The final Subway Series contest of the 2017 season takes place this evening at Citi Field, and if you put on the game, you might get the impression that the Yankees and Mets have a big-time rivalry going. It’s not that way for most baseball fans, however. The numbers show that only a minority actually like one team but not the other, while far more people hold the same opinion of both teams (good or bad) or just don’t care about one or both. In other words, most fans will probably be fine no matter the outcome tonight.

That’s according to data from a combination of two FiveThirtyEight-commissioned SurveyMonkey Audience polls conducted in June and July. SurveyMonkey asked baseball fans across the country how they felt — whether they had a favorable view, an unfavorable view or didn’t know enough to say — about each MLB team. Here, we’re examining a subset of that data, totaling 321 baseball fans who were asked specifically about the Mets and Yankees.

Of those, many fans (29 percent) held a favorable view of both the Mets and the Yankees. It’s not just that a fairly high percentage liked both teams. It’s that if you like one team, it actually increases your chance of liking the other team. While just 49 percent of the overall subsample held a favorable view of the Mets, 66 percent of fans who viewed the Yankees favorably felt the same way about the Mets. And a similar story holds in reverse. Only 44 percent of the fans in our subsample held a favorable view of the Yankees, but that percentage jumped to 59 percent among fans who held a favorable view of the Mets.

While the idea that someone could simultaneously like the Mets and the Yankees is unthinkable to this Yankee hater, it actually makes a lot of sense. Fans often root for the hometown team, whether it be in their city or even their state. So it’s not unreasonable to say you like both the Mets and the Yankees because they are both from New York. Indeed, among our subsample who live in New York state, the Mets and Yankees sport a 71 percent and a 67 percent favorable rating, respectively.

At the other end of the spectrum, 21 percent of baseball fans dislike both franchises. So that means 50 percent of baseball fans either like both the Yankees and Mets, or dislike both — not quite what you’d expect from a heated rivalry where battle lines are drawn and allegiances sworn. In fact, disliking the Mets or the Yankees actually makes one less apt to like the other team as well. The Mets sport just a 41 percent favorable rating among those who dislike the Yankees, 8 points below their overall favorable rating. And the Yankees do even worse among fans who dislike the Mets, with a 33 percent favorable rating — far below their 44 percent favorable mark overall.

Again, part of this may just have to do with disliking a city or a state. As an illustration of this, the Mets and Yankees sport favorable ratings of just 40 percent and 30 percent among our subsample that hailed from New England. New England, of course, is a natural geographic rival of New York.

Still, there are some people who do like the Mets and dislike the Yankees, and vice versa. One-fifth (20 percent) of fans hold a favorable view of the Mets and an unfavorable view of the Yankees. Meanwhile, 11 percent of fans hold a favorable view of the Yankees but an unfavorable view of the Mets. These fans, however, total only about a third of our subsample. That’s not much more than the 20 percent of fans who hold no opinion of at least one (if not both) teams.

Don’t tell that to the New Yorkers in the stands, jawing at each other about the two ballclubs. But the bottom line is that most baseball fans around the country won’t have much of anything on the line in tonight’s Subway Series finale.

Garry Kasparov, a former world chess champion and probably the best player ever to play the game, has come out of retirement and returned to competitive chess. He has suited up for this week’s Saint Louis Rapid & Blitz, a 10-player round-robin tournament that consists of relatively speedy games and features some scarily strong competition. Four of the 10 competitors are in the world’s top 10.

The chess world was abuzz with news of the return; Kasparov hasn’t played competitively since 2005. But the open question was how well he could perform against the young guns across the table. Kasparov is 54 years old, after all. To get some insight into how chess skill might decline with age, I downloaded the most recent FIDE rating list, from the beginning of August. This lists ranks all the players registered with the game’s international governing body according to their Elo rating.These lists are currently published monthly; they were published quarterly in earlier years.

“>¹ The end result was a data set with more than 280,000 players and their respective ratings. These are all the players currently rated by FIDE, although some of them, such as Kasparov, are flagged as “inactive,” meaning that they haven’t played a rated game in a year or more. (To estimate a given player’s age, we subtracted his or her birth year from 2017.)

The result is shaped like a large floating apostrophe of mortality. After a steep increase in players’ early years (youth is wasted on the young), the estimated trend in ratings peaks just after age 38, before beginning a long, slow, irreversible and depressing decline (kinda like real life).

But when the ratings are plotted this way, Kasparov’s outlier status becomes clear — his most recent rating, established before he retired in 2005, is 2812. If he were active in classical chess tournaments, that’d put him second in the world, behind the current world champion, Magnus Carlsen, who is 26.

Another former world champion, Vladimir Kramnik, who defeated Kasparov for the title in 2000, noted in a 2015 interview that he was in his mid-20s at the time. “In fact, chess is a game for the young,” he said.

As I write, Kasparov is near the bottom of the pack in St. Louis, with five draws and a loss through his first six games. Ian Nepomniachtchi, a 27-year-old Russian grandmaster, is in first place.

After the first day of play, Kasparov retweeted the following:

In this week’s politics chat, we discuss President Trump’s response to the violence in Charlottesville, Virginia. The transcript below has been lightly edited.

micah (Micah Cohen, politics editor): Welcome, all. Today I want to talk about President Trump’s continued insistence on treating the violence in Charlottesville — where white nationalists, neo-Nazis and the Ku Klux Klan held a march, and a suspected white nationalist has been charged with killing a woman and injuring others by plowing a car into a group of counterprotesters — as a “both sides” problem. After getting a ton of blowback because his initial statement, on Saturday, failed to explicitly condemn white supremacist groups, Trump made more explicit remarks on Monday. But then today, he returned to the position that “both sides” are to blame.

“You had a group on one side that was bad and you had a group on the other side that was also very violent,” Trump said. “And nobody wants to say that, but I’ll say that right now.”

It was really an amazing, depressing press conference, but we’re political reporters, so … WTF is the political calculus here? (For the sake of this conversation, let’s assume that there was such a calculus.) The idea I’ve seen floating around is that Trump won the White House, in part, by pushing messages and policies that white nationalists liked and is therefore hesitant to condemn those groups because doing so would anger his political base.

But the number of full-fledged neo-Nazis, for example, or KKK members is small. So what’s really going on here?

clare.malone (Clare Malone, senior political writer): I think if you pushed and pushed Trump on it, he would never say he supports white nationalists — today’s press conference saw some pretty ugly prevarication, though. When he said “not all of those people were neo-Nazis” of white nationalists who organized a march and were chanting KKK slogans — that was a pretty disturbing false distinction for a president to make.

But what Trump would be proud to say is that he doesn’t support “PC culture,” which is what a lot of people who hold racist beliefs use as a cover: I’m not racist, but I think we’re marginalizing white people. That spins into a whole lot of other things, many of them pretty ugly, but not always rising to the level of bringing out plastic riot shields and guns and beating up black people in Charlottesville and killing someone. A lot of times, racism in America is a lot more coded than neo-Nazi riots. Not always, though.

perry (Perry Bacon Jr., senior writer): Clare is making the right point. I think the actual number of neo-Nazis is small. They are not an integral part of Trump’s coalition.

harry (Harry Enten, senior political writer): You have to conclude that we saw the real President Trump in that press conference. He is who he is. I could add to that, but like … how hard is it to condemn white nationalists and neo-Nazis and stick to that condemnation?

In any case, I’d start with a number from Perry’s Charlottesville story: Nearly 20 percent of self-identified Republicans who think there’s “a great deal” of discrimination against whites. Almost half think there’s “a great deal” or “some” discrimination against whites. Those groups, which are bigger than neo-Nazis, are the ones I think Trump had on his mind.

perry: That is why I think he could have condemned them on Saturday, in the same way Marco Rubio or Jeb Bush did. But there is this “PC” culture thing that he campaigned against. So I was not surprised that he did not immediately react the way other Republicans did.

clare.malone: You look to Attorney General Jeff Sessions and what he said — he called the attack domestic terrorism. Sessions is not a guy who is known for being PC.

perry: Right.

clare.malone: Trump could and should have done that. But perhaps his initial statement and his press conference today are signs of the radicalism of people who are helping him write this stuff.

Or, to give them a more charitable read, their ignorance about the effect that certain rhetoric can have.

Or, very believably, these are the feelings Trump himself has about race — he refuses to see nuance in the issue. When a reporter at the press conference today asked him, “What do you think needs to be done to overcome the racial divides in this country?” Trump answered, “Well, I really think jobs can have a big impact.” Pretty telling answer.

perry: Right. Trump may be overdoing it, at least in this instance, in aligning himself against the media/establishment/political correctness.

micah: OK, so take that ~20 percent of Republicans who think there’s a lot of discrimination against whites. I don’t know if they are “white nationalists” per se, but maybe that’s a group — a sizable group — that feels like victims and found in Trump someone they thought would fight for them. Is Trump worried about turning that group off by condemning racism, white nationalism, etc.?

clare.malone: I guess Trump is worried about turning them off, but what I think he misunderstands is that probably the majority of those people who feel that way about whites being discriminated against have internalized the social stigma of being part of, say, the KKK.

Not all, but a lot. We’re still a pretty racist country, but up until at least recently, there’s been a heavy stigma on this kind of ugly belief. Maybe, though, that is changing. Which would be sad.

harry: According to the 2016 Cooperative Congressional Election Study, about two-thirds of Trump voters said they are at least somewhat angry that racism exists. We don’t know what’s in people’s hearts, but as Clare said, they’re at least aware of modern cultural norms. A very large chunk of Trump’s voters say they don’t like racism. So I’d imagine that they’d be fine with Trump saying the same thing.

perry: I don’t necessarily think feeling that there is a lot of discrimination against whites makes you a white nationalist. But white people who feel like they are victims of today’s politics and policies — that feels like something that undergirds Trump’s positions. He is proposing to limit legal immigration, for example, because he says it brings down wages of people already here. I guess I think Trump might agree in some ways with those who say whites are facing too much discrimination.

micah: Right — so there does seem like a political risk for him in not appearing as a champion of white, working-class Americans.

I guess, here’s what I’m trying to get at …

We’ve sometimes talked about whether a politician with Trump’s policy agenda and a more conventional, acceptable persona could do even better than Trump has in national politics. But maybe Trump thinks that’s not right — that the anti-PC stuff, the white nationalist rhetoric, is central to his appeal.

perry: It’s hard to know, because Trump rarely talks directly about his political coalition. And his advisers don’t talk about the white nationalism stuff as part of their political coalition. They talk about people opposed to illegal immigration.

clare.malone: But there’s such a thing as going too far on the anti-PC stuff. What’s been effective about Trump’s racial dog-whistling is that he hides it — to some extent — underneath this “law and order” umbrella.

So, MS-13 is going to kill people on Long Island, Mexican criminals are going to rape your daughters, etc.

Remember the GOP convention? The testimonials about people killed by undocumented immigrants?

perry: Yes, all signs are that Trump views this kind of identity politics as central to his politics. But I don’t know if Trump or even Stephen Bannon, Trump’s chief strategist, ever say that.

We know from Joshua Green’s book “Devil’s Bargain” that Bannon felt like the people who were really passionate about condemning racism were already Hillary Clinton voters.

harry: Can we break this down a little further?

micah: Yeah, go Harry!

harry: The American National Election Studies asked Clinton and Trump voters to give their opinion on different groups. They asked them to rate each group from zero to 100, with 100 being the warmest feelings. I took a look at different groups — specifically, how many Clinton and Trump voters gave each group a rating below 50 (which means they disliked the group more than they liked it).

Among Trump voters, 77 percent gave illegal immigrants a negative rating. But just 12 percent gave blacks a negative rating.

That’s a huge disparity.

clare.malone: That’s really interesting.

micah: Hmmm … That seems like a blunt, semi-misleading measure to me.

perry: That doesn’t tell me much, at all. Illegal immigration is illegal behavior. I’m not surprised people are against it.

harry: Let’s keep going.

micah: Keep going

harry: Forty-seven percent of Trump voters gave Muslims a negative rating.

clare.malone: Well, those demos intersect too …

micah: See, this seems hard to disentangle from the social stigma attached to “disliking” each group.

harry: Perhaps — although part of this survey was conducted among web participants, so among them, I wouldn’t think social stigma would be too much of a factor.

perry: This data set, from the Public Religion Research Institute, I thought was interesting

micah: Yeah, I think we need more indirect questions, like that PRRI study. Here’s a chart from that:

clare.malone: I’ve seen a lot of Confederate flags in very Northern states.

perry: This too:

harry: There was no subtlety in Charlottesville; there were Nazi flags, etc.

It’s one thing to be against removing the Confederate flag. It’s another to come out and say I don’t like black people — as most people would argue happened in Charlottesville.

micah: I mean, the way to do this, I think, is to look at a bunch of poll questions that, to various degrees, get at someone’s racial biases and prejudices without directly asking, “Are you racist?” Check these charts out, from a 2014 article we did …

micah: And here’s the aggregate of a bunch of those different questions:

perry: So I think we should consider two things in terms of Trump’s response. The rally had elements of being anti-black, anti-Semitism, anti-diversity. But it also had elements of being pro-white. Do parts of Trump’s coalition feel like they should be able to defend whiteness? Sure. The defense of Confederate monuments is not exactly the same thing as saying blacks should not marry whites. You can see in the PPRI data that the share of whites who see the flag more as a symbol of Southern pride than a symbol of racism is fairly high, even among the college-educated.

micah: Hmm …

perry: Secondly, we have to consider that, politics aside, Trump may agree at least partially with the ideas that whites/Christians/men are under threat from a society that won’t let them say what they think.

clare.malone: A lot of the white voters in Trump’s coalition take umbrage at the term “white privilege,” saying that they lack economic opportunity. And they resent, say, white men being treated as a powerful, monolithic group.

That’s a powerful political argument to a lot of people, especially if you live in a homogenous area where everyone is white and poor.

micah: It certainly proved powerful in 2016.

I mean, Obama made that point in his famous “A More Perfect Union” speech:

harry: Well, just 3 percent of Trump voters rated Christians, as a group, negatively in the ANES. For Clinton voters, it was 14 percent. I think Trump voters see that type of thing and think there’s a group of liberal elites who don’t like them.

clare.malone: I.e., wearing “deplorables” as a badge of honor, resenting that Clinton had boiled their Trump support down to racism.

harry: Indeed, this goes back to the point made earlier: Most Trump voters don’t see themselves as racist.

perry: I think that word is basically pointless to use — because we don’t have a shared understanding of what racist means in any real way. Beyond Bull Connor-style moves.

And I think it doesn’t do a particularly great job capturing what is happening in America.

harry: That’s a great point.

micah: OK, so we have a bunch of these labels/groups — Nazi, white nationalist, racist, deplorables, people who believe white people are discriminated against, people who are “uncomfortable” with America’s growing diversity, etc. — and those overlap some but are also very different.

But at least based on the numbers we referenced above, those feelings and grievances do represent a big chunk of Trump’s support. I don’t know if it’s 10 percent or 40 percent or whatever. But Trump lost the popular vote and won the Electoral College by a hair. So aren’t we in a situation where we have a president who is catering to those groups? He may have bungled that catering in response to Charlottesville, but he is doing it.

clare.malone: We have a president definitely catering to the group that believes white people are being discriminated against/people who are uncomfortable with diversity.

perry: Well, if we broaden things out that widely, didn’t Richard Nixon/Ronald Reagan/Bill Clinton appeal to some of that.

micah: Yeah, fair point.

perry: This is part of the problem: “Racist” is being defined too narrowly in some instances and too broadly in others. It irritates white and Republicans who feel like everything is labeled racist, but also liberals and minorities who feel like nothing is considered racist unless you are Bull Connor or George Wallace.

clare.malone: What’s new is that we can’t say beyond a shadow of a doubt that Trump isn’t dog whistling to white nationalist groups. I think today’s press conference was pretty unsettling to that end.

That’s new in the modern presidency.

harry: Yeah, I mean the difference is Trump couldn’t say neo-Nazis were bad on Saturday. That’s the difference.

perry: I guess I feel like Trump is getting this wrong for an obvious reason: Who else are these people who feel racial resentment or are outright racists going to vote for? Hillary Clinton? Kamala Harris?

He can offend David Duke.

He can go pretty far in offending David Duke and keep this part of the Republican Party behind him.

micah: Are we sure about that, Perry?

perry: Who else are they going to vote for?

micah: I guess my question is how much that bleeds over into the less overt groups?

Take the Bannon-level white nationalists …

They’re not wearing white hoods, but they have a pretty explicit, racialized set of policy goals. Doesn’t Trump need that group to believe that he’s a champion of white people?

I mean, Trump must think that, right?

How else to explain him not condemning neo-Nazis?

perry: He doesn’t like condemning people the media tells him to.

I happen to think this is less about some kind of grand political calculation than a petulant president.

micah: (Yeah, I agree with that.)

perry: He doesn’t like the media and elites telling him what to do, particularly about issues of race and culture.

harry: He knows that bashing the media is something that unites his party.

perry: I also think he and his team genuinely see white nationalists as like an alternative version of Black Lives Matter.

‘Obama never had to condemn Black Lives Matter; why should Trump have to condemn the radicals who like him?’

That is what it sounds like Trump thinks.

micah: IDK. I’m a little worried that we’re underestimating the size of the white nationalist vote.

perry: I guess I’m worried we can never calculate it.

harry: I think that’s right.

clare.malone: You’re likely never going to be able to get an explicit, actual polling read.

perry: What I’m not sure about is whether Confederate monument defenders are“white nationalists.” Or whether that term is only for those who say whites must control the country. And people who say blacks should not marry whites seems like a different issue.

Do all the various white power groups support Trump? Probably yes. In terms of policy, I don’t think he politically can afford to say that he supports affirmative action, for example. Could he call for taking down Confederate monuments? I think yes politically, but that’s a closer call. (Trump, to be clear, seems to oppose taking down those monuments.) He can certainly say that he doesn’t support white supremacy.

micah: See, that’s revealing. I don’t think he could call for taking down Confederate monuments without having big problems with his base. I’m much more willing to take out the broad brush.

clare.malone: He’s not going to do that. Look how he handled those questions today. He said if you take down the statues of Robert E. Lee, that might lead you to taking down statues of George Washington and Thomas Jefferson. Trump’s reasoning on this being that those other guys were slave owners too. Washington and Jefferson, of course, didn’t lead a rebellion against the U.S. government over the issue of slavery and states rights, though, certainly, yes, they did own slaves.

perry: But is there a huge political risk with his base? I can see Micah’s point. I’m not sure of it.

micah: OK, final question that gets at some of this in a different way: If Trump fires Bannon, will Trump have a meaningful political problem?

perry: I don’t have a great sense of who defines white nationalism in today’s politics. Is it Trump, David Duke, Breitbart or someone or something else? Who decides what violates the tenets of this kind of white nationalism? Who decides Trump has gone too far in the tolerance direction and says we must oppose him? Ann Coulter? Bannon when he is outside of the White House?

So if Bannon is fired but Trump remains generally anti-free trade, anti-immigration and Stephen Miller stays, Trump will be fine politically with his base.

clare.malone: I think Bannon would lob inflammatory criticism at the White House if he were let go.

Would that affect economic populist Trump supporters who read/watch a certain part of the right-wing media? Or would the prominence of Fox/Hannity as ever-loving supporters of Trump drown out the noise?

I don’t know, honestly!

Although, I guess I can see a scenario where Bannon is let go on good terms and he writes from a not-entirely-confrontational point of view from the outside.

perry: If Bannon is fired and it’s part of a general repositioning of Trump as a Jeb Bush/Rubio-style figure, yeah, then Trump will have a problem. If it means that H.R. McMaster/John Kelly/Ivanka Trump have taken over, Trump will have a problem with the Bannon wing of the party. But I doubt Trump is headed there.

Isn’t Donald Trump the leading voice of this kind of politics in the White House, not Bannon?

micah: Yes.

This week on the FiveThirtyEight Politics podcast, the team discusses the weekend’s events in Charlottesville, Virginia. President Trump, after not explicitly condemning white supremacists, neo-Nazis or the Ku Klux Klan in his initial response to the violence, made a more forceful statement on Monday. But was it too little too late? Also, FiveThirtyEight’s Perry Bacon Jr. joins the show to talk about the rise of white identity politics. Plus, the team previews Alabama’s special U.S. Senate primary.

You can listen to the episode by clicking the “play” button above or by downloading it in iTunes, the ESPN App or your favorite podcast platform. If you are new to podcasts, learn how to listen.

The FiveThirtyEight Politics podcast publishes Monday evenings, with occasional special episodes throughout the week. Help new listeners discover the show by leaving us a rating and review on iTunes. Have a comment, question or suggestion for “good polling vs. bad polling”? Get in touch by email, on Twitter or in the comments.

White nationalist protests in Charlottesville, Virginia, over the weekend drew bipartisan condemnation, particularly after a car plowed into counter-protesters, killing one person and injuring more than a dozen. Many observers called the apparent attack an act of domestic terrorism. “Go home,” Virginia Gov. McAuliffe, a Democrat, told white supremacists in a press conference Saturday. “You are not wanted in this great commonwealth.” GOP House Speaker Paul Ryan called white supremacism a “scourge” and said that, “Hate and terrorism must be confronted and defeated.”

President Trump’s response to the violence, by contrast, was comparatively mild and, in the view of many commenters, inadequate. Trump tweeted that we should “come together as one” in the face of hatred and violence and called the events in Charlottesville “sad!” In a short statement from his golf course in New Jersey on Saturday, he said Americans need to reject violence “from many sides.” But as of Sunday morning, he had yet to denounce the white supremacist protesters specifically, and he declined to label the car crash an act of terrorism. (On Saturday, Charlottesville police charged a man, apparently the driver of the car, with second-degree murder.)

Trump’s comments are striking for a couple of reasons. For one, Trump repeatedly denounced his predecessor, Barack Obama, for refusing to use the phrase “radical Islamic terrorism” to refer to attacks by Islamist radicals. For another, denouncing Friday’s white supremacist protest and Saturday’s (apparent) attack should have been comparatively easy for an American politician. In recent years, political norms emphasizing “colorblindness” in public life have made it tough for presidents to talk about structural racism, but rejecting rallies and groups like the ones coming together in Charlottesville should be straightforward. Photographs and press reports indicated that some of Friday and Saturday’s protesters gave Nazi salutes and chanted slogans associated with the Nazis, and at least one person carried a Nazi flag.

There is a long history of U.S. presidents proving reluctant to take strong stands in response to racial violence. Democratic and Republican presidents alike were unable and, often, unwilling, to address the most egregious abuses of the Jim Crow South. And that caution extended well into the modern era. Political realities have meant that presidents have rarely led the way on race relations, but Trump’s response to the events in Charlottesville stands out for lagging so far behind.

In 1906, for example, a group of African-American soldiers in Brownsville, Texas, was accused of shooting multiple people. They were acquitted by a court and there was no real evidence of their guilt — but President Theodore Roosevelt issued a dishonorable discharge for all of the accused soldiers. Roosevelt’s critics accused him of placating the angry mob for political reasons, as Roosevelt’s Republican Party had long tried to make electoral progress in the South.

Later in the 20th century, several presidents struggled to respond to lynchings, the violent, extra-judicial killing of African-Americans accused of crimes. (Recent estimates suggest that nearly 4,000 people died this way in the South between 1877 and 1950.) The NAACP had to lobby both Democrat Woodrow Wilson (who held and acted on racist views) and his Republican successor Warren G. Harding. Wilson did eventually speak out against lynching, but it took several years of lobbying by the NAACP to convince him to do so. As political scientist Megan Francis has written, “Only through an unyielding onslaught of protest was [the NAACP] able to obtain support from Wilson.” Harding, meanwhile, made some initial statements about lynching, Francis found, but did not continue to pressure Congress to adopt anti-lynching legislation. Like Theodore Roosevelt, he was limited by his party’s ambitions in the South.

Even in cases when presidents did end up taking more aggressive action on racial issues, they often did so reluctantly. In 1957, for example, Dwight Eisenhower sent federal troops (and federalized the Arkansas National Guard) to quell unrest in Little Rock, Arkansas, and enforce a court decision mandating the racial integration of schools. But Eisenhower took that step only after the crisis had been going on for three weeks, and he avoided addressing the substance of the ruling or the question of civil rights, instead citing the need to enforce the law. Eisenhower’s successor, John F. Kennedy, was also slow to move forward civil rights, although he eventually found his voice on the issue as political pressure mounted. In June, 1963, Kennedy addressed the nation on the question of civil rights and urged Congress to pass legislation, which he had previously been reluctant to pursue.

More recent presidents have faced a somewhat different set of issues. Since the passage of civil rights legislation in the 1960s, presidents have been able to embrace the principles of racial equality without fear of political backlash. But they have still often struggled to respond to racially charged situations. In 2005, President George W. Bush sparked outrage with his slow response as Hurricane Katrina wrought destruction in New Orleans, especially in predominantly black sections of the city. Members of the Congressional Black Caucus tied the slow federal response to the race of those affected by the flood. In response, Secretary of State Condoleezza Rice, the most prominent black official in the administration, defended its record on race.

In 2014, Obama urged calm after the announcement that the police officer who shot Michael Brown in Ferguson, Missouri, would not be charged, and many networks showed him speaking on a split screen alongside images of Ferguson descending into disorder. In both cases, the leaders appeared disconnected from the suffering of their citizens, at least in the moment. For different reasons, Bush and Obama faced delicate political situations. Bush led a party that had equated government assistance with moral degeneracy, a theme that came up as criticism piled up over the anemic federal response to the disaster. For Obama, the question of race was perpetually complex and fraught.

Presidential responses to racial violence and injustice have not all been discouraging. In the wake of Kennedy’s assassination and years of build-up from the civil rights movement, Lyndon Johnson staked his legacy on the issue. As a presidential candidate, Obama addressed the nation candidly about prejudices and fears. Obama’s eulogy for the slain pastor Clementa Pinckney is considered one of his most powerful speeches. And in a piece of rhetoric that gets less attention, George H. W. Bush responded to the Rodney King riots in Los Angeles by turning attention to the police violence against King.

Although racial politics have changed, the political dilemma facing presidents is dismayingly familiar. When it comes to race questions, presidents have sought to balance competing groups and their concerns. Presidents are products of their times — and they are politicians. In this sense, Trump’s bland equivocation fits right in. When it comes to race relations in the United States, presidents rarely cut through politics to express bold statements about equality; rather, they tend to be caught up in political conflict, and respond only to sustained pressure.

But history doesn’t absolve Trump. His tepid response to such overt and violent racism recalls a much earlier era, when people who espoused these violent ideologies held real political power. The political calculus for a contemporary president should be different. Congressional Republicans, for example, like Marco Rubio and Cory Gardner have asked the president to more strongly condemn what’s happened. Presidents have typically lagged behind the racial justice activists of their day — sometimes far behind. But Trump is unusual in also lagging behind today’s widely understood norms.

This weekend is not, of course, the first time that Trump has appeared reluctant to denounce white nationalists or other racist groups and individuals, many of whom supported his presidential campaign last year. He retweeted accounts and memes with ties to white supremacist groups, and he waited until deep into the campaign before firmly disavowing the support of former Ku Klux Klan Grand Wizard David Duke. That suggests that Trump’s cautious statements, like those of past presidents, may stem in part from his reluctance to alienate a key group of supporters; in Trump’s case, however, those key supporters include avowed racists.

We’ve all seen a pitcher when he’s zeroed in: His mechanics are clean, his curveball is dropping off the table and he’s painting the edge of the zone. But just as often, a hurler can lose command, and we see pitches that normally look sharp getting hammered into the stands. These streaks are confounding; for no apparent reason, a journeyman can look like a Hall of Famer, or a Cy Young winner can look like an ordinary junkballer.

Sabermetricians usually insist that such streaky performances are really just an artifact of fans and journalists forcing narratives onto random patterns. No matter how much it seems like a pitcher is getting hot, the more likely explanation is that they just happen to have bunched a few good innings together. But that’s not quite correct: Using a new method that focuses on fastball velocity, we found a way to detect whether a pitcher is actually throwing with a hot hand — and just how big of a difference it can make.

Arguments over streakiness in baseball are almost as old as the sabermetric movement itself, and for a long time, research seemed to disprove the notion of a “hot hand” effect or argue that it played only a severely limited role. But although the sabermetric community felt certain that these streaks were just coincidence, nearly every baseball player insists that hot streaks are real. And fresh evidence has muddied the debate. Recent papers have called into question some of the foundational research on which statheads built their skepticism. It turns out there might be room for hot streaks after all.

Of course, even if streakiness exists, predicting whether a player will go on a tear is even harder than proving tears are real. But it’s also much more useful. Knowing that a pitcher is on a hot streak, for instance, could tell you whether a team is primed for victory or defeat in a short playoff series. So we set out to find a way to forecast the hot hand using a method called a Hidden Markov Model. And not only did we find that hot streaks are real, but we can also tell whether a pitcher is hot or cold at any given moment.

The statistical details of a Hidden Markov Model are complex, but here’s a nontechnical description of the idea. Imagine that two pitchers were throwing from behind a curtain: flamethrowing Stephen Strasburg and soft-tossing Jered Weaver. The curtain completely conceals their uniforms and arm mechanics, and the two pitchers are each only allowed to toss a few dozen fastballs in a row before the other player takes a turn. The only way to tell who’s throwing is by looking at their pitches.

Despite the curtain, any dedicated baseball fan would be able to tell who’s who. Weaver’s average fastball clocks in at a pedestrian 84 miles per hour, while Strasburg’s zooms by at 96. With a glance at the radar gun, you’d easily be able to identify which pitcher was throwing, and you’d have a pretty good guess at how fast the next pitch would be.

Our analysis assumes that deep within every hurler, there’s a Strasburg and a Weaver lurking behind the curtain. When a pitcher is feeling healthy, or when he’s had a good night’s sleep, or when countless other factors fall into place to allow him to be in peak form, he can throw his hardest. On the other hand, if his mechanics are out of whack, or if he’s having troubles in his personal life, then maybe he starts to toss more like Weaver. Using a sequence of fastball velocities recorded by MLB’s pitch-tracking systemSpecifically, the data we used relied on PITCHf/x, the system MLB used to track pitches before it switched to Statcast this season.

‘>¹ for each pitcher in the 2014-2016 seasons, our model guesses who’s behind the curtain: the hot version or the cold version. We can then say whether a pitcher is likely to keep throwing hard or lose his flamethrowing touch.

To do this, though, we need to eliminate some common factors that can influence fastball velocity but don’t tell us anything about the pitcher’s condition. First, we focused on each thrower’s hardest types of fastball, which allowed us to avoid situations where pitchers were intentionally varying speeds, such as between two-seam and four-seam heaters.We used Pitch Info data to discern which fastballs are which. In rare cases in which a pitcher tended to use a cutter as his dominant fastball, we analyzed cutters instead of or in addition to four-seam fastballs.

“>² Individual ballparks’ speed measurements sometimes run hot or cold, which can make it look like a player is throwing harder or softer than usual, so we removed the effect of each stadium. We also accounted for the fatigue a pitcher experiences during the game, plus a host of other elements.Here’s a more technical explanation of our methodology: We begin by running a generalized linear model that predicts a pitch’s velocity based on who’s pitching and the number of pitches they’ve thrown. Then we took the residual from that model and controlled for external factors such as whether the bases were occupied, stadium elevation, park effects and game-time temperature, all of which can affect pitch velocity. We also looked at a number of other contextual elements, such as the difference in the teams’ scores, but we found that they did not significantly impact velocity. Finally, we applied a Hidden Markov Model to the residuals of the second model, searching for two hidden states — corresponding to hot and cold — within each pitcher.

“>³

Once we’ve done all that, we can go through a year’s worth of fastball velocity readings and determine when a starting pitcher is hot or cold.We limited it to pitchers who had thrown at least 800 fastballs in the 2016 season.

“>⁴ We found that the typical pitcher goes through 57 streaks in a season, jumping between hot and cold every 24 pitches. And not only did we find streaks, but we also found that the difference between being in the freezer and on fire is huge: The average pitcher moves up or down by an average of about two miles per hour when shifting between states.

Every starting pitcher in our data shows a noticeable pattern of switching between hot and cold states.We guarded against overfitting by scrambling the order of the fastball velocities for each pitcher and re-running the Hidden Markov Model. These randomized, fictitious sets of velocities produced smaller spreads between hot and cold states, as well as more random transition matrices than we saw in the real data, thus confirming that our model picked up on real streakiness in the authentic data.

‘>⁵ Some pitchers’ streakiness manifests in a pronounced downside when they’re cold, like what happens to Texas Rangers lefty Cole Hamels. When he’s on, Hamels’ fastball is just a tick faster than average for him. But when he’s off, he loses about two and a half miles per hour compared to his average fastball. The impact is massive: That almost 4 mph difference in heat translates to a 1.03-run difference in projected runs allowed per nine. If you apply those numbers to Hamels’ 2016 season, he had ace-level stats when hot (3.41 RA/9, 18th among 73 qualified starters), and mediocre ones when off (4.44 RA/9, 44th).

What’s more, the differences in Hamels’ performance seem to be steady from year to year. Running the same analysis on his 2014 and 2015 seasons shows that Hamels always fluctuates between about 2.5 mph down when cold and 1 mph up when hot. He’s not alone: Players who appeared in all three seasons we studied tended to show the same hot and cold effects from year to year, suggesting that we picked up on some of each pitcher’s true characteristics rather than just noise.

Unlike Hamels, some pitchers tended to gain and lose velocity in roughly equal measure. Masahiro Tanaka and Carlos Rodon, for instance, both gained about 1.5 mph when on and lost the same amount when off. But in general, pitchers in cold stretches lost more velocity than they gained when they were hot.

Although our approach can tell us when pitchers are on or off, it can’t tell us why. For some throwers, it’s obvious. Cleveland Indians’ star Danny Salazar suffered an elbow injury midway through the 2016 season, and his velocity tumbled, creating a cold streak, in his last two starts before he took a trip to the disabled list. It seems likely that the elbow was affecting Salazar’s mechanics even before the issue became bad enough to take him out of the game.

Salazar’s situation is not unusual. Many transitions between hot and cold streaks correspond with injuries. Pitchers on our list took 59 trips to the DL in 2016, and in 28 of those cases, they went through a notable frigid period in the two weeks before their injury took them out of the game.Specifically, their cold-state probability spiked above the 99th percentile of what you would expect to see if you randomly selected from their pitches.

“>⁶ The chance of that many pitchers going cold by chance just before a DL stint is very slim, so it’s likely that our method can also detect injuries. In particular, we found evidence that clusters of several slow pitches in a row are associated with a hurt pitcher.

In other cases, it’s not so clear what’s driving a streak. Hamels, for example, has stayed relatively healthy over the last few years, but that hasn’t stopped his fastball from fluctuating wildly. Any number of factors could explain Hamels’ performance: Maybe he is especially reliant on getting good rest between starts, or maybe he’s vulnerable to lingering, unreported medical issues — ones that never get bad enough to send him to the disabled list, but that diminish his performance nevertheless. Whatever the cause, his velocity does fluctuate in a meaningful way, so there must be more to it than noise.

Our approach isn’t just backwards-looking, either — we can also predict whether a pitcher will be hot or cold in the future. Using just the first two months’ worth of 2016 data, we tried to predict every pitcher’s subsequent fastball velocity.We ran our model on the first two months of pitches for each pitcher, and then used the Viterbi algorithm to generate updated state estimates for every subsequent pitch in the season.

‘>⁷ Our model was able to predict how hard the next pitch would be better than a guess based on the pitcher’s season-long average would be able to, suggesting that it’s able to pick up on when a pitcher is hot or cold at any point in the season after June 1. That’s useful information for managers who are deciding when a starter might be getting cold and should be pulled from the game or which bullpen arm to turn to in a jam.

And the predictions don’t just affect fastball velocity. The hotter a pitcher was projected to be on a given pitch, the greater the probability was that the next fastball would yield a swinging strike, even accounting for the increased speed of that heater. Similarly, a pitch was significantly less likely to go for a hit, and less likely to yield extra bases, if a pitcher was considered hot.We used generalized linear models that examined the hot-state probability of the previous pitch, the count, and the current pitch’s velocity as predictors. All p-values were less than p=.05.

‘>⁸ It’s no surprise that good velocity is correlated with better results, but it reinforces that these hot streaks aren’t just quirks in the speed readings — they also indicate that something extra that happens when a pitcher is sharp.

If hot streaks are real, as our results suggest, they probably apply to more than just pitchers. We started out looking at fastball velocity because it is one of the most consistent and important performance characteristics in baseball, but our method could be applied to anything, from how hard a batter is hitting the ball to how often he swings the bat.

As evidence mounts that player performances do vary from hot to cold, it’s probably time to revisit the long-held sabermetric belief that such streaks are a fallacy. Whether a player is in the zone or in a funk, it’s not just magical thinking — it actually tells us something real about how he will play in the near future. And although our eyes might not be especially reliable indicators of a pitcher’s state, fastball velocity doesn’t lie.

Special thanks to Harry Pavlidis, Pitch Info and Rob McQuown.

This month’s Sparks podcast has the team really excited because they got to talk about one of the biggest public science spectacles of the year (probably the decade): the total solar eclipse that will cross the entire United States on Aug. 21.

In the podcast, which runs in FiveThirtyEight’s What’s The Point feed, science writer and FiveThirtyEight contributor Rebecca Boyle joined former senior editor Blythe Terrell, lead science writer Christie Aschwanden and lead health writer Anna Maria Barry-Jester to talk about this year’s eclipse through the lens of David Baron’s new book “American Eclipse.” Baron chronicles a total solar eclipse that made a splash 139 years ago. The 1878 eclipse in the Western U.S. helped America make a name for itself in the world of science and brought out luminaries including inventor Thomas Edison and Maria Mitchell, a Vassar College professor and astronomer who made the case that women deserved a place in the world of science.

Christie will interview Baron about the book in the second part of this podcast. We’ll post that audio here when it’s available.

As Colin Kaepernick’s job hunt has crept into training camp, the parameters of debate have shifted. Just a few months ago, the contention was over whether or not Kaepernick was good enough to play in the league. That no longer seems to be the case. Last week, reports circulated that Baltimore Ravens head coach John Harbaugh and general manager Ozzie Newsome were both interested in signing Kaepernick, but were met with resistance by owner Steve Bisciotti, who framed hesitance over signing Kaepernick as a PR concern.

“Your opinions matter to us,” Bisciotti said at a fan event, referring to fan opinion over Kaepernick. “We’re very sensitive to it, and we’re monitoring it, and we’re still, as Ozzie says, scrimmaging it, and we’re trying to figure out what’s the right tact. So pray for us.”

Kaepernick’s ability to play the position no longer seems to be in doubt. Players have spoken in support of Kaepernick, and most serious analysis reliant on game study arrives at the conclusion that Kaepernick is not just a competent quarterback, but is also better than he was when he led the 49ers to the Super Bowl in 2013. Cian Fahey, who catalogues quarterback performance at Pre-Snap Reads, found Kaepernick to have outplayed Ravens starter Joe Flacco.

And yet Kaepernick doesn’t have a team. It’s obvious Kaepernick is being frozen out for his political opinions, but it’s less apparent how extraordinary it is that a player like him can’t find a team. Back in March, Neil Paine and I wrote about Kaepernick’s situation and noted that it was strange for even a halfway decent quarterback to remain unsigned so deep into free agency. Four months later, it’s no longer merely unusual — it’s practically unheard of.

Here are the free agent quarterbacks from the past five offseasons, charted by their Total Quarterback Rating in the previous season and how many days they remained in free agency before being signed by a team. (The size of the dots represent the number of pass attempts.)

No above-average quarterback has been unemployed nearly as long as Kaepernick this offseason. The most comparable scenario — Ryan Fitzpatrick’s contract showdown with the New York Jets last offseason — isn’t really comparable at all, since Fitzpatrick was the one exerting leverage over the team, not the other way around.

It’s easy to lose sight of the reality that good quarterbacks often never even reach free agency, let alone remain unsigned for so long. That’s especially the case for our discussion of Kaepernick, which has shifted from his merit as a player to concern-trolling and a consideration of business practicalities. So while Kaepernick is clearly an outlier on the chart above, the fact that he’s on it at all should be just as surprising.

Additional research by Neil Paine

This week on the FiveThirtyEight Politics podcast, the team sizes up the news that special counsel Bob Mueller has empanelled a grand jury in his investigation into President Trump’s campaign and Russian meddling in the 2016 election. Grand juries don’t necessarily lead to indictments, but they have in some past political scandals, including Watergate and Iran-Contra. The team also looks at persisting rifts in the Democratic Party after some progressives have spoken out against three rising black Democrats.

You can listen to the episode by clicking the “play” button above or by downloading it in iTunes, the ESPN App or your favorite podcast platform. If you are new to podcasts, learn how to listen.

The FiveThirtyEight Politics podcast publishes Monday evenings, with occasional special episodes throughout the week. Help new listeners discover the show by leaving us a rating and review on iTunes. Have a comment, question or suggestion for “good polling vs. bad polling”? Get in touch by email, on Twitter or in the comments.