Can You Construct The Optimal Tournament?

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

Riddler Express

From Tyler Barron, where in the square?:

You are given an empty 4-by-4 square and one marker. You can color in the individual squares or leave them untouched. After you color as many or as few squares as you’d like, I will secretly cut out a 2-by-2 piece of it and then show it to you without rotating it. You then have to tell me where it was (e.g., “top middle” or “bottom right,” etc.) in the original 4-by-4 square.

Can you design a square for which you’ll always know where the piece came from?

Submit your answer

Riddler Classic

From Erich Friedman, conscientious competition construction:

Imagine a competition in which players are ordered in ability, but we do not know what that order is. Assume the better player will win two-thirds of the time in any one game, independent of any other games. We want to construct a tournament to maximize the probability that the best player wins.

For example, if there are four players and three games, the best tournament is the standard simple elimination tournament: A vs. B, C vs. D, and the winners play for the championship. The best player wins this \((2/3)^2\) = 4/9 = 44.4 percent of the time. Not as good, say, is a lopsided tournament: A vs. B, winner plays C, and winner plays D for the championship. The best player wins this just \((2/4)(2/3)^3 + (1/4)(2/3)^2 + (1/4)(2/3)\) = 23/54 = 42.6 percent of the time.

Your challenge: Construct the optimal tournaments for four players and four games, and for five players and five games.

Extra credit: How often does the best player win the optimal tournaments for N players and M games?

Submit your answer

Solution to last week’s Riddler Express

Congratulations to 👏 Lucas Gredell 👏 of St. Louis, winner of last week’s Riddler Express and ROFL Coach of the Year!

Last week, every Riddler reader became the coach of a team in the Riddler Official Football League, or ROFL. Each coach prepared his or her team to take and defend a penalty kick. The goal was divided into two rows (upper and lower) and three columns (left, center and right). A shooter could aim at any one of these six areas, and a goalie could choose to defend any one of the six. If a goalie chose the same area as the shooter, the shot was blocked. If the goalie did not choose the same area as the shooter, the shot had a chance of scoring, per the probabilities shown below.

Knowing that, each coach then submitted a selection for his or her shooter and his or her goalie. I matched each coach’s plan against every other coach’s — there were over 1,520 teams in the league and millions of randomly generated penalty kicks — and adjudicated all the shootouts. Overall, a goal was scored on about two-thirds of the shots. The coach with the most net goals at the end of all that won.

And that coach was Lucas Gredell, who scored 1,218 goals and gave up 902 for a total of 316 net goals. Here were the league’s Top Five performers, a leaderboard dominated by coaches from the soccer powerhouse that is the American Midwest:

Riddler Official Football League’s top coaches
Goals
Name Hometown For Against Net
Lucas Gredell St. Louis 1,218 902 316
Matthew Beale Denver 1,211 898 313
Julian Wellman Ann Arbor, MI 1,223 911 312
Kevin Collins Davison, MI 1,204 893 311
Michael H. Streator, IL 1,216 905 311

All of the top performers had their shooter aim at the upper middle and their goalie defend the lower middle. But because the outcomes of many shots were random, there is a good deal of luck baked into the results, just as there is a good deal of luck baked into life itself.

Our winner explained his decision: “I chose to defend lower middle because it represents the largest risk — any shots attempted at that area will score. Eliminating that certainty means that all other shots have at least some probability of missing. I chose to shoot at upper middle because it is one of the 90 percent regions. I believe it likely that many will mirror my strategy of defending lower middle, so I wanted to maximize my shot probability against that strategy. Even for those who decided to defend a 90 percent region instead, there is only a 1/2 chance that they’ll select my shooting zone.”

Shooters go for the center
Left Middle Right
Upper 98 461 138
Lower 144 446 236

Indeed, shooters overall heavily favored the upper and lower middle areas, where there were 90 and 100 percent chances of scoring, respectively, if those zones were left unguarded.

And goalies very heavily favored the lower middle area — where an unguarded shot was sure to score. Fully half of all keepers defended it.

Goalies choose lower middle
Left Middle Right
Upper 56 191 89
Lower 109 753 325

And our winner’s 90-percent gambit clearly paid off: If a goalie did defend a 90-percent region, it was far more likely, for whatever reason, to be lower right rather than upper middle, despite their tactical identicality. Upper middle, therefore, became the juicy scoring spot. Lower middle, while very well defended and not juicy in the least, remained a popular choice among shooters given its scoring guarantee if the goalie doesn’t stay there.

We can also analyze this game through the lens of game theory, which is made easy with an online calculator. The Nash equilibrium of this game is in mixed strategies — that is, players randomize over their location choices with certain specific weights. The equilibrium of this game has the shooter placing the most weight on the riskiest upper left area (which ROFL did not do) and the goalie placing the most weight on the surest lower middle area (which ROFL did do). In equilibrium, the goalie also mixes equally between the two 90-percent zones (which definitely did not happen in ROFL). In equilibrium, a goal is scored about 70 percent of the time (somewhat more than in ROFL).

This column’s motto bears repeating … Riddler Nation: Out of equilibrium since 2015.

Solution to last week’s Riddler Classic

Congratulations to 👏 Christopher Clark 👏 of Boston, winner of last week’s Riddler Classic!

Last week’s Classic continued the sports theme, taking us in this case to the basketball court for a friendly game of HORSE. The two competitors, Alice and Bob, were equally good shots and both were perfectly aware of their abilities — they could select a particular shot that they knew they would make 90 percent of the time, for example, or 2 percent, or 50 percent, or whatever difficulty they chose. Alice and Bob were also both sharp strategists who selected their shots optimally in an effort to win the game. Your challenge: If Alice went first, what type of shot should she take to begin the game?

Alice should take the surest shot she can, perhaps one with a 99 percent chance of going in. (Bob, if and when it becomes his turn, should do the same.)

Intuitively, the only advantage Alice has in this game is that she goes first. It’s a bit like having the serve in volleyball — only you can score. Anything less than Alice’s surest shot cedes some of this advantage to Bob. The game may go on a very, very long time, but assuming she doesn’t have to go home any time soon, Alice does well to nurse this first-shooter advantage.

Mathematically: Let’s say Alice’s chosen shot has an \(X\) chance of going in. She has a \((1-X)\) chance of losing her “serve,” an \(X(1-X)\) chance of giving Bob a letter and an \(X^2\) chance of returning to the initial state of the game. The only thing that matters here, as solver Guy Moore explained, is the ratio of the first two outcomes. That is maximized by making \(X\) as close to 1 as possible.

Solver Laurent Lessard plotted the chances that Alice would eventually win the game depending on the surest shot available to her. As that surest shot approaches 100 percent, Alice’s chances of winning reach nearly 55 percent.

Speaking of “eventually,” let’s say that indeed the surest shot available to Alice is a 99-percenter. In that case, the game would take some 700 shots on average. If we assume the players are pretty quick and each shot takes 10 seconds, we’re looking at a two-hour game of HORSE. Let’s hope it’s not too close to dinner.

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 me at [email protected]

Why Is Bryce Harper’s Old Team Ahead Of Bryce Harper’s New Team?

For seven years, Bryce Harper was an integral part of the Washington Nationals both on and off the field. Harper remains the team’s fourth-best player by wins above replacement5 since the franchise moved from Montreal to Washington in 2005, trailing only Ryan Zimmerman, Max Scherzer and Stephen Strasburg. In 2015, he had one of the all-time great individual seasons by a batter, notching 9.7 WAR. At the same time, Harper was the face of the franchise in the press and probably the most famous player in baseball. When it became clear that Harper was leaving D.C. last winter, it looked like Washington had a huge void to fill — a concern only exacerbated when Harper went to the division-rival Philadelphia Phillies in a record-setting deal.

And yet, more than halfway into the Nationals’ first post-Bryce season, they appear to be just fine. While the Atlanta Braves are very likely to win the National League East, Washington is on track to snag the NL’s top wild card slot with 87 projected wins (according to the FiveThirtyEight forecast) and a 66 percent playoff probability. The Phillies, meanwhile, are only tracking for 83 wins and have just a 31 percent chance at the postseason. How is it possible that Harper’s old team has not only survived without him, but outperformed his new team up the Northeast Corridor?

For one thing, Washington always had a very underrated core outside of Harper — starting with future Hall of Fame pitcher Max Scherzer, who currently leads the major leagues in pitching WAR6 after finishing second in each of the previous two seasons. Scherzer began 2019 somewhat slow, but he’s been building a truly dominant campaign ever since; his fielding-independent pitching of 2.02 is 54 percent better than the MLB average and his strikeout rate of 12.6 per nine innings is one of the best in baseball history. If Scherzer maintains his current pace for a 9.6-WAR season — once he returns from injury — he would have the majors’ best pitching season since Randy Johnson in 2001 (and one of the 40 best of all-time).

Scherzer isn’t Washington’s only stellar starter, either. Strasburg and Patrick Corbin are on pace for 5.8 and 5.3 WAR, respectively, helping make the Nationals’ rotation the most valuable collection of starting pitchers in baseball this season. Add in a strong group of position players — including veterans such as Anthony Rendon and Howie Kendrick, plus up-and-comers like 20-year-old phenom Juan Soto (whose late home run stunned the Phillies in a Nationals win last week) and rookie Victor Robles — and the talent cupboard was far from bare in D.C. despite Harper’s exit.

Not everything is going perfectly right for the Harper-less Nats, of course: 26-year-old shortstop Trea Turner, who played like an All-Star (4.4 WAR) last season, is having a down year due to an early season injury and poor performance on defense. (Blending together the defensive metrics from Baseball-Reference.com and FanGraphs, Turner grades out as -9.2 runs worse than an average shortstop this season, after being basically average over the previous two years.)7 Outfielder Adam Eaton has been mediocre at the plate (.752 on-base plus slugging), and veteran second baseman Brian Dozier, who signed with Washington in the offseason, is hitting .231 and appears to be well past his prime. The team’s defense remains a weakness, and its bullpen has been very shaky (24th in relief WAR) beyond closer Sean Doolittle.

But all told, the Nationals have only suffered slightly on offense — their hitting WAR has gone from ninth last year to 13th this year — without Harper’s presence at the plate, and they’ve actually improved their leaguewide ranking in overall WAR from 11th with him in 2018 to 10th without him in 2019:

If the talent surrounding Harper in Washington was always underrated because of the gravitational pull of his star power, Harper’s own impact was probably always a bit overstated. That isn’t to say Harper is not a very good player; at age 26, he has already been roughly as good in his career as, say, Harold Baines (who at least some people thought should be in the Hall of Fame). But as my colleague Travis Sawchik and I wrote in March, Harper is also a flawed superstar — and he has played almost precisely to that form this season.

Looking at his previous three seasons, a reasonable expected baseline for Harper’s 2019 value for Philadelphia could have been set at about 3.1 WAR — three times his WAR from 2018 (2.4), plus two times his WAR from 2017 (4.7), plus his WAR from 2016 (2.2), divided by six. And lo and behold, if you prorate Harper’s current output (1.9 WAR in 95 games) to a full season, it comes out to … 3.2 WAR. Although there is a growing feeling among some Phillies observers that Harper’s Delaware Valley debut has been a disappointment, he has performed almost exactly how you might have predicted.

The only letdown might be this: Harper’s monster 2015 season did still imply some probability of an MVP-caliber performance — moreso than from the typical 26-year-old who’d had 9.3 WAR over his previous three seasons. So 2019 appears to be another season of Harper not converting what small chance there was of him ever reaching that hyper-productive ceiling again.

Harper’s path to that 3.2-WAR pace has been slightly different than usual. His strikeout rate continues to climb (somehow much faster than the MLB-wide rate), from 18.7 percent of plate appearances in 2016 to 26.2 percent so far in 2019, and his isolated power (.220) is the lowest it’s been in three seasons. Harper’s walk rate, which ballooned to 18.7 percent last season, is back down to 15 percent — more in line with his career rate of 14.8 percent. But his StatCast batting metrics have stayed relatively steady; his average exit velocity is actually up from MLB’s 82nd percentile to its 90th. Harper’s OPS has dropped from .889 to .845 on the season, thanks in large part to the decline in plate discipline, but he’s also hitting the ball just about as hard as ever. (He’s also heating up in July, with a .885 OPS this month, so we’ll have to keep an eye on Harper for a potential second-half surge.)

The best sign for Harper might be that his defense — which was conspicuously bad last season according to the advanced metrics — is back to being solid. Again averaging together the fielding values at FanGraphs and Baseball-Reference, Harper was 20.2 runs worse than average while playing mostly right field last season. That number was way out of step with his previous track record (4.3 runs above average over the previous two seasons) and easy to identify as a place for positive reversion to the mean in 2019. So sure enough, Harper has been 4.7 runs better than the average right fielder this season, which is enough to offset his OPS drop and leave him on pace for slightly more WAR in 2019 than in 2018.

Despite playing almost precisely to expectations, Harper is still just the fourth-best player on the Phillies, however, behind catcher J.T. Realmuto, first baseman Rhys Hoskins and pitcher Aaron Nola. (Shortstop Jean Segura and surging jack-of-all-trades Scott Kingery aren’t too far behind, either.) Philadelphia also has had its share of legitimately disappointing players, from starters Nick Pivetta and Vince Velasquez to outfielder Odubel Herrera (who was suspended for the season for domestic assault earlier this month), while injuries have largely robbed Philly of expected contributions from relievers David Robertson, Pat Neshek and Seranthony Dominguez.

The Phillies started the season with more (healthy) talent on paper than its current 83-win trajectory would suggest. But not by much. Harper’s fame always made his departure from Washington — and arrival in Philadelphia — feel more consequential than it actually was. The Nationals have survived without their erstwhile star because they made years of shrewd decisions filling out the roster around him. The Phillies have held steady this season8 in part because of bad injury luck and other underwhelming performances — but Harper can’t be included in that group, even if he isn’t playing to his ceiling. He’s been about as good as usual, and that was neither enough to tank Washington’s season in absentia or save Philadelphia’s by addition.

Check out our latest MLB predictions.

Bulletpoint: Bernie Sanders Is Running Ahead Of The Pack On Health Care

As we talked about on this week’s podcast, Bernie Sanders is having trouble differentiating himself from Elizabeth Warren and other candidates competing for liberal voters. And some of the arguments that Sanders has been making — like that he’s more electable than Warren, even when voters don’t necessarily perceive that to be the case — have been dubious. But one number jumped out at me in the new CNN/UNH poll of New Hampshire Democratic primary voters that’s really good for Sanders: 34 percent think that Sanders is best able to handle health care.

By contrast, only 19 percent of voters in the poll put Sanders as their first choice (tied with Warren for second and behind Joe Biden’s 24 percent), so he’s still getting some credit from voters even if they don’t necessarily have him as their first choice.

And frankly, he probably should be getting credit. I don’t mean that as any sort of endorsement of his plan. It’s just that he has a plan — Medicare for All — when several of the other Democrats don’t. Instead, a number of other Democratic candidates — Warren, Kamala Harris, Cory Booker and Kirsten Gillibrand — have signed up as co-sponsors of Sanders’s bill.

This is particularly strange for Warren, whose semi-official slogan is that “she has a plan for that.” As the Washington Examiner’s Philip Klein points out, there are plenty of plausible versions of plans that fall under the rubric of single payer or Medicare for All, some of which would allow Americans to keep some forms of private insurance (without which, Medicare for All becomes much less popular). Harris, meanwhile, despite having co-sponsored Sanders’s bill, has had trouble articulating what her health care stance actually is, exactly. In the category of unforced errors, I find it hard to fathom why Warren and Harris are ceding leadership on health care to Sanders, and even to Biden, who released his own plan health care plan this week. And it comes on an issue that matters: Health care ranked as the top issue for Democrats in that CNN/UNH poll.

NBA Free Agency Diary: Today’s NBA Superstars Won’t Stop Team-Hopping

Keep track of the chaotic NBA offseason with our Free Agency Diary.


Dear NBA Diary,

Remember when NBA players wearing different jerseys was new and novel? When you’d experiment with weird trades in NBA Live’s franchise mode, knowing that nothing so crazy as, I don’t know, Russell Westbrook in a Houston Rockets uniform or Kevin Durant as a Brooklyn Net would actually happen? And when the first wave of truly wild moves — such as LeBron James joining the Miami Heat in 2010 — did actually happen, do you remember the way our minds were blown as we imagined superstar combinations we’d never seen before?

All of that is old news in 2019, now that we’ve seen countless Big Threes and even Hamptons Fives. If James signing to play with Dwyane Wade and Chris Bosh was groundbreaking and Durant joining the Golden State Warriors still managed to shock, we’re pretty desensitized to huge names heading for new places by now. Yes, Kawhi Leonard becoming an L.A. Clipper was a big story, but mostly because of what it means for next season’s championship chase — not because the idea of him in a different jersey was all that tough to comprehend. (We’d just finished watching the longtime Spur win a title in a Toronto Raptors jersey anyway.)

This is the era of player empowerment, as it’s recently been designated, and NBA players are placing a major premium on freedom of movement and choice of teammates. You can see this in the sheer number of different franchises for which top players suit up, relative to in the past. From the 1980s through the 2000s, a top 25 NBA player of a given decade (according to consensus Wins Created)1 played for 1.99 teams during a 10-year span, on average. During the 2010s, however, the average top 25 player has played for 2.76 teams. And that bump in franchises played for holds across most of the ranking slots from No. 1 to No. 25, if we plot them out in a chart:

Not every player has taken quite the same path as Dwight Howard, who ranks No. 18 in the 2010s and is now on his seventh team of the decade after being traded away from the Wizards this summer. But James, for instance, has played for three teams this decade — the Heat, Cleveland Cavaliers and Los Angeles Lakers — while only one No. 1 player of the previous three decades — Kevin Garnett, who starred for the Minnesota Timberwolves and Boston Celtics during the 2000s — played for more than one team. The reality of today’s league is stars hop teams far more often than their counterparts did in earlier eras, controlling their own destinies rather than letting team executives slide them around like pawns on a chessboard.

It’s a trend NBA commissioner Adam Silver seems keenly aware of — if powerless to change, particularly with regard to the many deals that appeared to be made before the league’s mandated free-agency period was set to begin.

“My sense in the room today was, especially when it comes to free agency and the rules around it, that we’ve got work to do,” Silver told reporters last week, after the league’s board of governors meetings. “And as I said, it’s still the same principles of fair balance of power and a sense that it’s a level playing field. I think that’s what teams want to know. I think they’re put in difficult situations because when they’re sitting across from a player and whether it’s conversations that are happening earlier than they should or frankly things are being discussed that don’t fall squarely within the collective bargaining agreement, it puts teams in a very difficult position because they are reading or hearing that other teams are doing other things to compete.”

Even incentives put into place to theoretically curb player movement, such as larger maximum contracts (both in guaranteed length and total money) for players re-signing with their most recent teams, have failed to stop them from packing up and leaving town. Durant, for instance, left $57 million on the table to sign with Brooklyn rather than return to Golden State. Leonard gave up at least $80 million (!!) — if not even more — relative to what he could have gotten from a supermax deal with the Spurs, and about $30 million compared with what the Raptors could have given him by signing with the Clippers.

Today’s stars, as ESPN’s Rachel Nichols perfectly put it, can’t be bought. They’ve proven that they’re willing to give up mind-boggling sums of cash in order to make their own decisions.

Is all of this good for the league? Judging from the reaction on social media or in search traffic — where the NBA got playoff-level attention during the first week of July — the game’s popularity has seldom been higher, and the craziness of this offseason has only helped. I’ve said before that, if you view the modern NBA through a player-focused lens, it makes the most sense as a gigantic real-life soap opera. The concept of franchises is just incidental to all that, merely providing structure for the individual drama.

Of course, if you are a fan of a team, it hurts to see your favorite players leave. The Raptors did everything they possibly could to retain Leonard’s services, but they reportedly had practically no chance of re-signing him even as they were winning the title. Although the players should owe no loyalty to team owners (err, “governors”) beyond the contracts they sign, from a fan’s perspective it seems to make little sense to root for any specific NBA team. Even if a team is lucky enough to acquire a superstar, it’s far from guaranteed he would stay more than a season or two in today’s climate.

But the other side of that coin is that it’s more possible than ever for downtrodden teams to land a superstar in the first place. The Nets and Clippers have spent more of their histories as laughingstocks than contenders, particularly since both were seen as the “little brothers” in their markets (behind the Knicks — LOL — and Lakers). The franchises were not traditional free-agent destinations. But as stars become more focused on setting up the right situation for themselves and the players they want to play with, even teams without a history of snagging big-name players can make themselves an attractive option. It’s a different way of doing business — but in today’s era of superstar team-hopping, it might just be the new normal.

Check out our latest NBA predictions.

We Watched 906 Foul Balls To Find Out Where The Most Dangerous Ones Land

Chicago Cubs outfielder Albert Almora Jr. hit a 106 mph line drive in May that screamed into foul territory down the left-field line at Houston’s Minute Maid Park. The ball hit a 2-year-old girl, who was rushed out of the stadium. The game stopped as an emotional Almora dropped to a knee. Less than two weeks later, as the Washington Nationals played the White Sox in Chicago, a woman sitting just past the third-base dugout was struck in the face. Less than two weeks after that, a Dodger Stadium spectator sitting just past the netting on the first-base line was hit in the head by a hard line drive off the bat of right fielder Cody Bellinger.

Bloomberg News estimated in 2014 that 1,750 fans per year are hurt by batted balls at MLB games. Amid debates over how much protection teams should offer spectators, we wanted to find out which areas of stadiums might be the most dangerous, which could help us figure out what could be done to prevent more fan injuries.

Because there’s no central database of all of MLB’s foul balls, we had to compile a data set ourselves. To do that, we searched the batted-ball data for this season on Baseball Savant to find the 10 stadiums that produced the most foul balls up to June 5 and then analyzed the pitch-level data from the most foul-heavy game day at each of those stadiums (including one doubleheader). Because we had to individually research each foul ball, we couldn’t look at a whole season’s worth of fouls. By limiting the data set to the most foul-heavy days of play in those 10 stadiums, we aimed to keep the data set to a manageable size while also capturing the largest number of fouls we could from a variety of parks, since stadiums vary dramatically in architecture, altitude and seating arrangements.

Dozens of fouls per game in the most foul-heavy parks

The most foul-heavy day at each of the 10 stadiums that produced the most fouls this season, as of June 5

Most foul-heavy day
Stadium Average No. of Fouls per game Date Matchup No. of Fouls
Camden Yards* 57 4/20/19 Baltimore Orioles vs. Minnesota Twins 113
PNC Park 57 6/1/19 Pittsburgh Pirates vs. Milwaukee Brewers 111
Oakland Coliseum 53 6/2/19 Oakland A’s vs. Houston Astros 109
T-Mobile Park 53 5/18/19 Seattle Mariners vs. Minnesota Twins 100
Globe Life Park 55 5/3/19 Texas Rangers vs. Toronto Blue Jays 87
Dodger Stadium 51 3/29/19 Los Angeles Dodgers vs. Arizona Diamondsbacks 86
Miller Park 55 5/4/19 Milwaukee Brewers vs. New York Mets 85
Citizens Bank Park 53 4/27/19 Philadelphia Phillies vs. Miami Marlins 75
SunTrust Park 53 4/14/19 Atlanta Braves vs. New York Mets 73
Yankee Stadium 51 3/31/19 New York Yankees vs. Baltimore Orioles 67

* Includes both games of the doubleheader

Source: Baseball Savant

We watched clips of 906 foul balls hit during those games (excluding foul tips, which were never in danger of reaching the stands, and fouls that resulted in outs, because Baseball Savant groups those with other types of caught-ball outs, so we couldn’t get data on foul outs specifically), and we recorded whether the fouls were grounders, fly balls, line drives or pop-ups. Then we split the parks into “zones” to categorize the general area where each of those balls landed.

Zones 1, 2 and 3 include seats that are largely protected by netting — the area behind home plate and both dugouts — along with the corresponding areas of foul territory on the field. Zones 4 and 5 are mostly non-netted seating areas3 and the foul territory outside the baselines, from the dugout to the foul pole. Zones 6 and 7 cover the areas past the foul poles; the fly balls that land here typically have too much arc to be dangerous, and line drives rarely make it that far.

Less than half of the foul balls we charted were followed by a camera to where they landed. But by gauging angles,4 we estimated where all of the fouls — both those that were followed by a camera and those that weren’t — likely landed. We tested our predictions against the footage of the balls that were followed to check our accuracy.5

Nearly equal shares of foul balls ended up in zones with netting vs. zones that largely lack netting: 454 balls landed in zones 1, 2 and 3, while 452 balls fell in zones 4 through 7.

The scariest foul balls are those with high exit velocities, particularly the line drives, which give spectators only seconds — or fractions of a second — to react. Statcast was able to measure exit velocities for 580 of the 906 foul balls in our data set, and most of the hardest-hit of those 580 landed in areas that are primarily unprotected. Of the fly balls with recorded exit velocities of 90 mph or higher, 71.8 percent landed in zones 4 and 5.6 And all of the line drives that left the bat at 90 mph or more landed in those same zones. That’s the type of hit that injured the toddler at this year’s Cubs-Astros game or that blinded a man in one eye at Wrigley Field in 2017.

Major league stadiums have slowly been installing more netting around the field. Players have been pushing the issue, including Dodgers pitcher Rich Hill, who called the MLB Players Association to voice his support for more protective netting. In 2015, MLB encouraged teams to extend netting to the “near ends of both dugouts.” By 2018, all 30 stadiums had exceeded that recommendation, installing netting from one end of the dugout to the other. After the incident at Guaranteed Rate Field, the White Sox announced that they would implement netting from foul pole to foul pole, and crews worked during the All-Star break to install the new nets. The Washington Nationals also used the break to add netting.

But more netting won’t protect every fan. Linda Goldbloom was sitting high above home plate in Dodger Stadium — in zone 1, where netting is provided — last year when she was struck and killed by a high fly ball that had an exit velocity of just 73 mph. And a woman at Tropicana Field was hospitalized in 2016 after she was hit by a fly ball that found its way through a hole in the netting just to the left of the first-base dugout.

The efforts that other leagues make to ensure the safety of their spectators could serve as a blueprint for MLB. Take the Japanese Nippon Professional Baseball Organization, where the stadiums have netting from foul pole to foul pole. Whenever a ball is hit into the stands, fans are warned with loud whistles blown by staff stationed in their seating section, and animated warning videos are played before every game. As a result, unprotected seats are something of a luxury in Japan. The Tokyo Dome offers “exciting seats” near the foul lines, which come equipped with helmets and gloves.

Even with extensive netting, no one will ever be completely safe at a baseball game. But there are ways for MLB to protect its fans from foul balls — particularly in the most dangerous areas of the park.

“It’s something that you just hold your breath for a second,” Hill told The Los Angeles Times. “You just hope it hits a seat, not a person.”

Neil Paine contributed research.

Check out our latest MLB predictions.

CORRECTION (July 15, 2019, 5 p.m.): A previous version of this story referred to the data as having been collected from the 10 most foul-ball-heavy games this season. It was actually collected from the 10 most foul-ball-heavy game days — one day included a doubleheader.

Americans Say They Would Vote For A Woman, But …

A record number of women are running for president in 2020, and now two women look like serious contenders for the presidential nomination — Elizabeth Warren and Kamala Harris, both of whom rose in the polls after strong performances in the first Democratic debate. Joe Biden is still in the lead, but Warren and Harris may be starting to chip away at one of the central conceits of the 2020 race so far: the idea that Biden has the best shot at defeating President Trump.

For months now, voters have told reporters that they want to elect a woman — but after Hillary Clinton’s loss in 2016, they simply can’t imagine a woman winning against Trump. And this calculus is often justified by beliefs about other people’s sexism — an Ipsos/Daily Beast poll in June, for example, found that only 33 percent of Democrats and independents said they believed that their neighbors would be comfortable with a female president. But the performances of Warren and Harris in the first debate may have allowed some of those voters to envision a path to victory for these candidates for the first time.

Even with Warren and Harris on the upswing, though, it’s hard not to wonder if sexism will still make it more difficult for a woman to win the nomination. After all, the other women in the race — including Kirsten Gillibrand and Amy Klobuchar, who seemed at the outset like promising contenders — are still barely registering in the polls. Whether these women are struggling because of their gender is pretty much impossible to say right now; in part, this is because there is, of course, no research to tell us how six female candidates might fare against 17 male competitors in a presidential primary.

But that doesn’t mean we’re completely in the dark about how sexism affects women’s electoral chances. Political science research has established that women who run for elected office have to navigate a thicket of stereotypes and double standards that their male counterparts are unlikely to experience. And while most scholars agree that partisanship usually overpowers voters’ biases about female leaders, no matter how deeply held, a long and crowded presidential primary could be especially challenging.

So with the caveat that we will learn a lot about gender and elections over the next 16 months (not that we’re counting), here’s a link-heavy introduction to what we know already — and how that could influence the Democratic primary.

Americans say they will vote for a woman, but they’re still influenced by stereotypes

These days, it’s hard to find voters who openly admit that they’re reluctant to support a woman for president. Only 13 percent of Americans believe that men are better suited for politics than women, according to the 2018 General Social Survey. And a Gallup poll conducted in May found that 94 percent of Americans say they would vote for a woman for president.

But many people’s assumptions about what it means to be a woman and what it means to be an elected leader still don’t line up, which can put female candidates at a disadvantage when they step into the political sphere. The traits most people associate with politicians — for example, competence, ambition, aggressiveness, confidence, toughness — are linked to masculine behavior. And studies have found that as a result, men are often assumed to be viable candidates from the get-go, while women must work to be taken seriously. “Men have a leg up in politics because there’s a basic assumption that they’re qualified to run,” said Nichole Bauer, a professor at Louisiana State University who studies political psychology.

These stereotypes are mostly unconscious — these days they rarely emerge, fully formed, in our political discourse. But we can see them bubbling underneath the surface, like when female candidates are asked if they’re “likable” — a question that’s already in the air in 2020. (Gillibrand was asked this question within minutes of formally announcing her campaign.) And trying to seem “likable” can quickly morph into an impossible bind for female politicians because they’re trying to fill two roles with very different sets of expectations — “woman” and “leader.” Appearing both qualified and likable can mean walking a narrow tightrope between the stereotypically masculine qualities that are associated with political leadership and feminine qualities like warmth, kindness and empathy.

This can be a hard act to pull off. Research has shown that being liked has outsize importance for women because voters will support a man they dislike, but they will not support a qualified, unlikable woman. Take what happened in the 2016 presidential election: Trump and Clinton both had historically low favorability ratings, but Trump still eked out a victory despite Clinton’s political credentials. That speaks to another trap several political scientists told me that women often face: A long political track record can open a candidate up to more criticism, but without an established résumé, a woman might not be taken seriously at all. Men, meanwhile, can run with less experience and get away with talking more vaguely about their policy positions, according to Amanda Hunter, research and communications director at the Barbara Lee Foundation, a nonprofit group that has done research on gender bias and elections. “Women are judged more harshly if it seems like they’re learning on the job,” she said. “So that means they have to be uber-prepared to run, while men can kind of figure it out as they go.”

There are some stereotypes that can work to female candidates’ advantage — but they can be a double-edged sword. Women are more likely to be seen as having expertise on issues that are stereotypically associated with women, like health care or child care, which can give them a boost when those issues are at the top of voters’ minds — a nice edge until you learn that men have an advantage on issues like the economy or national security. Female politicians are generally assumed to be more liberal, too, which can be a good thing in the Democratic primary but can quickly go south in a general election. And studies have shown that women are generally perceived as possessing more honesty and compassion than men — qualities that many voters say are important for politicians. But Cecilia Mo, a professor of political science at the University of California, Berkeley, cautioned that even being seen as the more civil or morally upright candidate can become a liability because there’s more room for disappointment.

“We assume female political leaders are more of these good things — warm, honest, caring, smart,” Mo said. “But when women candidates are shown to be flawed in some way, voters are much less forgiving than they are of their male counterparts.” Mo’s recent research suggests that voters punish female candidates more than male candidates for scandals or political attacks, perhaps because voters have higher expectations for women’s judgment or integrity.

There are plenty of metaphors for the limitations female candidates face, but whether they’re on a pedestal or a tightrope, there isn’t much room to maneuver, and there’s a long way to fall. And all of these biases — helpful or not — end up narrowing the possibilities for how a viable female candidate can behave. Of course, the six women running for the Democratic nomination will navigate these stereotypes differently and won’t all be affected by them in the same way. Other factors like race, age and political ideology will also shape how the candidates are perceived by voters, which means that gender bias could have a bigger effect on some candidates than on others.

Stereotypes may not stop women from winning elections — but they probably make it harder

The question, then, is not whether women face gender stereotypes when they run for elected office — they do. But do women actually lose elections because of sexism?

It’s very difficult to get a definitive answer to this question when it comes to presidential races, since only one woman — Hillary Clinton — has ever run on a major party ticket. So instead, researchers have focused on lower-level races to figure out whether voters actually penalize women because of their gender. And they found that women do well at the ballot box, in spite of the barriers they face.

In congressional races, for example, several studies have shown that women win at about the same rate as men. To some political scientists, this suggests that the problem isn’t with voters, who seem entirely willing to elect women when given the opportunity. The logic here is fairly simple — if more women run, more elections will be like the 2018 midterms, in which a historic number of female candidates were elected to Congress.

Despite these promising statistics, some scholars still think sexism is fueling women’s underrepresentation, at least to some extent. For one thing, lurking within those studies of women’s performance in congressional elections is a revealing data point: Female candidates are generally more qualified than their male rivals. “That’s actually a sign that voters may still be biased against women because why else aren’t the higher-quality candidates winning at a higher rate?” said Sarah Anzia, a professor of political science at the University of California, Berkeley. And other researchers have found that when a man and a woman run against each other and are equally qualified, the woman is more likely to lose.

It’s also possible that gender bias still poses a significant risk, but women have just gotten better at figuring out how to neutralize it. “If you’re a woman in politics, you know voters are less likely to think you’re qualified or competent,” said Kelly Dittmar, a professor of political science at Rutgers University. “So your goal is to make sure that when Election Day rolls around, you’ve responded effectively to those concerns. But that means that on every other day of your campaign, gender bias is influencing your strategy and your experience.”

Presidential races are especially difficult for women, starting with the primary

So what does all of this mean for 2020 and, say, the chances of Harris or Warren in the Democratic primary? It’s hard to arrive at a definitive answer because the vast majority of the studies on how often women win look at general election matchups — not primary contests, in which the candidates are from the same party.

And Kathleen Dolan, a professor of political science at the University of Wisconsin, said that while these studies tell us a lot about the power of party loyalty, they can’t signal how voters will act in all elections. “Your uncle Joe could think that women aren’t as good as men,” she said. “But there’s no evidence that he will actually cross over and vote for the other party’s candidate to avoid voting for a woman.” How uncle Joe will behave when he’s choosing between two candidates of the same party is pretty much anyone’s guess.

Several political scientists told me that gender could play a bigger role early in a primary than it does later on. When voters don’t have much information about the candidates beyond basic information like gender, they’re more likely to rely on stereotypes. Several studies have even suggested that voters who make their choice with little or no outside knowledge are more likely to support a man. “There’s more room for gender bias to actually influence your decision if you know very little about who someone is beyond the fact that they’re a woman,” Anzia said. This could help explain why Harris’s and Warren’s standing rose after the debate, when they were able to make a strong impression on millions of potential primary voters who may not have known much about them before tuning in.

But voters’ prejudices about women may also just be stronger when it comes to the presidency. Studies have found that voters may be more biased against women when they run for executive offices. So women in a presidential campaign will likely have to do more than their male rivals to convince voters that they deserve to sit in the Oval Office, even if those voters also say they’re fine, in theory, with the idea of a female president.

If you’re a woman running for president, Democratic primary voters will probably be an especially friendly crowd. A recent experiment conducted by CBS and YouGov looked at the qualities prioritized by Democratic voters in a series of matchups between hypothetical candidates, and it found that Democrats showed a clear preference for female candidates. One of the studies about executive leadership indicated that Democrats are more likely than Republicans and independents to see women as viable leaders, and a meta-analysis of multiple studies also found that Democrats are more likely than Republicans to support female candidates, all things being equal.

This enthusiasm for female candidates, though, has to contend in voters’ minds with the still-fresh memory of the sexism Clinton faced on the campaign trail and her ultimate defeat in 2016. And Democratic voters also aren’t wholly immune to sexism, and some do seem more reluctant to vote for women. One ongoing study suggests that gender bias hurt Clinton in her race against Bernie Sanders in 2016. Political scientists Erin Cassese and Kevin Banda looked at how Democratic primary voters in 2016 scored on a scale designed to measure sexism. They found that some Democrats held hostile views toward women, and those voters were less likely to vote for Clinton in the primaries. Cassese expects these voters will be especially open to the notion that women are less electable than men. A survey conducted just before the first debate found that support for Warren and Harris was, in fact, lower among voters with more sexist views.

Scholars, meanwhile, are still divided about the role that sexism played in Clinton’s downfall. But the fact that she lost a campaign defined by her gender — and by Trump’s sexism — could make it hard for voters to imagine another woman charting a different path, at least while Trump is the opponent.

But it’s also too early to know exactly how all of this will play out. Two months ago, Warren’s campaign still hadn’t taken off, and now she has out-fundraised Sanders and is pulling ahead of him in some polls. Harris, similarly, has surged in the polls only in the past few weeks. Their recent success certainly doesn’t mean that they have figured out the key to running for president as a woman — everything can (and probably will) change over the coming months. And, of course, it remains to be seen whether any of the other four women will be able to emerge from the crowded purgatory of candidates who average around 1 percent or below in the polls.

It’s clear that female candidates can win despite sexism, but as the research shows, they probably can’t escape it entirely. This time around, voters and candidates alike are acutely aware of the barriers that remain for women seeking the White House. But will gender biases assume their familiar shape with an unprecedented number of women in the race? We’re about to find out.

Meredith Conroy contributed research.

Serena Williams Will Need To Serve Better To Tie Margaret Court

With one more win at Wimbledon, Serena Williams would tie Margaret Court, the only player in history with 24 Grand Slam singles titles. In Saturday’s final, the 37-year-old Williams will battle Simona Halep, who won the French Open last year but has never won a Wimbledon title. Williams appears to have shaken off the rust of earlier this season and seems, at last, to have returned to her perch as the most dominant player in the history of tennis.

There’s just one problem: Williams’s incredible serve is still a little shaky.

“I don’t know if I’ve had my best serves this tournament,” Williams said. “I’m just now starting to use my legs again.”

On Thursday, Williams beat Barbora Strycova, a 33-year-old who had never reached a Grand Slam singles semifinal. Strycova, who has a fine track record at doubles, reaching the semifinals in each major event, couldn’t control Williams, who won 6-1, 6-2.

But Williams hasn’t played anyone like the 27-year-old Halep. She’s great at receiving serves and, at times, pouncing on them, too. Halep has won 53 percent of return points — and that includes first and second serves. Williams, known as an all-time returner, has won 43 percent.

Halep also sounds eager and hungry. “I feel stronger mentally facing her,” she said. “We will see what is going to happen.”

Williams has yet to play against a top 15 player in this tournament. According to the WTA, Williams’s opponents so far had an average rank of 75.2, and only two of them were seeded (No. 30 Carla Suarez Navarro in the fourth round and No. 18 Julia Goerges in the third). A similar scenario unfolded a year ago, when Williams coasted to the finals with her average opponent ranked even lower at 80, until she faced Angelique Kerber in the final. Kerber, who has an attacking style similar to Halep’s, beat Williams 6-3, 6-3.

Williams needs to serve as well as possible to tie Court’s record, and so far, her serve has seemed vulnerable. Throughout the event, Williams has won 54.2 percent of second-serve points, which is solid and in line with her career numbers at Wimbledon. But the first serve counts the most, and Williams has not nearly been her best. She has won 74 percent of her first serves in her six matches. That’s lower than for all of her Wimbledon wins; her previous low at a Wimbledon in which she won was 75.8 percent in 2003. Her share of first serves won was much higher for her most recent match, at 89 percent, so perhaps she has started to find her footing.

At her best, Williams’s serves have been efficient and brutal. In 2010, she won 87.5 percent of the points for which she landed her first serve, the highest at Wimbledon in her career. (That year, Williams hit 23.5 percent of her total points served as aces.) Williams didn’t lose a set that year (she also lost no sets in 2002). In 2012, Williams had stats nearly as impressive, hitting 20.9 percent of her total points served as aces. That’s the only time Williams hit more than 100 serves as aces (102 in all) at Wimbledon.

Williams has played Halep 11 times, including three at a Slam. Halep has won just once, in 2014. But she played Williams close at the Australian Open this year and won a set from her in the 2011 Wimbledon, back in their first matchup. Williams knows this will be her biggest test, and she knows that Halep is ready.

“The biggest key with our matches is the loss that I had. I never forgot it. She played unbelievable,” Williams said. “That makes me know that level she played at, she can get there again. So I have to be better than that.”

NBA Free Agency Diary: The Rockets Don’t Have Superstar FOMO Anymore

Keep track of the chaotic NBA offseason with our Free Agency Diary.


Dear NBA Diary,

Time for a do-over. On Thursday morning, I wrote that the Houston Rockets would be just fine running things back with their existing core of James Harden, Chris Paul, Clint Capela and company, despite the narrative that they were falling behind in the Western Conference’s superstar arms race.

Then Thursday night happened. Daryl Morey and the Rockets offered up what feels like the millionth earth-shattering transaction of the NBA summer by dealing Paul to the Thunder for Russell Westbrook. Just like that, Houston had created an entirely new star combo in Harden and Westbrook — and we needed a new breakdown of their full-strength CARMELO rating:

Whoaaaa, look at this Rockets team now

Projected full-strength regular-season depth chart for the 2019-20 Houston Rockets, based on CARMELO plus/minus ratings

EXPECTED MINUTES PER GAME PLAYER RATING
PLAYER PG SG SF PF C TOTAL OFF. +/- DEF. +/- TOT. +/-
James Harden 8 25 4 0 0 37 +7.4 +0.9 +8.3
Russell Westbrook 31 5 0 0 0 36 +3.5 +0.5 +3.9
Clint Capela 0 0 0 2 29 31 -0.3 +2.3 +2.0
Eric Gordon 0 3 26 0 0 29 +1.1 -1.2 -0.1
PJ Tucker 0 0 3 25 0 28 -1.2 +1.1 -0.1
Austin Rivers 9 12 5 0 0 26 +0.1 -1.3 -1.2
Gerald Green 0 0 9 8 0 17 -0.7 -1.9 -2.6
Tyson Chandler 0 0 0 0 15 15 -2.9 +2.1 -0.9
Danuel House Jr. 0 3 1 10 0 14 +0.0 -0.4 -0.5
Deyonta Davis 0 0 0 1 4 5 -1.7 +1.0 -0.7
Isaiah Hartenstein 0 0 0 2 0 2 -1.7 +1.4 -0.3
Gary Clark 0 0 0 0 0 0 -1.9 -0.4 -2.3
Chris Chiozza 0 0 0 0 0 0 -0.9 -1.6 -2.5
Michael Frazier 0 0 0 0 0 0 -1.6 -1.3 -2.9
Trevon Duval 0 0 0 0 0 0 -2.5 -1.4 -3.9
Chris Clemons 0 0 0 0 0 0 -0.7 -1.0 -1.7
Team total 240 +6.8 +1.8 +8.4
Expected record: 58-24
CARMELO team rating: 1716

In the short term, this deal improves what was already a surprisingly strong-looking Rockets roster. Houston’s CARMELO rating was 1693 (good for a 56-win projection and a 19 percent championship probability) before the trade; now, that rating is 1716, to go with 58 projected wins and a 25 percent chance of winning the title. Morey paid two first-round picks (and two pick swaps) to make those marginal gains, but in a 2019-20 season that looks wide-open, every little bit could make all the difference.

Certainly, Westbrook (age 30) is younger than Paul (34) and projects to be better over the next few seasons, according to CARMELO’s wins above replacement metric, though he is coming off a worse season in 2018-19:

There are still plenty of questions about how the members of Houston’s new star pairing will coexist with each other. And the trade feels at least in part like a deal done just so the Rockets can say they made a big offseason splash on par with the West’s other heavy hitters. But it certainly further bolsters Houston’s case as the favorite in a loaded Western Conference.

UPDATE (July 12, 2019, 2:40 p.m.): This diary entry has been updated to reflect the signing of Tyson Chandler. Houston’s Elo didn’t change.

Check out our NBA player ratings.

Second Place In The Democratic Primary Is Crowded — That’s Not Good For Sanders

Welcome to Pollapalooza, our weekly polling roundup. Hope you didn’t miss us too much over the holiday weekend.

Poll(s) of the fortnight

You’ve probably heard that the first Democratic primary debate was bad for former Vice President Joe Biden’s polling numbers and good for Sen. Kamala Harris’s and Sen. Elizabeth Warren’s. But what about Sen. Bernie Sanders, who’s long been second to Biden in the polls? Well, his standing appears to be slipping — and his runner-up status is now in real danger.

For example, a CNN/SSRS poll conducted in the days after the debate gave Sanders 14 percent of the vote, which was down 4 points from late May, when CNN/SSRS last polled the primary. And a Quinnipiac poll from after the debate gave Sanders 13 percent of the vote; earlier in June, the pollster had him sitting at 19 percent.

Granted, not every poll showed Sanders losing ground. According to Reuters/Ipsos, Sanders enjoyed the support of 15 percent of Americans a few weeks before the debate and 16 percent right after it. And the poll we partnered with Morning Consult on to track debate reaction in almost real time found Sanders’s support virtually unchanged from before to after the debate. But RealClearPolitics’s overall polling average does suggest that Sanders did indeed lose a couple of points from the debate.

And his standing might be even more endangered because Warren and Harris improved so much that they are now in a rough three-way tie with Sanders for second place. That’s a problem for Sanders because there are now two newly competitive rivals whom he needs to vanquish to win the nomination. Your baseball team may be only a few games out of first place, but if four other teams are too, it hurts your odds of finishing first; not only must you perform well, but you also need multiple other teams ahead of you to stumble.

More importantly, Sanders is arguably in a worse position than Warren and Harris are, despite their nearly tied horse-race polling. And that’s because someone with near-universal name recognition like Sanders needs to be polling higher to have a good shot at winning the nomination (or at least that’s what our research on historical early primary polls has found). On the other hand, lower-name recognition candidates like Warren and Harris arguably have more room to grow than Sanders does, as there is still a pool of potential supporters out there who haven’t heard of them. And unlike Sanders, Warren and Harris both outperformed their polling average in the first half of 2019 when you adjust for name recognition.

Another potential pitfall for Sanders is that he has so far limited himself with a campaign strategy that doesn’t appear designed to expand beyond his base. But to win the nomination, he’ll need to win over some new fans — especially if he keeps losing old ones. Ardent progressives have more options (most obviously Warren) to choose from than they did in 2016, and Sanders may have underestimated how much of his 2016 support was simply a protest vote against Hillary Clinton. An Emerson College poll out this week found he was getting only 25 percent of the vote among those who said they supported him in 2016.

So yes, Sanders is going through a rough patch — but he could still recover. With eight months until the first ballots are cast, there is plenty of time for him to change campaign strategies. He certainly has the money — a reported $30 million cash on hand, plus the proven ability to fundraise even more — to go on the offensive again. Then again, so do his rivals — Warren reportedly raised even more money than Sanders in the second quarter. Sanders might want to act quickly to turn his campaign around, as his margin for error is rapidly shrinking.

Other polling bites

  • In an ABC News/Washington Post poll released this week, support for Roe v. Wade (the 1973 Supreme Court decision that established a woman’s legal right to an abortion) has tied its all-time high in their polling — 60 percent of Americans. Notably, Democrats (specifically, 71 percent of them) were more likely than Republicans (57 percent) to say abortion would be an important issue in their 2020 vote for president, yet another sign that Republicans may have lost their advantage in this arena.
  • In the first poll we’ve seen of the Democratic primary for U.S. Senate in Colorado (one of the Democrats’ best pick-up opportunities), former state House Speaker Andrew Romanoff took 23 percent, Secretary of State Jena Griswold (who isn’t running — yet) took 15 percent and former state Sen. Mike Johnston took 12 percent. The poll was conducted by Keating Research and Onsight Public Affairs but paid for at least in part by supporters of Griswold.
  • A new study from Pew Research found that 64 percent of U.S. military veterans do not think the Iraq War was worth fighting. In addition, 58 percent think the war in Afghanistan was not worth fighting, and 55 percent say the same about U.S. involvement in Syria. The numbers are almost identical among the general public.
  • YouGov researched the walk-up songs of 23 presidential candidates (the music that plays when they take the stage at rallies) and asked respondents to pick their three favorites. President Trump’s “God Bless the USA” took first place with 28 percent of the vote; Rep. Tulsi Gabbard’s “Ain’t No Mountain High Enough” took second with 18 percent, closely followed by Sanders’s “Power to the People” (16 percent).
  • Also according to YouGov, 28 percent of Americans said it is “very likely” the government is hiding information from the public about UFOs. Another 26 percent said it was “somewhat likely.” Now I’m just thinking about what the aliens’ walk-up music would be.
  • A new Nanos poll, released Tuesday, found that 35 percent of Canadians plan to vote for embattled Prime Minister Justin Trudeau’s Liberal Party in October’s parliamentary elections; 30 percent plan to vote for the Conservative Party, 18 percent for the National Democratic Party and 9 percent for the Green Party. Then, on Wednesday, Mainstreet Research also released a poll putting Liberals at 35 percent and Conservatives at 33 percent (the NDP and Green Party took 10 percent each). The polls were a surprise because Conservatives have long been leading in the polling average, although that advantage has narrowed in recent weeks.

Trump approval

According to FiveThirtyEight’s presidential approval tracker, 42.5 percent of Americans approve of the job Trump is doing as president, while 52.4 percent disapprove (a net approval rating of -9.9 points). At this time last week, 42.3 percent approved and 52.5 percent disapproved (for a net approval rating of -10.2 points). One month ago, Trump had an approval rating of 42.0 percent and a disapproval rating of 53.0 percent, for a net approval rating of -11.0 points.

Generic ballot

In our average of polls of the generic congressional ballot, Democrats currently lead by 6.4 percentage points (46.3 percent to 39.9 percent). A week ago, Democrats led Republicans by 6.1 points (46.2 percent to 40.1 percent). At this time last month, voters preferred Democrats by 5.8 points (45.9 percent to 40.1 percent).

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

A Midsummer Overview Of The Democratic Field

When people ask me who I think is going to win the Democratic nomination, I shrug my shoulders and say, “I have no freaking idea.” It’s worth keeping in mind that in a field of 20-something candidates with no runaway frontrunner, all of the candidates are fairly heavy underdogs. Joe Biden is probably going to lose. Kamala Harris is probably going to lose. Elizabeth Warren is probably going to lose. Bernie Sanders is probably going to lose. And so forth.

But the first debate last month, the subsequent polling and the latest set of fundraising numbers provide some clarity about where the race stands, sorting the candidates into what I’d consider to be four relatively distinct tiers. So after taking a couple of weeks mostly off to work on NBA metrics and vacation in Las Vegas playing poker,1 here’s how I currently see the race:

Nate’s not-to-be-taken-too-seriously presidential tiers

For the Democratic nomination, as revised on July 10, 2019

Tier Sub-tier Candidates
1 a Biden, Harris
b Warren
2 a Sanders
b Buttigieg
3 a Booker
b Klobuchar, Castro, O’Rourke
4 a Inslee, Gillibrand
b Gabbard, Yang
c Everyone else

We’ve used these tiers before, and as the headline says, they’re not to be taken too seriously. They’re mostly based on the polling — not just national polls, but also early state polls, favorability ratings, polling adjusted for name recognition, etc. — with some further adjustments upward or downward based on other factors, the most important of which I consider to be support from party elites and the ability to build a broad coalition. But they’re not based on any sort of statistical model, and they involve an element of subjectivity.

Let’s go ahead and start from the top, with the three candidates I’d consider to be front-runners.

Tier 1: The front-runners: Biden, Harris and Warren

Biden, Harris and Warren represent three relatively distinct, but fairly traditional, archetypes for party nominees:

  • Biden, as a former vice president, is a “next-in-line” candidate who is rather explicitly promising to perpetuate the legacy of President Obama and uphold the party’s current agenda. It might not be exciting, but these candidates have pretty good track records.
  • Harris is a coalition-builder who would hope to unite the different factions of the party — black, white, left, liberal, moderate, etc. — as a consensus choice.
  • Warren is offering more red meat (or should it be blue meat?) and would represent more of a leftward transformation from the status quo. But she’s simpatico enough with party elites and has broad enough appeal that she isn’t necessarily a factional candidate in the way that Sanders is. Instead, a better analogy for Warren might be Ronald Reagan; they are not comparable in terms of their backgrounds or their political styles, but they are both candidates who straddle the boundary between the ideological wings of their party and the party establishment.

On an empirical basis, the Biden and Harris strategies have produced more winners than the Warren one, although all three approaches are viable. That doesn’t mean that Biden, Harris and Warren are the only candidates pursuing these strategies. Cory Booker’s coalition could look a lot like Harris’s, for instance, were he ever to gain traction. But they’re the only candidates who are both (a) taking approaches that have worked well in the past and (b) polling reasonably well at the moment. That puts them in the top tier.

How you would rank them within the top tier is harder. But we should probably start with the fact that Biden is still ahead of the other two in the polls. It’s closer in early state polls, and it’s closer once you account for the fact that Harris and Warren still aren’t as well-known as Biden is. But Biden’s lead is nontrivial — he’s ahead of Harris by 12 percentage points (and Warren by 13) in the RealClearPolitics average.

And while you might claim that Harris and Warren have momentum, you need to be careful with that. Often, polling bounces from debates and other events fade, so it’s at least possible that Harris and Warren are at their high-water marks. Or not. But Biden is (POKER ANALOGY ALERT!) a bit like a poker player who’s just lost a big pot. Before, he had way more chips than Warren and Harris did; now, he has only slightly more than they do. But you’d still rather be the candidate with more chips than fewer, momentum be damned.

Unless … the way you lost that hand reveals something about your game that could come back to bite you again in the future. Biden wasn’t very effective in the debates, according to the voters we surveyed along with Morning Consult. And some of his decline in the polls has to do with what could be Biden’s two biggest vulnerabilities: his electability halo bursting and voters expressing concern about his age. The age problem isn’t going away. And while Biden can still make an electability case — there are plenty of polls showing him doing better than other Democrats against President Trump — voters are at least likely to scrutinize his argument rather than take it for granted.

Biden and Harris are a fairly clear No. 1 and 2 in endorsements, meanwhile, with Harris having recently picked up a number of endorsements from members of the Congressional Black Caucus, an indicator that coincides with her gaining support among black voters in polls. Warren lags in endorsements, meanwhile. Also, it’s worth noting that whichever candidate wins the plurality of black voters usually wins the Democratic nomination — something that Biden and Harris probably have a better chance of doing than Warren does. For those reasons, I have Biden and Harris a half-step ahead of Warren. That said, I see the dropoff from Biden and Harris to Warren as being considerably smaller than the dropoff from Warren to the rest of the field.

Tier 2: They can win Iowa, but can they win the nomination?

For Sanders and Pete Buttigieg, the data is a lot more mixed.

Let’s start with the good news for Sanders: He’s still roughly tied for second place in most polls. His favorability ratings are pretty good. He had a decent second-quarter fundraising number. He should have a pretty good on-the-ground organization in Iowa and other early states. He potentially has a fairly high floor relative to the other candidates, and voters know what he stands for.

The bad news: His polling is less impressive given his high name recognition; in fact, he’s in a zone (15 percent-ish in the polls with 100 percent name recognition) that’s usually associated with losing candidates. He’s polling worse in Iowa than he is nationally, a bearish indicator given that it should be a strong state for him demographically. He’s failing to win the support of influential progressive groups like MoveOn.org that backed him four years ago, or to receive many endorsements of other kinds. His fundraising totals are underwhelming as compared with the numbers from his best quarters in 2015 and 2016. Warren’s emergence has produced another strong candidate in his lane. And to the extent that age is a consideration for voters, it’s a problem for Sanders as much as it is for Biden.

That’s a pretty long list of negatives to weigh against decent-but-not-great topline polling numbers. And it leaves out what might be the biggest problem of all for Sanders, which is that even if he were to win Iowa — and New Hampshire — that might not slingshot him to the nomination in the way it would for the other candidates. That’s because Sanders doesn’t have a particularly broad coalition. He has some support among black voters but not a ton, he doesn’t perform well with older voters, and he’s alienated enough moderate and pro-establishment Democrats that he’s usually near the top of the list when pollsters ask voters who they don’t want to see win the nomination. Meanwhile, the party establishment probably won’t do him any favors in the event of a campaign that remains undecided late into the race.

I don’t want to go overboard. If you’re comparing Sanders against, say, Booker, all of Sanders’s liabilities aren’t enough to outweigh the fact that Sanders is at 15 percent in the polls and Booker is at just 2 percent. But they do explain why I don’t have Sanders in the same tier as Warren and Harris, who are in a superficially similar position as Sanders is in national polls. None of those candidates are in a position to win the race right now with 15 percent of the vote, but Sanders has the least obvious path toward expanding his coalition.

Buttigieg offers a different mix of positives and negatives. Pluses: the best second-quarter fundraising numbers of any Democrat; high favorability ratings among voters who know him; stronger polling in New Hampshire and Iowa than he has nationally. Minuses: his topline standing in the polls has reverted back to only about 5 percent of the vote as college-educated voters flock to Warren and Harris; his credentials aren’t as impressive as the other leading candidates; his media attention has atrophied from his initial bump to some degree.

And then there’s Buttigieg’s big challenge, which is similar in some respects to Sanders’s: It’s not clear if Buttigieg can build a broad-enough coalition to win the nomination. He has very little support among black or Hispanic voters and relatively little support among non-college Democrats. Is there a niche for college-educated white voters who think Warren and Sanders are too far to the left, but Biden is too old and/or too moderate? Sure, and it’s a niche that probably includes a lot of FiveThirtyEight readers. 😬 But it’s not a particularly large niche, and that helps explain why Buttigieg is at 5 percent in the polls instead of 20 or something.

With all that said, a Buttigieg win in Iowa would be expectations-defying enough that it could reset how the media covers him. It could also sway voters who like him, but don’t necessarily have him as their first choice, to overcome their doubts about his campaign.

Tier 3: There’s potential, but these candidates are underachieving — for now

One of the lesser-noticed aspects of polling after the first debates is how several candidates who were deemed to have performed well in the debates by voters didn’t really see their topline numbers improve. That especially holds for Booker and Julian Castro. Both got high marks for their debate performances, and both saw their favorability ratings improve, but they’re still polling at just 1 or 2 percent in the toplines. That ought to read as a bearish signal for Booker, Castro and other candidates in this tier. They can have a good night, and it still isn’t necessarily enough to move the vote choice needle for them.

Perhaps that’s a sign that the top four or five candidates are fairly strong. Biden, Harris, Warren, Sanders and Buttigieg collectively give almost every voter in the Democratic Party something to be happy with. Some of the other candidates are more redundant, meanwhile. A potential Beto O’Rourke voter probably sees a lot of what he likes in O’Rourke in Buttigieg, for instance; or a Booker voter could gravitate toward Harris, instead. So it’s not clear what’s distinctive about what these candidates have to offer to voters, although I should note that Castro is the only Hispanic candidate in the field.

With that said, it’s early, and an alternative way to interpret Harris’s and Warren’s emergence is that serious candidates with good résumés will get their opportunities sooner or later. And Booker, Castro and Amy Klobuchar are all serious, well-credentialed candidates.

O’Rourke is in a slightly different category. He’s a little bit like (BASEBALL ANALOGY ALERT!) a baseball player who gets called up from the minors and surprises everyone by hitting .330 in 100 at-bats in September, only to hit .206 when he’s named the starting third baseman the next season before promptly getting sent back to the minors. What O’Rourke accomplished against Ted Cruz in Texas’s U.S. Senate race in 2018 was genuinely impressive — but he may not get another chance to prove that he wasn’t a flash in the pan.

Tier 4: These candidates are also running for some reason

Pretty much everyone else is in asterisk territory in the polls, and is raising relatively little money, and so is in danger of missing the third debate in September. To the extent I have any of these candidates ranked ahead of any of the others, it’s pretty much entirely subjective. But I think Kirsten Gillibrand and Jay Inslee are well-enough credentialed and have distinctive-enough messages — Gillibrand around women’s issues, Inslee around the environment — that they’re slightly more likely to surge than the others.

Beyond that … I’m deliberately avoiding listing overall percentage chances (i.e. “Biden has an X percent chance of winning the nomination”) until and unless we release a statistical model to forecast the primaries. But just to be clear, once we get down to Tier 4, we’re not talking about candidates with even a 10 or 20 percent chance of winning the nomination. Maybe it’s 1 or 2 percent. Maybe it’s 0.1 or 0.2 percent. Maybe it’s even less than that. I haven’t really thought about it much. The chances are not high, though.

How to differentiate such small probabilities from one another is tricky. But other things being equal, if you’re betting on extreme longshots, you’d probably prefer weird candidates who have higher variance to milquetoast candidates with lower variance. Maybe 98 out of 100 times, Andrew Yang or Tulsi Gabbard fade out after failing to qualify for one of the debates and are never heard from again. But the two times out of 100, it turns out that American politics are way different than we thought — it wouldn’t be the first time! — and their eccentric approach proves to be effective. It’s a weird world where Gabbard becomes the Democratic nominee. But I’m not sure there’s any world where, say, Seth Moulton does.