing about special counsel investigations! If they don’t come to a conclusive result, it’s hard to know what to do with the findings politically.
clare.malone: Basically, Democrats have to keep their base on board with the long-term plan of winning back the White House and not the short-term impulse to impeach.
natesilver: What does it change going forward? I dunno. The Barr memo didn’t do much to shift public opinion in Trump’s favor, so Occam’s razor is that the Mueller report won’t do much to shift public opinion against him.
I do think it will make the press more skeptical of Barr and any efforts the White House makes to normalize its conduct.
ameliatd: And it does mean we’re going to keep hearing about the investigation, which could be good for Democrats because people are so fired up about it.
natesilver: It certainly describes a White House and a campaign that’s in total disarray. In the end, as Perry said earlier, I think it brings us back to where we were a month ago, where “the Russia stuff” is a negative for Trump and one of the reasons his approval rating is so low but not an acute crisis for him or the first (or second or third or fourth) thing that voters are thinking about.
Eight days ago, the FiveThirtyEight Soccer Power Index (SPI) gave Manchester City the best chance to win the Champions League. On Wednesday, Manchester City crashed out of the competition in spectacular fashion, conceding three goals at home to Premier League rival Tottenham Hotspur. The series finished 4-4 on aggregate, but Spurs get to play on because of the competition’s away-goals rule. Remember all that talk about City winning the historic quadruple? That’s all over now.
Pep Guardiola’s Sky Blues got off to a quick start, grabbing the lead via a strike from Raheem Sterling in the game’s fourth minute. Sterling’s goal canceled out Tottenham’s 1-0 aggregate lead, and the tilt was on. But it wasn’t long before Son Heung-min struck to give the lead back to Spurs, and it wasn’t long before he struck again. At that point it looked like City was doomed, but then they stormed back, scoring twice to tilt things back in their favor. Spurs were not done, however, and got the series-winning goal from unlikely hero Fernando Llorente in the 73rd minute. They still had to survive some end-of-the-game drama: City scored what appeared to be the winning goal, but VAR ruled that forward Sergio Aguero was offside in the buildup, and Tottenham was on to the semifinals to face Ajax.1
City is out, but the favorites to win the whole thing still hail from Northern England. According to our SPI, Liverpool has the best chance to conquer Europe. The Reds followed up their very professional 2-0 win over Porto at Anfield last week with a very professional 4-1 win over Porto at Estadio de Dragao on Wednesday. Porto needed to score at least two goals to send the series to extra time — and at least three to win it outright — and the first 35 minutes of the match reflected that: Porto completed twice as many passes in the attacking third as did its opponents from Merseyside en route to outshooting them 14 to 3.
But then Liverpool scored a goal in the 26th minute, and it was all but in the bag for Jurgen Klopp’s side. Eder Militao, future center back for Real Madrid, scored a late goal for Porto, but it was merely consolation. And Liverpool’s reward for its 6-1 aggregate victory? A date with Barcelona in the semifinals.
Speaking of the Catalonians, they made relatively light work of Manchester United in the quarterfinals on Tuesday. Lionel Messi did Lionel Messi things at Camp Nou, scoring twice from outside the box — one shot with his left foot, the other with his weaker right — in a matter of four minutes. The first was vintage Messi, a left-footed effort driven low that curled past the outstretched body of Manchester United goalkeeper David de Gea and into the bottom left corner of the goal. The second was less spectacular, a speculative effort that de Gea whiffed on uncharacteristically. Gift or not, the goal put Messi two clear at the top of the Champions League Golden Boot race. A goal in the 61st minute from old United foe Philippe Coutinho put the series out of reach for the Mancs. And now the soccer world can salivate over a Messi-vs.-Salah showdown in the semifinals.
If the result in Barcelona felt like a forgone conclusion, the result in Turin felt like anything but. Ajax’s 2-1 Tuesday win (3-2 aggregate) marked a sort of long-fermented revenge: In April 1997, the last time the Dutch giants played in the Champions League semifinals — a month before the team’s current best player, Frenkie de Jong, was born — they were eviscerated by Juventus, losing by an aggregate score of 6-2. That Ajax team featured club and country legends Edwin van der Sar, Frank de Boer, Marc Overmars and Danny Blind,2 but Lucky Ajax wasn’t very lucky on that occasion.
This time around, Ajax took the game to Juventus from the opening whistle, a strategy that should have stunned exactly no one who watched the team embarrass Real Madrid last month. Total shots and shots on target were nearly equal Tuesday in Turin, but Ajax created more big chances and completed a higher percentage of passes in the attacking third than Juventus. Crucially, the Dutchmen didn’t panic when Cristiano Ronaldo scored to give the Italians the lead in the 28th minute. They kept pressing, kept playing on the front foot, and midfielder Donny van de Beek bagged an equalizer just six minutes later. And even after it took the lead on a header from team captain Matthijs de Ligt in the 67th minute, Ajax didn’t sit back. The side smelled blood and attempted more passes inside the penalty area in the final 23 minutes plus stoppage time than its opponents. Ajax could have scored a couple more — and now it has a 16 percent chance in our SPI model to win the whole thing, up significantly from before the quarterfinal’s second leg.
It’s hard to predict whether Ajax pups like de Jong, de Ligt and van de Beek will go on to have the kinds of long, fruitful careers their elder countrymen did, but there’s little doubt that they’ve cemented themselves as club legends. They’ve made Ajax relevant again. Now all that’s left for them to do is to make Ajax champions again.
Presidential primary debates are a major media spectacle in American politics, so candidates, naturally, want to participate lest they become irrelevant. And with a historically large Democratic field in the 2020 cycle, the race is on to qualify for the first two debates, which are taking place this summer.9
Democratic hopefuls have two ways of getting onto the debate stage, according to a February news release from the Democratic National Committee. They can earn at least 1 percent of the vote in three different national or early-state polls conducted by qualifying pollsters, or they can receive donations from at least 65,000 unique donors, with at least 200 individual donors in at least 20 different states. And as you can see in the table below, of the 16 major candidates FiveThirtyEight is tracking — plus former Vice President Joe Biden, who hasn’t yet entered the race but is widely expected to — 15 have already met at least one of those two criteria, according to our research.
Which candidates have made the primary debates?
Democratic presidential candidates or potential candidates, by qualifying criteria for the first two primary debates, as of April 16, 2019
Qualifies for debates via …
Of the major candidates we’re tracking, only U.S. Reps. Tim Ryan of Ohio and Eric Swalwell of California have not yet qualified, but working in their favor is that they announced their campaigns in the past two weeks. Also considering that they both received 1 percent in a recent Iowa poll by Monmouth University (one of the qualifying pollsters), it’s not implausible that they could hit that mark in two more qualifying polls by early June, ahead of the first debate.
And remember that our tally above doesn’t include 2020 hopefuls whom FiveThirtyEight doesn’t consider “major.” Some of those candidates, including author Marianne Williamson, Miramar, Florida, Mayor Wayne Messam and retired Alaska Sen. Mike Gravel, could end up qualifying for the debates, as could candidates who have up to now been pondering a run but end up getting into the race in the next couple of months. Colorado Sen. Michael Bennet, Montana Gov. Steve Bullock and New York Mayor Bill de Blasio, for example, have not officially declared their candidacies, but each has already received 1 percent in at least onequalifyingpoll. So the number of candidates meeting the criteria to participate in the first debates could grow.
This means we could end up in a situation in which more than 20 candidates qualify to participate in the first debate. The Democratic National Committee indicated in its release that it will cap the debate at 20 candidates and that if more than 20 qualify, the candidates who meet both thresholds will be given preference. Based on our tally, which relies on self-reported figures, six currently do.10 But we don’t have a complete picture of who has met the donor criteria. (The DNC said in its release that candidates will be required to provide evidence of how many donors they’ve had.) So, theoretically, we could end up with more than 20 candidates who hit both marks.
What happens then? The party indicated in the release that it would then give debate spots to the candidates with the highest polling averages. So let’s suppose that the DNC needs to create a polling average to narrow the field to 20 participants — where do the candidates fall currently? Since late February, there have been four qualifying national surveys and three early-state polls (two from Iowa and one from New Hampshire).11 If we average these polls together, we can get a sense of how a polling average might help some candidates — and not others. As you can see in the table below, only eight candidates are polling above 2 percent, on average.
In a big field, many candidates are polling below 1 percent
Polling average of Democratic presidential candidates based on seven surveys from qualifying debate pollsters since late February
Number of polls included in
Seven candidates are polling at less than 1 percent, which could signal that they might be in trouble if the polling average comes into play. Granted, if there are more than 20 qualifiers by June, there will be more polls to include, which could boost — or hurt — a candidate’s standing. Not to mention that it’s unclear how the DNC would calculate a candidate’s polling average. FiveThirtyEight reached out for clarification, but the DNC wouldn’t specify how it would handle such a situation.
Additionally, the process for averaging polls could mean that tenths of a percentage point might determine which lower-tier candidates make or don’t make the stage, so Democrats could find themselves mired in controversy because pollsters don’t always ask about the same list of candidates and surveys have margins of error much larger than a tenth or two of a percentage point.12
If the polling averages aren’t enough — and the DNC has need for further tie-breakers to determine a final list of debaters — it said in its release that the number of “unique donors” would be taken into consideration (although it declined to specify how this would work). It’s no wonder then that candidates are also very focused on increasing their total number of donors. For example, former Maryland Rep. John Delaney is trying to hit the donor threshold by promising to donate $2 to charity every time someone new donates to him. His campaign said Delaney’s “debate challenge” will remain in place until he has 100,000 new donors, which could help him in the event of a tie-breaker.
Time will tell, but Democrats could very well have more than 20 candidates qualify for the debates. And if that happens, get ready for a debate about the debates, similar to what Republicans experienced in the 2016 presidential cycle.
Latinos became the nation’s largest minority group in the early 2000s. Next year, the country’s pool of eligible voters is expected to include more Latinos than African Americans for the first time. But more than 10 years after black voters proved pivotal in nominating and electing the first African American major party presidential candidate, a Latino candidate has never come particularly close to winning the Democratic or Republican presidential primaries.
Julian Castro, of course, hopes to change that. So far though, he’s polling in the low single digits. Whether it’s Castro or another candidate in another election cycle, will Latino Democrats mobilize behind electing one of their own for president, as black Democrats have in the past?
Before we get to Castro, let’s start with understanding the role of the Latino vote in the Democratic primary process. While the eligible voter pool is expected to include more potential Latino voters then black voters in the 2020 general election, black voters are still likely to outnumber Latino ones in the Democratic primary. That’s true for several reasons, most notably because African Americans tend to vote at higher percentages and because Latinos are more divided between parties (about 25 percent are Republican and about 60 percent are Democrats) than African Americans are (close to 90 percent are Democrats). So part of the reason media coverage of the 2020 Democratic primary, including the coverage at FiveThirtyEight, tends to emphasize the role of black voters more than Latino voters is simply that there will likely be more black voters in the primary. As a rough estimate, I would expect somewhere from 18-25 percent of Democratic primary voters in 2020 to be black and 10-20 percent to be Latino.
But the size of the black vote is not the only reason it’s important in the primary — black Democrats also sometimes vote as a big, unified bloc. In four modern, competitive Democratic primaries, black voters overwhelmingly got behind one candidate — Jesse Jackson in 1984 and 1988, Barack Obama in 2008 and Hillary Clinton in 2016 — with more than 75 percent of the African American voters backing a single candidate, according to exit polls.
The Latino vote, in contrast, has tended to be less unified, regardless of whether a Latino candidate was on the ballot. The most prominent Latino Democrat to run for president was then-New Mexico Gov. Bill Richardson in 2008. He dropped out after lackluster finishes in Iowa and New Hampshire, so his campaign didn’t last long enough to compete in states with large Latino populations. The overall Latino vote is much smaller on the GOP side, but neither Sen. Ted Cruz of Texas nor Sen. Marco Rubio of Florida did particularly well in 2016 with Latino voters in any of the three states where we have detailed exit poll results — each won a plurality of the Latino vote in their home states, but President Trump won at least a quarter of Hispanic voters in both Florida and Texas and a plurality in Nevada.
The candidate who has done best with Latino voters in recent primaries is Hillary Clinton, but even her performance was not dominant. In 2008, Clinton won more than 60 percent of the Latino vote in the Democratic primary. In 2016, few exit polls were conducted in states with sizable Latino populations,1 but of the four states where we do have detailed results, Clinton basically split the Latino vote in Illinois and Nevada against Bernie Sanders, while winning about 70 percent in Florida and Texas.
What does all this history mean for Castro’s candidacy? Castro, who served as mayor of San Antonio from 2009 to 2014 and then as secretary of Housing and Urban Development in the Obama administration, is not a civil rights leader in the mold of Jackson or an already famous political figure like Clinton. But you could see him taking a path somewhat similar to another Harvard Law School graduate who ran for president in his 40s: Barack Obama.
In 2007, before the voting began, polls suggested that Clinton and Obama were running neck-and-neck among black voters. Then, Obama won Iowa and narrowly lost New Hampshire, two states with very small black populations. Once the primary moved to the South, Obama overwhelmingly won the black vote. It’s impossible to know for sure, but it seems likely that black voters moved decisively toward Obama as they saw that he had a real chance to win. And that black support helped Obama win many Southern states, including a number with heavily black Democratic electorates.
For Castro, then, the ideal scenario is that he is a viable candidate when the primaries start in February, so he can galvanize Latinos behind him in three key states in particular: California, Nevada and Texas. Nevada (where about 20 percent of Democratic primary voters are likely to be Latino) is currently scheduled to be the third state to vote.2 California and Texas, the two states with the largest Latino populations, hold their primaries along with several other states on Super Tuesday, on March 3, but both states allow early voting, so lots of voters in both states will cast ballots in February.3
In short, Castro will have less time, post-Iowa, to show Latino voters he has a real chance. That means he’ll need to use Iowa and New Hampshire as a springboard as much as possible, while also trying to rally Latino voters for strong showings in Nevada, California and Texas regardless of what happens in the first two contests.
And it’s entirely possible that he will succeed in mobilizing Latino voters. Some research has shown Latino voters are more likely to vote if a Latino candidate is on the ballot and more likely to back the Latino candidate than a white one, even in an intra-party race. But that research largely looked at state- and city-level races — we haven’t had a major Latino presidential candidate on the Democratic side, where appeals to shared racial identity are easier to make than in the GOP.
“If Latinos think that Castro has a reasonable chance of winning, they will come out in large numbers to support him,” said Melissa Michelson, a political science professor at Menlo College and an expert on Latino political activism. She suggested having key Latino leaders embracing Castro’s candidacy would be important, with Michelson specifically naming journalist Jorge Ramos as a key potential validator for Castro.
Michelson’s caveat — “a reasonable chance of winning” — is important and goes back to the Obama comparison. Castro is currently polling at 1 percentin many surveys. He is raising significantly less money than some of his rivals, and it will take a lot of money to organize and win in big states like California and Texas. There are few polls that have large samples of Latino Democrats, but the fact that, in the few polls available, he’s not doing much better in California (where 30 percent of eligible voters are Latino) than in Iowa (where 3 percent of eligible voters are Latino) suggests that he is not overwhelmingly popular with that demographic.
For Castro to even test the potential for a Latino candidate to mobilize Latino voters in a Democratic primary, he needs to first do fairly well in contexts where Latino voters are not particularly powerful: fundraising, endorsements and debates.
When I asked Castro how he would present himself as “electable” to Democratic voters, he named six states that he felt he could flip: Michigan, Pennsylvania and Wisconsin, which Clinton barely lost in 2016, along with Arizona, Florida and Texas. Castro didn’t outright say this, but the implication was obvious: Arizona, Florida and Texas are the three states with the largest Latino electorates that did not vote for Democrats in 2016.
“It’s important to always campaign and to govern for everybody,” Castro said when I asked him about being the only Latino candidate in the race. “And I’ve always done that in public service.”
But, he added: “I recognize that there’s special meaning for the Latino community, especially now, because the community has been so targeted by this president, whether on the issue of immigration or his comments about the Mexican judge or any number of ways that he has scapegoated people. He has tried to paint people of color as the ‘other’ …. So I’m confident that my campaign is going to resonate with people of all different backgrounds, but of course there’s special meaning in the Latino community.”
Castro is doing exactly what he should be doing at this stage — trying to make himself a viable candidate to all Democrats while also laying the groundwork for Latino voters in particular to get behind him. But he probably has to be great at the first part to get a chance at the second part. And so far, the signs are not promising.
The first time Tiger Woods won the Masters, becoming the youngest to ever do it, he decimated the field and crumbled in his father’s arms. “We made it,” Earl Woods told his then-21-year-old son. Woods is now 43-going-on-60, still donning his trademark Sunday red. He scaled Augusta National this weekend for the fifth time,1 holding off a number of contenders, some of whom grew up watching him transcend the sport, on the back nine. What once seemed inevitable was anything but just a few years ago, as Woods battled surgeries and off-the-course maladies.
“Maybe the son of golf has returned,” broadcaster and former Masters champion Nick Faldo said as Woods left the 17th green.
It had been 3,954 days since Woods last won a major. Somehow, it felt even longer. Winning a major is an accomplishment reserved for a select few, but for a 10-year span beginning in the late 1990s, it was as synonymous with Woods as audacious drives and timely putts.
Suddenly a man who went five years without a win on tour has two in the past seven months. His turn-back-the-clock performance materialized when it mattered most. He now has three top-10s in his past four majors.
Just as he has previously, Woods bashed the par-5s (-8), going three-under on them over the final round. He approached the 15th hole in a three-way tie with Xander Schauffele and Francesco Molinari, detonated his tee shot and immediately began walking toward the hole as it soared through the sky. He two-putted his way to a birdie and an outright lead and never looked back.
The last time Woods won the Masters, his chip-in on the No. 16 green provided the signature highlight of his career. Playing the same hole 14 years later, Woods added to his legend. He struck an 8-iron to the center of the green, spinning it back down the hill where it stopped 4 feet from the pin. As pandemonium played around Woods at the tee box, a replay showed him at-ease cooing “come on” to his ball at it inched closer to history.
That wasn’t the only time precision paid off for Woods on par-3s, which he played four-under for the tournament, the best four-round score among his five wins. When Molinari and Tony Finau found the water on No. 12, it was Woods who found the green and two-putted his way to par.
Nine players entered the weekend within a shot of the lead, the most in Masters history. That historically congested scoreboard continued Sunday, as each hole seemed to carry implications for the top 15 in the standings. The win marked the first time Woods came from behind in the final round to win a major.
Most unbelievable was the winding path Woods had to take just to get back to Butler Cabin. His career first began to go off the rails with a knee injury that cost him half of the 2008 season, and although he played well in 2009 (leading the PGA Tour in money won), he also blew a Sunday major lead for the first time ever when Y.E. Yang overtook him at the PGA Championship.
Such a pronounced valley in performance (particularly relative to the rest of his career) led plenty of pundits to write off Woods’s chances of ever winning another major. Those takes look scorching hot in retrospect, but it’s difficult to find an established veteran player whose ranking dropped outside the top 600 and who managed to claw back to win a major. Then again, Woods is one of the greatest pure talents in golf history — if anyone was going to rewrite that record book and make such an astonishing comeback, it would be him.
Age comes for everyone, of course. And the aging curve for golfers heads south well before 45, which will be here for Woods in no time. But even as younger players increasingly dominate the sport, there’s still room for perhaps the greatest golfer of all time to enhance his legacy.
It was Woods’s first Masters victory in 14 years, snapping Gary Player’s all-time record of 13 years between wins, according to ESPN Stats & Information. The win is Woods’s 81st on the PGA Tour, one shy of Sam Snead’s all-time record. It’s also his 15th major championship, three shy of Jack Nicklaus’s record. When asked about Woods’s rekindled pursuit of history on Sunday, Nicklaus said, “he’s got me shaking in my boots.”
Golf’s prodigal son has officially returned, and what happens next is not known. But no one will again underestimate what Tiger Woods is capable of on a golf course.