On Monday, Donald Trump singled out American Muslims as supporting repression and violence, citing a discredited poll from an anti-Muslim group as evidence for imposing border restrictions. But if he is worried about extremist public opinion in the United States, he should take a broader look around.

Research shows that Muslim Americans are less likely to endorse violence against civilians than other religious groups. Moreover, the evidence suggests that a non-trivial minority of Americans of all faiths and backgrounds is willing to endorse the sorts of violence against the government and repressive legal measures that Mr. Trump accused Muslims of disproportionately supporting.

For instance, 27 percent of Americans endorsed violence against the government under some circumstances in a 1998 Pew poll — the same accusation he made against American Muslims. More recent surveys conducted by Nathan Kalmoe of Monmouth College indicate that support for anti-government violence extends for millions of Americans to specific actions such as sending threats to politicians who are “damaging the country” (9 percent), throwing a brick through the window of the “worst politicians” (6 to 13 percent) and fixing “some of the problems citizens have with government” with “a few well-aimed bullets” (5 to 6 percent).

Americans also frequently wish to remove legal protections from certain groups, which again echoes Mr. Trump’s fear-mongering about imposing Shariah law. James Gibson at Washington University in St. Louis found in a 2005 survey, for example, that more than half of Americans endorsed unconstitutional limitations on speech by the groups they liked least, which included widespread support for banning demonstrations by “radical Muslims” (57 percent), atheists (47 percent) and religious fundamentalists (39 percent).

Given these findings, Mr. Trump’s turn toward extremism can be understood as a result of his willingness to exploit existing undercurrents in public opinion. Some people have always been willing to support the types of policies he’s proposing. He’s betting that those tendencies and anti-Muslim sentiment are likely to grow in the wake of recent attacks in Paris and San Bernardino, Calif., which have heightened fears about terrorism that in the past have been found to be associated with negative views toward Arabs and support for restrictions on their entry to the United States.

At least in the short term, he may not be wrong — one poll released Wednesday reported that support for Mr. Trump’s proposal was unchanged when respondents were told that “leaders from across the political spectrum have condemned” it as making the United States less safe by alienating potential allies.

Can it be logical for a liberal to vote for Ted Cruz?

Judging by some recent comments from Upshot readers, the response would probably be a quick and Spock-like “No, highly illogical.”

That the answer is actually yes shouldn’t be too surprising when you allow for the possibility of strategic voting, or thinking one move ahead with your ballot: for example, crossing over to vote in a primary for someone you think is a weak general election opponent for your favorite candidate.

Research shows that the rate of so-called party-crasher voting in primaries is generally low. Voters in open primaries, in which you can vote in the primary of either party, are more likely to pick a candidate they like. In 2008, John McCain benefited from what evidence suggests was sincere crossover voting from Democrats and independents in winning the G.O.P. race, while the radio host Rush Limbaugh’s “Operation Chaos” to help Hillary Clinton defeat Barack Obama did not prevent an Obama presidency.

But the possibility of mischief always lurks, particularly in states, like Massachusetts, that don’t have closed primaries.

Steve Koczela, president of the MassINC Polling Group, said in an article in WBUR Politicker that the Massachusetts G.O.P. primary electorate in 2008 “was the most liberal of any state where exit polls were done” and that “the majority of voters in the G.O.P. primary are likely to be independents, or unenrolled voters, who make up the majority of all voters in Massachusetts.”

If Hillary Clinton pulls away from Bernie Sanders in Iowa and New Hampshire, for example, some Massachusetts liberals may want to participate in a primary in which their votes seem to matter more. And if Donald Trump fades, Marco Rubio and Mr. Cruz could well be the last men with a realistic shot in the G.O.P. race, as Charlie Cook of The Cook Political Report recently predicted in National Journal. On Sunday, Jonathan Martin and Jeremy W. Peters reported in The New York Times that Mr. Rubio was switching his focus to attack Mr. Cruz, who is moving up quickly in Iowa.

A reader, Anne-Marie Hislop from Chicago, wrote:

As someone clearly to the left of center, I’d much rather the Democrat face off against Cruz than Rubio. The former will turn off many more moderates than will the latter. I think with a little luck and skill Rubio could beat Hillary. In terms of where the country over all is, the pendulum swings. Recent terror fears certainly pull that pendulum to the right a bit, as fear always does. Best-case scenario from where I sit is for the G.O.P. to nominate one of their selection of extremists.

But it wouldn’t be easy for liberals to learn to stop worrying and love Ted Cruz: They’d have to walk into a polling place and actually vote for him. It’s not just Democrats who struggle with that thought, as Frank Bruni recently wrote in a Times column about his surge:

The political strategist Matthew Dowd, who worked for Bush back then, tweeted that “if truth serum was given to the staff of the 2000 Bush campaign,” an enormous percentage of them “would vote for Trump over Cruz.”

And the same goes for many who have known him beyond politics:

Anyone but Cruz: That’s the leitmotif of his life, stretching back to college at Princeton. His freshman roommate, Craig Mazin, told Patricia Murphy of The Daily Beast: “I would rather have anybody else be the president of the United States. Anyone. I would rather pick somebody from the phone book.”

Some voters may actually be praying that Mr. Cruz doesn’t win.

After my colleague Nate Cohn wrote that Mr. Cruz’s lopsided support among self-described “very conservative” voters wouldn’t necessarily preclude victory in the G.O.P. race, a reader wrote:

Dear God,

Please don’t let Ted Cruz be the president of the United States of America.

Thanks for your help

We’re getting desperate,

America’s 99%

Jim from Washington

And yet … it still might make sense for liberals to vote for Mr. Cruz. His head-to-head numbers against Mrs. Clinton, for example, were until recently the worst of the major G.O.P. contenders (Mr. Trump now holds that spot, having fallen sharply).

One caveat is that head-to-head numbers this early aren’t that significant. The bigger problem: If you vote for Ted Cruz because you don’t like the party of Ted Cruz, what happens if Ted Cruz goes on to become president?

One reader said, “I hope he wins the Republican nomination so that his brand of fear-mongering, income-inequality-defying ultraconservatism can be fully repudiated in the general election.”

To which a reader responded: “It might not be. Are you willing to risk that?”

Public opinion surveyed in the weeks before the San Bernardino, Calif., attack show that those voters who believe Muslims are dangerous have especially favorable views of Donald Trump.

What is somewhat more surprising is how Republican voters have efficiently sorted themselves on this issue among the many Republican candidates running for the nomination. Even before Mr. Trump called for a “total and complete shutdown” of Muslim entry into the United States, his supporters were in favor of the move. His call is unlikely to offend his strongest supporters, and in fact may have been an appeal to the pre-existing attitudes of his core constituency.

Public opinion data on attitudes toward Muslims collected over the last several years corroborate that Trump supporters already shared his views on that issue. The data show that a majority of Republicans view Muslims unfavorably and, according to the Pew Research Center, Republicans are cooler to Muslims than to other religious groups like Jews, Catholics and Buddhists.

To see how these anti-Muslim attitudes relate to support for Mr. Trump, I turned to data collected by YouGov from Nov. 19 through Nov. 23 — a little more than a week before the attack in San Bernardino. The survey of 2,000 people shows that Mr. Trump’s supporters are particularly suspicious of Muslims, and although the numbers get quite small, among all of the other candidates only Ted Cruz’s supporters look similar to Mr. Trump’s on this topic.

YouGov asked two questions about the threat of Islam on its final November survey. The first asked how serious a threat Muslims posed to the country. On average, 30 percent of Americans thought this group presented an “immediate and serious” threat, but there were large differences between Republicans and Democrats. Nearly half (46 percent) of Republicans believed Muslims were an immediate threat to the nation, while 23 percent of Democrats felt this way.

The second question asked what share of Muslims worldwide supported ISIS. Over all, about a third of the country thought more than half, most or all Muslims supported ISIS. Again there were large differences between the parties. Almost twice as many Republicans (45 percent) as Democrats (24 percent) believed a majority of Muslims supported ISIS.

Research by political scientists shows that there’s a strong correlation between people’s attitudes toward Muslims and their views of President Obama: Those who believe Muslims are dangerous have especially unfavorable ratings of the president.

Even bigger differences on the perceived threat of Muslims emerged within the Republican Party and across the candidates. For example, two-thirds of Mr. Trump’s supporters believed Muslims posed an immediate threat. The same is true among the smaller number of supporters of Mr. Cruz.

But supporters of Marco Rubio, Jeb Bush and Chris Christie were less inclined to believe Muslims posed an immediate threat. Less than one-third of their supporters fell into this category; a quarter of their supporters believed — 10 days before the California shootings — that Muslims as a group were less than a minor threat to the country. Supporters of Mr. Trump and Mr. Cruz were unique in their strong beliefs about the potential dangers Muslims posed.

Another way to see the importance of Muslim attitudes for Mr. Trump’s voters is to examine how increasing support for him connects to escalating beliefs about a Muslim threat. The data show that nearly half of Republicans who think Muslims pose an immediate threat to the United States support Mr. Trump over other candidates in the race, while only 13 percent of Republicans who think Muslims are not a threat to the country choose him over the others. Likewise, Mr. Trump is winning a majority of G.O.P. primary voters who believe most Muslims worldwide support ISIS.

Over half of Mr. Trump’s primary supporters, before the San Bernardino attack, thought that Muslims posed an immediate threat to the United States and that most Muslims in the world supported ISIS.

Last night, the Washington Redskins brought their much-debated appellation to “Monday Night Football.”

“Hail to the Redskins” was sung in the nation’s capital on national television at a taxpayer-subsidized event.

If the team today had the name “darky,” a word that Eleanor Roosevelt used in formal writing in the 1930s — in the same decade “Redskins” became a football franchise — there’s no chance the team would keep the name, no chance fans would sing a song with that name. So why is Redskins O.K.?

More on that below. First, on Saturday the 2015 Heisman Trophy winner will be announced. Here’s an insider tip: It won’t be a lineman. If John Heisman were alive today, he would not be considered for his own trophy.

Of the Heisman winners, just two, Larry Kelley from Yale in 1936 and Leon Hart from Notre Dame in 1949, played the line. That’s 2.5 percent of Heisman recipients who were linemen, though in football typically 40 percent of gents on the field are linemen.

The last time the winner was not either a quarterback or running back was corner Charles Woodson in 1997. Today Heisman, who played center and tackle for Penn and Brown back in the day, would draw no votes for the trophy that bears his name.

The award should be renamed the Heisman Trophy for the Quarterback or Running Back Who Receives the Most Publicity.

Suppose the Heisman voters were told that this year they were forbidden to cast ballots for quarterbacks or tailbacks. Many would have no idea for whom to vote. Here are T.M.Q.’s runners-up for the Non-Quarterback Non-Running Back Heisman:

Defensive end Emmanuel Ogbah of Oklahoma State. Best player at a program that won 10 straight before tailing off. Versus T.C.U., Ogbah recorded a sack while being held.

Offensive tackle Laremy Tunsil of Ole Miss. Perhaps the most talented player over all in college, his season was marred by a suspension that was classic N.C.A.A. galimatias. The N.C.A.A. will send in helicopter-borne commandos to stop a scholarship athlete from driving a loaner car or getting a short-term interest-free loan, two things Tunsil did.

But if the football players aren’t going to class, the N.C.A.A. does nothing. (Tunsil’s interest-free loan sounds disturbingly like the way the Federal Reserve funds the national debt, the difference between the Ole Miss player and Congress being that Tunsil repaid what he owed.)

Defensive end Joey Bosa of Ohio State. Quarterback Cardale Jones got the publicity for the Buckeyes’ January 2015 title victory; Bosa got it done. Some front seven stars boast of being triple-teamed, though actual triple teams are rare. Against Illinois, Bosa was the focus of actual triple-teams.

Guard Joshua Garnett of Stanford. This elite academic university finished 11-2 mainly because of an excellent line led by Garnett, who’s an honest-to-goodness student majoring in human biology.

And the Non-Quarterback Non-Running Back Heisman goes to the Clemson offensive line. Clemson finished No. 1 largely because it enjoyed college football’s best blocking. In the A.C.C. title contest, center Jay Guillermo snapped and then pulled and got the key block on the Tiger touchdown that ended the first half; most centers don’t even attempt to pull. Guard Eric Mac Lain once introduced Vice President Joe Biden. Giving awards to quarterbacks and running backs makes for good television. Linemen are the essence of the sport.

In other N.F.L. news, the Seahawks, whose Super Bowl formula has been rushing offense plus rushing defense, right now are first in rushing offense and third in rushing defense. Seattle just held Minnesota, which came in as the No. 1 rushing team, to 31 yards rushing on its own field.

The Panthers are 12-0 and have clinched a postseason date; stretching back to last season, they are on a 17-1 run. The best thing that could happen to Carolina is a loss, to get the monkey off its back about the pointless distraction of trying to go 16-0.

Back in September, this column began talking up New England’s little-known, undrafted free agent center David Andrews. Let me point out it’s now December and the Patriots are 10-0 when Andrews starts, 0-2 when he doesn’t.

Sweet Lend Me a Tight End Play. Tight ends behaving like wide receivers has become so common that now two tight ends need to go deep to count as an innovation.

Houston and Buffalo tied at 21-21, the Bills faced second-and-7 on the Moo Cows’ 40 just inside the two-minute warning. Given the game-management situation, Houston expected Buffalo to rush to drill the clock, then attempt the winning field goal as time expired. Buffalo fielded a heavy package with two tight ends and a fullback — just what the Texans expected. Megabucks pass-catching tight end Charles Clay lined up alongside blocking tight end Matt Mulligan. At the snap Mulligan ran a deep out while Clay ran a seam. Houston double-covered Mulligan — who came into the contest with one reception for 2 yards on the season – while no one covered Clay, who caught a 40-yard untouched touchdown. That’s as sweet as candy cane on the tree.

Sweet ‘n’ Sour Pair of Lend Me a Tight End Plays. Detroit leading 3-0 and facing third-and-3 on the Green Bay 2, the Packers lined up with no one across from Lions tight end Eric Ebron. Seeing the blown coverage, Matt Stafford called for an immediate snap, touchdown. Sweet for tight end advocates, sour for the defense. Green Bay had all its timeouts — realizing no one was lined up near Ebron, why didn’t the Packers call time?

Now it’s the game’s final, untimed down, Detroit ahead 23-20, ball at the Packers’ 39. On the previous snap Green Bay had attempted a Stanford Band play; Detroit expected another. But why was nose tackle Haloti Ngata on the field for Detroit — the Packers were unlikely to run up the middle — while pass-rush artist Ziggy Ansah was out? Not enough pressure on Aaron Rodgers meant plenty of time for Green Bay receivers to reach the end zone. With eight defenders to cover the five Green Bay receivers, how did the Pack’s Richard Rodgers get open for the winning touchdown? No defender even attempted to cover Rodgers, who was standing alone at the Lions’ 3 yard line as Aaron Rodgers’s pass approached.

As the winning pass was caught, there were five Detroit defenders in the end zone, three near Aaron Rodgers and three — where? The missing three were standing around midfield as if to defend another Stanford Band play, and never reacted to the fact that Green Bay was attempting a Hail Mary. Sweet for tight end advocates, sour for the defense. Detroit had a timeout. When the game appeared to end but a penalty created the untimed down, why didn’t Lions coaches call the timeout to make sure their ducks were in a row? At least now the unused timeout can be donated to charity.

Sour Play of the Week (Recurring Sour Play). Twice this season, versus Dallas and New England, the Giants have reached a late fourth-quarter commanding position near the opposition goal line, then have managed to blow games by throwing the ball, thus stopping the clock, rather than simply rushing. Both times the proper strategy hasn’t been some mystery, rather, TOTALLY OBVIOUS.

Now it’s Jersey/A 20, Jersey/B 10 with the Giants facing fourth-and-2 on the Jets’ 4 midway through the fourth quarter. Even go-for-it zealots like The Upshot’s 4th Down Bot expected a field-goal attempt. A field goal would have forced the Jets to score two touchdowns, with the clock remorselessly ticking down. But if trying for the first down, run the ball so that a failed try pins the Jets against their goal line. Instead pass, interception, Jersey/B returns to the 14 and goes on to win in overtime, though does not score two touchdowns. Near the opposition goal line late in the game, somehow the Giants can’t simply do what’s TOTALLY OBVIOUS.

Bot Note. Live tweeting while the score was still close, the Bot urged the Colts to go for it on fourth-and-1 from their 29. Chuck Pagano did the “safe” thing and moments later the score was no longer close, the Steelers hanging a 45-10 defeat on Indianapolis.

Worst Crowd Reaction. As the Flying Elvii melted down in the second half against Philadelphia, the home crowd booed. Sure you’re the defending champions, and stretching back to the start of the 2014 season you’re 26-6. But what have you done for us lately?

Stats of the Week. Denver is on a 15-0 road streak in its division.

The Falcons have followed a 5-0 run with a 1-6 run; the Chiefs have followed a 1-5 run with a 6-0 run.

Since the start of the 2014 season, at home Tennessee is 2-0 versus Jacksonville and 0-13 versus all other teams.

Chicago has lost 12 of its last 15 at home.

Baltimore has losses by 6, 5, 4, 4, 3, 2 and 2 points.

At 4-8, the Dallas Cowboys are one game out of first place in the N.F.C. East.

The Redskins, and a History of Racism. Again the Redskins name is in the news, with federal proceedings in which the team admitted the word is offensive but, like Lenny Bruce, argued that offensive is O.K.; and with Barack Obama’s praise for Adidas, which offered to help any high school that drops an American Indian mascot.

That the N.F.L. franchise representing the nation’s capital won’t stop using an offensive term — for a new name, the Washington Insiders has a nice ring — is more evidence N.F.L. owners view themselves as an unaccountable aristocracy. Changing the Redskins’ name would not have any impact on how American Indians live their lives or on unresolved issues regarding treaties with former North American nations. (If only there were a national version of the 1971 Alaska Native Claims Settlement Act.) But changing the Redskins’ name would show respect while generating good will. Still the league refuses, all the while demanding public subsidies.

Everyone understands that when fans chant “Redskins” or wear headdresses to games, they do not wish to cause hurt feelings — they just want to celebrate their team. Most Redskins faithful probably don’t know that the Redskins’ founding owner, George Preston Marshall, was an unrepentant racist who refused to sign African-American players for a full decade after other N.F.L. teams were integrated. Following scores last night in the nation’s capital, Redskins’ faithful sang,

Hail to the Redskins!

Hail victory!

Braves on the warpath

Fight for old D.C.!

Most probably don’t know that because Marshall promoted the Redskins as a segregated Southern team, in some years the song ended “Fight for old Dixie!” Most Redskins fans probably don’t know that American Indians were held as slaves in old Dixie and in colonial New England, including at colleges of what would become the Ivy League — see the troubling book ”Ebony and Ivy” by Craig Steven Wilder. Most probably don’t know that American Indians suffered indentured servitude in pre-statehood California.

Supporters of the Redskins name sometimes contend that although today the word is objectionable, that was not the case in 1933 when the Boston Braves became the Boston Redskins: because the name was used in polite speech when chosen, it should continue for historical reasons. But in that time, “darky” was not necessarily a slur; it too was accepted in polite speech. There’s no chance the N.F.L. would, today, have a team by that name. There’s no chance fans would sing after touchdowns using that name.

When you hear “Washington Redskins” in that song, mentally substitute the other name. Soon you’ll favor a name change.

The Football Gods Chortled. Two N.F.L. games in four days — Ravens-Browns on a Monday night, then Packers-Lions on Thursday — concluded with the winners scoring a touchdown as time expired, then taking a knee on the extra point.

An odd N.F.L. rule requires a try after every touchdown, even if an added score does not impact the outcome. In high school and college, the scoring team can simply tell the referee it waives the try. In the N.F.L., 11 guys must trot out, snap and kneel.

This 1998 contest ended with New England scoring a touchdown on an untimed down that followed a clearly wrong pass interference flag in the end zone against the Bills as time expired. Furious with good reason, Buffalo Coach Wade Phillips pulled his team off the field for the meaningless try that the referee insisted upon. New England sent out 11 and hiked to place-kicker Adam Vinatieri, who jogged across the goal line for a deuce scored against air. It’s believed to have been the sole down in modern N.F.L. annals on which only one team was on the field.

Note 1: Put this year’s bad-officiating headlines into perspective by noting that bad N.F.L. officiating was a 1998 story line, too. Note 2: because of the phantom deuce, Vinatieri’s career totals now are 1 two-point conversion and 736 single-point conversions.

Unhappy Hour in Hell’s Sports Bar. Hell’s Sports Bar offers unlimited free chicken wings, but patrons must bite them off a live rooster. Sunday, northern Florida, Tennessee and parts of Alabama became an actual Hell’s Sports Bar as viewers were shown the Jacksonville at Tennessee pairing, combined records 6-16, rather than playoff-atmosphere Jets at Giants. The food-cart version of Hell’s Sports Bar was Maine, where viewers saw the Bengals at 2-9 Browns rather than Seahawks at Vikings, combined records 14-8.

Ravens Play in the Pick-Six Lotto. Since 2013, Matt Schaub has thrown 13 touchdown passes to teammates and seven touchdown passes to defenders. Who’s worst in that span for the pick-six? Would you have guessed Matt Ryan or Philip Rivers?

To Each, His Dulcinea. Vikings trailing Seattle 38-0, Minnesota’s Cordarrelle Patterson scored a touchdown and celebrated wildly, waving the ball to the home crowd.

Let’s Hope His Dulcinea Noticed. Late in a home loss to Denver, San Diego’s Jason Verrett intercepted a pass. Verrett turned to the audience and did a stage bow.

Oh Ye of Little Faith. Trailing 15-0 versus Miami, Baltimore kicked a field goal to avert a shutout; trailing 20-0 versus Cincinnati, Cleveland kicked a field goal to avert a shutout; trailing 10-0 versus Arizona, St. Louis kicked a field goal to avert a shutout. All three teams that kicked while being shut out and trailing by at least 10 points went on to lose.

Opening Soon: Star Wars and the Goblet of Fire Go to the Two Towers with Katniss. At this point it’s becoming hard to tell the many “Star Wars” sequels from the many “Harry Potter,” “Hunger Games” and “Lord of the Rings” sequels. “Star Wars” is science fiction, so one may presume whatever one wishes about a galaxy far, far away. But would societies based on super-advanced technology really fight with hand weapons?

If trailers are any indication, the new “Star Wars” movie will feature endless combat among storm troopers, clones, droids and heroes conducted mainly using the high-tech equivalent of rifles and swords. As in the previous six “Star Wars” iterations, soldiers arriving in troop transports will fan out with light arms and try to chase down enemies on foot, rather than, say, dropping bombs. Already in our own Milky Way, the United States military is replacing short-range hand-held weapons with long-range self-guided munitions. Engineers of the Star Wars galaxy have mastered space warps and antigravity, but can’t figure how to make a missile.

Is Hollywood Convincing People Climate Change Is No More Real Than Darth Vader? Katy Perry just called for action against climate change: “Today we’re seeing more extreme weather everywhere ... conditions will worsen.” The scientific proof of artificially triggered global warming is solid. But does that mean greenhouse gases cause “extreme weather?” Far from known.

Entertainment-industry types like to talk greenhouse action. It’s not just the hypocrisy — they fly in private jets, then demand other people conserve fossil fuels. It’s more that filmmakers churn out nonsense about climate change destroying the world. Numerous big-budget movies have depicted warming as the agent of doomsday. For instance, Steven Spielberg, who recently received the Presidential Medal of Freedom, had climate change ending human life by the year 2100 in “A.I. Artificial Intelligence.” This makes it seem global warming is just more Hollywood drivel. Celebrities talking about climate change may serve mainly to discourage people from believing in the reality of the problem.

Adventures in Officiating. The face-masking penalty against Detroit that set the stage for the longest final-play game-winning touchdown in N.F.L. annals was a dicey call. At game speed it looked like face-masking. In slow-motion the contact seemed O.K., since the defender let go immediately, which is what a player is supposed to do if making accidental contact with the face mask. Officials watch at game speed, and responded to the game-speed view.

J.J. Watt Watch. This column has taken issue with J.J. Watt’s incessant immodesty. On the other side of the coin, this season Watt, the Houston defensive end, has been held more than anyone in the league. At Buffalo, on a long completion to Sammy Watkins, guard Richie Incognito wrapped his arm around Watt’s neck, no flag. On a third-down conversion leading to a touchdown, Buffalo’s Jordan Mills pretty much tackled Watt, no flag.

Late in the fourth quarter, Watt was blocked well by the backup guard Kraig Urbik, then simply stood watching, making no attempt to pursue, as LeSean McCoy ran for 20 yards. Mills, an emergency starter just promoted from the practice squad, neutralized Watt on the 40-yard touchdown pass that was the game’s decisive score. With the Bills fielding a backup at guard and a street free agent at tackle on the side of the line Watt was attacking, the Pro Bowler and advertising pitchman was held to no sacks and no hits on the quarterback. That wasn’t because of holding, that was Watt being outplayed by who-dats.

Scout’s Note. At the goal line versus Seattle, Cincinnati drew the defenders wide, then Andy Dalton went up the middle for a touchdown. Sunday versus the Browns, the Bengals went for it on fourth-and-1. A tight end lined up in the backfield, then split wide, drawing defenders, and Dalton went up to the middle for a first down. Reaching the Cleveland 3-yard line, Cincinnati used the rare “quad” set — four wide receivers on the same side — drawing the defense wide, then Dalton went up the middle for a touchdown.

The league has now seen this Cincinnati tactic, and fool me once shame on you, fool me twice shame on me. Drawing defenders wide and then sending Dalton straight up the middle is likely to stop working. Why did Bengals coaches use up this clever move against the Browns, whom they were all but certain to paste?

Rare Moment of Perspective in N.C.A.A. Sports. Stephen Curry of Golden State is tearing up the N.B.A. At his current rate of improvement, Curry soon will ascend directly to a higher plane of existence.

He is doubly interesting because he chose Davidson, an excellent academic college, over bigger-deal basketball programs. Davidson is well regarded for educational quality and also graduates nearly all of its student-athletes. But not Curry. Until he earns his degree, Davidson will not retire his jersey. Three cheers for the Wildcats, and here’s to you, Davidson alums.

What Do the Football Gods Have Against the Detroit Lions? Stretching back to last season’s playoffs, the Lions have lost three of their last 13 games largely on late fourth-quarter officiating decisions that were either outright blunders or questionable judgment. Defensive pass interference against the Cowboys seemed to put Detroit in a commanding position deep in Dallas territory, then officials picked up the flag and the Lions punted, going on to lose by four points. Officials should have awarded Detroit possession at the Seattle 1 after the batted-ball call late in the Seahawks-Lions game, and instead mistakenly awarded possession to the Hawks, Detroit going on to lose by three points. And of course the face-masking call that allowed the extra down on which Green Bay defeated Detroit was sketchy.

A rule of human nature is that we tend to recall what harms us while forgetting good luck; mistakes and disappointments live in our minds in cinematic detail while we retain only hazy reminiscences of pleasure. Natural selection seems better to have prepared us for wariness than happiness.

In sports, fans bitterly remember the flags that go against their teams while not remembering the flags that went against opponents. During the Lions’ streak of bad luck with officiating, they’ve also gotten calls in their favor. But all the Lions’ faithful will recollect from this season is the calls Detroit didn’t get.

Coaching Error of the Week. Kansas City and Oakland tied at 20-20, the Chiefs faced second-and-10. Kansas City showed trips right; the Raiders lined up two defensive backs across from the three wide receivers. Seeing this, Alex Smith quick-snapped and threw sideways; Jeremy Maclin walked in for an untouched touchdown. Raiders coaches saw the same thing Smith saw. Why didn’t they call a timeout?

Authentic Games Standings. For those who came in late, this concept was introduced last week. Remember, I can’t disclose my methodology because I don’t have one.

In the Authentic Games metric, a team’s ranking changes as much based on its opponents as on its own performance. For example, the Packers won in Week 13 but dropped in these standings because the Lions are not an Authentic opponent, while Green Bay lost credit for their opener defeat of the Bears, who were punched out at home by a second-echelon club.

I reserve to right to retcon the Authentic Games standings at any time. Last week the Eagles weren’t a factor and now they are, since defeating the defending champion on its own field is Authentic. This week the Falcons and the Raiders drop out.

The Patriots, losers of two straight, have the most big-game experience, which augurs well for New England. Others that have appeared in the most Authentic contests are Buffalo and Kansas City. Neither has a sterling record, but lots of big-game tests suggests at least one will receive an engraved invitation (or maybe an email) at playoff time.

Carolina: 6-0

New England: 7-2

Cincinnati, Denver 4-2

Kansas City 4-4

Green Bay, Philadelphia 3-2

Arizona 2-1

Jets 3-4

Houston, Pittsburgh, Seattle, Washington 2-4

Buffalo 3-5

Giants, Indianapolis 2-5

Minnesota 1-3

Retcon/White House Crossover Note. Retconning — “retroactive continuity” — is a major factor in superhero movie reboots. It’s shaping up as big in the 2016 presidential campaign, too.

The 500 Club. In California high school playoff action, St. John Bosco put up 52 points and lost by two scores. The final of Corona Centennial 62, Bosco 52 in a 48-minute game extrapolates to an N.F.L. final score of 78-65.

Obscure College Score. Wisconsin Whitewater 31, Wisconsin Oshkosh 29 (Division III playoffs). Located in Oshkosh, the University of Wisconsin Oshkosh has a “new, forward-looking strategic plan.” Are there plans for the past? Division I football is all about recruiting. In theory Division III doesn’t recruit, but the winning programs do. Here’s the recruiting form for Wisconsin Whitewater.

Much of the reaction to Donald Trump’s call “for a total and complete shutdown of Muslims entering the United States” casts him as a cynical populist who is simply supplying the sorts of proposals an Islamophobic electorate demands. By this view, we’re learning about the ugly side of America. But economics offers a different and arguably more optimistic lens for interpreting Mr. Trump’s statement. And it suggests that his statement is less a calculated attempt at feeding a demand for bigotry and more an effort to fuel the hunger for authenticity.

Here’s the crucial idea: It’s not that the American electorate is looking for prejudiced policies. Rather, it’s tired of career politicians and is looking for a leader who breaks the mold. I’m not sure exactly what it is that people are looking for, but let’s call it authenticity. Every politician could claim to be “authentic,” but the truth is, we know that most of them are just saying that to get our vote. This is where the economic theory of signaling comes in.

How can you convince voters that you are in fact the real deal — a trustworthy person who speaks his mind — rather than yet another poll-driven politico? The answer is that you do something that a poll-driven politico would never do, such as making a statement that will alienate many voters. Mr. Trump’s call is outrageous, and it’s politically risky. But that riskiness can be a feature, not a bug. It’s devised to make you infer that he’s not like other politicians.

I’ve long called this the Ventura theory of politics, after the former professional wrestler Jesse “The Body” Ventura, who was elected governor of Minnesota in 1998 as a third-party candidate, after asking people not to “vote for politics as usual.” Soon after his election, Mr. Ventura gave an interview for Playboy magazine in which he said that “organized religion is a sham and a crutch for weak-minded people who need strength in numbers.” It’s not a view that I subscribe to, but more important, it’s not a view that any electorally minded politician would ever admit to.

Given Mr. Ventura’s rising political star, the only explanation for his statement was that he both believed it to be true and was pathologically honest. The statement was politically risky, and offended many voters. Yet that’s the point, and from that day onward, I simply believed any statement that Mr. Ventura made, because that single episode made it hard to believe that he was a poll-driven politician.

An economist recognizes this as the theory of signaling. It’s the same logic that biologists speculate leads male peacocks to grow beautiful but useless tail feathers. Brightly colored feathers are a useful signal of health, because only a healthy male could afford to divert energy to growing them. A result is that peahens, looking for a healthy mate, are attracted to males with attractive but pointless plumage. Likewise, Mr. Trump’s statement wasn’t a serious attempt at articulating policy; it was the political equivalent of a peacock’s feathers, although rather than try to signal his reproductive fitness, he was trying to signal his authenticity.

The good news in this story is that behavior that appears superficial or thoughtless may actually reflect something more important. A peahen may look shallow as she chases the male with the most colorful tail feathers, but in reality, she’s looking for something more serious — a healthy mate. And likewise, it may be that a share of Mr. Trump’s supporters are not drawn to his nativist policies, but rather are looking for something more serious, like a politician who is willing to present his authentic self.

The Ventura strategy is a risky one. Believe me, I’ve tried it, and it means that date night with an economist can be an unusual experience. For sure, I might try to tell my partner that her little black dress looks lovely, but she understands that this is the sort of thing that all men say and so dismisses such compliments. Realizing this, I’ve tried the Ventura strategy: Begin by saying that her lipstick is smudged, so that she knows that I’m the truth-telling type, and then tell her that I like her dress. I don’t think I violate any confidences in revealing that this doesn’t always work well.

This simple interpretation of Mr. Trump’s antics is that he’s betting his campaign on H.L. Mencken’s claim that no one “has ever lost money by underestimating the intelligence of the great masses of the plain people; nor has anyone ever lost public office thereby.” Perhaps this explains some fringe of the electorate, but I think that it sells the American people short.

The economic theory of signaling tells a more optimistic story: Mr. Trump’s outrageous statements signal that he has some other political virtue some voters value. But if authenticity is more important to voters than specific policies, we’re left with an unusual paradox: Some of his supporters may be willing to vote for what his policies signal about his personal character, even as they find these policies repugnant. And if Mr. Trump loses support over the next few weeks, it will reveal the other truth: Risky strategies often fail.

Can machines outperform doctors? Not yet. But in some areas of medicine, they can make the care doctors deliver better.

Humans repeatedly fail where computers — or humans behaving a little bit more like computers — can help. Even doctors, some of the smartest and best-trained professionals, can be forgetful, fallible and prone to distraction. These statistics might be disquieting for anyone scheduled for surgery: One in about 100,000 operations is on the wrong body part. In one in 10,000, a foreign object — like a surgical tool — is accidentally left inside the body.

Something as simple as a checklist — a very low tech-type of automation — can reduce such errors. For example, in a wide range of settings, surgical complications and mortality fell after implementation of a basic checklist including verification of patient identity and body part for surgery, confirmation of sterility of the surgical environment and equipment, and post-surgical accounting for all medical tools. Though simple procedures would all but eliminate certain sources of infections in hospitals, thousands of patients suffer from them in American hospitals every year.

Limits on how much information we can process and manipulate make it hard or impossible for even the smartest and most adept doctors to keep up with new evidence. In 2014 alone, more than 750,000 additional medical studies were published. Granted, a physician might need to keep up only with the evidence in her specialty, but even at a fraction of this rate, it is unrealistic to expect even the best physicians to assimilate every new development in their fields. In cancer alone, 150,000 studies are published annually.

Computers, on the other hand, excel at searching and combining vastly more data than a human. I.B.M.’s Watson — the computer that won Jeopardy! — is among the best at doing so. Teams of physicians at Memorial Sloan Kettering Cancer Center in New York, the University of Texas MD Anderson Cancer Center in Houston, and the Cleveland Clinic are helping to train Watson to apply humanity’s huge store of cancer knowledge to the delivery of more personalized treatment.

At Boston Children’s Hospital, Watson will help diagnose and treat a type of kidney disease. It will team up with Apple to collect health care data; with Johnson & Johnson to improve care for knee and hip replacements; with medical equipment manufacturer Medtronic to detect when diabetes patients require adjustments to insulin doses; and with CVS to improve services for patients with chronic conditions. Another computer-assisted approach to cancer treatment is already in place in the vast majority of oncology practices. Other automated systems check for medication prescribing errors.

To many patients, the very idea of receiving a medical diagnosis or treatment from a machine is probably off-putting. Apart from the sense that it just doesn’t feel right to some, there’s a fundamental question of whether medicine is or can be purely data driven. If the only thing between your illness and its diagnosis and cure is the manipulation of evidence, then, in principle, a computer should one day be able to deliver care as well or better than a human.

But healing may rely on more than the mere processing of data. In some cases, we may lack data, and a physician’s judgment might be the best available guide. A good deal of health care’s benefits may also be in the human interaction between doctor and patient. Placebo effects can be real and strong. Many people engage the health system for reassurance and hope, even when no cure is available. Studies show that patients with close, personal bonds with their doctors and shared engagement with their care are more likely to follow their prescribed treatments. To the extent medical treatment relies on the human touch, on the trust of patients in their doctors and on physicians’ embodiment of authority, a computer-delivered cure may never feel complete.

Patients also may be skeptical that a computer can deliver the best care. A 2010 study published in Health Affairs found that consumers didn’t believe doctors could deliver substandard care. In contrast, they thought that care strictly based on evidence and guidelines — as any system for automating medical care would be — was tailored to the lowest common denominator, meeting only the minimum quality standards.

But algorithms can be put to good use in certain areas of medicine, as complements to, not substitutes for, clinicians. A Princeton University economics professor, Janet Currie, and colleagues developed a simple algorithm to improve care for heart attack patients. Their analysis found that about one-fifth of patients arriving in Florida hospital emergency departments with heart attacks between 1992 and 2011 received treatments not ideally suited to their condition, increasing their chances of dying in the hospital. Their algorithm based on patient characteristics could be used to indicate when treatments were not well matched to patients, potentially improving their outcomes.

Just because algorithms can assist in making decisions doesn’t mean humans should check out and play no role. It is important not to over-rely on data and automation. Bob Wachter, a physician, relates a story about how automated aspects of an electronic medical system contributed to the overdose of a child at the University of California San Francisco Medical Center.

Notwithstanding the cases in which reliance on automation contributes to harm, automation can improve safety, and has. Our ambition to protect us from ourselves inevitably leads to automation, even in medicine. The reason is simple: Some things humans do better than algorithms, but not all things.

Two young campers were sleeping in Yosemite Valley this August when a tree branch snapped and fell on their tent, killing them both. “We don’t know what caused the limb to fall,” said the park’s spokeswoman, Jodi Bailey. “It seems like just a freak accident.”

Ms. Bailey was right: Being killed by a falling object is extremely rare. On average, about 680 Americans each year die this way, or about two people per million. The accident was seen as so unusual that it became national news, covered by CNN, The Los Angeles Times, MSN and The Daily Beast.

Yet in other developed countries, there is another cause of death that is just as rare: homicide by gun.

In Germany, for example, about two out of every million people are fatally shot by another person each year — making such events as uncommon there as the campers’ deaths in Yosemite. Gun homicides are just as rare in several other European countries, including the Netherlands and Austria. In the United States, two per million is roughly the death rate for hypothermia or plane crashes.

In Poland and England, only about one out of every million people die in gun homicides each year — about as often as an American dies in an agricultural accident or falling from a ladder. In Japan, where gun homicides are even rarer, the likelihood of dying this way is about the same as an American’s chance of being killed by lightning — roughly one in 10 million.

In the United States, the death rate from gun homicides is about 31 per million people, which is similar to the rate at which Americans die in car accidents (not including van, truck, bus or motorcycle accidents). The homicides include losses from mass shootings, like those Wednesday in San Bernardino, Calif., and the week before in Colorado Springs. And of course, they also include the country’s vastly more common single-victim killings.

These comparisons help highlight how exceptional the United States is. Here, where the right to bear arms is cherished by much of the population, gun homicides are a significant public health concern. For men 15 to 29, they are the third leading cause of death, after accidents and suicides. In other high-income countries, gun homicides are unusual events. The recent Paris attacks killed 130 people, which is nearly as many as die from gun homicides in all of France in a typical year. But even if France had a mass shooting as deadly as the Paris attacks every month, its annual rate of gun homicide death would be lower than that in the United States.

The accompanying table shows the mortality rates for gun homicides in a variety of countries, along with a correspondingly likely cause of death in the United States.

Our gun homicide numbers come from the Small Arms Survey, a Swiss nonprofit affiliated with the Graduate Institute of International and Development Studies, and represent the average gun homicide death rates in those countries between 2007 and 2012. Our United States death rates come from the Centers for Disease Control and Prevention over those same years. We focused on the rates of gun homicides; the overall rate of gun deaths is substantially higher, because suicides make up a majority of gun deaths in the United States and are also higher than in other developed countries.

The table is not meant to make light of rare causes of death. Instead, we show them as a way to help think meaningfully about the differences among gun death rates.

The rate of gun violence in the United States is not the highest in the world. In parts of Central America, Africa and the Middle East, the gun death rates are even higher — close to those from heart attacks and lung cancer in the United States. In neighboring Mexico, where a drug war rages, 122 people per million die in a gun homicide, a rate slightly higher than Americans’ death rate from pancreatic cancer. But the countries with those levels of gun violence are not like the United States in many other ways, including G.D.P., life expectancy and education. Among developed democracies, the United States is an outlier.

How can my team make the N.F.L. playoffs? It’s a simple question, but answering it can be devilishly complicated.

At the moment, there are 109 games remaining in the season, which, without counting ties, translates into over 649 nonillion possible ways the season could end. (That’s 649 followed by 30 zeros.) Yes, it’s good if your team wins all its remaining games. But then what?

Which outcomes help your team get its best shot at winning the division, getting a first-round bye or having home-field advantage throughout the playoffs? For a normal fan, it’s surprisingly difficult to cheer like a smart person.

It’s always bothered us, too, so we built an interactive tool to help us understand.

Our N.F.L. Playoff Simulator is built for one purpose: to help you explore the paths to the playoffs for every team in the N.F.L. It works like this: We let you choose the outcomes of any game you select and simulate every other game remaining in the 2015 season. (Last year, we considered each game a coin flip; this year we’re using Sagarin ratings, which reflect the fact that, even though anything can happen on a given Sunday, not all teams are created equal.)

For example, we estimate that the Giants have about a 40 percent chance of making the playoffs. But what if they beat the Redskins on Sunday? Their odds move up to 60 percent. The Giants’ most important game after that becomes obvious: their last game, at home against the Eagles on Jan. 3. If they win that, too, we estimate their odds are closer to 90 percent.

Our simulator is not just about assessing your team’s chances of making the playoffs. At 9-0, while not technically a sure thing, the New England Patriots are a safe bet to go to the playoffs this season. (We estimate they have better than a 99.99 percent chance of making it, if anyone’s asking.) But Patriots fans don’t care about making the playoffs — they’re thinking about getting the No. 1 seed in the A.F.C. and home-field advantage. Right now, we give the Patriots about an 80 percent chance of doing so, but a win in Week 12 against the Broncos in Denver would put them in great shape.

Finally, we offer this tool as a bit of an escape. Most teams will not make the playoffs, and many have no real shot, even with seven weeks remaining in the season. Yet not having a realistic chance does not mean “mathematically eliminated,” and our tool can help indulge the most improbable fantasies.

For example, it’s safe to say the Browns, at 2-8, are not thinking about the postseason. Even by winning out, they would end with an 8-8 record, which is almost never good enough. But it is possible — technically, the Browns could even get the top wild-card seed with that record! And now you know precisely how that could happen.