Donald Trump Jr. and Very Big Numbers

Recently, Donald Trump, Jr. – son of the Republican nominee/possible lizard person – tweeted out this graphic:


The insinuation, of course, is that any Syrian refugee could possibly be an ISIS sleeper agent trying to gain access to the United States. The comparison was quickly denounced in some circles, roundly praised in others, and given a stern rebuke by the Wm. Wrigley Jr. Co., the maker of the fruity candy, who said, “Skittles are candy. Refugees are people. We don’t feel it’s an appropriate analogy. We will respectively refrain from further commentary, as anything we say could be misinterpreted as marketing.”

Perhaps the most interesting response came from Alex Nowrasteh of the Cato Institute. Nowrasteh argued that the Skittles meme is an appropriate metaphor, but only if utilized properly. It is, after all, a very different story if our bowl holds fifty Skittles or if it holds a million. Per Nowrasteh:

Imagine a bowl full of 3.25 million Skittles that has been accumulated from 1975 to the end of 2015.  We know that 20 of the Skittles in that bowl intended to do harm but only three of those 20 are actually fatal.  That means that one in 1.08 million of them is deadly.  It gets even better though.  There are over three hundred million Americans and not everyone can get a Skittle.  This means that the chance of any American actually eating the fatal Skittle and perishing is about one in 3.64 billion a year during the 41-year time period. Do you eat from the bowl without quaking in your boots?  I would.

The odds of an American being killed by a refugee in any given year are one in 3.64 billion. That is an absurdly small number. But is it correct?

Nowrasteh arrived at his estimate by finding the number of refugees admitted to the United States who were either convicted of planning a terrorist attack or actually carried one out. There were twenty such individuals. “Refugees were not very successful at killing Americans in terrorist attacks,” Nowrasteh writes. “Of the 20, only three were successful in their attacks, killing a total of three people.”

Nowrasteh then comes to his yearly average by dividing three by the sum total of the American population from 1975-2015 (roughly 10.9 billion) to arrive at his one in 3.64 billion figure. (The most dangerous form of immigrant is the one here on a tourist Visa: the odds of dying to such a person in any given year are one in 3.6 million. The second most dangerous? Students.)

“The three refugee terrorists were Cubans who committed their attacks in the 1970s,” Nowrasteh adds. “(They) were admitted before the Refugee Act of 1980 created the modern rigorous refugee-screening procedures currently in place.” According to Nowrasteh, there have been no such murders committed by foreign-born refugees since that act passed.

There are a couple things to consider here. The first is that translating a yearly probability into an absolute probability is a fairly tricky process. The absolute probability over the span from 1975-2015 is roughly 1 per 166 million people. (The sum of Americans who are alive today plus the number who have died since 1975 gives the total number of Americans alive at any point since 1975. That number is approximately 500 million. If three died in refugee-related terrorist activities over that span, that gives us approximately one in 166 million.) But 41 years does not cover the average American life-span. If we can expect to live to 75, on average, and we can expect this rate to remain constant at 1 in 3.64 billion, then the odds of being killed by a refugee-terrorist are now one in 49 million, or roughly the odds of winning the Powerball if you buy four tickets.

Second, if we use the number of refugee-terrorists (whether or not they were successful in their attacks) as our numerator, the odds get a little worse. The number of victims in any given terrorist attack is highly variable. Sometimes these attackers are victims of their own incompetence and there are no victims except for an amateur bomb-maker and the application of common sense. Future attacks, if they are ever indeed carried out, might be more effective at producing casualties. According to John Mueller, professor at Ohio State University, there have been approximately 3.2 million refugees admitted to the United States since 1975. Of those, 20 have attempted acts of terror, or about one for every 162,000 refugees. That’s almost identical to our current rate of mass shooters, which begs an uncomfortable question: are comfortable with the current level of mass shooters in our country?

That leads us to the final, most important factor: is there any reason to expect that the current rate of one in 3.64 billion should stay constant? This is the question at the heart of the debate. “Perhaps future Skittles added into the bowl will be deadlier than previous Skittles but the difference would have to be great before the risks become worrisome,” says Nowrestah. Total refugees from ISIS-controlled territories have increased steadily. According to the State Department, there were 31 total Syrian refugees admitted into the United States. In 2015, that number was 1,682. Refugees from high-percentage Muslim countries have increased a small amount since 2008 (30,934 last year compared to 23,490 in 2008).

Of the twenty refugee-terrorists on Nowrasteh’s list, nine of them entered the US after 9/11. Four of them – Yassin Aref, Najibullah Zazi & Zarein Ahmedzay, and Abdullatif Aldosary – came from regions affiliated with terror groups. Given the high numbers of refugees from these areas, the relative risk for such refugees is one in 44,000 – four times higher than the average rate for refugees. (None of these men were successful in carrying out their crimes).

Depending on how you frame the question, you have between a one in 49 million and a one in 166 million chance of being killed by a refugee-terrorist on American soil. Somewhere between one and 44,000 and one in 162,000 refugees will attempt such an act. Those numbers may seem high, maybe even intolerably high. But stop to consider the fact that you are 7300 times more likely to die in a car accident than at the hands of a refugee-terrorist. Have you stopped driving yet?

The refugee vetting process starts with the UNHCR, which is the U.N.’s refugee agency. The U.N. performs interviews, biological screenings, and attempts to do background checks to weed out criminals and military combatants. After the U.N. refers candidates to the U.S., the Resettlement Support Center initiates an interagency background check, sending the relevant information through the FBI, NCC/IC, the State Department, and Homeland Security. (Syrian refugees receive an even more thorough screening than the average refugee.) Basic biometrics are collected and a medical screening is done. Less than half of referrals are accepted. Finally, an NGO determines where refugees will be settled.

Refugees are subject to the highest level of scrutiny and security checks of any traveler to the United States. The process takes 18-24 months to complete. Refugees have little influence on where and when they will be resettled. As a recipe for spreading terror across an ocean, this method has serious drawbacks. It’s no wonder why the most deadly terrorists came here on student and travel visas. Though we may squabble about particular numbers, the current risk posed by refugees is absurdly low.


Mike Zimmer and Strategic Deception

A couple of years ago, during a famous hand at the London event of the European Poker Tour, an amateur player named Shlomi Angel looked down at his cards to see two kings staring back at him. In Texas Hold ‘Em, the default variant at these events, each player is dealt two cards face down. These are known as the “hole cards,” and pocket kings are the second-best set of hole cards a player can be dealt – only pocket aces are better. Shlomi peered stoically at his opponents before throwing out his bet. Two players called. The first was an Iranian pro named Farzad Banyani. The second was a Canadian player named Daniel Negreanu.

In 1998, Daniel Negreanu became the youngest player ever to win a World Series of Poker bracelet, earning him the moniker “Kid Poker.” Since then, Negreanu has made tens of millions of dollars in tournament winnings to go along with countless endorsement deals and a Netflix documentary about his life. Kid Poker might be the closest thing to a celebrity that the poker world has produced since Wild Bill Hickok.

After the flop – the first three community cards that are dealt face up on the table – Shlomi bet again, and he continued to bet big. Banyani folded. Negreanu paused and studied Shlomi carefully. “He looked at me and I could see he was nervous,” said Negreanu, recalling the hand. “But it was a different kind of nervous. He didn’t look like he wondered if he had the best hand or like he was bluffing. He looked nervous like he was thinking, ‘Please fold.’” So Negreanu called. When a queen hit on the turn, the fourth community card, Shlomi bet again, and again Negreanu called. After the river – the fifth and final community card – was dealt, Shlomi bet somewhat meekly, about a third of the pot.

Daniel seized the opportunity.  He raised big, pushing out a bet four times the size of Shlomi’s. “I figure you have aces or kings,” he said, calm as a millpond.

But if he knows I have aces or kings, Shlomi may have thought, he must have me beat. Looking equal parts awed and humbled, Shlomi quietly pushed his cards to the middle of the table and folded.

Robert Greene, writing on misperception strategies in warfare, notes that “People’s perceptions are filtered through their emotions; they tend to interpret the world according to what they want to see.” Shlomi Angel filtered Daniel Negreanu’s perfect read through fear: fear of losing his chips, fear of getting knocked out of the tournament, perhaps even fear of looking silly on television. If he could have steeled his nerves for a moment, perhaps he would have been able to ask himself an extremely important question: If Daniel’s hand is better than mine, why is he encouraging me to fold?

In poker, these kinds of mind games are known as levels. A rank beginner might bet big only when dealt a strong hand while immediately folding his bad hands, and in doing so is essentially playing his hole cards face up for his opponents to see. A slightly more sophisticated player will take the opposite tack. As the film Rounders put it, “If a fish acts strong, he’s bluffing. If he acts meek, he’s got a hand. It’s that simple.” An even more sophisticated player, realizing this, will reverse his strategies again, on and on and on until it reaches a sort of parity: any size bet a player might make with the top of her range should be the same sort of bet she would make at least occasionally with the bottom of her range.

Compare this to a short, blink-and-you-miss-it anecdote from Moneyball, Michael Lewis’ relentlessly entertaining account of Billy Beane’s efforts to build a functional major league roster on a small-market budget. About halfway through the book, Lewis introduces us to Scott Hatteberg as Hatteberg is trying to prepare to hit against a particularly difficult pitcher named Jamie Moyer. “Moyer was one of the few pitchers in baseball who would think about Scott Hatteberg,” writes Lewis. “Moyer would know that Hatteberg never swung at the first pitch – except to keep a pitcher honest – and so Moyer might just throw a first-pitch strike. But Moyer would also know that Hatteberg knew that Moyer knew. Which brought Hatteberg back to square one.” If these evolutions sound at all like the Battle of Wits from The Princess Bride, it’s because it is exactly the same process.

But in poker, as with pitching or The Princess Bride, high stakes and a time constraint lead people to make bad decisions they might have avoided under more relaxed circumstances.

“Feed (your opponent’s) expectations, manufacture a reality to match their desires, and they will fool themselves,” continues Robert Greene. “The best deceptions are based on ambiguity, mixing fact and fiction so that the one cannot be disentangled from the other.” Put another way, the best deceptions tell a plausible story. This is as true in poker as it is in warfare or spycraft. For the top players, a hand of poker is akin to a highly specific genre of interactive storytelling that uses a combination of bet sizes and emotional cues, in lieu of words, to imply certain climaxes. A player whose stories “make sense” – that is, the player with enough sophistication convince her opponents she is strong when she is weak and weak when she is strong – is a player who is poised to cash in.

Stories of this genre, filtered through the fear or anxiety of their specific (often, but not always, one-person) audience are also a fixture of competitive spots. Football writer Matt Waldman has made this observation explicit. “I’ve arrived at the conclusion that good route running is like telling a suspenseful story,” he observed as he described the subtle factors that help a smaller, less-physically gifted player like Wes Welker break away from his coverage with astonishing regularity. In football, as in poker, this becomes more and more true at the highest levels of the game, as abilities converge and the so-inclined can put more time into studying their opponents.

The football analyst Brett Kollman underscored this theme in a video about the matchup between Oakland receiver Amari Cooper and Kansas City cornerback Marcus Peters. His analysis invokes the tension between what Cooper is trying to make Peters believe he’s seeing, and what he’s actually trying to accomplish. “About four to five yards into his route he stutters just a little bit as if he’s running a hitch,” Kollman describes. “Now, that in itself isn’t really special, but keep in mind what that little stutter means to a corner like Peters. He knows he’s not as fast as Cooper, and he knows that the Raiders are eventually going to try to exploit that difference of speed with a route like a stutter go.” A stutter go is, as it sounds, a play where a wide receiver chops his feet quickly (the stutter), trying to make it seem like he’s going to turn back and look for the ball, but instead just accelerates and runs as deep as he can. What Kollman is saying is that Cooper is trying to take advantage of what Peters expects will come after that stutter. “That’s the fear that Peters is working with here,” continues Kollman. “He’s thinking ‘Stutter go!’ because that’s a great route to get rid of his cushion immediately, and that goes double because Peters isn’t really that fast to begin with. So as soon as he sees Cooper come out of that stutter, look at Peters’ hips.” Here, Peters’ hips turn counterclockwise, rotating his body towards the sideline. “He’s starting to flip and run immediately, because in his mind, he’s thinking, ‘Shit, it’s the stutter go. I need to get over the top of this thing right now or I’m going to get burned.’”

But on this particular play, Cooper wasn’t running a stutter go. He was running what is called a dig: he turns at a 90 degree angle and cuts straight across the field. At the exact moment Peters’ hips are facing the sideline, Cooper snaps his own to the inside of the field, and in an instant Peters has his back turned to his opponent. Cooper is as wide open as you’re likely to see a wide receiver be in the NFL – but despite the fact that he won his matchup, the ball wasn’t thrown his way. His quarterback, Derek Carr, threw it underneath for a three-yard loss. “Carr ignores him, for whatever reason,” Kollman adds with an air of disappointment. “Literally the next play after that, one play later, I’m sure Cooper told Carr in the huddle, ‘Hey, I’m beating the shit out of this guy over here, please throw me the ball.’ And Carr does exactly that for a 23-yard gain. Again, he gets Peters with a double move – a post corner this time – and Peters can’t do anything about it, because when you’re that far off, and you’re giving that much runway to a wide receiver, you really have no shot of getting your hands on them.”

The combination of high stakes, a time constraint, and a narrative built on exploiting fear can create a powerful competitive advantage. But fear is not the only state of mind that can be exploited in this manner. When the Twenty Committee, the World War II British espionage service, launched Operation Mincemeat, it was a direct attempt to exploit Hitler’s belief that the Allied Forces would invade Europe through Greece and the Balkans. The Twenty Committee showed Hitler what he thought he wanted to see. The intelligence they fed to Hitler simply convinced him he was right to believe what he knew all along.

In a film study session with the NFL Network, Richard Sherman, the brash and brilliant Seahawks cornerback, describes how he brings the same elements of deception to his game. “People are like, ‘Ah man, the best corners, man, nobody throws to their side,’” he says. “You’re not a ‘best corner’ if nobody’s throwing to your side. Because the best corners get picks. And they get picks because they bait quarterbacks into throwing to their side, showing them exactly what they want to see. They want to see a picture of me closer to the number one receiver than the number two receiver? I will give them that at the snap. But by the time the ball comes out, I will be where I intended to be. I’ll give him what he wants, what he thinks he’s seeing, and he’ll throw it and he’ll be like, ‘You sneaky sneaky!’”

Next, Sherman describes intercepting Rams quarterback Sam Bradford on a play that effectively knocked the Rams out of the playoffs. “To tell you the truth, he hadn’t really tried me all day. I was kind of pissed.” Sherman is referring to the fact that he was second in the league in interceptions to Chicago’s Tim Jennings. Sherman is legendary for his competitive nature. He once gave an interview with the ESPN personality Skip Bayless where the two argued viciously over which was more accomplished in their respective fields. To Richard Sherman, finishing second is unacceptable: this is, after all, a man who says you cannot be the best cornerback if you cannot lure quarterbacks into your traps. “Tim Jennings had just gotten another pick, I just watched him before we played. So he was at nine, and I was like, ‘You’re not going to give me the chance to get to eight?’”

“For quarterbacks like Sam Bradford, who are just off of rhythm, like ‘Bam bam bam bam bam BALL,’” – here, Sherman pantomimes a quarterback working through his progression in quick, percussive movements – “you have to be a little more sneaky. You have to let them get the picture they want. I’m showing them what they want to see. I’m giving them an illusion of sorts.” The Seahawks’ bread-and-butter coverage is called Cover-3, which in its simplest form means they have three defenders playing deep, each responsible for a third of the field. A common counter-tactic to Cover-3 is a play called Four Verticals – if you send four players deep against their three defenders, more often than not one of them should be undefended. That was exactly what the Rams tried to do on the play in question. “They were in trips, they ran three verticals (to the near side of the field,” Sherman explains. “The inside vertical is simply to pull the safety out of it, and (isolate) me against two receivers.” To play a deep zone against two receivers, the defender has to split the difference. “You have to play it more 80-20. 80% to the outside, 20% to the inside receiver. I was watching the quarterback’s eyes and reading, and the way I played it was more 60-40 than 80-20. I thought his shoulders were aimed at number 2. He got past the point of no return, and there was a play to be made.” As Bradford released the ball, Sherman cut under the inside receiver and intercepted the ball.

Whether or not they were consciously aware of doing so, Richard Sherman and the spies of the Twenty Committee were actively exploiting cognitive biases, in this case confirmation bias. Confirmation bias is the tendency to search for and interpret information in a way that confirms what we already believe or what we expect to see. The Nobel laureate Daniel Kahneman put it like this: “Contrary to the rules of philosophers of science, who advice testing hypotheses by trying to refute them, people (and scientists, quite often) seek data that are likely to be compatible with the beliefs they currently hold.” Robert Greene said that feeding your opponent a story that matches their desires will often cause them to fool themselves. What desire is more powerful than the desire to be right?

In September, 2016, during the weak leading up to their home contest against the Green Bay Packers, Minnesota Vikings head coach Mike Zimmer refused to report whether his starting quarterback for the game would be the aging Shaun Hill or the newly-acquired Sam Bradford. “I try to keep my cards close to the vest,” Zimmer explained. It was reasonable, of course, to have not yet decided. Hill had just completed a solid, if unspectacular, performance against a middling Tennessee Titans squad, while Bradford was busy learning his third offensive playbook in four years. (If you’re tempted to think that sounds easy, University of Minnesota neuroscientist David Redish has compared this process to trying to master “a musical instrument that’s scheming against you.”) All other things being equal, however, Bradford is a better quarterback than Hill. Adamant that his public secrecy would earn him a competitive advantage, if only a slight one, against the Packers, Zimmer would not budge. “You’ll have to wait ’til Sunday.”

But isn’t this just one more example of that same leveling war we see in poker games, or between Scott Hatteberg and Jamie Moyer, or with Westley and Vizzini in their Battle of Wits? Is there any reason to think that Mike McCarthy, the coach of the Packers, would be paralyzed with indecision about how to prepare for such similar players?

Shlomi Angel folded to Daniel Negreanu because Negreanu told a story that was consonant with his fears. Marcus Peters flipped his hips to run deep because he expected Amari Cooper to run a stutter-go sooner or later. Sam Bradford threw an interception to Richard Sherman because Sherman painted a picture of an open receiver in the gap of the Cover-3. All three took what their opponents either expected or feared and combined that with the added pressures of high stakes and a time constraint. A suspenseful story combined with high stakes and no time to analyze will, more often than not, lead a person to make a bad decision. It should be no surprise that many of the spies of the Twenty Committee became novelists after the war. After all, storytelling is the heart of deception .

If there were a real strategic advantage to be gained here, Mike Zimmer could have taken a lesson from Negreanu, Cooper, or Sherman, or any of the geniuses from the Twenty Committee. He could have said the team was doing everything possible to bring Bradford up to speed, but perhaps add that he wasn’t making as much progress as they would like. He could have had a player leak to the media that Shaun Hill was taking most of the first-team reps in practice. He could imply since that Shaun Hill led the Vikings to a win and he deserved another shot to start. After all, inviting Packers coaches to be prepared to deal with both quarterbacks would be less helpful than convincing them they need only worry about the wrong one. In short, he could have tried to tell a story.

But that was never going to happen. On September 18th, Sam Bradford took the field as the Vikings’ starting quarterback, and promptly led his new team to a hard-earned victory against their division rival on the strength of what was possibly his best game as a professional football player. It is unclear whether Zimmer’s attempted subterfuge had any impact on the result.