No Justice, No Peace

 

‘She’s never found peace since she left his arms, and never will again till she’s as he is now!’
—Thomas Hardy. Jude the Obscure. (1895).

Done because we are too menny,” writes little “Father Time,” in Thomas Hardy’s Jude the Obscure—a suicide note that is meant to explain why the little boy has killed his siblings, and then hanged himself. The boy’s family, in other words, is poor, which is why Father Time’s father Jude (the titular obscurity) is never able, as he wished, to become the scholar he once dreamed of becoming. Yet, although Jude is a great tragedy, it is also something of a mathematical textbook: the principle taught by little Jude instructs not merely about why his father does not get into university, but perhaps also about just why, as Natasha Warikoo remarked in last week’s London Review of Books blog, “[o]ne third of Oxford colleges admitted no black British students in 2015.” Unfortunately, Warikoo never considers that possibility suggested by Jude: although Warikoo considers a number of reasons why black British students do not go to Oxford, she does not consider what we might call, in honor of Jude, the “Judean Principle”: that minorities simply cannot be proportionately represented everywhere always. Why? Well, because of the field goal percentages of the 1980-81 Philadelphia 76ers—and math.

“The Labour MP David Lammy,” wrote Warikoo, “believes that Oxford and Cambridge are engaging in social apartheid,” while “others have blamed the admissions system.” These explanations, Warikoo suggests, are incorrect: due to interviews with “15 undergraduates at Oxford who were born in the UK to immigrant parents, and 52 of their white peers born to British parents,” she believes that the reason for the “massive underrepresentation” of black British students is “related to a university culture that does not welcome them.” Or in other words, the problem is racism. But while it’s undoubtedly the case that many people, even today, are prejudiced, is prejudice really adequate to explain the case here?

Consider, after all, what it is that Warikoo is claiming—beginning with the idea of “massive underrepresentation.” As Walter Benn Michaels of the University of Illinois at Chicago has pointed out, the goal of many on the political “left” these days appears to be a “society in which white people were proportionately represented in the bottom quintile (and black people proportionately represented in the top quintile)”—in other words, a society in which every social strata contained precisely the same proportion of minority groups. In line with that notion, Warikoo assumes that, because Oxford and Cambridge do not contain the same proportion of black British people as the larger society does, that necessarily implies the racism of the system. But such an argument betrays an ignorance of how mathematics works—or more specifically, as MacArthur grant-winning psychologist Amos Tversky and his co-authors explained more than three decades ago, how basketball works.

In “The Hot Hand in Basketball: On the Misperception of Random Sequences,” Tversky and company investigated an entire season’s worth of shooting data from the NBA’s Philadelphia 76ers in order to discover whether there was evidence “that the performance of a player during a particular period is significantly better than expected on the basis of the player’s own record”—that is, whether players sometimes shot better (or “got hot”) than their overall shot record would predict. Prior to the research, it seems, everyone involved in basketball—fans, players, and coaches—appeared to believe that sometimes players did “get hot”—a belief that seems to predict that, sometimes, players have a better chance of making the second basket of a series than they did the first one:

Consider a professional basketball player who makes 50% of his shots. This player will occasionally hit four or more shots in a row. Such runs can properly be called streak shooting, however, only if their length or frequency exceeds what is expected on the basis of chance alone.

In other words, if a player really did get “hot,” or was “clutch,” then that fact would be reflected in the statistical record by a showing that sometimes players made second and third (and so on) baskets at a rate higher than that player’s chance of making a first basket: “the probability of a hit should be greater following a hit than following a miss.” If the “hot hand” existed, in other words, there should be evidence for it.

Unfortunately—or not—there was no such evidence, the investigators found: after analyzing the data for the nine players who took the vast majority of the 76ers shots for the 1980-81 season, Tversky and company found that “for eight of the nine players the probability of a hit is actually lower following a hit … than following a miss,” which is clearly “contrary to the hot-hand hypothesis.” (The exception is Daryl Dawkins, who played center—and was best known, as older fans may recall, for his backboard shattering dunks; i.e., a high-percentage shot.) There was no such thing as the “hot hand,” in short. (To use an odd turn of phrase with regards to the NBA.)

Yet, what has that to do with the fact that there were no black British students at one third of Oxford’s colleges in 2015? After all, not many British people play basketball, black or not. But as Tversky and his co-authors argue in “The Hot Hand,” the existence of the belief in a “hot hand” intimates that people’s “intuitive conception of randomness depart systematically from the laws of chance.” That is, when faced with a coin flip for example “people expect even short sequences of heads and tails to reflect the fairness of a coin and contain roughly 50% heads and 50% tails.” Yet, in reality, “the occurrence of, say, four heads in a row … is quite likely in a sequence of 20 tosses.” In just the same way, in other words, professional basketball players (who are obviously quite skilled at shooting baskets) are likely to make several baskets in a row—not because of any special quality of “heat” they possess, but instead simply because they are good shooters. It’s this inability to perceive randomness, in other words, that may help explain the absence of black British students at many Oxford colleges.

As we saw above, when Warikoo asserts that black students are “massively underrepresented” at Oxford colleges, what she means is that the proportion of black students at Oxford is not the same as the percentage of black people in the United Kingdom as a whole. But as “The Hot Hand” shows, to “expect [that] the essential characteristics of a chance process to be represented not only globally in the entire sequence, but also locally, in each of its parts” is irrational: in reality, a “locally representative sequence … deviates systematically from chance expectation.” Since Oxford colleges, after all, are much smaller population samples than the United Kingdom as a whole is, it would be absurd to believe that their populations could somehow exactly replicate precisely the same proportions as the larger population.

Maybe though you still don’t see why, which is why I’ll now call on some backup: professors of statistics Howard Wainer and Harris Zwerling. In 2006, the two observed that, during the 1990s, many became convinced that smaller schools were the solution to America’s “education crisis”—the Bill and Melinda Gates Foundation, they note, became so convinced of the fact that they spent $1.7 billion on it. That’s because “when one looks at high-performing schools, one is apt to see an unrepresentatively large proportion of smaller schools.” But while that may be so, the two say, in reality “seeing a greater than anticipated number of small schools” in the list of better schools “does not imply that being small means having a greater likelihood of being high performing.” The reason, they say, is precisely the same reason that you don’t have a higher risk of kidney cancer by living in the American South.

Why might you think that? Turns out, Wainer and Zwerling say, that U.S. counties with the highest apparent risk of kidney cancer are all “rural and located in the Midwest, the South, and the West.” So, should you avoid those parts of the country if you are afraid of kidney cancer? Not at all—because the U.S. counties with the lowest apparent risk of kidney cancer are all “rural and located in the Midwest, the South, and the West.” The county characteristics that tend to have both the highest and lowest rates of cancer are precisely the same.

What Wainer and Zwerling’s example shows is precisely the same as that shown by Tversky and company’s work on the field goal rates of the Philadelphia 76ers. It’s a “same” that can be expressed with the words of journalist Michael Lewis, who recently authored a book about Amos Tversky and his long-time research partner (and Nobel Prize-winner) Daniel Kahneman called The Undoing Project: A Friendship That Changed Our Minds: “the smaller the sample, the lower the likelihood that it would mirror the broader population.” As Brian S. Everitt notes in 1999’s Chance Rules: An Informal Guide to Probability, Risk, and Statistics, “in, say, 20 tosses of a fair coin, the number of heads is unlikely to be exactly 10”—the probability, in fact, is “a little less than 1 in 5.” In other words, a sample of 20 tosses is much more likely to come up biased towards either heads or tails—and much, much more likely to be heavily biased towards one or the other than a larger population of coin flips is. Getting extreme results is much more likely in smaller populations.

Oxford colleges are, of course, very small samples of the population of the United Kingdom, which is about 66 million people. Oxford University as a whole, on the other hand, contains about 23,000 students. There are 38 colleges (as well as some other institutions), and some of these—like All Souls, for example—do not even admit undergraduate students; those that that do consist largely of a few hundred students each. The question then that Natasha Warikoo ought to ask first about the admission of black British students to Oxford colleges is, “how likely is it that a sample of 300 would mirror a population of 66 million?” The answer, as the work of Tversky et al. demonstrates,  is “not very”—it’s even less likely, in other words, than the likelihood of throwing exactly 2 heads and 2 tails when throwing a coin four times.

Does that mean that racism does not exist? No, certainly not. But Warikoo says that “[o]nly when Oxford and Cambridge succeed in including young Britons from all walks of life will they be what they say they are: world-class universities.” In fact, however, the idea that institutional populations ought to mirror the broader population is not only not easy to obtain—but flatly absurd. It isn’t that that a racially proportionate society is a difficult goal, in other words—it is that it is an impossible one. To get 300 people, or even 23,000, to reflect the broader population would require, essentially, rewiring the system to such an extent that it’s possible that no other goals—like, say, educating qualified students—could also be achieved; it would require so much effort fighting the entropy of chance that the cause would, eventually, absorb all possible resources. In other words, Oxford can either include “young Britons from all walks of life”—or it can be a world-class university.  It can’t, however, be both; which is to say that Natasha Warikoo—like one character says about little “Father Time’s” stepmother, Sue, at the end of Jude the Obscure—will never find peace.

Hot Shots

 

… when the sea was calm all boats alike
Show’d mastership in floating …
—William Shakespeare.
     Coriolanus Act IV, Scene 3 (1608).

 

 

“Indeed,” wrote the Canadian scholar Marshall McLuhan in 1964, “it is only too typical that the ‘content’ of any medium blinds us to the character of the medium.” Once, it was a well-known line among literate people, though much less now. It occurred to me recently however as I read an essay by Walter Benn Michaels of the University of Illinois at Chicago, in the course of which Michaels took issue with Matthew Yglesias of Vox. Yglesias, Michaels tells us, tried to make the argument that

although “straight white intellectuals” might tend to think of the increasing economic inequality of the last thirty years “as a period of relentless defeat for left-wing politics,” we ought to remember that the same period has also seen “enormous advances in the practical opportunities available to women, a major decline in the level of racism … and wildly more public and legal acceptance of gays and lesbians.”

Michaels replies to Yglesias’ argument that “10 percent of the U.S. population now earns just under 50 percent of total U.S. income”—a figure that is, unfortunately, just the tip of the economic iceberg when it comes to inequality in America. But the real problem—the problem that Michaels’ reply does not do justice to—is that there just is a logical flaw in the kind of “left” that we have now: one that advocates for the rights of minorities rather than labors for the benefit of the majority. That is, a “cultural” left rather than a scientific one: the kind we had when, in 1910, American philosopher John Dewey could write (without being laughed at), that Darwin’s Origin of Species “introduced a mode of thinking that in the end was bound to transform the logic of knowledge, and hence the treatment of morals, politics, and religion.” When he was just twenty years old the physicist Freeman Dyson discovered why, when Winston Churchill’s government paid him to think about what was really happening in the flak-filled skies over Berlin.

The British had a desperate need to know, because they were engaged in bombing Nazi Germany at least back to the Renaissance. Hence they employed Dyson as a statistician, to analyze the operations of Britain’s Bomber Command. Specifically, Dyson was to investigate whether bomber crews “learned by experience”: if whether the more missions each crew flew, the better each crew became at blowing up Germany—and the Germans in it. Obviously, if they did, then Bomber Command could try to isolate what those crews were doing and teach what it was to the others so that Germany and the Germans might be blown up better.

The bomb crews themselves believed, Dyson tells us, that as “they became more skillful and more closely bonded, their chances of survival would improve”—a belief that, for obvious reasons, was “essential to their morale.” But as Dyson went over the statistics of lost bombers, examining the relation between experience and loss rates while controlling for the effects of weather and geography, he discovered the terrible truth:

“There was no effect of experience on loss rate.”

The lives of each bomber crew, in other words, were dependent on chance, not skill, and the belief in their own expertise was just an illusion in the face of horror—an illusion that becomes the more awful when you know that, out of the 125,000 air crews who served in Bomber Command, 55,573 were killed in action.

“Statistics and simple arithmetic,” Dyson therefore concluded, “tell us more about ourselves than expert intuition”: a cold lesson to learn, particularly at the age of twenty—though that can be tempered by the thought that at least it wasn’t Dyson’s job to go to Berlin. Still, the lesson is so appalling that perhaps it is little wonder that, after the war, it was largely forgotten, and has only been taken up again by a subject nearly as joyful as the business of killing people on an industrial scale is horrifying: sport.

In one of the most cited papers in the history of psychology, “The Hot Hand in Basketball: On the Misperception of Random Sequences,” Thomas Gilovich, Robert Vallone and Amos Tversky studied how “players and fans alike tend to believe that a player’s chance of hitting a shot are greater following a hit than following a miss on the previous shot”—but “detailed analysis … provided no evidence for a positive correlation between the outcomes of successive shots.” Just as, in other words, the British airmen believed some crews had “skill” that kept them in the air, when in fact all that kept them aloft was, say, the poor aim of a German anti-aircraft gunner or a happily-timed cloud, so too did the three co-authors find that, in basketball, people believed some shooters could get “hot.” That is, reel off seemingly impossible numbers of shots in a row, like when Ben Gordon, then with the Chicago Bulls, knocked down 9 consecutive three-pointers against Washington in 2006. But in fact hits and misses are reliant on a player’s skill, not his “luck”: toss a coin enough times and the coin will produce “runs” of heads and tails too.

The “hot hand” concept in fact applies to more than simply the players: it extends to coaches also. “In sports,” says Leonard Mlodinow in his book The Drunkard’s Walk: How Randomness Rules Our Lives, “we have developed a culture in which, based on intuitive feelings of correlation, a team’s success or failure is often attributed largely to the ability of the coach”—a reality that perhaps explains just why, as Florida’s Lakeland Ledger reported in in 2014, the average tenure of NFL coaches over the past decade has been 38 months. Yet as Mlodinow also says, “[m]athematical analysis of firings in all major sports … has shown that those firings had, on average, no effect on team performance”: fans (and perhaps more importantly, owners) tend to think of teams rising and falling based on their coach, while in reality a team’s success has more to do with the talent the team has.

Yet while sports are a fairly trivial part of most peoples’ lives, that is not true when it comes to our “coaches”: the managers that run large corporations. As Diane Stafford found out for the Kansas City Star a few years back, it turns out that American corporations have as little sense of the real value of CEOs as NFL owners have of their coaches: the “pay gap between large-company CEOs and average American employees,” Stafford said, “vaulted from 195 to 1 in 1993 to 354 to 1 in 2012.” Meanwhile, more than a third “of the men who appeared on lists ranking America’s 25 highest-paid corporate leaders between 1993 and 2012 have led companies bailed out by U.S. taxpayers, been fired for poor performance or led companies charged with fraud.” Just like the Lancasters flown by Dyson’s aircrews, American workers (and their companies’ stockholders) have been taken for a ride by men flying on the basis of luck, not skill.

Again, of course, many in what’s termed the “cultural” left would insist that they too, stand with American workers against the bosses, that they too, wish things were better, and they too, think paying twenty bucks for a hot dog and a beer is an outrage. What matters however isn’t what professors or artists or actors or musicians or the like say—just as it didn’t matter what Britain’s bomber pilots thought about their own skills during the war. What matters is what their jobs say. And the fact of the matter is that cultural production, whether it be in academia or in New York or in Hollywood, simply is the same as thinking you’re a hell of a pilot, or you must be “hot,” or Phil Jackson is a genius. That might sound counterintuitive, of course—I thought writers and artists and, especially, George Clooney were all on the side of the little guy!—but, like McLuhan says, what matters is the medium, not the message.

The point is likely easiest to explain in terms of the academic study of the humanities, because at least there people are forced to explain themselves in order to keep their jobs. What one finds, across the political spectrum, is some version of the same dogma: students in literary studies can, for instance, refer to American novelist James Baldwin’s insistence, in the 1949 essay “Everybody’s Protest Novel,” that “literature and sociology are not the same,” while, at the other end of the political spectrum, political science students can refer to Leo Strauss’ attack on “the ‘scientific’ approach to society” in his 1958 Thoughts on Machiavelli. Every discipline in the humanities has some version of the point, because without such a doctrine they couldn’t exist: without them, there’s just a bunch of people sitting in a room reading old books.

The effect of these dogmas can perhaps be best seen by reference to the philosophical version of it, which has the benefit of at least being clear. David Hume called it the “is-ought problem”; as the Scotsman claimed in  A Treatise of Human Nature, “the distinction of vice and virtue is not founded merely on the relations of objects.” Later, in 1903’s Principe Ethica, British philosopher G.E. Moore called the same point the “naturalistic fallacy”: the idea that, as J.B. Schneewind of Johns Hopkins has put it, “claims about morality cannot be derived from statements of facts.” The advantage for philosophers is clear enough: if it’s impossible to talk about morality or ethics strictly by the light of science, that certainly justifies talking about philosophy to the exclusion of anything else. But in light of the facts about shooting hoops or being killed by delusional Germans, I would hope that the absurdity of Moore’s “idea” ought to be self-evident: if it can be demonstrated that something is a matter of luck, and not skill, that changes the moral calculation drastically.

That then is the problem with running a “left” based around the study of novels or rituals or films or whatever: at the end of the day, the study of the humanities, just like the practice of the arts, discourages the thought that, as Mlodinow puts it, “chance events are often conspicuously misinterpreted as accomplishments or failures.” And without such a consideration, I would suggest, any talk of “values” or “morality” or whatever you would like to call it, is empty. It matters if your leader is lucky or skillful, it matters if success is the result of hard work or who your parents are—and a “left” built on the opposite premises is not, to my mind, a “left” at all. Although many people in the “cultural left,” then, might have the idea that their overt exhortations to virtue might outweigh the covert message being told by their institutional positions, reality tells a different tale: by telling people they can fly, you should not be shocked when they crash.

Luck of the Irish

 … I hear him mock
The luck of Caesar, which the gods give men
To excuse their after wrath.
Antony and Cleopatra V, ii

Stephanie Wei, the ex-Yalie golf blogger, recently got her press credentials revoked for the crime of filming tour players during a non-televised Monday practice round at the WGC-Match Play using a live-stream video app. According to her own account, the tour said that her “live-streaming of behind-the-scenes content had violated the Tour’s media regulations.” Wei has admitted that the tour did have a right to take away her credentials (it’s in her contract), but she argued in response that her work produced “fresh, interesting and different content,” and thus enhanced the value of the tour’s product. Wei’s argument however, as seductive as it might be, is a great example of someone manipulating what Thomas Frank has called “the titanic symbolic clash of hip and square” for their own ends: Wei wants to be “hip”—but her actual work is not only just as “square” as any old-school sportswriter who didn’t see fit to mention that Ty Cobb was one of the meanest and most racist men in America, or that Mickey Mantle was a nihilistic drunk, but in fact might be even more harmful.

As Thomas Frank was writing so long ago as the 1990s, the new digital economy has been sold as an “economic revolution,” celebrating “artists rather than commanders, wearers of ponytails and dreamers of cowboy fantasies who proudly proclaim their ignorance of ‘rep ties.’” In contrast to the old world of “conformity, oppression, bureaucracy, meaninglessness, and the disappearance of individualism”—in a word, golf—the new would value “creativity” and “flexibility.” It’s the bright new world we live in today.

So inevitable does that narrative appear that of course Deadspin, the hipsters’ ESPN, jumped on it. “It’s not surprising,” proclaimed Samer Kalaf, “that the PGA Tour, a stuffy organization for a stuffy sport, is being truculent over something as inconsequential as this, but that doesn’t make it any less ridiculous.” The part of Judge Smails (Caddyshack’s prototypical stuffed shirt) is played in this drama by the PGA Tour’s Ty Votaw, who told Golf.com that in the eyes of the tour, what Wei did was “stealing.” On the theory of the tour, what Wei did extracted value from the tour’s product.

Wei herself, to be sure, had a different theory about her actions. Wei wrote that her purpose in transmitting the “raw, alternative footage”—excellent use of buzzwords!—was to “spread fanfare.” In other words, Wei was actually doing the PGA Tour a favor because of her hip, new kind of journalism. It’s an argument you are probably familiar with, because it is the same one the venues that don’t pay bands, or the companies that tell you to take an internship, or people who tell you to “get on YouTube” make: think of the exposure, man!

Yet while Wei pleads her case on the basis of her hepcat, app-using new jive journo-ing, in fact her stuff isn’t much, if any, different from the bad old days of sports reporting, when writers like Grantland Rice were more interested in palling around with the athletes (and, more worryingly, the owners) than with the audience. The telling detail can be found in her coverage of Rory McIlroy’s win at the very same tournament she got busted at: the Match Play.

The Match Play, obviously, is conducted under match play rules and not stroke play, which meant that, to win, Rory McIlroy had to win seven consecutive matches. In several of those matches, McIlroy came from behind to win, which prompted the following from Wei: “What I found the most interesting [what? Wei is missing a noun here] about McIlroy’s victory,” Wei wrote, “and his route to the winner’s circle was the way he found another gear when he was losing late in the match.” This McIlroy is not the same McIlroy as the one “we knew two years ago”—he is “a more mature one that knows how to dig deep.” Wei thusly repeats one of the most standard sorts of sportswriting cliche.

What of it? Well, the difficulty with this particular cliche, the reason why it is not “on a par” with those jolly old-school fellows who didn’t mention that a lot of ball players took speed, or cheated on their wives, or beat them, or that the owners were chiseling everyone for pennies on the dollar while looking the other way as men’s brains were slowly battered into jello—oh wait, that still happens—is that it justifies a species of rhetoric that gets repeated in many other arenas of life. (The most important of them being, of course, the economic.) That is the rhetoric of “toughness,” the “intangibles,” and so on—you know, the ghosts that don’t exist but are awfully handy when justifying why nobody’s getting a raise.

The belief in a player’s “toughness” or whatever words a given sportswriter can invent—the invention of such terms being largely what sportswriting is about—has been at best questionable, and at worst a knowing cynicism, ever since Gilovich’s, Tversky’s, and Vallone’s landmark 1985 paper, “The Hot Hand in Basketball: On the Misperception of Random Sequences.” The “hot hand,” the three proved, is merely a product of cognitive bias: when people are asked, for instance, to predict sequences of coin tosses, they inevitably expect the tosses to be half heads and half tails—even though such an even breakdown, no matter how many tosses are made, is nearly impossible.

So too in sports: writers continually ask their audience to believe that an athlete has “matured,” or “dug deep,” or what have you, when the more likely explanation is just that the athlete’s inherent talent level eventually expressed itself—or, in the case of a losing effort, the other side “got lucky.” Outcomes in sports are determined by skill (and the lack of it), not by “grit” or “will.” Rory won because he is a better golfer than nearly anyone on the planet, and while that skill can be masked by chance, over time it is more likely to expose the other player’s relative lack of skill.

Rory McIlroy won his tournament because he is a good golfer, not because he has some kind of psychological strength the rest of us lack. The fact that Stephanie Wei participates in this age-old sporting charade demonstrates that, for all her pretensions to the contrary, there isn’t a great deal different between her “new school” approach and that of her “stuffy” opponents. There is, perhaps, even reason to cheer for the PGA Tour in this dispute: at least they, unlike many in the age of the New Economy, believe people ought to get paid.