Significant Digits For Wednesday, July 31, 2019

You’re reading Significant Digits, a daily digest of the numbers tucked inside the news.

Dozens of families

At least dozens of wealthy families in suburban Chicago are ceding the legal guardianship of their college-bound children to “a friend, aunt, cousin or grandparent” so that these children can call themselves financially independent and thereby qualify for federal and state financial aid. “It’s a scam,” the director of undergraduate admissions at the University of Illinois at Urbana-Champaign told ProPublica. [ProPublica]

200 million “bathroom miniatures”

By 2021, InterContinental Hotels Group, the owner of Holiday Inn, plans to swap out the 200 million “bathroom miniatures” — those little shampoos and so forth — that it uses in its 843,000 guest rooms each year in favor of bulk-size amenities in an environmentally-minded effort to cut plastic waste. Guess we’ll just have to find new stuff to steal. [Associated Press]

3-meter-wide ball

Scientists at the University of Wisconsin, Madison, built a 3-meter-wide plasma containment chamber called the Big Red Ball, inside of which they created a model of the mysterious, charged, flowing environment of the sun. Their experiment, published in Nature Physics, was “able to mimic a region around the sun where the plasma hangs in a precarious balance.” [Quanta Magazine]

224 fights

There were a total of 224 fights in the 1,271 regular season games of the 2018-19 NHL campaign. That number was down from 280 fights the season before, and in fact the number of fights has dropped every season for the past decade from a high of 734. Why? “Today, the fourth-liners are cost-efficient skill players instead of goons, and staged fights are a rarity without those pugilists on the rosters,” Greg Wyshynski writes. [ESPN]

2-second clip

Kraftwerk, the pioneering German electronic band, has won a 20-year case in the European Court of Justice concerning a 2-second clip of its song “Metal on Metal.” The court ruled that two hip-hop producers could not sample the track without permission. The ruling “could have huge implications for the music industry” and also comes as an American court ruled against Katy Perry, holding that she copied 2013’s “Dark Horse” from a Christian rap song that Perry claims she had never heard. [BBC]

2.12 carats

A Nebraska schoolteacher visiting Crater of Diamonds State Park in Arkansas discovered, well, a diamond. A 2.12-carat diamond, to be precise, the largest of the 300 or so found at the park this year, where visitors pay up to $10 to search a 37-acre field on top of a volcanic crater. However, the raw brown diamond, large though it may be, is probably only worth about $1,000, based on comparable stones for sale online. [The Washington Post]

From ABC News:
SigDigs: July 31, 2019

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What We’re Watching For In The Second Democratic Debate

Welcome to FiveThirtyEight’s weekly politics chat. The transcript below has been lightly edited.

sarahf (Sarah Frostenson, politics editor): It’s hard to believe it’s been a month, but the Democratic primary debates are baaack. And on Tuesday and Wednesday evening, 20 candidates (10 each night) will take the stage, with one potentially big new showdown (Elizabeth Warren vs. Bernie Sanders) on the first night and one big rematch (Kamala Harris vs. Joe Biden) on the second night.

For reference, here’s Tuesday’s lineup: Bernie Sanders, Elizabeth Warren, Pete Buttigieg, Beto O’Rourke, Amy Klobuchar, Marianne Williamson, John Delaney, John Hickenlooper, Tim Ryan, Steve Bullock.

And Wednesday’s: Joe Biden, Kamala Harris, Cory Booker, Andrew Yang, Julián Castro, Tulsi Gabbard, Michael Bennet, Jay Inslee, Kirsten Gillibrand, Bill de Blasio.

So yes, let’s talk about the lineups and matchups, but first let’s also take a step back to talk about the role of primary debates — how do they change the race?

nrakich (Nathaniel Rakich, elections analyst): I think it’s clear that debates can change the race. But the effects might be fleeting, as after one debate the race might move in one direction while subsequent debates might push things in a different direction.

natesilver (Nate Silver, editor in chief): Debates also tend to ramp up in importance as the campaign goes along. It might feel like we’ve been covering this race forever. But we’re still in the rather early stages, as far as voters are concerned.

julia_azari (Julia Azari, political science professor at Marquette University and FiveThirtyEight contributor): I think I might have a slightly different take on this than Nate. My sense, based on the research, is that the debates will produce diminishing returns as opinions become solidified, but that might apply more for minor candidates than for contention between major ones like Harris and Biden. (Though there’s still a notable big name-recognition gap between the two.)

nrakich: I’m with Julia on this one. In 2016, the first Democratic primary debate had the highest ratings.

natesilver: But in some sense, the purpose of these early, very-inclusive debates is to see if any of the minor candidates can break through. Which didn’t really happen after the Miami debates, although you could argue the case for Castro I guess.

sarahf: Castro was interesting. His favorability numbers shot up, but he didn’t really see as much of a swing in support, or at least that is what we found in our poll with Morning Consult.

nrakich: But Castro is a great example of someone for whom the debates could build on each other to increase his support. He got people’s attention in the first debate; maybe, with another good moment this week, he’ll start to get their support. Or at least get enough backing to clear the third-debate thresholds.

natesilver: I’m skeptical that Castro is likely to break through. I mean, shouldn’t we take the opposite lesson from the first debates, in fact? That you can have a good debate and it doesn’t help you break through because the top of the field is pretty entrenched?

nrakich: We didn’t say he was likely to, though — just that the possibility existed.

He’s already at 130,000 donors, the threshold for the third debate, in large part due to his first debate performance.

natesilver: I guess I’m just saying that I think people are maybe underestimating how much voters like the top-tier candidates when they say they expect a middle-tier candidate to break out.

julia_azari: What we’ve seen so far leaves me questioning whether the top tier is really open to newcomers at this point. I think there’s contention over who will be in that second tier of candidates who meet the requirements for the fall debates, but most of those candidates won’t come close to winning the nomination.

sarahf: Or maybe even making the next debate!

This might be the last time we see many of these candidates on stage because September’s qualifying thresholds will be difficult for them to meet. (Candidates must have at least 2 percent support in four recent qualifying polls1 and 130,000 unique donors.2)

natesilver: There are a lot of middle-tier candidates, so what are the odds that at least one of them will break into the top tier at some point in the race? Maybe fairly high. Let’s say it’s 60 percent, just to make a number up. But that 60 percent is divided between a lot of different candidates.

sarahf: OK, so as to this top-tier vs. middle-tier debate …

Let’s look at night one and unpack some of the dynamics there. As a reminder, night one includes: Sanders, Warren, Buttigieg, O’Rourke, Klobuchar, Williamson, Delaney, Hickenlooper, Ryan, Bullock.

So given the lineup, there’s potential that some of the more moderate candidates — say, Buttigieg, O’Rourke and Klobuchar — maybe try to position themselves against Warren or Sanders, right? And that can maybe help them break through to the top tier? Or at least make the top tier look less fixed?

julia_azari: Yeah, “Can a middle-tier candidate move up?” seems like the unofficial slogan of night one.

sarahf: More so than night two?

julia_azari: I think so. But I reserve the right to flip-flop if one of you convinces me.

nrakich: Agreed, and in fact I’d pay even closer attention to the lower-tier candidates: Hickenlooper, Ryan, Bullock, Delaney. They know that this is their last chance to make a splash before the third debate’s stricter thresholds. And they all have little love for Sanders’s socialism/Warren’s progressivism.

I think they will lash out pretty hard.

julia_azari: And, in fact, I might convince myself to flip-flop because of the timing. If Buttigieg, O’Rourke or Klobuchar has a strong performance (say, on the level of Castro last time) and emerges as the official Biden Alternative for the Heartland Moderate (or whatever, don’t @ me), I think there’s still a strong chance that something else happens on night two that overshadows it.

nrakich: I also think the potential for Sanders-Warren fireworks is overrated. Despite their ideological similarities, they aren’t really competing for the same bloc of voters. Warren supporters are more likely to be higher-income or have a college degree, while Sanders’s support is more working-class.

natesilver: I strongly disagree with Rakich on the Sanders-Warren lanes thing!

sarahf: 🍿

nrakich: 🎆

natesilver: 🍿

sarahf: Finally, the two in-house Nathaniels fighting!

julia_azari: I’m just here for the ratio.

natesilver: But OK, I don’t think looking at the characteristics of Sanders’s current voters is the right way to go about it.

Because he’s lost a shit-ton of support since his last presidential run.

Roughly two-thirds of his supporters from 2016 have gone to other candidates. We know that because he got more than 40 percent of the vote then and is now polling in the mid-teens.

And a lot of those voters probably went to Warren.

Probably some went to Buttigieg, Biden, etc. too.

nrakich: Indeed — according to an Emerson poll conducted earlier this month, 25 percent of Sanders’s 2016 voters still support him, but 20 percent now support Biden, 15 percent support Warren, and 9 percent support Harris.

natesilver: I’m just saying, Sanders has already lost a lot of the voters that he was gonna lose to Warren. Maybe he lost most of them at the start of the cycle and then a few more as she’s gradually gained ground. The voters who are still with Sanders now might be fairly lukewarm on Warren, but that reflects a type of selection bias: They’re the ones who haven’t defected to Warren yet.

nrakich: I take your question, Nate.

And I agree with you generally that Sanders needs to go on the attack more. But that doesn’t necessarily mean he will. Especially when he and Warren are reportedly good friends.

natesilver: Friends, schmends, people are trying to WIN THE PRESIDENCY!!!!

sarahf: And what does that mean for the debate? Does Sanders have an incentive to go hard on Warren?

natesilver: Sanders probably — maybe definitely — needs some of Warren’s current voters to have a shot at the nomination. It doesn’t necessarily mean he needs to go after her, though, which could fairly easily backfire.

His staff, at times, has seemed a little prickly about Warren. Maybe they thought it was Sanders’s turn — he was the second-place finisher last time, after all. But she’s the one who seems to have momentum and whose chances the media is taking more seriously.

But, again, that doesn’t necessarily mean it’s a good look for Sanders to go after her. I’m not sure what he’d even say, exactly.

He has, at times, tried to emphasize his electability vis-a-vis Warren, a strategy that I think is a bit dubious.

nrakich: I feel like that won’t win him a lot of friends among people who already don’t like the way he treated the last woman he faced in a primary.

natesilver: He has sometimes tried to act like he was the OG Democratic Socialist and she’s stepping on his turf, which I don’t think is a particularly compelling message either.

julia_azari: One thing I want to note about Warren and Sanders is how we (media, voters, everyone) understand what goes on within parties in a nomination contest. Because you essentially have two people competing who have somewhat different approaches to their shared ideological lane. So is this competition about candidates and their personalities? Or is it about which approach gets to bear the standard for the economically left wing of the party? It’s kind of remarkable that we’re seeing public contestation at this level — not just between factions but within them.

nrakich: I definitely think it’s a competition of personalities, not ideologies. I think a lot of elites who support Warren really don’t like Sanders because of his “revolution” rhetoric and somewhat ornery personality.

sarahf: What are some other dynamics we expect on night one? Do we think, tactically speaking, it makes sense for the other candidates to position themselves against the front-runners, i.e. Warren and Sanders?

natesilver: I think it makes sense for Klobuchar to push back against them.

nrakich: Yeah, I think it makes a lot of sense for the moderates like Klobuchar, Hickenlooper and Delaney to set themselves up as a foil against Sanders or Warren.

julia_azari: The smart move for Klobuchar-O’Rourke-Buttigieg is to try to emerge as the leader of that pack. I think, if we conceptualize the nomination as a process of coalition-building, there’s potential for Klobuchar to build on her status as a woman, a Midwesterner and a pragmatic candidate. But the staff stuff may have sunk her, I don’t know.

natesilver: Klobuchar might actually have a shot at the nomination. I’m not sure I care what Delaney does though.

nrakich: DeLaNeY sHoUlD bE aT cEnTeR sTaGe

(Nate, did I do that right?)

natesilver: I don’t think you can troll effectively with Delaney.

It’s not like Yang or Williamson, where there’s something inherently trollish about their candidacies.

sarahf: And Steve Bullock, while I don’t think he has a shot at winning the nomination, could still be an interesting addition. At the very least, he wasn’t in the first debate, so voters won’t have heard him make his case yet.

nrakich: Yes, Bullock is a strong candidate on paper: two-term governor of a red state, and he has some institutional support in Iowa. Unlike some of the other lower-tier candidates, you can see a path to the nomination for him, however faintly.

But I would guess that virtually no one has heard words come out of his mouth, so this week will be big for him.

julia_azari: Bullock also has anti-establishment cred from being excluded from the first debate. Will anyone care? I don’t know. As someone writing about party legitimacy, I’m way into watching that unfold.

natesilver: Overall, the moderates would rather be on the stage against Biden, no?

nrakich: Yeah, I think so, Nate, but with Sanders, they’ll still have material to work with.

sarahf: Is the idea here it’s better to be on a stage where you can show what you have in common with someone who’s polling better than you? Rather than showing how you’re different?

julia_azari: Yeah, I think this debate might be a good test of whether it’s good for these kinds of candidates to be on a stage with the front-runner in their “lane” or if it’s better to go up against the front-runner not in their “lane” to establish themselves as the main alternative.

nrakich: I think it’s just because you can make the most effective attack on Biden in person (as Harris showed), and if it lands, you’re likely to be the beneficiary.

natesilver: I think a lot of the moderates need Biden to implode to have a shot, so you’d rather just be on the stage with him so that you can benefit directly from him imploding. It’s harder if you have to count on a parlay of you doing well in one debate and then Biden doing poorly in the other debate but somehow none of the candidates from the other debate get credit for dismantling Biden.

sarahf: OK, on to night two!

Reminder, the stage is: Biden, Harris, Booker, Yang, Castro, Gabbard, Bennet, Inslee, Gillibrand, de Blasio.

nrakich: All of the nonwhite candidates are debating on this night. I find this fascinating.

Also, Biden sharing the stage with them is fascinating.

Harris and Booker in particular have shown that they are eager to attack Biden on racial-justice issues.

sarahf: Right, and we’ve got the potential for a rematch on our hands. What are the non-probabilistic odds, you think, that Harris and Biden spar again?

nrakich: High.

And I think Biden will be readier for it. (Or at least he should be — he has no excuse now.)

natesilver: I think Harris-Biden Round 2 is fairly likely to be the headline that emerges, yeah.

sarahf: My bet is that Booker joins the headline, largely because, as Nathaniel mentioned earlier, he’s also taken Biden to task on issues of race.

Booker also is a pretty strong debater, I think.

natesilver: Could Harris, in theory, rely on Booker to be the more aggressive one and try to remain a bit above the fray?

I’m not saying it’s a good strategy or a bad strategy, but it’s one she could consider.

Biden is still very popular with Democrats and she doesn’t necessarily want to alienate his voters.

julia_azari: I think that’s definitely a possibility and a strategy she could consider. The dilemma with tackling Biden’s record on race is that candidates may want to do it as long as something like reparations isn’t pinned to them when the general election rolls around. Not saying this is right or wrong morally or strategically, but I do think it’s a calculation.

And to some degree, I think that’s sorta the larger dilemma of this primary (I’m really liking the word “dilemma” today, leaning into it) — how does one compete fiercely in this kind of field without alienating the supporters of other candidates?

sarahf: And as we’ve talked about before, if Biden were to falter, both Harris and Booker have some chance of benefiting from supporters switching to them instead. So it will be a fine balance between weakening Biden while not alienating his base too much.

nrakich: FWIW, I think Harris’s attack in the first debate was excellent precisely because it conveyed respect to Biden while also totally destroying him.

sarahf: Yeah, she even started her attack by saying how much she respected Biden.

natesilver: Ohhhh I don’t really think it conveyed much respect.

I mean, it wasn’t out of bounds.

But saying you respect someone as a rhetorical strategy is only loosely correlated with actually conveying respect.

julia_azari: I’m not sure about the respect thing either.

But I think it was a great piece of political theater, and there’s some evidence that debates are good for changing people’s impressions of how viable or electable a candidate is. Harris perhaps helped people envision her on a debate stage with Trump.

nrakich: I have no idea if Harris actually respects Biden, but it’s about how people interpret it, and I think she managed to land a devastating attack in a way that didn’t come off as mean. So I don’t think it alienated anyone but the most diehard Biden fans who think he is above reproach.

Harris’s unfavorable rating went up just 1.4 points after the debate, according to our tracking poll, so few voters seemed put off by her approach.

sarahf: OK, let’s wrap. Top line, what will you be looking for on Tuesday and Wednesday?

nrakich: It’s kind of a boring answer, but I’ll again be looking to see if any of the middle- or lower-tier candidates have a moment that earns them a burst in support. Otherwise, it’s going to be the same old cast of characters on the September stage, and you’ll probably see multiple people drop out. (Note: That may happen anyway.)

natesilver: I’d be interested in if O’Rourke, Buttigieg and/or Klobuchar explicitly play to the center.

Klobuchar seemed reluctant to do that in the first debate.

julia_azari: The four things I’ll be looking for are: 1) movement among top-tier candidates; 2) the porousness of the top tier, i.e. can anyone else get into it; 3) who is competing against whom (e.g. what “lanes” emerge); and 4) what issues emerge as the ones that will define the primary race?

Because how the candidates link themselves to and prioritize issues might give us a sense of how fault lines will emerge as the primary season progresses.

FiveThirtyEight's most memorable debate moments

15 Percent Is Not A Magic Number For Primary Delegates

If you hear the phrase “delegate math” and remember 2016, you might have some nightmares. That’s because Republicans, who briefly kinda sorta looked like they might have a contested convention, have incredibly complicated delegate-allocation rules. Some states were winner-take-all in the GOP primaries. Some were proportional. Some states didn’t even really vote at all (!) or had voters chose delegates directly. It was a mess.

Democratic delegate rules are far more uniform from state to state — and they’re much simpler. But there are a couple of nuances that I can imagine people are going to get wrong.

One of them concerns the 15 percent threshold, which is a number that you’re going to be hearing a lot about. Democrats allocate their delegates proportionately among candidates who get 15 percent or more of the vote in a given state or district. So, for instance, if Bernie Sanders gets 42 percent of the vote in a certain state, Kamala Harris gets 18 percent, Joe Biden gets 14 percent, Pete Buttigieg gets 11 percent, Cory Booker gets 10 percent and Marianne Williamson gets 5 percent, then only Sanders and Harris would get state-level delegates, with Sanders getting 70 percent of the delegates1 and Harris getting the other 30 percent.

The part that’s easy to miss is in that term state-level delegates. In the Democratic primaries, only about 35 percent of delegates are actually allocated at the state level. The remaining 65 percent are allocated by district — usually by congressional district, although some states use different methods such as by county (Montana and Delaware) or state legislative districts (Texas and New Jersey).

This can make a big difference. In the example above, for instance, if Biden were to get 14 percent of the vote statewide, he probably would get some delegates because he’d likely be at or above 15 percent in at least some districts.

How many delegates is harder to say; it depends on how much variation there is from district to district. But for some rough guidance, I looked back at candidates who finished with between 10 and 20 percent of the vote in the Republican primaries in 20162 in states that allocated some of their delegates by congressional district.3 In the average district, there was about a 3-point gap between a candidate’s statewide vote share and that candidate’s districtwide vote share.

By performing a little math,4 we can extrapolate how many district delegates we’d expect a candidate to get given a certain statewide vote share. For instance, a candidate who gets 14 percent of the vote statewide, as Biden did in this example, would expect to achieve at least 15 percent in somewhere around 40 percent of districts, thereby receiving delegates there. Even a candidate who got 10 percent of the vote or less statewide might have a couple of strong districts where he or she received delegates, especially in a large, diverse state such as California.

On the flip side, a candidate who finished just above 15 percent statewide, such as Harris’s 18 percent in this example, would probably still miss out on a few district-level delegates by falling below 15 percent in some districts.

Overall, considering both state and district delegates, the relationship between statewide vote share and the share of statewide delegates looks something like this:

There’s still a big spike at 15 percent when the statewide delegates kick in, but it isn’t completely an all-or-nothing proposition; you’ll still get some delegates if you finish a bit below 15 percent, and you’ll still miss out on some if you finish just above 15 percent. The safest bet, of course, is to finish at 20 percent or higher, in which case you’ll not only get almost all of your delegates but will also have the chance to actually win the state.

Can We Play NBA Jam … With MLB Teams?

It takes an entire 25-man roster to make a winning baseball team — just ask the defending-champion Boston Red Sox. Sure, Boston had plenty of top-line talent at its disposal, but it also got key playoff contributions from the likes of Steve Pearce and Nathan Eovaldi, neither of whom was especially heralded when the Red Sox picked them up in midseason deals. Postseason history is littered with similarly unsung heroes from down the roster who step up in big moments.

But what if teams didn’t need to rely on all of those non-star contributions? Instead, we want to find the opposite: teams that are too top-heavy, with lots of star power but few quality role players to help fill out the rest of the roster. These are teams who lack for diamonds in the rough — though the stars sure do shine brightly.

For instance, if there was an NBA Jam for baseball, where teams could only use two players (let’s say a pitcher and a hitter), which club would come out on top? Here are the best team hitter-pitcher tandems in MLB this season,1 according to the sum of the wins above replacement2 per 162 games across both players:

Major League Baseball’s most dynamic duos of 2019

MLB teams with the best combination of a top hitter and top pitcher, according to the sum of both players’ WAR per 162 games

Rk Team Top Batter (WAR/162) Top Pitcher (WAR/162) Sum
1 Dodgers Cody Bellinger 10.1 Hyun-Jin Ryu 6.1 16.2
2 Nationals Anthony Rendon 5.9 Max Scherzer 9.0 14.9
3 Brewers Christian Yelich 9.3 Brandon Woodruff 4.3 13.6
4 Diamondbacks Ketel Marte 7.4 Zack Greinke 5.6 13.1
5 Angels Mike Trout 10.5 Ty Buttrey 2.6 13.1
6 Astros Alex Bregman 7.0 Gerrit Cole 5.9 12.9
7 Rangers Joey Gallo 5.1 Lance Lynn 7.6 12.6
8 Mets Pete Alonso 6.1 Jacob deGrom 5.7 11.8
9 White Sox Yoan Moncada 5.2 Lucas Giolito 6.2 11.3
10 Athletics Matt Chapman 7.3 Frankie Montas 4.0 11.3
11 Twins Jorge Polanco 6.7 Jose Berrios 4.6 11.3
12 Red Sox Xander Bogaerts 6.7 Chris Sale 4.3 11.0
13 Cubs Kris Bryant 6.3 Cole Hamels 4.4 10.7
14 Rockies Trevor Story 6.0 Jon Gray 4.6 10.7
15 Braves Ronald Acuna Jr. 5.8 Mike Soroka 4.7 10.5
16 Rays Brandon Lowe 4.2 Charlie Morton 5.8 10.0
17 Yankees DJ LeMahieu 6.7 Masahiro Tanaka 3.1 9.8
18 Indians Carlos Santana 4.9 Shane Bieber 4.6 9.5
19 Padres Fernando Tatis Jr. 5.5 Kirby Yates 4.0 9.5
20 Reds Eugenio Suarez 3.1 Luis Castillo 5.4 8.6
21 Phillies J.T. Realmuto 4.1 Aaron Nola 3.8 7.9
22 Blue Jays Eric Sogard 3.2 Marcus Stroman 4.3 7.6
23 Tigers Nicholas Castellanos 2.4 Matthew Boyd 5.1 7.5
24 Pirates Josh Bell 4.1 Joe Musgrove 3.1 7.2
25 Royals Whit Merrifield 4.5 Brad Keller 2.6 7.1
26 Orioles Trey Mancini 2.7 John Means 4.3 7.0
27 Cardinals Paul DeJong 4.4 Jack Flaherty 2.2 6.6
28 Marlins Miguel Rojas 3.2 Caleb Smith 2.9 6.0
29 Mariners Edwin Encarnacion* 2.9 Marco Gonzales 3.0 5.9
30 Giants Evan Longoria 2.5 Madison Bumgarner 3.1 5.6

* Player is no longer with club. Data through July 23.

WAR is based on JEFFBAGWELL — the Joint Estimate Featuring FanGraphs and B-R Aggregated to Generate WAR, Equally Leveling Lists.


In terms of two-man teams, the Los Angeles Dodgers’ combination of Cody Bellinger (10.1 WAR per 162) and Hyun-Jin Ryu (6.1) is easily the best in baseball this year. The former is having one of the best seasons in baseball history, and the latter has been the surprising pillar of one of baseball’s best rotations. Bellinger’s ability to play three outfield positions plus first base also helps in this hypothetical universe where he has to field all of the balls hitters put in play against Ryu. (In related news, no, I didn’t completely think through the mechanics of how MLB Jam would work.)

Of course, the Dodgers are also arguably baseball’s best team in the real world. So that doesn’t do us much good here; we are, after all, looking for the teams whose fortunes would change the most depending on whether we look at their stars or the entire team. To that end, let’s break down the teams with the biggest differences in WAR ranking between their top hitter-pitcher duo and their full roster.

According to that method, the team that would most benefit from an MLB Jam-style roster construction is the Chicago White Sox, whose top pairing of pitcher Lucas Giolito (6.2 WAR/162) and third baseman Yoan Moncada (5.2) is ninth among pitcher-batter combos. That placement for Giolito and Moncada is much higher than the White Sox’s overall team ranking in WAR (No. 26), making them baseball’s top-heaviest team in terms of leading twosomes. The Pale Hose edge out the Texas Rangers, whose top combo of pitcher Lance Lynn (7.6) and Joey Gallo (5.1) ranks seventh in MLB despite the team sitting only 15th in WAR overall.

The Tampa Bay Rays, meanwhile, are on the opposite end of the spectrum to the White Sox and Rangers. Their leading duo of pitcher Charlie Morton (5.8 WAR/162) and second baseman Brandon Lowe (4.2) ranks just 16th among MLB’s top 1-2 hitter-pitcher punches, but Tampa as a whole is fourth in WAR on the basis of its impressive depth. Eleven different Rays are on pace for at least 2.0 WAR — the mark of a solid season — and, perhaps more importantly, only 10 Rays have 0.0 WAR or fewer (which is tied for the fewest of any team). Although Tampa Bay lacks star power, it has been able to build its 47 percent playoff probability by avoiding what Jay Jaffe calls “replacement-level killers”: players who produce little or no value in substantial playing time.

Expanding the scope to the top five players on each team — and now looking at the ranking irrespective of positions — the Colorado Rockies emerge as another markedly top-heavy team. Colorado has four players on pace for at least 4.0 WAR — shortstop Trevor Story (6.0), third baseman Nolan Arenado (5.2), and pitchers German Marquez (4.7) and Jon Gray (4.0) — which helps to drive a top five tally that ranks 14th in the league. However, the Rockies also have 22 players producing at or below the replacement level. Several of those players were expected to have much better seasons (most notably Kyle Freeland and Daniel Murphy), but their actual performances have left Colorado ranking 22nd overall in spite of its productive core.

A similar top-heavy split applies to the Milwaukee Brewers and Washington Nationals. Milwaukee‘s top five is led by reigning National League MVP Christian Yelich (9.3 WAR/162) and rounded out by Brandon Woodruff (5.0), Mike Moustakas (4.6), Yasmani Grandal (4.3) and ghost-ball master Josh Hader (2.8). Given that group, it would seem impossible that the Brewers are merely an average team (14th in MLB) according to overall WAR. Milwaukee’s problem isn’t even that the team uses a ton of replacement-level scrubs — it’s just that the Brewers lack solid role players beyond their top handful of stars. (In no small part due to down years from Lorenzo Cain, Jesus Aguilar, Jhoulys Chacin and Travis Shaw.)

The Nationals are in a comparable situation. In terms of star-level production, you’d take Washington’s top-line group — Max Scherzer (9.0 WAR/162), Stephen Strasburg (6.8), Anthony Rendon (5.9), Patrick Corbin (5.1) and Juan Soto (3.6) — against just about anybody’s in baseball. By WAR, only the Dodgers have a better top five than the Nats, and only the Dodgers and Houston Astros have a better top 10. Yet Washington only ranks 10th in total WAR because the supporting cast has largely failed to meet expectations. (Trea Turner counts among that group, though his recent hot streak — highlighted by hitting for the cycle Tuesday — could at least signal another top performer reemerging in Washington’s galaxy of stars.)

Finally, you have the New York Yankees who, like the Rays, consistently show up as a better overall team than their top performers would indicate. For instance, New York leaders DJ LeMahieu (6.7 WAR/162) and Aaron Judge (4.2) only rank 15th in tandem WAR — and the team’s top 10 also ranks just 15th — despite the Yankees ranking fifth in overall WAR. Some of that is a bit misleading because of the Yankees’ injury problems: Judge, Giancarlo Stanton, Didi Gregorius, Aaron Hicks and Miguel Andujar have all missed significant playing time this year, among others. But it also speaks to how deep the Yankees’ roster truly is, with lesser-known contributors such as Luke Voit, Mike Tauchman and Gio Urshela keeping the team afloat in the face of so many star absences.

If you had the choice, clearly it’s ideal to be a team like the Dodgers, who have the best star power and the best supporting cast. But teams like the Rays and Yankees prove that a deep stable of contributors can outperform more star-powered teams such as the Nationals, Brewers, Rockies, White Sox and Rangers — even if the latter group of teams would be a lot better if we could just play baseball using “NBA Jam” rules.

Check out our latest MLB predictions.

Is The NBA’s Small-Ball Revolution About To End?

It’s rare in life that you can look back and identify the specific moment that marked the end of the way things were and the beginning of the way things are. That is not the case when it comes to the creation of the style of play that dominates the modern NBA, which now sees teams eschewing size advantages in favor of loading the floor with as much shooting as possible. It’s worth examining the origins of the small-ball revolution, even if there are indications that the trend may reverse itself — perhaps as soon as this season.

Though the seeds for this shift were planted by teams like the Houston Rockets of the mid-1990s, the Phoenix Suns of the 2000s and, particularly, the 2009 Orlando Magic, everything changed for good on May 13, 2012. During the Miami Heat’s 95-86 win over the Indiana Pacers in Game 1 of the 2012 Eastern Conference semifinals, Heat star Chris Bosh suffered an abdominal strain and was ruled out indefinitely.

To that point in both the regular season and the playoffs, the 6-foot-11 Bosh had played almost exclusively at power forward. He’d played 2,174 minutes combined regular season and postseason minutes, spending 1,901 of them (87.4 percent) next to one of Joel Anthony, Udonis Haslem, Ronny Turiaf, Dexter Pittman or Eddy Curry in the frontcourt.1 With Bosh sidelined for the remainder of that Pacers series and the first four games of the ensuing Eastern Conference Finals against the Boston Celtics, however, Heat coach Erik Spoelstra slid the 6-foot-8 Shane Battier into the starting lineup in his place.

Battier had played just 3 percent of his regular-season minutes at power forward in 2011-12, per Basketball-Reference, but he remained in the role for the rest of Miami’s run to the 2012 title. Bosh returned at first as a reserve. But when he moved back into the starting lineup for Game 2 of the NBA Finals, it was as a center next to Battier and LeBron James in the frontcourt. With that group providing more space in which James and Dwyane Wade could operate, the Heat blitzed the Oklahoma City Thunder with four straight wins, capturing the first of two championships of the Big Three era.

After the Heat rode the same configuration to another championship in 2013, the NBA saw a massive drop in two-big lineup usage the following season. That trend may have steadily continued anyway, but it was hastened by the Golden State Warriors going even smaller, playing the 6-foot-7 Draymond Green at center in order to beat LeBron’s Cleveland Cavaliers teams. Pretty soon, damn near the whole league was reorienting around trying to compete with the Warriors’ Death Lineup.

Consider the following chart, which plots regular-season “two-big” lineup usage for each of the NBA’s 30 teams, as well as the league average, from the beginning of the Heat’s Big Three era through the just-completed 2018-19 campaign. See if you can identify the turning point; it should be pretty easy.2

Two-big lineup usage peaked at 58.8 percent of minutes leaguewide during the 2011-12 season, but the shift to small ball sliced that number in half within four seasons. Last season, two-big lineups played just 6.4 percent of regular-season minutes. During LeBron, Wade and Bosh’s second season together, 19 of the league’s 30 teams used two-big lineups at least 50 percent of the time. Last season, no team even crossed the 40 percent mark in two-big lineup minutes.

Such a stark trend might make it seem like we have reached a point of no return. But given several developments of this offseason’s free-agent period, it seems fair to wonder whether we may have actually passed Peak Small Ball and might be in for a reversal during the 2019-20 campaign.

The Philadelphia 76ers, for example, signed Celtics center Al Horford to a four-year deal, and presumably plan to play him as their primary power forward alongside Joel Embiid. Contrary to popular belief, the 6-foot-10 Horford has actually been a center for the majority of his career — he’s played 83 percent of his minutes at the position, per Basketball-Reference — but Celtics general manager Danny Ainge has said that he believes a desire to return to the power forward slot — where Horford played in college — factored into his decision.

Assuming Ainge is correct, Horford is not the only big who’s moved to a new team hoping to slide back to the four. New Los Angeles Lakers star Anthony Davis expressed a firm desire to resume playing the four during his introductory press conference. According to Basketball-Reference, Davis has spent 55 percent of his career at center, peaking last season at 96 percent.

Other teams’ offseason moves indicate they could potentially lean into two-big lineups as well.

The Sacramento Kings signed centers Dewayne Dedmon and Richaun Holmes, who could potentially play either together or alongside Harry Giles. The Portland Trail Blazers let small-ball power forward Al-Farouq Aminu leave in free agency and traded combo forward Moe Harkless, at the same time adding former Heat center Hassan Whiteside to last season’s primary starter Jusuf Nurkić,3 and they seemingly plan to start former backup center Zach Collins at power forward.

The New York Knicks have Mitchell Robinson as their presumed starting center and should probably let 2018 lottery pick Kevin Knox play at least some of his minutes at power forward; but they still used a significant portion of their free-agent budget to sign non-shooting power forward Taj Gibson, as well as Bobby Portis, who in a 28-game stint with the Wizards last season played 77 percent of his minutes at center. Even the team’s most high-profile signing, Julius Randle, only started shooting threes last season, and he often gets treated by opposing defenses as a non-shooting big man.

The Indiana Pacers let power forward Thaddeus Young and small forward Bojan Bogdanovic leave in free agency, and plan to start backup center Domantas Sabonis at power forward next to Myles Turner, who has been the starting center since midway through his rookie season. Sabonis has played 79 percent of his minutes at center with the Pacers, per Basketball-Reference, but he was primarily a power forward both in college and during his rookie season with the Thunder. The Utah Jazz — previously among the heavier users of two-big looks — pivoted smaller by signing the aforementioned Bogdanovic, but in so doing sent Derrick Favors to the New Orleans Pelicans, where he could potentially play alongside either Jaxson Hayes or Jahlil Okafor when he’s not manning the pivot next to Zion Williamson.

Several additional teams may end up using two-big lineups more often due to other types of roster changes. The defending champion Toronto Raptors, after losing Kawhi Leonard to the L.A. Clippers, could use more of the Marc Gasol-Serge Ibaka frontcourt that worked so well for them in the playoffs. The Clippers figure to load-manage Leonard, as the Raptors did last season, but even when he’s in the lineup, it’s entirely possible we see Montrezl Harrell — who has played 83 percent of his career minutes at center, including 96 percent last season — playing the four next to Ivica Zubac. Even the Warriors — who took small-ball even further than the Big Three-era Heat — could end up using more two-big lineups featuring, say, Kevon Looney and free-agent signee Willie Cauley-Stein when Draymond Green has to rest, given that they lost Kevin Durant in free agency and traded away Andre Iguodala.

Already, that’s a significant portion of the league seemingly preparing to devote non-trivial minutes to two-big lineups. Not even mentioned are four of the seven squads that used two-big units at least 10 percent of the time last season, and could conceivably do so again. (They are the Minnesota Timberwolves, Cleveland Cavaliers, San Antonio Spurs and Denver Nuggets, in addition to the Trail Blazers, Jazz and Pacers.) With multiple contenders in the East and West seemingly planning to use two-big lineups more often, it doesn’t appear as necessary for teams to ensure that they are well-equipped to go small against the very best opponents. Much of the league appears to have reacted by returning to the comfort of using size as an advantage.

Can You Escape This Enchanted Maze?

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,6 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, Riddler Nation’s Master Mazist, a jumbled journey:

Walking through an enchanted land, you are informed that you are coming up to a maze. You reach a very odd set of words arranged in hexagonal patterns. Accompanying them are instructions for how to navigate through the hexes to arrive at the maze’s end. You see the words:


“OK, what,” you ask yourself. Luckily, you find further instructions, involved though they may be:

  • These letters form the pattern of how to navigate this maze. Once you enter, you must follow the options provided.
  • Your goal is to exit the maze (“Win!”).
  • When moving from one hex to another, you must obey the basic two rules:
    • If you come to a hex with a consonant, you must turn left: either a mild left (60 degrees, or one hex to the left), or a sharp left (120 degrees).
    • If you come to a hex with a vowel (“Y” is a vowel), you must turn right: either a mild right (60 degrees, or one hex to the right), or a sharp right (120 degrees).
  • You may never proceed straight or back directly up.
  • If you travel outside of the pictured hexes, or enter the dreaded gray hex, you must return to the start.
  • You must pass through the letter “M” before you are allowed to finish.

Can you navigate your way to the end of the maze?

Submit your answer

Riddler Classic

From Benjamin Danard, a navigational challenge of a different kind:

There are 48 contiguous states in the United States. Each of these states shares at least one border with another state. You are planning a road trip in order to visit as many states as possible. The only restriction is that you can only cross a border from one state to another one time. You can visit a state any number of times, as long as you do not enter or leave it from a border you have already crossed.

How many states can you visit without crossing the same border twice?

Submit your answer

Solution to last week’s Riddler Express

Congratulations to 👏 Jonathan Chow 👏 of Ottawa, Ontario, winner of last week’s Riddler Express!

Last week, you were given an empty 4-by-4 grid and a marker. You could color in any of the individual squares you liked and leave any of them untouched. After you did that, I would then secretly cut out a 2-by-2 piece of the square and show it to you, without rotating it. You then had to tell me where the piece was (e.g., “top middle” or “bottom right,” etc.) in the original 4-by-4 square. The challenge: Could you design a square for which you’d always know where the piece came from?

Indeed you could. In fact, there were 6,188 different ways to do so. This puzzle’s submitter, Tyler Barron, illustrated 150 of them:

Perhaps the most elegant solution is to simply color in a small 2-by-2 square smack in the middle of the big 4-by-4 square. One might call it the donut. It’s quick to check whether that one, for example, works as a solution to challenge. No matter what piece I cut, the pattern you’ve colored will be different — a colored piece in the lower right, or along the bottom, and so on — and so you’ll be able to tell me where I cut in the original square.

Mmm, donuts.

Solution to last week’s Riddler Classic

Congratulations to 👏 Sjoerd De Vries 👏 of Nancy, France, winner of last week’s Riddler Classic!

Last week you were charged with constructing an optimal tournament which consisted of some predetermined number of players and number of games. Specifically, you wanted to devise a tournament in which the best player won most often. All the players were ordered by a skill level, though you didn’t know the order, and the better player won each individual game two-thirds of the time. Your challenges were to devise these tournaments for four players and four games, and for five players and five games.

For four players and four games: First, name the teams A, B, C and D. Have A play B, and then have the winner play both C and D, and finally have the winners of those two games play for the championship. (If the winners are the same, that player wins the championship). The best player wins this tournament 38 out of 81 times, or about 46.9 percent of the time. (Note that this is a somewhat higher chance than the standard three-game bracket-style tournament in which the best player wins about 44.4 percent of the time.)

For five players and five games, it’s a bit more involved: As before, name the teams A, B, C, D and E. First, pit A versus B, and have the winner (say it’s A) play C. If A wins, have A play D and E, and have the winners of those games play for the title. If A loses, have A play D. If A wins, A plays E and the winner plays C. If A loses, have C play E and that winner play D. The best player wins this one — which I would love to hear explained on SportsCenter — about 1,496 out of 3,645 times, or about 41 percent of the time.

This puzzle’s submitter, Erich Friedman, has put together a handy table — frankly, one of my all-time favorite tables — with the optimal tournaments and their relevant probabilities for various combinations of numbers of players and games. Not too surprisingly, the chance that a tournament produces the best player as its winner increases with the number of games, and decreases with the number of players.

May the best player win … you know, some of the time.

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]

The Teams That Should Be Buying And Selling At This Year’s Baseball Trade Deadline

Major-league teams are on the clock and must decide whether they want to buy or sell — and this decision comes with perhaps more urgency than in any previous July. MLB’s annual trade deadline is one week away, and the deadline carries a new sense of finality this season, as baseball eliminated August waiver trades in favor of a single July 31 cutoff for deals. Although the early read on the market has been one of uncertainty, at the very least we should see an intriguing chess match develop between rival general managers in the leadup to next Wednesday afternoon.

Granted, we don’t exactly know how those GMs will react to the compressed timeline when making deals this year. But here at FiveThirtyEight, we do have a tool to help assist with the overall deadline decision-making process: the Doyle Number. (So named for an infamous 1987 Detroit Tigers deadline trade when they shipped future Hall of Famer John Smoltz to Atlanta for pitcher Doyle Alexander.) Basically, Doyle measures the amount of future talent (i.e., total projected wins above replacement added over the next six seasons) a team should be willing to give up — in the form of prospects or other team-controlled assets — in exchange for adding an extra WAR of rental talent in 2019, with the goal of maximizing its total expected championships in both the short and long term.

In other words, Doyle is all about the tradeoff between how adding talent improves a buyer’s present-day championship odds and reduces those odds in the future.1 So when we say the Los Angeles Dodgers have a Doyle Number of 2.17, it means they should be willing to sacrifice 2.17 future WAR in exchange for every WAR of talent they add at the 2019 deadline. (This is a textbook definition of a buyer; the Dodgers’ Doyle Number is the highest in baseball.) Meanwhile, the lowly Tigers are clear sellers: They have a Doyle of 0.00, meaning there is literally no amount of rental talent they could add this season that would justify giving up any future WAR.2

Those are the easy cases. A team with a Doyle Number around 1.00 has a tougher choice, and would essentially be equally served by either buying or selling, depending on the particulars of a given trade. Here are the Doyle Numbers for each of 2019’s MLB teams, taking into account games played through July 22:

Who are 2019′s trade-deadline buyers and sellers?

Postseason chances (according to the FiveThirtyEight prediction model) and Doyle Numbers* for 2019 MLB teams

Dodgers >99% 26% 2.17 Angels 5% <1% 0.16
Yankees >99 19 2.16 Giants 8 <1 0.13
Astros >99 17 2.09 Rockies 5 <1 0.07
Twins 94 6 1.70 Reds 5 <1 0.06
Braves 96 6 1.64 Pirates 5 <1 0.06
Indians 70 4 1.48 Padres 2 <1 0.04
Cubs 63 4 1.34 Mets 4 <1 0.03
Athletics 49 3 0.95 Rangers <1 <1 0.03
Nationals 62 3 0.92 White Sox <1 <1 0.00
Cardinals 44 3 0.86 Blue Jays <1 <1 0.00
Red Sox 35 2 0.76 Mariners <1 <1 0.00
Rays 48 2 0.75 Royals <1 <1 0.00
Brewers 40 2 0.73 Marlins <1 <1 0.00
Phillies 35 1 0.48 Orioles <1 <1 0.00
Diamondbacks 31 1 0.31 Tigers <1 <1 0.00

*The Doyle Number represents how many wins of future talent a team should trade away now for one extra win of talent in 2019.

Playoff and World Series odds are as of July 22.

Source: FanGraphs

One of the key lessons from Doyle is that the best candidates to buy at the deadline aren’t the ones that conventional wisdom might suggest. Instead of teams that are on the cusp of the playoffs, the most committed buyers ought to be teams whose playoff odds are already solidified — but whose World Series chances could get a big boost with a few important additions. This is a consequence of how talent relates to winning championships in baseball: Because even the best teams usually only have a 15 to 25 percent chance at the title, a mega-talented roster can still get a sizable increase in World Series odds by adding extra star power. As long as it doesn’t create too many positional logjams (and even those can be worked around), there are effectively no diminishing returns between your team’s talent and its odds of holding a parade in November.

Of course, you also have to possess prospects that will convince sellers to part with veteran talent. Among the teams with the highest Doyle numbers, the best farm systems belong to the Atlanta Braves, Houston Astros, Minnesota Twins, Dodgers and — to a lesser extent — Cleveland Indians, according to FanGraphs’ estimates of total farm-system value. (The Tampa Bay Rays also have an incredible amount of prospect talent in their pipeline, though their Doyle of 0.75 suggests a slight preference towards selling, not buying, despite the team’s position in the thick of the American League Wild Card race.)

Houston and Minnesota are in particular need of pitching, in a year when the most desirable trade targets are disproportionately pitchers. So if the Astros deal for, say, Texas Rangers starter Mike Minor (whose long-term track record is that of about a 5-WAR pitcher3 per 162 games), Doyle says the Astros should be willing to part with as many as 12 wins of future talent to add Minor’s five wins to their current talent level. Each amount — five wins now or 12 over the next six seasons — is worth about 0.071 expected championships added.

Not every team has such a stark split between the importance of present wins and future ones. The Washington Nationals, for instance, are one of the teams whose Doyle is currently closest to 1.00, the point of true indifference between buying and selling. They could buy 5 WAR of current talent and have it be worth the equivalent of 1.3 additional WAR in the future, so it would still make sense in terms of balancing expected championships. But they could also sell 5 WAR of current talent, and get back the equivalent of 2.3 extra future WAR if we again assume the championship odds are balanced. This is a delicate situation, although it also can give a team many options in the trade marketplace. Here are all of the 2019 teams who could either add or subtract players — in increments of either 2 WAR (a solid regular starter, per Baseball-Reference’s WAR guide), 5 WAR (an All-Star level player) or 8 WAR (an MVP-level player) of present-day talent — and still potentially create a surplus in total wins after balancing the championship odds:

Time to switch up the roster

After adjusting for the effect on championship odds, net equivalent wins gained if a team buys or sells 2, 5 or 8 WAR at the trade deadline for teams on the buy/sell fence

Team Doyle 8 WAR 5 WAR 2 WAR 2 WAR 5 WAR 8 WAR
Cubs 1.34 +1.0 -0.2 -0.3 +1.0 +3.7 +8.4
Athletics 0.95 +5.4 +2.1 +0.4 +0.1 +1.4 +4.3
Nationals 0.92 +5.8 +2.3 +0.4 +0.1 +1.3 +4.1
Cardinals 0.86 +7.1 +2.9 +0.6 +0.0 +0.9 +3.6
Red Sox 0.76 +8.8 +3.8 +1.0 -0.3 +0.2 +2.1
Rays 0.75 +9.4 +4.1 +1.0 -0.3 +0.2 +2.1
Brewers 0.73 +10.1 +4.4 +1.1 -0.3 +0.1 +2.1

The Doyle Number represents how many wins of future talent a team should trade away now for one extra win of talent in 2019.

Source: FanGraphs

When it comes to teams on the buy/sell fence, the details of their trade options are important. The Milwaukee Brewers — who have just 84 wins of talent on their roster, a 40 percent chance of making the playoffs and 2 percent World Series odds — could only get a big surplus from buying if they were to somehow land an MVP-caliber player4; otherwise, they’d get a lot more out of just selling assets and reloading for the future. By contrast, the Chicago Cubs would only make sense as sellers if they blew up everything and got a massive haul of prospect value back in return. But the Oakland A’s, St. Louis Cardinals and Boston Red Sox, in addition to the Nationals, could benefit from either buying or selling, as long as they commit to a strategy.5 In fact, for all of these teams, some kind of activity at the deadline is better than standing pat and doing nothing.

A few interesting teams are not on that list of on-the-fence clubs. The San Francisco Giants have played themselves into the larger deadline conversation in the media, thanks to a recent stretch of surprisingly good play (they’re 15-3 in July). But Doyle says holding onto rumored trade candidate Madison Bumgarner would be a big mistake. With 77 wins of underlying talent (according to Elo) and a still-slim 8 percent playoff probability, even a massive 10-WAR improvement in current talent (think trading for Mike Trout) would result in a net long-term loss of expected championships if bought at a fair price.6 Just let the dynasty end already!

Likewise, the Rangers, Philadelphia Phillies and Arizona Diamondbacks — all teams with .500 records or better — are logical candidates to make a deadline push based on traditional baseball thinking. But similar to San Francisco, Doyle sees the Rangers as a team with 75-win talent who has overachieved to its current record and, trailing three division rivals in the standings, possess less than a 1 percent chance of making the playoffs. With attractive trade assets such as Minor and fellow starter Lance Lynn potentially on the block, Texas would be well served to sell. Philadelphia and Arizona have better talent than the Rangers, but neither has much chance of winning their respective divisions, so the wild-card game appears to be each team’s ceiling. Doyle explicitly accounts for how much that fact slices into a team’s World Series odds, which helps explain why each team has a Doyle Number under 0.50. (Then again, I would have considered the Phillies a good candidate to buy a month ago, so these things can change quickly.)

Whatever happens over the next week, it should be fascinating to watch teams react to the finality of this year’s deadline. Even before the new hard July 31 cutoff, deadline activity has been increasing in the past few seasons anyway, and recent history tells us the deals made now could have a significant effect in the postseason. While there aren’t as many massive rental-candidate stars on the market as last year — maybe Arizona’s Zack Greinke qualifies? — the added sense of urgency could keep things interesting, whether teams follow Doyle’s advice or not.

Check out our latest MLB predictions.

What Endorsements Matter Most In The Democratic Primary?

Welcome to FiveThirtyEight’s weekly politics chat. The transcript below has been lightly edited.

sarahf (Sarah Frostenson, politics editor): Here at FiveThirtyEight, we’re interested in tracking presidential endorsements as they’re often a good indicator of which candidates the party is rallying behind.

So today let’s talk about the Democratic Party’s Kingmakers — or those endorsers that can make or break a candidate. First of all, who are they? And then second, what does a winning strategy in the endorsement primary look like? Should candidates prioritize endorsements from early-voting primary states? Does the type of office an endorser holds/held matter? Or is it all about the constituencies an endorser can bring to the table?

clare.malone (Clare Malone, senior political writer): What’s interesting to me is how few people have endorsed! I guess it’s still very early, but the clearest example I can point to of the endorsement primary already being underway is when all the candidates (or so it seemed) headed to Jim Clyburn’s South Carolina fish fry in June.

He, of course, is a big deal in the national party as well as in an early primary state.

And I think the fight over Clyburn is demonstrative of the battle over important black endorsers. In fact, between Kamala Harris, Cory Booker and Joe Biden, I’d say there is already a pretty big push to win endorsements from members of the Congressional Black Caucus.

natesilver (Nate Silver, editor in chief): Yeah, a Clyburn endorsement would definitely be in my top five or 10. But the thing about this year is that since Everybody’s Running, the endorsements you probably want the most are actually from the other candidates. In particular, Bernie Sanders, Elizabeth Warren and Biden, who all command large, loyal constituencies.

clare.malone: Very true, though the big candidate endorsements likely won’t happen until next summer, right?

Or next spring, if things shake out neatly.

galen (Galen Druke, podcast producer and reporter): At this point, it seems like a lot of these candidates are going to have enough money to keep them going well into the primary season, so I’m not holding my breath on those endorsements happening anytime soon.

clare.malone: Maybe, though some candidates might see the writing on the wall and they’ll want to have their endorsement actually matter.

Speaking of a BIG endorsement — and a new one at that — who Alexandria Ocasio-Cortez decides to back is going to be big. My guess is it will come down to Warren or Sanders, but she’s said that she wants to wait to endorse, so I’ll definitely be keeping an eye out to see what she does.

galen: An endorsement from AOC would definitely confer progressive bona fides on a candidate, so it’ll be important to see who she endorses. And as we talk about endorsers, it’s important that we keep in mind what they represent: a demographic group, an ideological wing of the party, a certain state, or say, a figurehead like Obama.

natesilver: I mean, Obama is THE kingmaker.

But I don’t know if he’s going to endorse.

If does though, he’s like 10x more important than any other endorsement.

sarahf: But will Obama endorse?!

galen: NO

Unless it is Biden vs. Marianne Williamson at the end.

natesilver: I could see some circumstances where he would.

Especially if, like, a candidate he liked was ahead, but it seemed like Democrats were headed toward a contested convention, and he wanted to avoid that.

clare.malone: Yeah, Obama could endorse by early summer next year if things are still looking very crowded.

There will certainly come a point in the primary season where people start writing think pieces along the lines of “Have Democrats learned any lessons from the GOP’s disastrous 2016 primary??”

People will CLICK on those.

sarahf: But to the point Nate made earlier about people dropping out of the race and how their endorsements could be some of the most important endorsements this cycle … I have a question: How come their endorsements don’t get extra points in our tracker?

I, for one, would think they’d have a higher point value based on what we’ve discussed so far.

But I digress!

galen: Agree. I don’t understand why we give former Presidents Jimmy Carter and Bill Clinton the same number of points as Obama in the tracker.

So … explain that.

natesilver: I don’t think we should be thinking about this stuff in terms of the tracker.

The tracker tracks everyone, and we’re asking here if there are endorsements that carry SYMBOLIC and SUBSTANTIVE importance beyond that.

The value of endorsements isn’t in like “ohhh, Random Senator X endorsed Candidate Y,” it’s more that it’s a proxy for the “party deciding.” But some endorsements, e.g. Obama’s, really might persuade voters to think differently about the race.

sarahf: OK, so who are some other Democrats that might fall into this category, the “big names,” if you will?

We’ve got Obama, AOC and Clyburn.

galen: Apart from Barack, there is Michelle. Do you think the Obamas endorse together?

clare.malone: I think I disagree with Galen’s point about the weight of Jimmy Carter and Bill Clinton’s endorsements.

Clinton’s endorsement might be toxic in today’s party, but Carter is still seen as a moral leader.

galen: I agree with that, but I still don’t think his endorsement is as powerful as Obama’s.

clare.malone: No.

natesilver: HiLlArY ClInToN

sarahf: Oooh, I know Clare was talking about Bill Clinton’s endorsement being toxic, but I’m not so sure Hillary Clinton’s endorsement would be much better.

natesilver: Oh, you guys are totally wrong, the Clinton endorsements would still be a big deal.

clare.malone: Well, Hillary’s endorsement would certainly carry more weight than Bill’s at this juncture. Even if Bill still resonates with some communities, his sins (that were kinda forgiven in the past) are viewed very differently today by party elites.

galen: I honestly couldn’t tell you how this would play out, but I think candidates will play it safe and just try to keep the Clintons out of the conversation.

It is worth remembering that as of the 2018 midterms, Hillary Clinton’s approval rating among the broader public was still in the mid-30s.

natesilver: But Clinton won the primary by a WIDE margin four years ago! And a lot of Democrats like her! They didn’t want her to run again, but they still like her!

clare.malone: I don’t think she’ll endorse until there’s a named nominee.

Though, who knows–she might want to make waves! She does seem to occasionally throw bombs.

galen: Who of the top four would actively seek her endorsement?

natesilver: I think Harris and Warren, in particular, would seek her endorsement.

clare.malone: Harris for sure.

Warren I’m less sure about, though you could be right, Nate.

sarahf: OK, last call for the heavyweights. Who else?

natesilver: NaNcY PeLoSi

galen: Proxies for heavy hitters also matter — Valerie Jarrett, Eric Holder, for example.

natesilver: Ohhhh I totally disagree on the proxies.

clare.malone: I like the idea of proxies…

Why, Nate?

natesilver: Because who the hell cares who, say, Valerie Jarrett endorses. Nobody knows who she is.

galen: But party people know who she is and they might take it as a sign of what “Obama world” is thinking.

And that matters.

natesilver: ZZZZZ

clare.malone: Oh, I have one.

Pod Save America.

If they endorsed, they would be decently influential as a group.

galen: Hooo boy

clare.malone: I’m serious.

They’re a big platform for a core slice of the party.

natesilver: WHAT ABOUT CHAPO

sarahf: Hold on, I think Galen has a point about proxies, especially if many of these heavyweight endorsers won’t endorse until later. Sure, many people might not know who Valerie Jarrett is (she’s one of Obama’s longest-serving advisors), but say she and others from “Obama world” come out in support of one candidate. That matters, no?

Or at least political journalists (aka us) will write about it.

clare.malone: It would drive mini news cycles (maybe…)

natesilver: It matters in the “party decides” sense but not in the “kingmaker” sense. And we’re debating king- and queenmakers today.

sarahf: 👑


sarahf: Warren. So that’s one heavyweight(?) down …

galen: Speaking of past presidential nominees … didn’t Walter Mondale endorse Amy Klobuchar?

natesilver: Mondale is for the Klob, yeah.

clare.malone: “The Klob” is the worst nickname ever.


sarahf: OK, let’s move away from who the heavyweights are (or aren’t) and back to the different endorsement strategies candidates should be using.

If a lot of these heavyweights are off the table, what lower-level king- and queenmakers should candidates be trying to win over now? Does it make sense to concentrate on just one state? Or maybe a state-specific strategy doesn’t matter?


clare.malone: In Iowa, at least, you want people with a history of activism who drive people to the caucuses–so state lawmakers really matter there.

That’s why people always talk about the importance of courting activist types in those early states–it’s very retail politics driven.

galen: The upper Midwest just elected some new Democratic governors in 2018, who could make the argument that they know how to win those states as Democrats, and that they have a good sense for who should be the nominee.

I’m thinking Gretchen Whitmer (Michigan) or Tony Evers (Wisconsin).

natesilver: Yeah, Michigan seems like it’s a state that could be up for grabs.

galen: What if the Democratic governors of Wisconsin, Michigan and Pennsylvania all endorsed together??

That could be kinda interesting

clare.malone: I don’t think it would happen, but sure! Interesting!

sarahf: What is a smart on-the-ground endorsement strategy at this point to win over these state kingmakers?

natesilver: Is there any strategy apart from kissing people’s asses a lot?

clare.malone: In the early states, a lot of national candidates go to local elected officials’ events, which makes the officials seem more high profile, in return for getting their on-the-ground/word-of-mouth push to voters.

So, yeah, ass kissing.

natesilver: Look, even Al Sharpton is getting a fair among of ass-kissing. That’s what this process involves.

clare.malone: What do you mean “even” Al Sharpton, Nate?

He’s a big name in Democratic politics.

natesilver: I mean that he’s pretty unpopular outside of narrow circles. Even in NYC, his favorability ratings are quite meh.

sarahf: So does this mean that candidates looking to have a strong performance in the early-voting states should concentrate their on-the-ground efforts there? Because I have to say, for all the talk of Iowa and New Hampshire as the first caucus and primary in the nation, it’s not exactly clear to me who the kingmakers are?

galen: Well, we know Clyburn is the kingmaker in South Carolina.

Perhaps Harry Reid is a kingmaker in Nevada?

And maybe there just fewer high-profile Democrats in Iowa and New Hampshire at this point?

clare.malone: Unions are big in the Nevada caucuses, too.

In 2016, Clinton heavily courted Latino members of unions, for instance.

So maybe in Nevada things are more organized around unions.

natesilver: Nevada is also sort of a machine state, so I think Reid is one of those endorsements that could matter a lot in a very direct sense.

Nevada is a pretty hard one to figure out otherwise.

clare.malone: I think in Iowa, at least, there are clearer kingmakers in the GOP primary — for instance, Steve King and conservative family organizations have tended to be very influential.

sarahf: And there doesn’t seem to be the same Democratic equivalent, right?

But maybe that’s because the endorsement primary in these early states works differently and involves a much broader array of endorsers, including state legislators, labor unions, interest groups and even celebrities.

And so, say, the union vote matters more than anyone prominent individual.

Or at least this is the “party decides” view.

galen: Can we talk about endorsements from #NeverTrump Republicans? Does anyone think that these endorsements could matter?



clare.malone: Bret Stephens will endorse Bill Weld or something.


I’m so excited about Mark Sanford running (potentially).

Never forget the Appalachian Trail.

natesilver: I tend to think the media will overrate the importance of those cross-partisan endorsements. But I also think they COULD matter. In many states, the primaries are open to independents and Republicans, or there isn’t party registration at all.

sarahf: I don’t think we’re going to see anyone making explicit appeals to Never Trumpers in the primary, though.

clare.malone: Yeah, I don’t think Biden would seek out John Kasich’s endorsements in the primary, but it definitely wouldn’t hurt in the general.

natesilver: If Biden were to win the primary, I think it’s probably going to be a big part of his message.

sarahf: So it seems as if when it comes to the endorsement primary, there are two parts of it: 1) You want to build a broad coalition of support in the early states amid core constituencies whether that’s activists, unions or the like. 2) But you also want that extra boost from king- and queenmakers, except they often wait until very late in the process to make their endorsement … so how do you set yourself up for success there?

galen: Promise cabinet positions and ambassadorships.

I’m joking.

clare.malone: …. but are you?

galen: Yeah, I might not be joking.

Because what else can you do? You can make them feel special by wining and dining them and offer them something for their endorsement, or you can start winning so that people feel like they are on the winning team when they endorse you.

The first is easier to do. Winning is harder.

natesilver: I think it’s maybe more idiosyncratic and random than that. These are famous people with big egos. You build relationships, network, ass-kiss and yeah, maybe you can promise a few people a cabinet job or ambassadorship or even (!!!!!!!) the vice presidency (!!!!!!!!!). But there’s not THAT much you can do beyond that.

To the extent you’re spending more time in X state, it’s for all sorts of reasons — mostly that you think you can win that state — and not to gain more endorsements there.

clare.malone: And you as the candidate don’t need to make promises of jobs–people will assume they have your ear/a shot at influence, etc.

People like to think that their support for you will matter if you win.

natesilver: And they also like to endorse winners.

Sometimes the endorsements that matter the most are the unexpected ones. Like, if Beto O’Rourke were to get a big, unexpected endorsement, that might help him quite a bit right now because he’s sort of sucking wind otherwise.

Or if Bernie were to get Hillary Clinton’s endorsement, that would shake things up!

galen: Is anyone willing to argue that endorsements don’t matter anymore in Trump’s America?


clare.malone: No, because here’s the thing: People like it when other people help them navigate the political process.

And I don’t mean this condescendingly–there is A LOT going on in this election and people have A LOT going on in their lives. So they form bonds of trust in people/institutions and use those to guide their decisions. It’s the same way a lot of us make big decisions.

In politics as in life, endorsements matter.

natesilver: Yeah, I really … endorse that comment from Clare.

Voters aren’t able to pay as much attention to the race as we reporter-editor-journo-analysts might because they Actually Have Lives. So having a trusted person or institution endorse a candidate matters a lot.

galen: I also agree with Clare. The lesson from 2016 was not that the party can’t decide, but that the party wasn’t coordinated enough to decide, at least on the GOP side.

natesilver: We wrote about this a lot when we launched our endorsement tracker.

There’s plenty of reason to think endorsements still matter.

Also, EVERYTHING IS DIFFERENT BECAUSE TRUMP is generally bad analysis, sorry, Galen.



clare.malone: I LOVE IT WHEN WE FIGHT

natesilver: IT WAS LONELY HERE

Will Hearing From Mueller Really Change Americans’ Minds About His Report?

After months of calling on special counsel Robert Mueller to testify about his investigation into Russian interference in the 2016 election, House Democrats’ wish is about to come true. Mueller, who has studiously avoided the political firestorm around his findings, will now appear in back-to-back public hearings before the House Judiciary and Intelligence committees on Wednesday.

The hearings have the potential to reignite the public debate about Mueller’s report, in which he pointedly said the president was not exonerated of obstruction of justice but didn’t say whether future prosecution or impeachment charges would be warranted. But the enigmatic special counsel is appearing reluctantly, only after House Democrats issued a subpoena demanding his appearance. So while an explosive televised hearing could help Democrats make the case that Trump is unfit for office, Mueller likely is not eager to help anyone make political hay out of his testimony — which means Democrats (and Republicans) will be on their own when it comes to crafting the narrative they want to emerge from the hearing.

It’s also been several months since Mueller’s report was released in April, which means there’s been plenty of time for people to develop opinions about the investigation’s conclusions. A lot will depend on how the hearings unfold, but polling shows that Democrats and Republicans are divided, so there’s also a very real question about how much Mueller’s testimony can actually move the needle. Democrats, for instance, are much more likely to approve of Mueller’s job performance than Republicans, and only Democrats support starting impeachment proceedings.

But even if the hearings don’t succeed in changing minds about the report’s findings — which, let’s face it, seems likely — hearing from Mueller could still energize Democrats and maybe help to weaken Trump’s approval rating as part of House Democrats’ broader investigations. On the other hand, in our era of hyper-partisan politics, even high-profile congressional investigations might not be as damaging to a president as they were in the past.

Republicans like Mueller a little less than they did when the report came out

When Mueller was appointed special counsel in May 2017, he was embraced on both sides of the political aisle as a trustworthy and impartial investigator. But that bipartisan warmth was fleeting. As the Russia investigation progressed, opinions about the special counsel became increasingly politically polarized, with more and more Republicans saying they distrusted Mueller, while his fan base among Democrats grew. That partisan acrimony mostly disappeared after the release of Barr’s summary, when support for Mueller rose among Republicans and fell among Democrats, but as the chart below shows, Mueller’s favorability among Republicans has dipped once again over the past few weeks, and he’s more popular again among Democrats.

Meanwhile, there’s still a seismic divide between Republicans and Democrats about what Mueller’s report concluded — specifically whether Trump obstructed justice by interfering with the special counsel’s investigation. According to a YouGov/The Economist poll conducted in late June, 83 percent of Democrats think Trump attempted to obstruct justice, compared to only 16 percent of Republicans. That gap has stayed basically consistent since the report was released, according to YouGov’s polling, which suggests that changing a significant number of minds about Trump’s behavior will be a tall order.

Of course, hearing the findings directly from Mueller could make a difference, since many Americans (and some members of Congress) admit they haven’t read the report. But while Democrats will be eager to draw out the parts of the report that look bad for the president, Republicans on both committees also will be ready to undermine Mueller’s credibility — which could just end up reinforcing the opinions that everyone already had.

Impeachment is popular among Democrats but nobody else

Some House Democrats are hoping Mueller’s testimony could help reinvigorate the push to start impeachment proceedings against the president. But that would require a big shift in public opinion. Right now, impeaching Trump still isn’t a broadly popular position. As the chart below shows, about half of Americans still oppose starting the impeachment process, and that really hasn’t changed much since the report was released.

Granted, the vast majority of Democratic voters do favor impeachment, but House Speaker Nancy Pelosi has been holding the line against impeachment proceedings for months now, so it’s not clear what would alter her calculus. Congressional Democrats are very divided on the topic — last week, the House blocked a proposal to impeach Trump with about 60 percent of Democrats on Pelosi’s side. Higher support for impeachment, particularly among Republicans or independents, could theoretically push more Democrats into the impeachment camp — but if Mueller’s testimony is bland or inconclusive, the necessary sea change in public opinion seems unlikely, particularly with the summer recess just days away.

It’s proving hard to weaken Trump with congressional investigations

This hearing is particularly high stakes for Democrats because so far, their investigations of the president and his administration haven’t made a dent in Trump’s approval rating. As I wrote earlier this year, political scientists have shown that sustained congressional investigations generally do have the power to weaken the president’s approval rating over time — making them a powerful weapon for the president’s opposing party.

But that was when presidents’ approval ratings tended to fluctuate over time and responded to events in the news. Opinions on Trump’s job performance, on the other hand, have been remarkably stable so far. (To be fair, so were Obama’s.) “It’s really hard to change people’s minds about Trump,” said Eric Schickler, a political science professor at the University of California Berkeley who studies congressional investigations. “So it’s very possible we’re in a new reality where congressional investigations just don’t do that much to weaken the president.”

This outlook seems bleak for the Democrats, but it’s possible that Mueller’s testimony could work in their favor, even if it doesn’t do much to shift views of Trump overall. They’ve faced across-the-board stonewalling from the Trump administration in response to requests for testimony and documents, so getting Mueller to testify at all was a rare bit of success because they’ve had very few splashy public hearings so far. If Mueller’s testimony does, in fact, turn out to be a “public spectacle” — as Attorney General Bill Barr has predicted — that could help refocus Democratic voters and the 2020 candidates on the report’s findings and potential misconduct by the president. After all, Mueller’s news conference in May, at which he spoke for less than 10 minutes and restated the report’s primary conclusions without taking questions, was enough to spark a new wave of calls for impeachment. Transforming the report into a true priority for voters could be harder, though — when a CNN poll in March asked respondents to name their top issue for 2020, none mentioned the Russia investigation.

There is another possible upside to Mueller’s testimony for Democrats, though — hearing from Muller could stop people from developing a more positive opinion about Trump. After all, his approval ratings remain low despite a strong economy, and they haven’t improved substantially since Mueller’s investigation ended. “We shouldn’t conclude that the Democrats are failing because they’re not having an impact on Trump’s approval rating,” Schickler said. “If their steady drumbeat of investigations and hearings can prevent Trump’s approval rating from increasing, that’s another kind of success.”