## James Holzhauer Broke ‘Jeopardy!,’ But Is Broken So Bad?

Note: This article discusses the results of the June 3, 2019, episode of “Jeopardy!”

James Holzhauer claims not to remember many particulars of how he lost on “Jeopardy!” for the first time, other than that he blanked on a clue about the city of Albany and his opponent quickly took control of the board, landing a game-changing Daily Double. Before long, it was all over. Monday’s episode marked the end of Holzhauer’s two-month reign as one of the winningest, and certainly the most radical, champions in the decades-long history of the trivia game show “Jeopardy!”

Holzhauer finished Monday’s game in second place with $24,799 behind Emma Boettcher’s$46,801. But during his 32-win run, he averaged about $77,000 per game — an average nearly identical to the record for the single richest game ever played before he took the podium in early April. In the process, he laid claim to the entirety of the top 10 highest-scoring games of all time, including one single half-hour haul of$131,127. It was a historic run driven by immaculate trivia knowledge, disciplined strategy and calculated aggression.

But other records will forever remain just out of reach. Holzhauer’s streak ended with total winnings of $2,462,216 — less than$60,000 shy of Ken Jennings’s record $2,520,700 which was amassed over a nearly incomprehensible 74 straight wins in 2004. Holzhauer will sit second on the all-time money list until the arrival of some other great champion. (Or he might sit there forever, which seems more likely.)2 “I played every day exactly according to my game plan, so I have no regrets,” Holzhauer told FiveThirtyEight a few days before the fateful episode aired. Holzhauer rewrote swaths of the show’s record books. But his biggest contribution may be to “Jeopardy!” strategy. Holzhauer exploited the game’s Daily Doubles to their fullest, hunting them down and betting big on them. Over his 32 wins (and one loss), Holzhauer — a professional sports bettor from Vegas — not only got significantly richer but likely changed how the venerable game show will be played. Holzhauer was such an effective and alien force that opponents began to mimic his style out of desperation, like growling at a hungry lion in hopes of scaring it away. They hopped wildly around the game’s board whenever they could, picking big-dollar clues early, searching madly for the Daily Doubles and betting big when they found them — just the sort of unalloyed aggression that had quickly become Holzhauer’s trademark and the fuel for his success. “Many of my opponents played like I do, but I’m not sure they would have done so without provocation,” Holzhauer said. “You don’t want to inadvertently make your opponents play a better strategy. In a sense, I may have helped bring about my own downfall.” Life as a longtime “Jeopardy!” champion is a strange one, chronologically speaking. Holzhauer has been watching the world wonder when his streak will end, all the while knowing exactly when it would happen. On its taping dates, the show records five episodes back-to-back, with just a change of clothes in between. The episodes don’t air until much later. If he could alter time, maybe buy a time machine with that$2,462,216, would he have approached the game any differently?

“The only things I would do differently from the start of my run: never wear a sport coat, which interfered a little with my buzzer form, and use gel insoles in my dress shoes,” Holzhauer said.
“Both were fixed by the second taping day.”

The insoles seem to have worked. Holzhauer has earned a spot in the pantheon of the “Jeopardy!” greats, and he gives himself prominent placement there. “I think there is a nebulous top three of Ken Jennings, Brad Rutter and me,” he said. “Ken’s 74-game streak remains the most impressive achievement in the show’s history.”

Rutter is no slouch, either — he has won more money than any other “Jeopardy!” contestant, and he’s a man who has never lost to a human. Rutter’s initial winning streak was ended by the show’s rules at the time, which limited a defending champion to five appearances. But between those appearances and the show’s Tournament of Champions, Ultimate Tournament of Champions and Million Dollar Masters, Rutter won $4,688,436. (Here’s a free idea for the “Jeopardy!” producers: Holzhauer vs. Jennings vs. Rutter in the Ultimate Tournament of Ultimate Champions.) A couple of days after we first emailed, however, Holzhauer followed up to amend his initial assessment. “Amidst all the people comparing me to Ken and Brad, I totally forgot about the two greatest Jeopardy champions of all time: Cindy Stowell, who won six games while dying of cancer, and Eddie Timanus, who’s … blind and was an undefeated five-time champ in his initial run. It’s impossible for me to compare myself to them, so perhaps they should be in their own category.” Holzhauer’s plan for now is a return to normalcy. “The 19-year-old version of James would be thrilled by the opportunities” that the winning streak has brought his way, “but married parent James is hoping to keep his home life settled.” The game that made him famous, however, has been left unsettled. Lots of esteemed competitive pursuits have been “broken” lately. Baseball. Basketball. Even the spelling bee just last week. An innovative strategy or an outlier talent can deeply alter the games we’ve played for decades. In the process, the cadence or tenor of the game might be rendered unrecognizable for someone who hadn’t seen it in a few years. These innovative strategies are often driven by mathematical analysis, data and statistical rigor — things that a sports bettor from Vegas must embrace in order to eat. I asked Holzhauer if “Jeopardy!” now belonged in this category of sabermetrically altered pursuits. “I can see the parallels, for sure,” he said. “At its heart, all these shifts are just attempts to increase your chances of winning. Why would anyone not want to maximize their chances?” Plenty of outlets have written that, thanks to Holzhauer, “Jeopardy!” is now broken. But there’s art in that. While the game may look a bit different than it did before, it may also be closer to perfection — to an ideal expression of trivia game-show strategy. Broken is beautiful. From ABC News: ## How Tottenham Could Shock Us One More Time This could finally be the year when a true underdog wins the Champions League again. The last time a club not among the world’s very elite hoisted the trophy was in 2012, when Chelsea won it all.1 In the six years since, the ruling class of Bayern Munich, Barcelona and Real Madrid captured Europe’s most prestigious club tournament each year. In this context, if Liverpool triumphs on Saturday, despite being clearly among the best teams in the world according to the FiveThirtyEight Soccer Power Index, the Reds would still be breaking ground. But the real underdog here is Tottenham. Spurs rate as the 12th-best club in the world by SPI. And in many ways, the story of Tottenham is the incredible journey it took just to get close to the world top 10. Spurs languished in the middle of the English Premier League table through most of the 2000s, and unlike Manchester City, which also made the leap to the EPL elite in this millennium, Tottenham didn’t luck into an owner willing to spend at a massive deficit to take the club up the ladder. Instead, Spurs had to ratchet up their spending slowly and play the market carefully. Of the Premier League’s current “big six” clubs,2 only Tottenham has come close to breaking even on its transfer dealings over the past decade — receiving about as much money in transfer fees as it has paid out. In this same time, Tottenham has managed to increase its wage spending from about$85 million in 2009-10 to 187 million reported last season. The money saved on transfers has, to a significant degree, been reinvested into wages. By carefully managing the club’s incoming and outgoing funds on transfers, chairman Daniel Levy has built up the quality of the squad and paid to keep better and better players. And it’s worked. Tottenham has finished at least sixth in every season this decade, including now four consecutive berths in the Champions League.3 In the previous decade, Spurs finished in the top six only twice (back-to-back fifth-place finishes in 2005-06 and 2006-07). Tottenham has become a regular Champions League competitor through a process of careful business management backing up good player development. This same “do more with less” mentality is reflected in the team’s performances this season under the management of Mauricio Pochettino. Faced with injuries up and down the squad, Pochettino has had to improvise. His team has given at least 1,500 minutes to 14 different outfield players,4 most among the big six sides in the Premier League. Tottenham’s 10 most-used outfield players have covered only 66 percent of the team’s total minutes, the smallest share among the big six. The team’s injuries have hit the midfield particularly hard: Eric Dier missed most of the second half of the season after an appendectomy, Harry Winks has missed time with ankle and groin injuries, Victor Wanyama was unavailable for most of the season with knee problems, and Mousa Dembele was injured in November and has not played for Tottenham since.5 Dier, Dembele and Wanyama were three of Spurs’ four leading midfielders in tackles and interceptions won per 90 minutes this season; without them, the club had no true ball-winners in the center of the pitch. The loss of these more defensively sound midfielders changed Tottenham’s approach, forcing Pochettino to dial back his preferred high-pressing, high-possession style. The team’s pressing rate has dropped to its lowest level under Pochettino at 47 percent.6 Instead, Pochettino has had to develop a more counterattacking approach. Tottenham has remained one of the best attacking teams in the league, with about 50 open-play expected goals created — good for fifth overall. But unlike the other clubs that rank high in this metric, Spurs complete surprisingly few passes into or within the penalty area. Arsenal completed 459 open-play passes into or within the penalty area to Tottenham’s 310. And yet Spurs have created only about three fewer expected goals from open play. This speaks to an unusually direct attacking style. Tottenham no longer pins its opponents back with a strangling high press but instead builds its attacks quickly to free individual players to run at the defense, in an attacking style that has been compared to college football’s “air raid.” To make passes inside the penalty area, a team must have multiple players already in the vicinity, and if one of these high-risk passes is left incomplete, fewer players are in position to stop a potential counterattack. Without the ball-winners in midfield to recover possession, such a deliberate approach would put Tottenham under too much pressure in transition. So instead, the team works more directly, bypassing midfield and quickly feeding a forward to face a defender one-on-one. This is the attacking style that Liverpool will have to defend against on Saturday in Madrid. Liverpool has consistently been able to use its midfield press to control matches and hold possession. But against Spurs, Jurgen Klopp’s side will have to be particularly wary of the direct counterattacks that have become the team’s go-to play. If Liverpool takes risks to overload Spurs defensively in possession, looking for some of these killer penalty area passes, it will be the Reds who are at risk of being countered. The table may be set for a more slow-paced and tactical Champions League final than either Klopp’s or Pochettino’s reputations might suggest. In the most recent meeting of the two sides on March 31, there were just 2.6 expected goals created from 25 shots. This is almost exactly average for a Premier League match7 but is far from the high-scoring barn-burner one might hope for from the matchup. If Liverpool won’t risk sending extra runners to support its forwards, while Tottenham invites some pressure and looks to counterattack, the game may slow down as it did at Anfield in March. The final, then, could come down to one team or the other relying on its superstar forward for a moment of magic. For Liverpool, this is not such a complicated question. Mohamed Salah had a great season, has returned to fitness after a head injury and is expected to be ready to go at full strength. Harry Kane is a bigger question for Tottenham. The English striker suffered his fifth ankle injury in the past three seasons against Manchester City in April and has not played since. He has rejoined the team and traveled to Spain, but can Spurs hope to get a vintage Kane performance? Last season when Kane returned from an ankle injury, his performance fell off badly. He had been running hot, averaging 0.98 expected goals and assists per 90 minutes in the 10 matches before he got hurt, and he dropped to about 0.73 in the 10 matches after his return. The same thing happened again this season after Kane suffered an ankle injury against Manchester United: His shot statistics declined from 0.88 xG+xA/90 to 0.52. But his ankle injuries in the fall of 2016 and spring of 2017 didn’t result in such a drastic downturn in performance. In 2017, he seemed to come back stronger than he was before the injury, going on a rampage down the stretch with 1.04 xG+xA/90 compared with 0.74 beforehand. Tottenham’s counterattacking style, and the team’s efficiency in turning passes around the penalty area into scoring chances, run best through an elite center forward. If Kane can return to form within a single game, that would give Spurs the best chance at a Champions League update. Getting an upset win probably requires a little bit of good fortune, and there is no better possible stroke of fortune for Tottenham than a fit Harry Kane. Check out our latest soccer predictions. ## Does Toronto’s Game 1 Win Spell Doom For The Warriors? sara.ziegler (Sara Ziegler, assistant sports editor): One game into the NBA Finals, and #WarriorsIn4 is already over. But what a first game! The Toronto Raptors led for most of the contest but weren’t able to put away the Golden State Warriors until the very end. tchow (Tony Chow, video producer): I’m gonna be honest. I was second screening Game 1 because my eyes were glued to the Scripps National Spelling Bee. I learned some new words that I’m gonna try to sneak in here, so you all better have your dictionaries ready — I’m about to drop some neil (Neil Paine, senior sportswriter): Omg, Tony sara.ziegler: Tony Though, I’m not gonna lie, I turned to that after the game was over. neil: Fortunately, the NBA can’t declare an eight-way tie for the championship. (Sorry, Celtics.) sara.ziegler: Chris, you’re in Toronto right now. What was the game like up close? chris.herring (Chris Herring, senior sportswriter): The atmosphere was incredible, and loud — both during the game and then pretty wild after. The fans here are insane. I think the game was what we hoped it would be, after years of watching relatively uncompetitive series with a team that couldn’t defend Golden State well enough. The Raptors’ defense is no joke, and it challenged the Warriors all game long. Toronto presents real problems for a club missing someone like Kevin Durant. neil: Yeah, Chris, this was the Warriors’ 20th-worst shooting game of the season by effective field-goal percentage. They still managed to get to the line, but they had a lot of turnovers, and Toronto held the non-Steph Curry scorers mostly in check. Fred VanVleet even did an admirable job keeping Curry from truly exploding. chris.herring: The Warriors shot 23 percent on contested shots last night, the worst mark they’ve had in a playoff game in the Steve Kerr era, according to ESPN Stats & Information Group. neil: And you have to think that Durant — one of the best tough-shot makers in history — would have boosted that some. chris.herring: Yeah. I’m really curious as to where Curry is going to have problems with VanVleet — we mentioned in our preview that he’d done very little scoring this season — averaging just 10 points per 100 possessions when VanVleet is the man defending him. That continued last night. sara.ziegler: FiveThirtyEight’s most valuable player (valuable in the most literal sense), Pascal Siakam had an amazing NBA Finals debut, scoring 32 points on 14-of-17 shooting. How surprised were you at how well he played? tchow: You could say Siakam was shining bright like a pendeloque last night. neil: LOL Our model definitely thinks highly of Siakam as a player, but I’m not going to say I saw him scoring 30+ going in. He had 32 points on 82 percent shooting!!! That’s the fourth-best shooting percentage in a 30-plus-point finals game EVER, according to Basketball-Reference.com. chris.herring: The Warriors got a lot of questions here about Siakam after last night’s performance. Draymond Green said it’s clear that Siakam is “a guy” now — meaning that we might not have treated him as a difference-maker before, but we sure as hell will now. sara.ziegler: He’s a now. chris.herring: Golden State basically acknowledged leaving certain guys open to begin the game in hopes of taking away Kawhi Leonard. That process worked, in a way. Leonard wasn’t efficient. But as a result, everyone else — particularly Siakam and Marc Gasol, who played brilliantly — got going. Danny Green was also himself again. And Golden State was never able to turn off that faucet. neil: Siakam might be a problem for the Warriors going forward. They didn’t have many good options to stop him. He scored 16 directly on Draymond. He also showcased his dangerous range as a 3-point shooter when rotations broke down or he trailed the play. chris.herring: I understand why GSW was willing to take that gamble with Siakam. He’s become very good from the corners but is right around 30 percent — if not worse — from above the arc. The real issue was letting him get whatever he wanted in transition. He was 5 of 5 in transition and hit 11 shots in a row at one point — the longest streak in a finals game over the last 20 years. As good as he is, that simply can’t happen in a game like that if you’re the Warriors. Golden State gave credit to Siakam but also largely chalked the game up to them not having seen this Raptors club before. They hadn’t played since early December, and Toronto has added Gasol, while Kawhi obviously took turns in and out of the lineup to rest. sara.ziegler: Yeah, no one was expecting this from Siakam, so game-planning it would have been tricky. chris.herring: I feel like I should get my apology in now. Although I don’t know if I’m apologizing to a person or an algorithm. neil: Or are you apologizing directly to CARMELO Anthony? Lol. chris.herring: Our model narrowly had Toronto winning this series. I ruled that possibility out pretty swiftly last week. But Thursday’s game was enough for me to think that their defense is good enough to win the series — particularly if Durant doesn’t return, and perhaps even if Durant is back but doesn’t jell right away after the long layoff. neil: I wanted to go back to what you said about loading up to stop Kawhi. Klay Thompson and Andre Iguodala did a good job limiting his efficiency, although it seems like that played a little into Toronto’s hands. Jackie MacMullan had a great reaction story about just how many other efficient options the Raptors have now if a team tries to focus too much on Kawhi. Only two of the seven Raptors who played at least 10 minutes averaged fewer than 1.2 points per individual possession, according to Basketball-Reference. (For reference, the Warriors as a team averaged 1.17 points per possession in the game.) sara.ziegler: And even with Kawhi bottled up, he still scored 23. neil: And! I worry about Iguodala’s health after he came up limping late. He did the bulk of the job guarding Leonard. tchow: So far, it looks like he’ll be OK, though. chris.herring: Yeah. That was the one other concern we mentioned in the preview: While the Warriors clearly could use Durant on offense, their defense becomes really, really thin on the wings without him. Especially if Iguodala is hurt or isn’t himself. This is now the second time he’s been banged up — he didn’t play in Game 4 against the Blazers, either. Speaking of Durant: The Raptors’ starting front court outscored Golden State’s 75-18. neil: sara.ziegler: Wow How much of a problem is that for the Warriors? If there’s no scoring help for Steph and Klay? neil: Certainly Draymond wasn’t much of a factor. Yes, he got the rare 10-10-10 triple double, but he also shot 2 of 9 from the floor and was a minus-8. chris.herring: They’re now 29-2 when he records a triple-double. neil: And both losses have come this postseason. chris.herring: I think what we saw yesterday is this: The Warriors, without KD, don’t have anyone who can shoot outside of Curry and Thompson. sara.ziegler: That seems … bad. chris.herring: I think Quinn Cook is probably the most reliable guy outside of those two. neil: How weird is it to think about the Warriors not having enough shooting? chris.herring: That’s where Durant’s ability to get his own shot comes in handy. He forces enough defensive attention to where he can play other guys open. Generally speaking, Steph often commands a second defender’s attention, so that’s enough to get someone else open and get the ball moving. It’s a tougher task when the other team can guard him and everyone else straight up. sara.ziegler: And Klay doesn’t really create his own shots. chris.herring: We haven’t talked much about DeMarcus Cousins’s return, but that’s both the blessing and the curse of having him You hope he can create an occasional double-team. But by the same token, his spot could have been used on a guard — and I think some people were of that opinion when they first got him: that the Warriors might have been better served by having another shooter. neil: Yeah, I thought the Warriors might go smaller and take somebody like Gasol out of the game, but either Kevon Looney or Jordan Bell played most of the game, and Gasol logged nearly 30 minutes. Meanwhile, Cousins played eight minutes and didn’t really do much of note. chris.herring: He looked a little rusty, but he made a few really nice passes. It’s tough to get your first playing time in weeks and weeks at this level, in the finals. Same may be true of Durant, honestly, if and when he comes back. tchow: It feels like it might be too soon to judge Cousins, but this is the problem of reintroducing someone like him back into the lineup during the finals. chris.herring: Exactly. neil: And that might be one of the ways our model was overrating the Warriors. It considered him one of the biggest talents of the series, which is true, but didn’t factor in the injury comeback. chris.herring: Not to mention the fact that Golden State has been better with Cousins off the court this season. Albeit with Durant playing more often than not. tchow: Yeah, Neil, it probably did overrate the Warriors because of his return. He ranked as the fifth most valuable player (behind Curry, Durant, Leonard and Lowry) according to our projections. neil: And at full health, that might be true in terms of skills. But that was a lot to expect with him easing back into playing. sara.ziegler: While Cousins did play a bit, the other injured Warrior was spotted high-fiving teammates behind the scenes. What did you make of Durant traveling with the team? neil: It has to be an encouraging sign for his chances of returning sooner rather than later, right? sara.ziegler: Is there a chance he plays in Game 2? chris.herring: No, it sounds like he won’t. Kerr was pretty firm about him needing to practice before having a chance to play. They’ll have another two practices — today and again on Saturday — before Game 2. But it doesn’t sound like he’ll be ready to practice here in Toronto before they suit up again Sunday. neil: The good thing about the finals is the sheer gap in days between games. Game 1 on a Thursday — Game 2 … all the way on Sunday. sara.ziegler: He has at least resumed “basketball activities,” which is my favorite phrase in all of basketball. neil: That reminds me, I need to go to the gym and “resume basketball activities” as well. sara.ziegler: So what do the Warriors need do to even the series? neil: Well, it seems obvious that Siakam won’t be down for 30+ again, so they have that going for them. chris.herring: Be a little less focused on stopping Kawhi to make sure that the other Raptors don’t overtake Jurassic Park again. And they have to slow Toronto down in transition, where the Raptors can be wildly efficient. It’s more of a question as to what they do differently on offense. But getting more stops and creating more opportunities to get out and run off those misses will ease some of that concern, I’d think. neil: Yeah, and that probably played a part in Toronto’s 24-17 disparity on fast-break points as well. Not enough stops turning into chances the other way. tchow: They have to play with rhathymia. (Am I using that right?) Just be the fun-loving Warriors we know. sara.ziegler: LOL tchow: I also agree with Neil in that the Warriors could afford to play smaller and get Gasol out of the game. He’s been solid all playoffs like an imbirussú for the Raptors. Otherwise, the Raptors could embarrass you again. Calembour intended. (OK, now I’m just forcing it.) neil: Tony, you’re banned from watching the spelling bee at work ever again. chris.herring: It’s a lot tougher for the Warriors to dictate the tempo without Durant. Playing smaller alone doesn’t get it done if you don’t have enough shooting to force the Raptors to come out and guard you on the perimeter. sara.ziegler: It’s interesting to me, too, that Kyle Lowry didn’t add much on offense again. He had as many field goals as charges forced. If he heats up, that’s a different wrinkle for Toronto. neil: Lowry continued his trend of being associated with strong Raptors play (+11) despite garbage individual stats. chris.herring: Frankly, if they’re getting what they got from everyone else — Green, Gasol and Siakam — they don’t need Lowry to do anything but bring energy. He had massive moments in that last series, and he’s always going to give you what he has on defense. It also helps a ton that VanVleet can stay attached to Curry so well in the minutes that Lowry is taking a breather. tchow: VanVleet was draped over Curry like a ferraiolone and actually guarded Curry for more possessions than Lowry in the end (33 possession vs. 16). chris.herring: O_______o neil: I’ve come around on this, Tony, and I applaud your spelling work here. tchow: Can we all pretend to be a marmennill for a minute? What do you think is going to happen now? Do the Warriors still three-peat? Do the Raptors pull this off? sara.ziegler: Our model (which accepts Chris’s apology) now has the Raptors at 63 percent to win it all. That feels right to me. chris.herring: The Raptors are the lone team that the Warriors haven’t beaten this season, and they have now won all three matchups against Golden State. I expect Golden State to respond. But stuff will get SO interesting if Toronto takes Game 2 as well. neil: 63 percent kinda makes more sense than our pre-series projection, to be honest. Home teams that win Game 1 of the NBA Finals win the series 78 percent of the time, historically. So this suggests that Toronto has far less of a talent edge than the typical home team that takes a 1-0 finals lead. Which is definitely true. tchow: This is anecdotal, but I was chatting with my cousin who lives in Toronto during last night’s game, and he said: “There’s just one guy outside our building somewhere screaming at the top of his lungs, ‘Let’s go, Raptors, over and over.” I can’t imagine what that guy will scream if the Raptors pull this off. That city is gonna be WILD. neil: I love seeing how excited Toronto fans are. (Drake aside.) Nav Bhatia was going nuts trying to distract Warrior free-throw shooters. chris.herring: I decided to walk home last night, about 35 minutes to my hotel. These two people were shouting “Let’s go, Raptors!” for entire blocks. I thought it was a crowd of people, and it was actually just those two guys. But between that, and all the car horns going off last night, people are on a noisy cloud here right now. Sort of how Milwaukee was to begin the last series. So we’ll see how it plays out. tchow: The city is gonna be as loud as a large flock of emberizines. From ABC News: Check out our latest NBA predictions. ## Can You Win The Lotería? 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,8 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 Taylor Firman, the unluck of the draw: Lotería is a traditional Mexican game of chance, akin to bingo. Each player receives a four-by-four grid of images. Instead of a comically large rotating bin of numbered balls, the caller randomly draws a card from a deck containing all 54 possible images. If a player has that image on their grid, they mark it off. The exact rules can vary, but in this version, the game ends when one of the players fills their entire card (and screams “¡Lotería!”). Each of the 54 possible images can only show up once on each card, but other than that restriction, assume that image selection and placement on each player’s grid is random. One beautiful day, you and your friend Christina decide to face off in a friendly game of Lotería. What is the probability that either of you ends the game with an empty grid, i.e. none of your images was called? How does this probability change if there were more or fewer unique images? Larger or smaller player grids? ## Riddler Classic From Ben Wiles, a mathematical trip across the pond: My favorite game show is “Countdown” on Channel 4 in the UK. I particularly enjoy its Numbers Game. Here is the premise: There are 20 “small” cards, two of each numbered 1 through 10. There are also four “large” cards numbered 25, 50, 75 and 100. The player asks for six cards in total: zero, one, two, three or four “large” numbers, and the rest in “small” numbers. The hostess selects that chosen number of “large” and “small” at random from the deck. A random-number generator then selects a three-digit number, and the players have 30 seconds to use addition, subtraction, multiplication and division to combine the six numbers on their cards into a total as close to the selected three-digit number as they can. There are four basic rules: You can only use a number as many times as it comes up in the six-number set. You can only use the mathematical operations given. At no point in your calculations can you end on something that isn’t a counting number. And you don’t have to use all of the numbers. For example, say you ask for one large and five smalls, and you get 2, 3, 7, 8, 9 and 75. Your target is 657. One way to solve this would be to say 7×8×9 = 504, 75×2 = 150, 504+150 = 654 and 654+3 = 657. You could also say 75+7 = 82, 82×8 = 656, 3-2 = 1 and 656+1 = 657. This riddle is twofold. One: What number of “large” cards is most likely to produce a solvable game and what number of “large” cards is least likely to be solvable? Two: What three-digit numbers are most or least likely to be solvable? ## Solution to last week’s Riddler Express Congratulations to Adam Martin-Schwarze of Sequim, Washington, winner of last week’s Riddler Express! Last week we met a soccer coach who was trying to assemble a team of 11 players in a very specific way. He had an infinite pool of players to choose from, each of whom wore a unique number on their jersey such that there was one player for every number. That number also happened to be the number of games it took on average for that player to score a goal. The coach wanted his team to average precisely two goals per game, and he also wanted his weakest player to be as good as possible. What number does the ideal weakest player wear? What are the numbers of the other 10 players the coach should select? The weakest player selected for the team wears the number 24. The other 10 players wear the numbers 1, 5, 6, 8, 9, 10, 12, 15, 18 and 20. Let’s quickly check that everything adds up correctly. If a player’s number is 5, say, then that player scores an average of 1/5 goals per game. If their number is 6, they average 1/6 goals per game, and so on. So our team as a whole averages 1/1 + 1/5 + 1/6 + 1/8 + 1/9 + 1/10 + 1/12 + 1/15 + 1/18 + 1/20 + 1/24 = exactly 2 goals per game, just like the coach wanted! I’m not aware of a more elegant method of solving this coaching conundrum than basic guess-and-check. There are many possibilities to consider, but one thing we do know is that the fractions we’re adding up to try to get to a sum of 2 are of a specific type: 1 divided by a whole number, which are also known as Egyptian fractions. These made a prominent appearance in the so-called Rhind papyrus, which also happens to be the oldest known collection of math puzzles. We also know that we want the worst player on the team to be as good as possible — that is, to have as big a fraction as possible — and that there are 11 players on the team. So first we might check 1/1 + 1/2 + 1/3 + … + 1/11, i.e., the best possible team, but that sum equals about 3, too big for our coach. We then might check the sums of the possible sets of fractions between 1/1 and 1/12, and then the possible sets between 1/1 and 1/13, and so on, rejigging the sums until we find something that gets us to exactly 2. It turns out that none of these will add up to exactly 2 until we get to testing out those fractions between 1/1 and 1/24, and specifically those fractions listed above. Solver David DeSmet shared a handy computer program he wrote to churn through all these possibilities, and Martin Piotte shared his thorough accounting of the possible teams. ## Solution to last week’s Riddler Classic Congratulations to Curtis Bennett of Long Beach, California, winner of last week’s Riddler Classic! Last week, three astronauts were at the edge of their Mars lander, staring down at the surface of the red planet. Each wanted to be the first human to step foot on the planet, but they wanted to pick who it would be using a fair and efficient method. They could, for example, use a fair coin, assign each astronaut an outcome — heads-heads, heads-tails and tails-heads — and flip the coin twice. If the result was tails-tails, they could simply restart the process. However, that method could take a long time and there was exploration to be done. Another approach, however, would be to use an “unfair coin” — one for which the probabilities of heads and tails are not equal. Is it possible to make a fair choice among three astronauts with a fixed number of flips of an unfair coin? You were able to set the coin’s probability of heads to any number you like between 0 and 1. You could flip the coin as many times as you like, as long as that was some known, fixed number. And, you could assign any combination of possible outcomes to each of the three astronauts. Indeed it was possible, though who knew coin flips could get so complicated. This puzzle’s submitter, Dean Ballard, walks us through his solution: What makes this problem interesting is that at first glance it appears to require searching an overwhelmingly large space of possibilities. The trick to solving this more easily lies in a simplifying assumption. Instead of dealing with three different probability functions for the three different astronauts, we can assign two of them sets of head-tail combinations that will give them the equal chances of winning, independent of the weighting of our coin. This way, we can only worry about two things at once rather than three. We will need at least four coin flips to make this work. Let $$p(H)$$ be the probability that our specially designed coin lands heads. With four flips we have 16 possible outcomes: HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH and TTTT. Note that subsets of these 16, such as {HHHT, HHTH, HTHH, THHH}, all have the same probability — in this specific case, $$p(H)^3 (1 – p(H))$$. So let’s call these “3H1T” — three heads, one tail. Expressing the 16 outcomes this way gives us: one 4H, four 3H1T, six 2H2T, four 1H3T and one 4T, or in another piece of shorthand, [1, 4, 6, 4, 1]. Let’s say we assign Astronaut A just the HHHH and TTTT outcomes, and evenly divide the other 14 between Astronauts B and C. This gives us A = [1, 0, 0, 0, 1], B = [0, 2, 3, 2, 0], and C = [0, 2, 3, 2, 0]. Each of these defines a probability function for each astronaut. (Note that the sum A + B + C = [1, 4, 6, 4, 1], so all outcomes have been assigned.) The probability for Astronaut A equals 1 when $$p(H) = 0$$ or $$p(H) = 1$$, so it is concave up. The function for B and C equals 0 when $$p(H) = 0$$ or $$p(H) = 1$$, so it is concave down. Since both functions are continuous, as long as A’s value is less than B’s and C’s value when $$p(H) = 0.5$$ (which is true in this case), there must be a solution between 0 and 0.5, and another between 0.5 and 1. Here is what those solutions look like graphically. On the x-axis is $$p(H)$$ and on the y-axis is the probability that an astronaut wins the contest. Let’s quickly check the solution at point A, where the $$p(H)$$, the probability of our coin landing heads, equals about 0.24213. As we mentioned above, Astronaut A gets to take the first step if the coin lands with four heads or four tails. This happens with probability $$0.24213^4 + (1-0.24213)^4$$ = 0.3333, or a third, which is exactly what we want. Since the other two astronauts have been assigned probabilistically equivalent outcomes, we know they must have equal chances, which must also be a third. So we’ve successfully devised a fair method that will give us a result in a known and fixed number of unfair coin flips! For extra credit, you faced the same question but with five astronauts. I’ll spare you all the gory details, but suffice it to say that solver Zach Wissner-Gross devised one method that used eight flips of a coin that came up heads about 81.7 percent of the time. The colors correspond to the lucky astronaut who will get to make history based on the flips shown on the axes of the diagram. So, for example, if the coin came up eight straight heads — relatively likely given the weighting of the coin — then Astronaut Yellow gets to take those first steps. ## 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] ## Hiring An SEO? Hear From Google What SEOs Do This Google video “How to hire an SEO” isn’t new but it’s to the point and vital to setting expectations. I encourage both SEOs and clients to watch this video and learn what Google says you should look for in an SEO. ## How to hire an SEO [embedded content]  Transcript hi I’m Maile Ohye and I work with Google search I like to share advice to help you hire a useful SEO and prevent hiring a bad SEO one who you might pay a lot of money without positive results or even worse one who implements shady practices on your website that result in a reduction in search rankings SEO stands for search engine optimization – some SEO seems like black magic having worked with Google search for over a decade what I’ve learned is that first it’s not black magic and second if you want long-term success there aren’t any quick magical tricks that an SEO will provide so that your site ranks number one it’s important to note that an SEO potential is only as high as the quality of your business or website so successful SEO helps your website put your best foot forward so that it ranks appropriately in the spot where an unbiased potential customer would expect your site to be seen a successful SEO also looks to improve the entire searcher experience from search results to clicking on your website and potentially converting a good SEO will recommend best practices for a search friendly site from basic things like descriptive page titles for a blog or small business to more complex things like language markup for a multilingual global site SEO is ensure that you’re serving your online customers a good experience especially those coming from a search engine and that your site is helpful whether they’re using a desktop computer or mobile phone in most cases the SEO will need four months to a year to help your business first implement improvements and then see potential benefit my strongest advice when working with an SEO is to request if they corroborate their recommendation with a documented statement from Google either in a Help Center article video or Google a response in a forum that supports both one the SEO description of the issue that needs to be improved to help with ranking and to the approach they prescribed to accomplishing this tasks requesting these two bits of information will help prevent hiring a poor SEO who might otherwise convince you to do useless things like add more words to the keyword meta tag or by links because if you search for google advice on this topic you’d see blog posts and videos from us that clearly explain that adding keywords to the meta tag wouldn’t help furthermore while google uses links for page rank our documentation highlights that we strongly advise against the approach of buying links for the purpose of increasing page rank one basic rule is that in a majority of cases doing what’s good for SEO is also doing what’s good for your online customers things like having a mobile-friendly website good navigation and building a great brand additionally if you’re a more established brand with complicated legacy systems then good search friendly best practices likely involved paying off some of your site’s technical debt such as updating your infrastructure so that your website is agile and able to implement features faster in the long term if you own a small local business you can probably do the initial work yourself check out our 30-minute video series on how to build an online presence for your local business now if you still believe you want to hire an SEO here’s a general process one conduct a two way interview with your potential SEO check that they seem generally interested in you and your business to check their references three act four and you’ll probably have to pay for a technical and search audit 4 decide if you want to hire let’s break this down and start with step 1 conduct a two-way interview in the interview here are some things to look for a good SEO doesn’t focus only on search engine ranking but how they can help your business so they should ask questions like what makes your business content and/or service unique and therefore valuable to customers they want to know this information to make sure it’s highlighted on your website for your current and potential new audience – what does your common customer look like and how do they currently find your website 3 how does your business make money and how can search help for what other channels are you using offline advertising social networks 5 who are your competitors what do they do well online and potentially offline if the SEO doesn’t seem interested in learning about your business from a holistic standpoint look elsewhere it’s difficult to do good SEO without knowing about a business’s goals their customers and other existing marketing efforts SEO should complement your existing work the second step in hiring an SEO is to check references if your potential SEO provides prior clients be sure to check their references you want to hear from past clients that the SEO was able to provide useful guidance and worked effectively with their developers designers UX researchers and our marketers a good SEO should feel like someone you can work with learn from experiment with and who generally cares about you and your business not just getting your site the highest rank as ultimately those techniques rarely last long if they work at all they’ll want to educate you and your staff on how search engines work so that SEO becomes part of your general business operations step 3 is to request a technical and search audit if you trust your SEO candidate give them restricted view not full or right access to your Google search console data and even your analytics data before they actually modify anything on your website have them conduct a technical and search audit to give you a prioritized list of what they think should be improved for SEO if you’re a larger business you can hire multiple SEO to run audits and prioritize improvements see what each has to say and then determine who you could work with the best in the audit the SEO should prioritize improvements with a structure like one the issue to the suggested improvement 3 an estimate on the overall investment in other words the time energy or money it would take for your developers to implement the improvement and for Google search as well as searchers and customers to recognize the improvement the SEO will need to talk with your developers to better understand what technical constraints may exist for the estimated positive business impact the impact might be a ranking improvement that will lead to more visitors and conversions or perhaps the positive impact comes from a back-end change that cleans up your site and helps your brand be more agile in the future five a plan of how to iterate and improve on the implementation or perhaps how to experiment and fail fast should the results not meet expectations that covers the structure of the technical and search audit now let’s talk about each of these audits individually in the technical audit your SEO should be able to review your site for issues related to internal linking crawl ability URL parameters server connectivity and response codes to name some if they mention that your site has duplicate content problems that need to be corrected make sure they show you the specific URLs that are competing for the same query or that they explained it should be cleaned up for long term site health not initial growth I mention this because lots of duplicate content exists on web sites and often it’s not a pressing problem in this search audit your potential SEO will likely break down your search queries into categories like branded and unbranded terms branded terms are those with your business or website’s name like a search for Gmail is a branded term while the search for email is an unbranded or general keyword an SEO should make sure that for branded queries such as Gmail your website is providing a great experience that allows customers who know your brand or website to easily find exactly what they need and potentially convert they might recommend improvements that help the entire searcher experience from what the searcher sees in search results to when they click on a result and use your website for unbranded queries an SEO can help you better make sense of the online competitive landscape they can tell you things like here are the types of queries it would make sense for your business to rank but here’s what your competition is done and why I think they rank where they do for instance perhaps your competition has great reviews really shareable content or they run a highly reputable site an SEO will provide recommendations for how to improve rankings for these queries and the entire searcher experience they’ll introduce ideas like update obsolete content they might say your site is suffering because some of your well ranking content is obsolete has poor navigation a useless page title or isn’t mobile-friendly let’s improve these pages and see if more website visitors convert and purchase or if they can micro convert meaning that perhaps they subscribe or share content improve internal linking your SEO might say your site is suffering because some of your best articles are too far from the homepage and users would have a hard time finding it we can better internally link to your content to feature it more prominently generate buzz the SEO might say you have great content but not enough people know we can try to get more user interaction and generate buzz perhaps through social media or business relationships this will help us attract more potential customers and perhaps garner natural links to your site learn from the competition your SEO might explain here’s what your competitors do well can you reach parity with this and potentially surpass them in utilities or can you better show customers your business’s unique value again a good SEO will try to prioritize what ideas can bring your business the most improvement for the least investment and what improvements may take more time but help growth in the long term once they talk with you and other members of your team such as developers or marketers they’ll help your business forge a path ahead the last thing I want to mention is that when I talk with SEO s one of the biggest holdups to improving away site isn’t there recommendation but it’s the business making time to implement their ideas if you’re not ready to commit to making SEO improvements while getting an SEO audit may be helpful make sure that your entire organization is on board else your SEO improvements may be non-existent regardless of who you hire so that wraps it up thanks for watching and best of luck to you and your business Hits: 2 Hiring An SEO? Hear From Google What SEOs Do ## The WNBA Is Uniquely Suited To Survive Its Many Star Absences When it was announced this week that Seattle Storm point guard Sue Bird would miss the 2019 WNBA season with a knee injury, it was just the latest in a long line of maladies that have struck the league this year. In addition to Bird, the sport has seen absences take out her teammate Breanna Stewart (reigning WNBA MVP), 2014 MVP Maya Moore of Minnesota,1 Atlanta’s Angel McCoughtry, Dallas’s Skylar Diggins-Smith,2 Indiana’s Victoria Vivians, Las Vegas’s Lindsay Allen and Phoenix’s Diana Taurasi for either all or most of the 2019 season. It’s a shocking and unprecedented spate of missing stars that figures to drastically change the championship picture for multiple teams, including — probably first and foremost — the Storm, who won the 2018 WNBA title based on huge contributions from Stewart and Bird. Together, the players listed above generated 30.5 wins last season according to Wins Created — a combination of Basketball-Reference.com’s Win Shares and the Player Efficiency Rating-based Estimated Wins Added metric.3 If all of them do miss the whole year, it would represent the most wins from any single season that were then completely removed from the WNBA ecosystem in the next: Even if we hedge on Taurasi, who currently plans to come back in the second half of the season after missing 10 to 12 weeks of action, the resulting 24.5-win tally would rank fifth-highest in WNBA history before accounting for any of the additional players who will inevitably join the ranks of the absent as the season goes on. (Diggins also plans to return from her pregnancy leave before season’s end.) The season structure of women’s pro basketball — including the year-round overseas grind that stars must engage in to make money — probably has contributed to the WNBA’s problems this spring. With so much mileage being put on top players’ bodies, a nightmare offseason like this was bound to happen sooner or later. But if there is a silver lining for the WNBA (and there isn’t much of one when considering the prospect of a season spent without players of Moore’s or Stewart’s caliber), it’s that the WNBA draws from an exceptionally deep pool of talent. With only 12 teams in the league and an entire world of basketball players to pull from, it might be the most competitive sports league on the planet — at least in terms of the likelihood that any given youth player actually makes the highest level of the sport. My colleague Ben Morris wrote a few years ago about this depth of talent in women’s basketball. He found that for every player who makes a Division I college roster, there are 87 high school players participating in girl’s basketball across the U.S. The only sport whose rosters were more competitive was men’s basketball, in which 101 high schoolers participate for every player who manages to make a Division I team. And, again, that was framed in terms of college basketball. Relative to the number of roster slots available in the WNBA, the amount of talent swimming in the pool becomes even more staggering. In the 2018 season, 157 players suited up for one of the WNBA’s 12 teams. According to an updated version of the same data set Morris used, there were 412,407 girls basketball players in U.S. high schools during the 2017-18 season — meaning there were about 2,627 high school girls playing basketball for every roster slot available in the (American) pros. By comparison, over the same span, there were 540 NBA players and 551,373 participating boys basketball players — or 1,021 for every top-level pro roster slot. By this accounting, it’s more than two and a half times easier (!) for the typical U.S. boys basketball player to make the NBA than it is for his counterpart in girls basketball to make the WNBA. Even if you grant the presence of extra roster slots available overseas,4 the amount of untapped talent in women’s basketball is mind-boggling. That depth of talent won’t necessarily be able to easily replace all of the stars who’ll be missing this season’s WNBA action. But it does mean there are more opportunities than ever for players in the next tier to showcase their skills. And that could be a good thing — because as the numbers show, the WNBA (perhaps more so than any other sport) has a group of unheralded players waiting in the wings, ready to take advantage of the chance. ## Are The Democratic Debates Already A Mess? Welcome to FiveThirtyEight’s weekly politics chat. The transcript below has been lightly edited. sarahf (Sarah Frostenson, politics editor): Republicans struggled with setting debate criteria during the 2016 presidential election because of their large and unwieldy field, and Democrats seem as though they’ll have their own issues in 2020. We already count 20 candidates who have qualified for the first two debates via one of the two criteria the Democratic National Committee has set up: receiving at least 1 percent in at least three qualifying polls or having 65,000 people donate to their campaign, with at least 200 donors in 20 different states. The DNC has said that it will cap participation at 20 candidates, so the next candidate who qualifies, via one of the two criteria for entry, will trigger the tiebreaker rules. Those get complicated fast, but the topline is: If more than 20 candidates qualify, then meeting both the polling and donor requirements will be paramount for candidates — those who do will get first dibs on debate lecterns. But why is it so hard to figure out a fair metric for inclusion? Is there a better way to determine who makes the debate stage? julia_azari (Julia Azari, political science professor at Marquette University and FiveThirtyEight contributor): It’s difficult to figure out a fair metric for inclusion because the whole process is weird. Ideally, it’s both inclusive and efficient (i.e., it narrows options for a nominee relatively quickly), but it’s not really possible to do both at the same time. geoffrey.skelley (Geoffrey Skelley, elections analyst): Right, and in the aftermath of the 2016 Democratic nomination, when the DNC was criticized for “rigging” the debates for Hillary Clinton, the DNC really wants to seem transparent and inclusive. natesilver (Nate Silver, editor in chief): So, 1) It’s good to have objective criteria, 2) as objective criteria go, fundraising and high-quality polling is perfectly fine, but 3) the DNC set the bar too low. Getting donations from 65,000 people is not that hard. And polling at 1 percent in any of three polls out of the many, many polls out there is even easier, probably. sarahf: Although, to be clear, the DNC is not counting all polls from all pollsters. It has said, however, that it’ll consider both national and early-state polls, and qualifying polls can come from 18 different organizations). geoffrey.skelley: Yeah, it’s still pretty easy to qualify via three polls at 1 percent or more — 19 Democrats have already done that. However, if the DNC had set the threshold at 2 percent or more, just eight candidates would meet that mark. ##### Only 8 candidates are polling at 2 percent or more Democratic presidential candidates by whether they have received at least 1 percent or 2 percent support in at least three polls that would qualify them for the first Democratic presidential debates, as of May 21, 2019 IN at least 3 DEBATE-QUALIFYING POLLS, HAS SUPPORT OF … Candidate 1 percent or more 2 percent or more Joe Biden Cory Booker Pete Buttigieg Kamala Harris Amy Klobuchar Beto O’Rourke Bernie Sanders Elizabeth Warren Steve Bullock Julian Castro Bill de Blasio John Delaney Tulsi Gabbard Kirsten Gillibrand John Hickenlooper Jay Inslee Tim Ryan Eric Swalwell Andrew Yang Michael Bennet Seth Moulton Marianne Williamson For candidates deemed “major” by FiveThirtyEight. Sources: Polls, Media reports natesilver: Yeah, hitting 1 percent is soooooooooo easy. Like people can literally just pick your name at random almost. The DNC is spending too much time trying to avoid mistakes they think were made in the previous Democratic nomination process when there are probably more lessons to be learned from the Republican nomination process. geoffrey.skelley: Well, part of what the DNC wanted to avoid was the mistakes the Republicans made in the 2016 cycle with prime time and undercard debates. nrakich (Nathaniel Rakich, elections analyst): I think the Democrats have already done a better job than Republicans did in 2016. The DNC has said that they’ll randomly distribute candidates across the nights, rather than hold “varsity” and “junior varsity” debates. I think that’s a good move. natesilver: Oh, I’m not sure I agree with that, Nathaniel. nrakich: How is a junior varsity debate better, Nate? My problem with splitting the candidates up by tier is that it requires splitting hairs between a candidate who gets, say, 3 percent in a poll and a candidate who gets 4 percent. (Margins of error are real!) I guess it’s fine to argue that you think the threshold should be higher and there should be only one main debate, but if you are going to split the candidates into two debates, I think randomly doing it is the only good way. natesilver: Well, if you wind up stuck in the JV debate because you poll at 2 percent rather than at 3 percent, I don’t have much sympathy for you, even though that’s a minor difference. nrakich: But the debates are candidates’ chance to raise their polling numbers up from that 2 or 3 percent. Debates should start off inclusive but probably get less inclusive as we get closer to voting. Like, the New Hampshire debate three days before the primary should probably only have the candidates with a serious chance of winning that primary. nrakich: My beef with using polling averages as a debate criterion is that they assume that candidates can be precisely ranked by their standing in the polls. But in reality, polls are imprecise instruments, and you can’t do much more than lump candidates into rough categories (and even those have fuzzy boundaries). For example, all candidates polling between 0 and 5 percent are basically in the same spot. julia_azari: I agree with Nathaniel here. I would also add that these differences don’t, in my mind, clearly differentiate candidates. And does it really matter if it’s 20 or 22 candidates on the stage? Either isolate the top-tier candidates or let everyone in. sarahf: Julia, the number of evenings we have to devote to watching the debates is at stake! julia_azari: If other people haven’t blocked off all of 2019 and 2020 to watch debates, that’s not my problem. People want an open nomination process. This is where that goes. nrakich: Some pollsters have also said that they are uncomfortable with their work influencing elections. Their role is as measurers, not active participants. natesilver: Meh, the pollsters complain too much. If you believe in the quality of your poll, you shouldn’t have any problem with it being used as an objective metric. I think they should literally have tiers on stage based on where you’re polling. nrakich: Nate take natesilver: So like Joe Biden and Bernie Sanders are on the top tier and have big giant podiums. And Swalwell is in the cheap seats in like a broom closet. julia_azari: This chat is a serious warning about overpopulated debates, and there are only five of us. natesilver: I do think for this first debate, they might as well just let everyone in. And then set the criteria a lot higher for future debates. geoffrey.skelley: But the polling average tiebreaker might not even solve things. Say there are a few candidates who have a bunch of polls in which they are hitting only 1 percent. If the polling average can’t settle a tie, it comes down to the number of qualifying polls a candidate has. But what if three or four candidates have the same number of qualifying polls? It’s going to be a mess one way or the other. natesilver: Again, though, I’m realllllllly not sympathetic to the borderline cases. The primary has been underway for a while now, and if you can’t both get 65,000 donors AND poll at 1 percent in three polls, there’s probably something pretty wrong with you. And I’d rather give more time to, say, Cory Booker or Amy Klobuchar to make their cases and less to Eric Swalwell or Bill de Blasio. julia_azari: This is a recurring problem for parties. They try to solve a lot of these problems informally by limiting who runs.But when these conversations break down like they did in 2016, the formal solutions — like trying to come up with a fair threshold for inclusion in a debate with so many candidates — show why those problems were being solved informally: It’s a mess. natesilver: Do we think the debate rules factored into how many candidates have decided to run? Mike Gravel, whom we don’t consider a major candidate yet, explicitly seems to have run based on the possibility that he’d get 65,000 donors and therefore some sort of platform to talk about U.S. imperialism or whatever. nrakich: Good question. Probably not? There are other ways to get media attention aside from the debates — it looks like every candidate is getting a CNN town hall, for example. And a few candidates have jumped in so late that it’s not clear whether they’ll make the debates at all, like Seth Moulton and Michael Bennet. So why are they running? geoffrey.skelley: I don’t know — it could have pushed a few candidates who were on the fence. julia_azari: That’s hard to know, but what’s interesting to me is that not that long ago, debates were mostly about getting the top-tier candidates to show up. Now, even though the evidence that they matter is somewhat mixed, they’ve taken on this whole different significance because of the record number of candidates and the scramble for inclusion. sarahf: So what good are debates, Julia, especially this far out? julia_azari: Well, the default position in political science tends to be that not that many people are watching and that those who are have already made up their minds. But the latter point is a bit different for a primary debate, since partisanship doesn’t shape decisions in the same way. sarahf: Right, here at FiveThirtyEight, we’ve been saying things won’t get interesting until the debates! julia_azari: So on the one hand, there’s not really hard evidence that debates affect who wins the primary. (Studies do suggest that debates might affect citizens’ perceptions of personality and viability to win the nomination.) But usually the primary is … not that competitive. The 2008 Democratic primary really stood out in this regard, because there were two strong contenders through most of the primary season, making the contest a real competition. sarahf: Yeah, I think the debates will stand out this year, too, as they’ll be one of the first opportunities for people to get to hear from the candidates directly (outside of a CNN town hall, which, as FiveThirtyEight’s Clare Malone has noted, can be overly orchestrated to begin with). geoffrey.skelley: And primary debates can certainly make or break a candidate — earlier this year, I examined their effects. Rick Perry in the 2012 GOP primary debates really stands out to me because after he defended Texas’s in-state tuition policy for undocumented immigrants, his standing among Republicans plummeted. It was much worse than when he forgot the name of the third federal agency he wanted to dismantle! nrakich: I feel like the debates are one of the events in the Olympic Games that are the primary season. You have to participate in them and be rated favorably by the judges (the media) in order to win gold. natesilver: But quite a few people watch at least relative to the size of the Democratic electorate, don’t they? Here’s some ratings data on the 2016 Democratic primaries from Wikipedia: By comparison, 31 million people voted in the Democratic primaries in 2016. So having an audience of 16 million for the first debate isn’t bad compared with 31 million! nrakich: It’s interesting how viewership dropped off so starkly after the first debate. natesilver: That may have happened because I don’t think either Sanders or Clinton were particularly interesting debaters. They were perfectly competent, but not interesting. sarahf: Do you think candidates who go the second night will be disadvantaged? I realize Democrats aren’t splitting the debates into a varsity and JV debate, but maybe one debate will be enough for folks? geoffrey.skelley: Depends on who is in each debate. If it’s a random draw but a number of leading candidates end up in one debate, that debate will probably get the most attention. natesilver: There might be a wee bit of fatigue, Sarah, but it probably depends more on the draw. If Biden, Sanders and Warren are all on the second night, that’s the one most people will care about. But if the heavyweights are all on the first night, the second night could feel like more of a JV affair. geoffrey.skelley: Yeah, but if the heavyweights are all grouped together, I think that could still be good for some of the underdog candidates. It could give them an opportunity to stand out without facing the same “main event” vs. “undercard” judgment that was explicit in how the GOP handled things in 2016. julia_azari: I don’t know. I’m going to remain on team skepticism about 2016 Republican type ratings. It’s possible that people will tune into these debates with a genuine eye toward actually deciding between candidates or learning more about some candidates. But I don’t expect that these debates will draw in Trump-level ratings. The Democratic field is crowded, but it doesn’t have an animating rivalry between two candidates and it’s not a clown show. sarahf: … at least not yet! There’s still so much we don’t know. julia_azari: But people weren’t watching in 2016 because they wanted to hear the finer points of Marco Rubio’s tax plan vs. Ted Cruz’s. There was a show-biz factor with Trump, to put it politely. And he delivered consistently enough. nrakich: I dunno, Julia, I’m pretty worked up about the Swalwell vs. Hickenlooper rivalry. sarahf: Nathaniel Is there another debate matchup you all are looking forward to? natesilver: Trump was uniquely unpredictable in the context of the debates, so I’m not sure whether there will be a point of comparison. But you will have the dynamic of other candidates working to take the front-runner down, which has both potential risks and rewards for the front-runner. I think the first debate is probably more likely to hurt Biden than help him, however. geoffrey.skelley: The lack of a Trump-like figure will certainly make a difference. But it could get really interesting if Biden and Sanders are on stage the same night. One could easily imagine Sanders going after Biden straight away, just as he did with Hillary Clinton in 2016. natesilver: I mean, I think debates sometimes tend to cause reversion toward the fundamentals. So if we think Biden’s numbers are a little bit inflated right now by a post-announcement boost, and I think they probably are, he’s more likely to decline than improve. julia_azari: Counterpoint: Biden is actually quite good in these settings. His experience helps as he’ll be less likely to go deer-in-the-headlights on a specific question. And he really knows how to work emotion, if you recall his performance in the 2008 VP debates. natesilver: Who do we expect to be an effective debater? Kamala Harris? Elizabeth Warren? Pete Buttigieg? Although, maybe it’s not a good thing if expectations are high. Everyone’s going to expect Harris to be super incisive with every response and for Buttigieg to speak Norwegian or something. julia_azari: I am OUT if I have to learn Norwegian for these debates. I think people expect Warren to be wonky and unlikable, but my impression is that she’s actually pretty good in front of a crowd, so maybe she’ll do well. natesilver: For Warren, I think you can argue that she is someone for whom the fundamentals are misaligned. She’s an “objectively” strong candidate and “should” be doing better (I know how loaded those terms are — it’s a chat, so give me a break). Maybe the same is true for Harris. So they both stand to gain. Or to put it another way, if Harris and Warren don’t benefit from the debates, then maybe we have to start concluding that they’re products that voters just don’t like very much for whatever reason. sarahf: So who … do we think won’t make the debate stage? Because it does seem as though we’re headed toward some sort of tiebreaker, right? nrakich: Maybe Marianne Williamson? She’s the only candidate currently who’s qualified via the donors criterion but not the polling criterion. sarahf: If Marianne Williamson is the one who’s cut … it’s kind of like what was the point of the DNC introducing the 65,000-unique-donor threshold anyway. geoffrey.skelley: But Williamson only needs to earn 1 percent support in one more survey to qualify via polls. So I actually like her chances if it comes down to a polling-average tiebreaker because she might hit both the polling and donor criteria. And yeah, Sarah, that’s a big question mark: How many of the candidates who have qualified via polls but not via donors will actually get 65,000 donors? It sounds like Inslee is close on the donor count, for instance. But what about John Hickenlooper or Kirsten Gillibrand or John Delaney, etc.? I haven’t found any new information about their donor counts. natesilver: There’s no particular reason to limit it to 20 candidates instead of 21 or whatever. nrakich: We live in a base 10 world, Nate. Get used to it. natesilver: But it just sort of seems to defeat the purpose of being inclusive if you’re excluding just Williamson. Moulton might not make it. geoffrey.skelley: Yeah, Moulton is the one who is really up a creek without a polling paddle — he doesn’t have a single qualifying survey yet. nrakich: The new hot take: I should be considered a serious candidate for president even though I have raised no money whatsoever. natesilver: Sorry, but you’re not a major candidate according to our criteria, Rakich. sarahf: OK, so as we’ve discussed, there are pros and cons to having a debate stage as wide-ranging and inclusive as what the DNC has settled on. But it’s also really hard to do any of this fairly. So to end today’s chat, what would you have liked to see the DNC do differently? julia_azari: I mean, the DNC is in somewhat of a no-win position, but given that I’m not sure they can actually regain (or gain) legitimacy by having 20-candidate debates, it might have made sense to just raise the thresholds to begin with. nrakich: Overall, I think the DNC did well. The criteria are arbitrary, sure, but they’ve turned out to be well-calibrated, at least for someone like me who wants initial debates to include (almost) everyone. geoffrey.skelley: I think 10 Lincoln-Douglas debates between pairs of candidates would be the best approach. Oh sorry, Newt Gingrich took over my Slack account for a second there. But seriously, I think the DNC could’ve made a case for higher thresholds, such as polling at 2 percent instead of 1 percent. nrakich: I think this chat did convince me that stricter thresholds are appropriate for later in the primary season, closer to the actual voting. We’ll see if the DNC agrees. natesilver: I think maybe there should have been both a money qualifier and a donors qualifier for the donor threshold. Like, you have to raise donations from 65,000 people and raise at least5 million, or something.

That’s basically what airlines’ frequent flier programs do now — you have to fly a certain amount of miles and spend a certain amount of money.

nrakich: The DNC should be more like airlines — there’s a winning electoral position!

natesilver: ThE AiRLiNe InDuStRy Is UnFaIrLy MaLiGnEd

julia_azari: This debate has been canceled due to mechanical failure. Tomorrow, we fly you to Poughkeepsie instead of Atlanta.

natesilver: And if I were the DNC, I’d stipulate my criteria for future debates sooner rather than later. Because otherwise it’s going to look like they’re engineering the rules around which candidates they do/don’t like.

geoffrey.skelley: Which would defeat the point of being so inclusive in the first place.

## It Turns Out The Vintage Warriors Are Still Pretty Good At Basketball

sara.ziegler (Sara Ziegler, assistant sports editor): The NBA conference finals are just three games old, but we’ve already seen two of the most entertaining games of the entire playoffs.

After Golden State easily dispatched Portland in Game 1 in the West, Milwaukee needed a furious comeback to take down Toronto in the East’s first game. And then came Thursday night, when the Trail Blazers led the Warriors by as many as 17 points in the third quarter, but Golden State used a 27-8 run to get back into the game. The teams traded leads down the stretch, but the Warriors prevailed.

tchow (Tony Chow, video producer): The “Warriors are better without Kevin Durant” crowd has gotten REALLY loud.

I’m not stupid enough to say they’re better without KD, but I can see the argument being made that they might be more fun to watch?

natesilver (Nate Silver, editor in chief): Tony, that feels like a way to rationalize the idea that KD will feel dejected or something by the Warriors because they can win without him so he’ll have to come to the Knicks.

sara.ziegler: LOL

tchow: I’m still auditioning for my Knicks GM job, Nate.

chris.herring (Chris Herring, senior sportswriter): I think they are more fun to watch this way, for sure. It’s a good reminder of what they were before Durant ever signed with them. The up-tempo, heavy ball-movement, “we can be down by 15, but still come back to beat you” Warriors.

I think Portland losing on Thursday was pretty brutal. It’s sounding more and more like Durant won’t be back in the conference finals, and a win would have gone a long way toward making this a series again. It’s hard to imagine them winning four of the next five.

tchow: You’re not kidding about the heavy ball movement, Chris. Per Second Spectrum, the Warriors have averaged 42 more passes per 100 possessions when KD was not on the floor during these playoffs.

natesilver: I guess the question is whether the Warriors could win grind-it-out, slower-paced, half-court-type games at the same rate without KD.

chris.herring: And that’s the thing. When the Warriors play that way, it’s changing the pace of the game. If you have a game with fewer possessions, I’d venture to guess it leaves things to random chance more often and helps the underdog.

Kind of why Virginia was seen as vulnerable in the NCAA Tournament for so long. (A loss to UMBC helps with that, too.)

natesilver: Beating Portland twice at home is just not all that rigorous a test, however.

tchow: That’s important to keep in mind. All the Warriors did was hold home court.

chris.herring: It may not be. But the Blazers played really well on Thursday, and then that third quarter happened. I just think we’re used to these sorts of onslaughts at this point.

tchow: Yeah, even with that scoreline at halftime, after the first three minutes of the third quarter, I think all of us kinda went, “Oh, the Warriors are winning this.”

natesilver: The Game 6 closeout against Houston, in a game where the Rockets played pretty well, was impressive. But I’m still not sure I really have a great sense for how Golden State is going to match up with Milwaukee or Toronto, with or without KD.

sara.ziegler: A Portland win would have completely changed the tone of this series. And it was close to happening — even after the Warriors stormed back!

natesilver: “Were the Blazers actually close to winning or was it all just an illusion” is a fun epistemological question. I mean, obviously, a win probability model or whatever would have them ahead for a lot of the game. But the Warriors have made SO many third-quarter comebacks over the years that I just don’t really know.

sara.ziegler: When the Blazers were up 8 with 4:28 left, I thought they could really win it.

Silly me.

chris.herring: I grow somewhat tired of the Curry vs. Curry storyline at times. But it was pretty awesome to see Seth play so well last night, and to try to get into his brother’s head at one point.

Crazy to think that, if Pau Gasol were healthy, there would be two sets of brothers playing against each other this round.

tchow: That’s very interesting. I’m kinda loving the Curry vs. Curry storyline. It’s pretty cool IMO to have siblings play against each other at such high stakes.

I found myself pingponging between “Where’s Steph? OK, where’s Seth now?” when they were both on the court.

chris.herring: I like the storyline. I just think it’s being milked pretty heavily in terms of showing their parents in the crowd, that’s all. But Seth was huge last night.

I think the challenge for Portland is that there’s a lot of “your turn, my turn” from Damian Lillard and CJ McCollum. McCollum owned the first half, and then Dame got hot in the second half.

And it kind of feels like they may need more of a balance, or another huge bench performance from someone, to get over this hump.

natesilver: What if Seth Curry woke up one day and had Steph Curry’s skills, and vice versa? That feels like a weird/bad movie plot.

tchow: “Freaky Friday 2”

natesilver: Would the Blazers play McCollum at the 3 or something? It would be a really weird team.

chris.herring: I already feel like it’s a weird team as is.

Credit to them for adjusting heavily after how bad Game 1 was.

tchow: You knew they had to do something about that pick-and-roll defense.

chris.herring: Enes Kanter was back at the free-throw line in Game 1 and then moved much farther up to contain their pick and rolls in Game 2. That made Golden State’s looks far more challenging, which you almost have to do in order to have a chance.

sara.ziegler: The Blazers didn’t get much on offense from Kanter on Thursday, though. What was going on there?

chris.herring: His impact is going to be a bit less on a night where they shoot as well as they did from three. Because he doesn’t get any offensive rebounds that way.

But also, when he’s playing so much higher up on D, it probably wears him down a bit.

Not to mention the fact that he’s fasting during daylight hours, which seems like such a tough thing to do during such a high-stakes series.

sara.ziegler: That does seem brutal.

chris.herring: Now THAT storyline I find fascinating.

sara.ziegler: I can barely edit when I’m hungry. Can’t imagine trying to play basketball at the highest level!

natesilver: If I fasted during daylight hours, I don’t think I could even do a Slack chat, let alone play in an NBA game.

sara.ziegler: Haha

tchow: Muslim soccer players do it all the time! (during Ramadan)

It is pretty cool the Blazers have three Muslim players on the roster (Kanter, Jusuf Nurkic and Al-Farouq Aminu).

chris.herring: Hakeem Olajuwon did it as well, and apparently Kanter reached out to him to figure out what all he did to maintain his game during that stretch of the postseason.

natesilver: I didn’t realize that the dates of Ramadan shift around a lot from year to year. It doesn’t always coincide with the playoffs.

sara.ziegler: What, if anything, can the Blazers do to turn the tide as the series heads back to Portland?

chris.herring: I think it goes without saying that they did enough to win Thursday.

You’d imagine they can control the tempo better at home than they did at Oracle, where the Warriors play extremely fast and in transition during those ridiculous comebacks. I think maybe Terry Stotts would call timeout when he feels one of those runs coming on. And they need to clean up some mistakes, in terms of fouling and taking care of the ball. Andre Iguodala made a great steal on Lillard on the final play, and Lillard had that pretty brutal foul on Steph while he was shooting a three late.

tchow: I’m actually not sure what else they can do. They played well on Thursday and still lost. I feel for Portland fans, I really do. But our predictions give them a 6 percent chance of making it to the finals which seems … high?

chris.herring: Realistically, unless Golden State has another major injury, that was probably it. I don’t see a whole lot of adjustments for a scenario where you were in control most of the game. You just have to finish the game. Period.

natesilver: I guess the one piece of good news for Portland is that it’s not obvious that KD’s going to play any time soon.

tchow: Chris mentioned that they needed another huge bench performance to have a chance, but both Rodney Hood and Seth Curry had pretty decent games. I don’t know where else it could come from. Zach Collins?

sara.ziegler: Meyers Leonard! He had a pretty good game.

chris.herring: Collins had five fouls in eight minutes yesterday, somehow. Leonard was impactful, though.

tchow: Yeah, some of those Collins fouls were bad fouls, too.

chris.herring: That’s why it’s hard to see Portland doing this: Everything seems really scattered right now.

Also, props to Draymond Green for raising his game to a ridiculous level lately. You can’t mention the Warriors looking like the Warriors of old without talking about how incredible he’s been on both ends.

natesilver: Maybe Draymond secretly hates KD and so ups his effort level when KD is out?

sara.ziegler: LOL. I kind of want that to be true. Since the NBA is just a soap opera, at its core.

tchow: “The Plays of Our Lives”

I’m sorry.

sara.ziegler: OMG, yes.

Moving on to the East: Chris, you wrote after Game 1 that the Raptors would likely be kicking themselves for letting that get away from them. How important was that outcome to the series?

chris.herring: Not nearly as much of a killer as Game 2 for Portland. But still potentially big.

There’s that saying that a series hasn’t begun until a road team wins a game. And on some level, that may be true. I just think that if you’re going to beat Milwaukee, it makes sense to grab the winnable game when it’s there. And the Bucks played really poorly in some regards, yet they still won. They are a complete team, whereas the Raptors look very stilted on offense at times.

And it’s part of why I continue to like Milwaukee’s chances of winning this whole thing.

tchow: It’s been really impressive seeing how well the Bucks have continued to play when Giannis Antetokounmpo is not on the floor.

natesilver: The thing I’d hate if I were a Raptors fan is that I felt like my team played pretty well in Game 1, and it still wasn’t enough. Obviously, not everything was perfect — the cold shooting in the fourth quarter — but it felt like a relatively fair contest.

chris.herring: Yeah. I guess there are two ways to view it:

1) Lowry is probably never going to shoot like that again.

2) There’s probably no way they’ll ever get less of a contribution from the rest of the team than they did in Game 1.

tchow: 3) Brook Lopez will not have a game like that again.

sara.ziegler: Lopez was EVERYWHERE.

chris.herring: I’m not completely sure about No. 3! If Toronto doesn’t go smaller, the Raptors are going to have to sacrifice something defensively. I don’t know that he’ll have almost 30 again, but the Raps are going to dare Brook and guys like him to prove they can make that shot as opposed to letting Giannis run wild in the paint.

That’s the risk.

sara.ziegler: To your second point, Chris, you can’t imagine a scenario happening again where no Raptor aside from Lowry makes a single shot in an entire quarter.

chris.herring: Yeah, those stats — 0 for 15 aside from Lowry in the fourth, and 1 for 23 in the second half outside of Lowry and Leonard — were some of the more insane ones I’ve ever seen.

And the one second-half basket that someone else made was a buzzer-beating 3 by Pascal Siakam in the third! One he wouldn’t have even taken if not for how much time was left.

tchow: The last time Lopez had a double-double while scoring more than 20 points was … one second, I’m still scrolling up on Basketball-Reference.

sara.ziegler: LOL

chris.herring: That part is true. But him scoring a bunch wouldn’t shock me based on how they’re defending him. Brook isn’t the biggest rebounder, in part because he’s more concerned with boxing out and making sure a teammate collects the miss. (But also, their minutes are longer in the playoffs, meaning he’ll have more chances.)

tchow: Found it! Nov. 3, 2017, when he was on the Lakers. And it was the Lopez revenge game because they played the Nets.

chris.herring: Remember: Milwaukee was 11 of 44 from three! That’s 25 percent. So the Bucks left a ton of points on the table. And many of them were wide-open shots.

As I was saying, I think Toronto may want to consider playing a little smaller. That would potentially crank up the tempo to a level Lopez isn’t comfortable with, and potentially give him more defensive responsibility, to where he has to come out farther to defend.

natesilver: I dunno, I feel weird about slicing-and-dicing the Raptors’ shooting stats into so many little pieces. Overall, they shot 15 of 42 on threes, which is pretty average/good.

chris.herring: Lowry was 7 of 9 by himself!

natesilver: They didn’t shoot great on twos, but a lot of teams don’t do that well against MIlwaukee. They made 85 percent of their free throws.

chris.herring: The other Raptors will likely shoot better. But Milwaukee did plenty to make Kawhi Leonard get his points. This team is really great at pushing star scorers to drive with their weaker hand.

tchow: Sixers should take note. Too soon?

sara.ziegler: LOL

chris.herring: The statistics illustrated that in Game 1. Leonard drove 15 times, and 11 of them were to his left. During the season, he drove to his right a little more than 57 percent of the time.

sara.ziegler: That seems to be a huge focus for the Bucks — and it looks like it’s paying off. But again, the Raptors almost stole Game 1. It would be huge for them to get Game 2 tonight.

chris.herring: Agreed.

While I still think Milwaukee is clearly the stronger team in this matchup, I wouldn’t be foolish enough to say that Toronto is out of this, regardless of what happens tonight. This is a more evenly matched set of opponents than with Portland and Golden State, clearly.

sara.ziegler: So let’s end on some soft predictions. How long will each series go?

tchow: I’m predicting a gentleman’s sweep for the Western Conference finals.

natesilver: Yeah, five games seems like the smartest bet.

sara.ziegler: It would be only fair to the Curry parents.

tchow: I believe Dame and CJ can do enough to get at least one win in Portland.

chris.herring: Agreed on the West.

In the East, I’ll go six, with the Bucks winning. Though if Milwaukee wins tonight, I wouldn’t be shocked if they closed it in five.

natesilver: I’m going to go seven games for the East. Despite what I said earlier about Game 1 being a bearish indicator for Toronto, I still think they’re a liiiiiiittttle underrated, and Nick Nurse probably has more ways to make adjustments than Mike Budenholzer does.

tchow: I think it’ll be Bucks in six, too.

natesilver: I have a hot take.

sara.ziegler:

WHAT IF DURANT HAS PLAYED HIS LAST GAME FOR THE WARRIORS?!?!?

sara.ziegler: Oooooooh

tchow: * searches in google * Durant Knicks jersey

chris.herring: That doesn’t sound as crazy to me as some people might think.

If it’s a more serious strain, and it’s closer to a month than it is a one-week or two-week injury, then the NBA Finals or the middle of the finals would be more realistic for him.

But if the finals aren’t competitive …

natesilver: So Knicks fans should be rooting for a Warriors sweep?

chris.herring: I don’t know. It would be really interesting. If the Warriors win easily without him, it would be weird for him to stay if he wants validation. If the Warriors LOSE, it gets interesting. Because, obviously, the last time the Warriors lost, he went and signed with them.

tchow: I just really want Curry to win his first finals MVP trophy.

sara.ziegler: Would THAT push KD to the Knicks?

natesilver: I think the BEST-case scenario for the Knicks would be if the Warriors are like up 3-1 over Milwaukee in the finals, and then KD comes back and they LOSE.

tchow: grinchgrin.gif

Check out our latest NBA predictions.

## A Lot Of Americans Say They Don’t Want A President Who Is Over 70. Really?

Welcome to Pollapalooza, our weekly polling roundup.

## Poll of the week

Gallup recently released new data on Americans’ willingness to vote for presidential candidates with certain traits. About 1,000 adults were asked3 whether they’d vote for a well-qualified candidate who was nominated by their party and was black, gay or had one of 10 other characteristics that are rarely or never seen in presidential nominees.

Almost all Americans said they’d be comfortable voting for a woman (94 percent), or a Catholic (95 percent), Hispanic (95 percent) or black (96 percent) candidate. But there are characteristics that big swaths of Americans said would be disqualifying — in particular being older than 70, being an atheist and being a socialist.

##### What types of candidates would Americans NOT vote for?

Share of respondents to an April survey who said they would not vote for a “generally well-qualified” presidential candidate from their own party if the candidate had each of the following characteristics

Democrats Independents Republicans Overall
Socialist 24% 48% 80% 51%
Atheist 28 33 56 39
Older than 70 35 37 37 37
Muslim 14 26 62 33
Younger than 40 21 28 34 28
Gay or lesbian 17 18 39 24
Evangelical Christian 27 20 6 18
Jewish 5 9 5 7
Woman 3 6 9 6
Catholic 4 6 3 5
Hispanic 3 3 8 5
Black 1 4 5 3

Source: Gallup

These results are fairly similar to what Gallup found when it previously asked this question, in 2015. There were a couple of interesting exceptions, however. Americans in 2019 said they were slightly more comfortable with a candidate who is an evangelical Christian (the share who said they’d vote for such a candidate rose from 73 percent in 2015 to 80 percent this year) or a Muslim (from 60 percent to 66 percent). Socialists, meanwhile, remained unpopular (47 percent in both 2015 and 2019).

So with Democrats obsessed with finding an “electable” candidate, does this mean that Bernie Sanders (who’s over 70 and identifies as a democratic socialist) and Joe Biden (who’s over 70) have big problems? Not so fast. So how seriously am I taking these numbers?

For the 2020 presidential election, I’m not taking them too seriously. Thirty-seven percent of Republicans said they would not back a GOP presidential candidate over the age of 70. Well … yep, President Trump was 70 on Election Day in 2016, and he’ll be 74 in 2020. I’ll bet that more than 63 percent of Republicans will vote for him — his job approval rating among GOP voters is currently in the 90s. In short, it’s important to remember that the survey question asks about categories of people, not individuals. The negative feelings that some Americans might have toward the idea of a gay or socialist presidential candidate, for example, might not apply to Pete Buttigieg or Sanders specifically.

On the other hand, these numbers could be understating some Americans’ resistance to certain characteristics. In particular, I’d view the numbers on ethnicity, race and gender skeptically. It could be true that virtually all Americans are comfortable with a black, female or Hispanic president, as the Gallup data implies. But I’d expect Americans who aren’t comfortable to be unlikely to express that view to a pollster. So I wouldn’t use this data to suggest that, say, Julian Castro wouldn’t run into electoral problems caused by racism or Elizabeth Warren because of sexism if either were the Democratic nominee.

In terms of which groups might face overt discrimation in the U.S., I’m taking these numbers more seriously. The results generally lined up with my expectations of which categories of people Americans are both somewhat wary of and willing to say so to another person.

Being a socialist is an expression of left-wing political views, so it’s natural and unsurprising that a lot of Americans, particularly Republicans, would openly oppose a socialist candidate. Similarly, it’s not surprising that some Americans wouldn’t want a president who is in her 70s as president (maybe they suspect that person wouldn’t have the energy for the job) or who is younger than 40 (a lack of experience). This is also a view that is perhaps not particularly controversial to express — columns suggesting that Biden (76) and Sanders (77) are too old to be running for president are published regularly.

What views about candidates are more controversial? Disqualifying people based on gender, race, ethnicity or sexuality. Again, I’d expect some Americans with negative attitudes toward certain religious groups, racial groups and sexual orientations not to admit that to a pollster.

Here’s where it gets interesting, however: The share of Americans who were willing to tell a pollster that they would not back an atheist, evangelical Christian, gay or Muslim presidential candidate was nonetheless fairly high. That lines up with how these four groups are treated in American culture — they face open, direct criticism based on their identities. (I don’t want to cast all parties as equal here — Republicans’ high level of opposition to an atheist or Muslim candidate jumps out.)

In terms of understanding the diversity of the Democratic Party, I’m taking these numbers very seriously. I’ve written that Biden is essentially the candidate of the un-woke Democrat (or maybe “less woke” is more accurate) and that those voters still represent a substantial bloc of the Democratic Party. This data is more evidence of that bloc’s existence. I was surprised that the share of Democrats who are uncomfortable with an evangelical Christian president was matched by about an equal share wary of a president who is an atheist or a socialist, since the Democratic Party is often characterized as becoming less religious and more liberal on economic issues. The share of Democrats who said they would not vote for a gay or Muslim candidate was also larger than I anticipated.

## Other polling bites

• 46 percent of likely Democratic primary voters in South Carolina say they would vote for Biden, according to a new Post and Courier/Change Research poll, with only two of his rivals reaching double digits. Sanders (15 percent) and Kamala Harris (10 percent) are far behind the former vice president, as is the rest of the 2020 Democratic field.
• Biden leads in Pennsylvania too, with 39 percent of the vote, according to a new Quinnipiac University survey. The only other candidate in double digits was Sanders (13 percent).
• The Quinnipiac survey also found Biden leading Trump 53 percent to 42 percent in Pennsylvania in a hypothetical general election matchup. Sanders also bested Trump (50-43).
• In the Republican nomination contest, Trump leads former Massachusetts Gov. William Weld 72 percent to 12 percent in New Hampshire, according to a recent Monmouth University survey.
• 61 percent of Americans support same-sex marriage, and 31 percent oppose it, according to a Pew Research Center survey. Support for same-sex marriage varied by party (75 percent of Democrats and Democratic-leaning independents, compared with 44 percent of Republicans and GOP-leaning independents). It varied by race (62 percent of white Americans, 58 percent of Hispanic Americans, 51 percent of black Americans). And it varied by religion (79 percent of those who are religiously unaffiliated, 66 percent of white mainline Protestants, 61 percent of Catholics, 29 percent of white evangelical Protestants).
• 47 percent of registered voters rated the economy as “excellent” or “good,” according to a new Fox News poll.
• Also from that Fox News poll: The share of voters who said Trump hasn’t been tough enough with North Korea is up to 50 percent; that number was 19 percent in September 2017.

## Trump approval

According to FiveThirtyEight’s presidential approval tracker, 42.0 percent of Americans approve of the job Trump is doing as president, while 53.1 percent disapprove (a net approval rating of -11.1 points). At this time last week, 42.4 percent approved and 52.7 percent disapproved (for a net approval rating of -10.3 points). One month ago, Trump had an approval rating of 42.1 percent and a disapproval rating of 52.3 percent, for a net approval rating of -10.2 points.

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

## How Many Soldiers Do You Need To Beat The Night King?

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 Tom Hanrahan, three colorful journeys:

In grade school, you may have learned about the three primary colors — blue, yellow and red — and the three secondary colors — green (blue + yellow), purple (red + blue) and orange (yellow + red).

And now it’s time to put that knowledge to use. Try to get through the maze below, a nine-by-nine grid of lines, three times: once as blue, once as yellow, and once as red.

If you are blue, you may only travel on lines that include the color blue. So you may travel on lines that are blue, green, purple or white (which contains all colors). You may not travel on orange, yellow, red or black (which contains no colors). The analogous rules hold for your trips as yellow and red.

In all three cases, you are attempting to travel between the same two points on the maze’s edge. Send me links, pictures or descriptions of your strategy!

## Riddler Classic

From Greg Burnham, it had to happen eventually, at long last and not a moment too soon, The Riddler meets “Game of Thrones”:

At a pivotal moment in an epic battle between the living and the dead, the Night King, head of the army of the dead, raises all the fallen (formerly) living soldiers to join his ranks. This ability obviously presents a huge military advantage, but how big an advantage exactly?

Forget the Battle of Winterfell and model our battle as follows. Each army lines up single file, facing the other army. One soldier steps forward from each line and the pair duels — half the time the living soldier wins, half the time the dead soldier wins. If the living soldier wins, he goes to the back of his army’s line, and the dead soldier is out (the living army uses dragonglass weapons, so the dead soldier is dead forever this time). If the dead soldier wins, he goes to the back of their army’s line, but this time the (formerly) living soldier joins him there. (Reanimation is instantaneous for this Night King.) The battle continues until one army is entirely eliminated.

What starting sizes of the armies, living and dead, give each army a 50-50 chance of winning?

## Solution to last week’s Riddler Express

Congratulations to Stuart Tooley of Edinburgh, United Kingdom, winner of last week’s Riddler Express!

Last week I gave you the following sequence of numbers and asked you what number came next?

2
6
10
3
8
9
4
7
?

The correct missing number is 8.

The numerical solution actually had more to do with letters, and with my favorite game, Scrabble. Starting at the top of the list: The number 2 is spelled “two,” which is worth six points if spelled with Scrabble tiles, so 6 becomes the next number in the list. The number 6 is spelled “six” which is worth 10 points in Scrabble, so 10 comes next in the list, and so on. To find the missing number, we write 7 as “seven” and tally that it’s worth eight points, so 8 is our answer.

## Solution to last week’s Riddler Classic

Congratulations to Brian Hare of Raleigh, North Carolina, winner of last week’s Riddler Classic!

Last week we were introduced to five brothers who had joined the Riddler Baseball Independent Society, or RBIs. Each of them enjoyed a career of 20 seasons, with 160 games per season and four plate appearances per game.5 Given that their batting averages were .200, .250, .300, .350 and .400, what were each brother’s chances of beating DiMaggio’s 56-game hitting streak at some point in his career? (Streaks could span across seasons.)

Their chances of besting DiMaggio were, respectively, approximately 0, 0, 0.01, 0.8 and 13.9 percent. Put another way, their chances were roughly 1-in-9,000,000,000, 1-in-3,000,000, 1-in-8,000, 1-in-130 and 1-in-7.

To get there, first we need to compute the chances that each brother get at least one hit in any given game. Suppose a brother’s batting average is A. The chances that that brother does not get a hit in a given game is (1-A)^4, because he gets four at bats. So the chances a brother does get a hit in any given game is 1 minus that. That gives the brothers a chance of 0.5904, 0.683594, 0.7599, 0.821494 and 0.8704.

We then need to turn those individual game chances into streak chances. To put a bit of mathematical structure on this problem, we are looking for the probability $$P$$ that at least $$r$$ consecutive games with a hit appears in a sequence of total length $$n$$ games given a probability $$p$$ of a hit in each game. In our case, $$r=57$$, $$n=3,200$$ (20 seasons of 160 games), and we calculated $$p$$ in the paragraph above.

As solver Michael Branicky explained, this probability, assuming the number of games played is large enough to contain a sufficiently long streak, must satisfy the following recursion:

\begin{equation*} P_{n+1} = P_n + ( 1 – P_{n-r} ) (1-p) p^r \end{equation*}

This is because a streak of length $$r$$ in $$n+1$$ games either occurred in $$n$$ games, or occurs for the first time in game $$n + 1$$. From there, the calculation can be done with a bit of computer code. Michael also illustrated the chances of breaking the streak by a player’s batting average:

As it happened, the brothers also had a cousin with a whopping .500 average, but he would get banned from the league after 10 seasons after testing positive for performance enhancers. What were his chances of beating the streak? Despite the shortened career, they were about 93.3 percent, an answer we can arrive at with the same approach described above.

As solver Chris Jones concluded, “Moral of the story: Doping pays off for record-breaking, bros.”

## 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]

CORRECTION (May 17, 2019, 10:48 a.m.): An earlier version of the Riddler Express displayed the wrong color for one line. The leftmost horizontal bar in the fourth row from the top should be white, not black. The graphic has been updated.