Let’s get the terrible stuff out of the way first. Characters in the movie keep wondering where God is and why he isn’t doing more to help them. God’s answers may not reach the questioners but we definitely get them, transmitted through an epigraph from the Book of Job (‘Where were you when I laid the foundations of the earth?’), a sequence of graphics (lots of lava, oceans, shots of the edges of the earth taken from outer space) that makes you admire the superior creativity of almost any screensaver, and a prehistoric inset revealing to us that this God is a Darwinist. The fittest surviving creature we see is a sort of oversized scaly ostrich, which steps on the head of a fallen lesser animal and trots off into the woods looking very pleased with the experience. The effect is that of 2001 not quite meeting Jurassic Park.

There’s some modern material that’s pretty bad too. The date seems to be the present, there are glassy skyscrapers everywhere, and Sean Penn seems to be a mid-career architect. We can’t be sure of this because he doesn’t do anything, just sits in meetings thinking about his murderous Oedipal days as a boy, and occasionally wandering through mental landscapes represented by deserts and small rooms, suggesting that neither his nor Malick’s imagination runs to anything very exciting by way of inner scenery.

God’s answer to his questioners, or what it would be if they could see the movie, seems to be: don’t bother me, can’t you see I’m still recovering from creating the world? And who are you anyway? Equipped with this generous response we may become – I became – less irritated by the large-scale drivel and more sympathetic to the tiny central characters of the film’s story, stuck with such a God and effectively abandoned by their creator and their director alike.

Well, Malick hasn’t abandoned them, he’s just isolated them from his own metaphysical insights, and this could be seen as a form of care or respect. The bulk of the movie – one critic has calculated the quantity at 90 minutes out of 138 – is set in small-town Texas in the 1950s, when the Sean Penn character was a boy, Jack, played by Hunter McCracken with a worried, stoic stubbornness that is really engaging. All the acting is persuasive, understated, in tune with what we might think of as the quiet strangeness of ordinary life once you stop to look at it. We are watching not so much a piece of American naturalism as the film equivalent of a hyper-realist painting. It seems merely real and highly stylised in equal degrees.

Brad Pitt is the father, terse, solemn, anxious to follow the precepts of the Darwinian proto-ostrich, and to make men – that is, bullies – out of his three sons. It’s to the character’s credit that he’s not very good at this, or at being the ruthless man of commerce he likes to think he is. We learn that he believes he has missed a career as a musician, but this is the one false note within this dry and rather moving non-idyll. It’s not that Brad Pitt can’t do the soulful fellow playing Bach on the church organ: he’s become good enough to do most things. It’s that the soulful fellow seems wheeled in to get a spiritual effect without too much work on the script. Jessica Chastain as the mother drifts prettily around the house as if she were waiting to be called for some as yet unknown saintly activity – at one point she does levitate a little, to make sure we get the mood, or perhaps just to show how Jack feels about her in memory. All three boys are wary and sceptical throughout, but none of them seems deeply unhappy, even in their bad moments. They have small smiles that suggest they know childhood will soon be over, and a good thing too. There is a fine, hands-off scene in which Jack watches his father lying under the car fixing something. The car is propped up at an angle. This is at a moment when Jack really hates his father and has said so to him. All he has to do now – we read his mind without needing any kind of cue – is to kick the prop away and the deed will be done, the father crushed. Jack doesn’t think about it for very long, just turns away. Oedipus should have been so lucky, or so patient.

The big events later in the movie are the father losing his temper and, in a more restrained mode, his job; Jack and his two brothers racing around, teasing each other; Jack stealing into the empty house of a girl he likes, and making off with her slip, which he throws into the river; Jack almost wounding one of his brothers with an air rifle. The street where the family lives has almost no traffic, the road is like an extension of the garden; the neighbour’s property begins at some invisible point on the broad lawn between houses. No fences make no neighbours. This is America in its disconnected, depopulated solitude. There is a grandmother, played by Fiona Shaw, but I didn’t know she was a grandmother till I read the credits.

And the big event early in the movie is the death of Jack’s brother, the middle child, at the age of 19. No one seems likely to get over this, least of all the mother, who travels through her grief as if it were just blank, unmeasurable time, and as if all the religious consolations that echo through the movie were ponderously, cruelly fraudulent, offering wisdom and solace as long as you don’t really need either, and entirely vacuous as soon as the crash comes and you reach for help. After the epigraph from Job, we hear the mother’s voice citing a lucid and at first compelling instruction: ‘The nuns taught us there were two ways through life – the way of nature and the way of grace … Nature only wants to please itself … It finds reasons to be unhappy when all the world is shining around it … Grace doesn’t try to please itself. Accepts being slighted, forgotten, disliked.’ This sounds uplifting when you hear it, and when the boy is not yet dead. On anything like a second thought, or under any sort of pressure, we see that a doctrine that so denies and demonises nature is headed for trouble, and can’t succour anyone in real need.

There is a grandeur about the sheer helplessness and loneliness of the family, as if their own ordinariness were baffling to them. But the film only half-believes in this form of grandeur, even if it’s the one thing it’s good at, and it finally decides both to take pity on the family and to show God in a better light. In someone’s sentimental imagination, the grown-up Jack’s or the kindly Malick’s, the whole story turns out well - that is, goes soggy. The family, including the dead boy, meets up on some beach of the other world, a sort of De Chirico setting for the afterlife, and wanders along the sand with the zonked-out look that seems to be obligatory for the dead in high-toned situations. The message presumably is that they are all at peace now, that grace has redeemed them from nature. What the images unmistakably say is that they are more lost than ever, along with the movie. At a stretch, we might say we are seeing how desperately this consolation is needed, how poor the chances are of such a reunion in the world the film has shown us, and how little conventional ideas and images are going to do for these suffering people. But it’s hard to avoid the feeling that the film is trying wrongheadedly to take away from them what matters most: their dogged dignity, their helplessness and their sorrow.

Well, sure — who can read “Dover Beach” without picturing naked Bunnies frolicking in the waves? Ward strives manfully to render his argument plausible, or at least non-preposterous, and he almost manages it. By 1972, it was still not possible to incorporate visual aids, but the scholarship took an important step forward that year when Harry Joe Jaffe published “The Stars of Playboy“ in the journal Western Folklore. This short article, barely one and a half pages long, reported on “a current item of folklore circulating at the Ohio State University” concerning the star(s) appearing near the “P” of the magazine’s title on the cover. Surveying 175 students in freshman English during the fall of 1970, Jaffe collected variations on the belief that, to quote one informant, “The stars on the inside of the ‘P’ indicate the number of times that Hugh Hefner has had intercourse with the Playmate of the Month. If the stars are on the outside of the ‘P’ that means that he has not had intercourse but came close.”

Among male respondents, this urban legend (or rather “contemporary legend,” to use the term folklorists now prefer) was quite widespread, but only 7 of the 53 female subjects had heard it. Jaffe contacted the magazine and learned from an editor that “since 1955 the stars have been used to denote regional editions which are offered as a service to advertisers.” Their placement was “determined by artistic considerations, that is, whether the ‘P’ is dark or light as well as the color of the cover.” The name of this editor was Auguste Comte Spectorsky, and it seems fitting that his response may count as the beginning of positivist Playboy scholarship.

Are the stars still there? It’s been such a long time since the last time I saw the magazine that I didn’t know, but according to the Internet, they aren’t. That it is still publishing at all seems remarkable, given the competition. Among the images in Carrie Pitzulo’s Bachelors and Bunnies: The Sexual Politics of Playboy, published by the University of Chicago Press, is a picture of Linda Summers, also known as Miss August 1972, who became familiar to my pre-adolecent peer-group, a couple of years later, when someone filched that issue from a parental hiding place. Seeing it again now is not just a matter of nostalgia but a reminder of the historicity of experience. Once, long ago, it was difficult for a boy to locate such a picture, with its valuable but normally unavailable information. Hormones would etch the images into the depths of the brain. There may be Amish teenagers who still respond to Playboy that way in 2011, but the photographs have lost their power, which came in large part from scarcity.

At the same time, the magazine itself was all about abundance, both material and erotic. The world in its pages was utopian. And the utopia rested on an ideology: “the Playboy Philosophy,” worked out by Hefner, that Socrates in a smoking jacket. This was an enlightened hedonism — part libertine, but mostly libertarian, with repressive morality understood to be the great evil in the world. For the serious Playboy, sex was recreational, while true passion involved high-end consumerism.

How Playboy brought carnal and acquisitive desires into alignment is the central concern of Pitzulo’s study. She focuses on the magazine’s first two decades, from its debut in 1953 through a mutually polemical encounter with radical feminism in the early 1970s. In the uncorrected page proofs sent out to reviewers, she refers to the book a couple of times by the title For the Articles — a nod to the old joke explaining why one read Playboy. Presumably this was the title it bore when the project started out as a dissertation. (Pitzulo is now assistant professor of history at the University of West Georgia.) This has been corrected in the final version — and in any case, Bachelors and Bunnies is both a better title and more fitting, since its argument is that Playboy‘s agenda was, at heart, emancipatory for men and women alike.

As the magazine came on the scene in the 1950s, pundits were in the midst of brow-furrowing over a “crisis in masculinity.” Expansion of the professional-managerial class meant that there were more guys working at desks than ever. Women had increasing power in the marketplace, and lots of them were having careers. Some of the rough-hewn male virtues of yesteryear, such as indifference to fashion and a distaste for luxury, were becoming inappropriate in an affluent society. However suitable in the day of the covered wagon, they now slowed the wheels of commerce. “This translated into a cultural angst over the ability of middle-class men to maintain their traditional authority in the home, workplace, and world,” Pitzulo writes.

A new, alternative code of masculinity could be found in the pages of Playboy. It was completely urban and tended towards a sophistication verging on dandyism. While displaying an aversion toward being domesticated by women, it was unambiguously (even strenuously) heterosexual. A man had to know how to consume, and women were there for the consuming. You used the best available hi-fi to play the coolest possible jazz album for that secretary you met in the elevator; soon she would be wearing only a smile, just like this month’s centerfold.

It was a new design for living. Pitzulo’s assessment is the bachelors to whom the magazine was addressed were not the only ones to benefit. The “objectification” of women in its pages was only part of the story. The centerfold was always accompanied by the model’s account of her life and interests; the women portrayed were presented as having lives outside the erotic gaze. They even had agency in their encounters with men. Pitzulo includes a memorable image from 955 showing a woman, mostly naked, leading her male companion up the stairs. (Presumably this is set in his split-level bachelor pad.)

Drawing on letters from readers found in the magazine’s archives, Pitzulo shows that by the late 1950s its audience included women who appreciated its lack of hypocrisy and fairly egalitarian attitude towards sex roles. And while there was the occasional bit of homophobia in Playboy’s pages, this was the exception and not the rule. Well before Stonewall, its attitude towards gay men and lesbians was by far more generous than that of any other mainstream media outlet. “In the December 1967 issue alone,” Pitzulo notes, “just under one-third of the letters published were about homosexuality, with five discussing police and government entrapment…” Thus Playboy philosophy moved from libertinism to a form of libertarianism — and no one the worse for it, or so goes the argument.

Previous studies of Playboy have made similar points about its cultural impact. Bachelors and Bunnies is so
quick to situate itself in a dialogue with earlier writers that it can be difficult to determine what is new about its interpretation. This may be a matter of shading. Framing the magazine’s stance as quasi-proto-feminist means dealing with some fairly overt expressions of hostility toward women. Pitzulo acknowledges this, while stressing that such attitudes were common enough in the culture of the time. We ought not to distract us from what was innovative about Playboy.

But anticipating the worldview of “Sex and the City” is not necessarily an unmixed good. Neither is redefining masculinity through competitive status-driven consumption. The quotations Pitzulo gives from Playboy articles advising readers on what to buy start to sound, after a while, like the interior monologues of Patrick Bateman from American Psycho.

In The Hearts of Men: American Dreams and the Flight from Commitment (Anchor Press, 1983), Barbara Ehrenreich quotes various specimens of misogynist ranting that appeared in the magazine over the years. An example: “All a woman wants is security. And she’s perfectly willing to crush man’s adventurous, freedom-loving spirit to get it.” (Similar deep thoughts are available upon request from some drunk in the nearest bar.) “From the beginning,” writes Ehrenreich, “Playboy loved women – large-breasted, long-legged young women, anyway – and hated wives…. The real message was not eroticism, but escape – literal escape, from the bondage of breadwinning.” As Pitzulo shows, this is not a fair characterization of the whole history of the magazine. By 1971, an article in Playboy included the Bartlett’s-worthy line: “The lack of sex is an inconvenience; the lack of love is a tragedy.” This is true. But there was never any legend claiming that the stars near the “P” showed how much Hefner loved that month’s Playmate.

Reed’s last few novels have been a lot heavier on the “six o’clock news” side of things. Whereas his earlier fiction—with its deliberate anachronisms, gallows humor, grotesque characters, misappropriations of historical figures and documents, and dei ex machina—created a powerful sense of dislocation, his recent fiction has been surprisingly linear and topical. With his latest novel, however, Reed seems to have struck a winning balance between the old and the new. Juice! successfully combines the sharp thematic focus of later works like Japanese by Spring with the technical daring of Mumbo Jumbo.

The novel tells the story of Paul “Bear” Blessings, an aging African-American cartoonist at KCAK, a television station that once espoused an edgy, leftist agenda but now, after falling under new corporate ownership, seeks to entertain the more socially conservative suburban set. At the behest of his new bosses, Blessings transforms his subversive cartoon character Attitude the Badger into the “less threatening” Koots Badger, “a harmless old curmudgeon who was always threatening individuals and institutions with his cane.” The execs reward him with a raise, a spacious new condo, and a cozy downtown studio.

But Blessings’s private obsession with documenting the mainstream media’s racist depictions of black males, particularly O.J. Simpson, eventually gets the best of him. Bewitched by the never-ending media circus surrounding Simpson’s legal troubles, Blessings gradually returns to drawing militant cartoons. Of course, this leads to a series of heated confrontations with the higher-ups, but, thanks to some bizarre behind-the-scenes machinations, he is kept on the company payroll.

Juice! raises serious questions about the bowdlerization of art and the unique forces that conspire to corrupt African-American artists searching for legitimacy and acceptance. But more importantly, Juice! interrogates readers’ expectations of the well-made literary novel. The chapters, for instance, seem to have been thrown together almost willy-nilly. They jump around wildly in time and subject matter, alternating between acerbic, often cogent disquisitions on the Simpson murder trial and comic descriptions of the narrator’s deteriorating personal and professional life. Out of nowhere, Blessings will sound off on anything from the consumer habits of so-called progressives to the history of graphic art in America.

The book is also padded with drawings, courtroom documents, television transcripts, and quotations from news articles and scholarly journals. With this deluge of information and narratives, this constant shifting from social commentary to outlandish personal drama, Reed somehow manages to construct a wonderfully textured and absorbing work of art. Indeed, it is the sheer range of references and techniques that he marshals to indict the American media and illustrate his characters’ complicity with its racist agenda that make Juice! a strangely fulfilling book. In other words, this novel deserves our attention because it shows one of our nation’s top writers, in prose that is both graceful and witty, expanding the possibilities and pleasures of novelistic form.

So what causes it? First, Moskowitz and Wertheim rule out the conventional explanations, starting with the support of the home fans. How do you isolate the effect of the crowd on a team’s performance? They do it by comparing how well home and away players perform when faced with identical tasks, save only for the presence or absence of a hostile audience. Take basketball: when a player is fouled, he (or she) is awarded free throws at the basket from 15 feet. No one is allowed to interfere, apart from the home fans, who can do what they like to put off the opposition. If you’ve ever seen an NBA game in the States you’ll know this often includes shaking rattles and waving balloons from behind the basket. The result? Nothing. The stats show that away players perform just as well as home players from the free-throw line, despite all the barracking. The same applies to goal-kicking in American football, and penalty shoot-outs in our version. The home side has no better chance of winning at penalties than the away team. Home fans often think they can help the ball into the net with their hushed support, or keep it out with their whistling derision. It seems they might as well save their breath.

If it’s not the fans, maybe it’s the travel. Away teams often have to cross long distances (especially in the US), sleep in unfamiliar beds, and deal with all the discomfort of being far from home. This one is easy to disprove. The record of away teams across all sports is just as bad in local derbies, despite the fact that getting to the ground is no more inconvenient than for the home players. Everton’s and Liverpool’s grounds are less than a mile apart – but Everton are still much more likely to beat Liverpool when they don’t have to make the short journey to Anfield. The historical data back this up. Travelling conditions for top athletes have got immeasurably better over time – where once it might have been as slow and difficult for them to get around as for the rest of us, now it tends to be pampered luxury all the way. But their performances away from home have not got better at all. As Moskowitz and Wertheim put it, ‘the home field advantage is almost eerily constant through time.’ You can do what you like to ensure your players do not suffer all the little inconveniences of being on the road – they are still liable to let you down when they arrive. (The one correlation Moskowitz and Wertheim do find between travel and performance is for those sports where away teams are sometimes forced to cram games together on a single road trip, meaning they have a tighter schedule than their opponents. This is true for US college basketball, where away sides are often disadvantaged by having to rush from town to town while the home teams get a day off – and in college basketball home court advantage runs as high as 69 per cent. But here the test is European soccer, where there are no scheduling anomalies, and where home teams win almost as often.)

What about local knowledge? Every ground is slightly different, so perhaps teams take advantage of their familiarity with their home environment. Even football pitches vary: some are wider, some are narrower, some are blowy, some are sheltered, some are rough, some are smooth. The differences are most noticeable in baseball, where some teams play at stadiums that suit hitters, and others at stadiums that suit pitchers (it’s a question of size, shape and atmospherics). Yet even in baseball, Moskowitz and Wertheim find it makes no difference. Teams that play in hitter-friendly stadiums do not outhit their opponents by any greater margin than teams that play in pitcher-friendly stadiums. This despite the fact that managers can pack the team with sluggers, sure that they will play at least half their games in advantageous conditions. Knowing what you need to do well in your own yard doesn’t help you do it any better. Home advantage seems to be entirely outside anyone’s power to control.

It’s not the crowd, it’s not the travel, it’s not the stadiums, it’s not the players or the managers. So what’s left? Well, there are always the referees (or umpires as they are known in most American sports). And that’s who it is – Moskowitz and Wertheim say home advantage is almost entirely down to the officials. Players aren’t put off by the barracking of the home fans, but the umpires are. It makes sense when you think about it – if tens of thousands of semi-hysterical people were scrutinising your performance, you’d want to try to please them if you could, if only subconsciously. The away players have nothing to gain from the home fans – if they do well they’ll get abuse, if they do badly they’ll get mockery. But the officials can make the home crowd happy and then surreptitiously bask in the warm glow. Away players can’t alleviate the pressure of being in a hostile environment. Referees can.

Moskowitz and Wertheim find plenty of evidence to back this up. In football, it turns out that referees consistently award more injury time when home teams are losing, and less when they are winning (on average, four minutes in the first case and two minutes in the second, enough to make a difference in plenty of matches). Home teams get far fewer players sent off, and receive many more free-kicks. Maybe this is down to the fact that the home side simply plays better and the away players are reduced to desperate measures. But Moskowitz and Wertheim find evidence that crowd effects make a real difference. In the German Bundesliga, for instance, where many of the teams used to play in stadiums incorporating running tracks, putting the crowd much further away from the action, the bias referees normally show to the home side was cut in half. In the British, Spanish and Italian leagues, attendance also has a marked effect on the number of red cards shown to the visitors. The bigger the crowd, the more likely the away team are to end up with fewer players on the pitch at the end.

However, the most compelling evidence for referee bias comes from those sports that have introduced technology to check on the decision-making of the officials. In baseball, a system called QuesTec (similar to Hawk-Eye in cricket and tennis) now shows whether a pitch was in the strike zone or not (the area over the home plate between a batter’s armpits and his knees). Moskowitz and Wertheim have looked at a mass of data and discovered that when a pitch is clearly a strike, baseball umpires do not advantage the home hitters. Equally, when a pitch is way outside the strike zone, they call it against the pitcher. But when it’s on the edges, the home team were getting a large percentage of favourable calls. This shows two things. First, given the choice, umpires prefer to please the locals who are breathing down their necks (in many baseball stadiums almost literally). Second, they know what they are doing – they restrict their bias to areas where it won’t be so obvious (in stadiums that have installed QuesTec umpires have started to eliminate their home bias, now that they realise it’s there for all to see). Moskowitz and Wertheim find the same thing in ice hockey and American football, where the introduction of instant replay reviews showed that for close calls, and in tight games, the officials tend to favour the home team by a significant margin (calls against the away side are more likely to be corrected when impartial technology is called in evidence). Tight games are by definition the ones that can turn on one or two key decisions. And it appears that tight games are also the ones in which the officials go out of their way to help the home team. That’s enough for Wertheim and Moskowitz to finger them as almost entirely responsible for the phenomenon of home advantage.

It’s a lovely theory – simple, elegant and in tune with what most of us believe about human nature (and with what many fans have long suspected but never been able to prove about referees). There’s only one problem – it’s not true. I don’t doubt that referee bias has something to do with home advantage, but the idea that it’s the crucial determining factor is absurd. Just think about it – or rather, think twice about it. The first time you’re told it’s the referees you will probably go ‘aha!’, as I did. But the second time you’ll go ‘huh?’ Look at a football game. Yes, the home side does sometimes seem to get the benefit of the doubt from the referee, and yes, injury time does seem to go on for ever when Manchester United are playing at home – the image of Alex Ferguson consulting his watch as United push forward for a winning goal in the 97th minute at Old Trafford is probably the one that defines the Premier League. But why do the home side always seem more likely to score at the end? Why are they the ones pushing forward? Look, really look. It’s not just because the referee is letting them, it’s because something is making them play better. They believe.

At this point the freakonomists will tell me that I’m the one being absurd. The whole point of trusting to the numbers is that we can’t trust our eyes. We think we know what’s really going on only because we have all sorts of cognitive biases that lead us to misread individual situations. The freakonomics approach is designed to rule out what we assume is happening, forcing us to accept that we have been blinded to the truth by our preconceptions. Didn’t Moskowitz and Wertheim rule out all the plausible-seeming alternatives? Well, no they didn’t. They used the numbers to make it look like that was happening. But really they were just expressing their own bias. This is the trouble with the freakonomics approach. It’s not that the numbers misrepresent human nature by treating us all as twitchy little utility maximisers. Doubtless that’s what most of us are most of the time. The problem is that the freakonomists misrepresent the numbers.

Let’s spool back. Moskowitz and Wertheim claim that the performance of players from the free-throw line or the penalty spot shows the crowd doesn’t have an impact on the performance of the home team. But that’s not what it shows at all: it shows that the crowd doesn’t have an impact on individuals. What if home advantage is a team phenomenon? There is plenty of evidence not considered by Moskowitz and Wertheim to suggest that it is. British tennis players have never seemed to gain much advantage playing at Wimbledon, despite the presence of thousands of people willing balls that are in to be called out (I’m talking pre-Hawk-Eye here). Are phlegmatic British line judges somehow impervious to these pressures in a way that football referees are not? It’s not just us Brits. No Frenchman has won the French Open since 1983; no Australian has won the Australian Open since 1976. Where’s the home advantage? One explanation might be that playing at home really makes a difference only when you’re part of a team. It’s a collective experience, in which case it dissipates for isolated individuals (including the individuals standing at the free-throw line in a basketball game or at the penalty spot in a football match). Somehow, playing at home breeds a sense of solidarity, or what used to be called team spirit, which means that players have more confidence in each other and work better as a unit. I’m not saying that’s definitely what happens. But Moskowitz and Wertheim haven’t proved that it doesn’t.

The key figure that they don’t really discuss is the disparity between home advantage in baseball and football. Baseball has a relatively low home advantage ratio – the lowest for all major sports – at around 54 per cent for the major leagues. This is a huge difference from the 63-67 per cent that holds for the big European soccer leagues. What explains it? Moskowitz and Wertheim spend a lot of time describing how the bias of baseball umpires can account for almost all the home advantage in that sport – if it sways around 3 per cent of games (and they give good reasons for thinking that it does), then that’s practically the whole of it. But what about the extra 10 per cent in football? Their answer is that football is a sport where the referee’s decisions count for more. But they provide no statistics to support this. In fact, they read it backwards: since they are committed to their theory that referee bias accounts for home advantage, and since home advantage is much greater in football, QED referees must have more influence on the games. So who’s suffering from cognitive bias now?

What’s striking about Scorecasting is that there are numbers that could prove Moskowitz and Wertheim’s thesis, but they don’t provide them. Take the German case: if the presence of a running track cuts referee bias in half then it also ought to have cut the home advantage of the teams playing at those stadiums in half. Did it? They don’t say, but somehow I doubt it. Similarly, it should be possible to provide some numbers to decide the question of how much difference refereeing errors make to the outcome of football matches. Moskowitz and Wertheim don’t even try (all they tell us is when a team gets a player sent off, it is considerably more likely to lose – no kidding!). So I’ll have a stab, though I’m only guessing. Let’s say the mistakes of football referees favour the home side by a ratio of 60:40 (corresponding with the basic home advantage ratio). It also seems reasonable to believe that the mistakes of referees decide perhaps 20 per cent of all football matches. But that would still only give a home win advantage of 4 per cent. To get to 20 per cent it would either have to be the case that every refereeing error favoured the home side, or that every football game was decided by a refereeing error. That’s absurd. I am also prepared to believe that the extra 2 per cent of home advantage in Spain, and 4 per cent in Italy, is down to more suggestible referees (though whether it’s the crowds that are influencing them or something more sinister is open to question). But whichever way you spin it, it seems that the bulk of home advantage in football is still unexplained by refereeing bias.

So here’s an alternative explanation: home advantage is lower for baseball because it’s less of a team sport. It’s primarily a series of individual encounters between batters and pitchers. It’s more like tennis than like football. Playing at home makes the biggest difference to passing sports, where the players have to rely on each other. (There is some passing in baseball, from fielder to fielder, but much less than in football or other sports where home advantage is very pronounced, like basketball and ice hockey.) Baseball is also a more disjointed sport (again like tennis): it consists of lots of discrete plays. Team spo
rts where the action flows are the ones in which playing at home really counts. Why? I’m not sure. But Moskowitz and Wertheim have not ruled it out.

I can’t prove my theory, but I can defend it. It chimes with what you can see happening in any team sport – the away players don’t quite believe in themselves in the way the home players do. This is especially true near the end of a close game between two otherwise evenly matched teams, when the home side will usually be the one pressing for a winner. Moskowitz and Wertheim say that’s because the referee is allowing it to happen: what we think is a quality belonging to the players is actually a quality we have misattributed to them because of the indulgence of the officials. But that’s not really convincing – not only does it not tally with the evidence of our own eyes (the home team attacks even during the periods when the referee has no influence on the game) but it doesn’t fit with another claim they make in Scorecasting. As well as identifying a bias in favour of the home side, they also show that officials prefer to avoid making decisions that might make them stand out, especially near the end of a game. This is a widespread phenomenon, and it applies to football as much as any other sport. As Moskowitz and Wertheim report, having studied 15 years of data from the Premier League, La Liga and Serie A: ‘Fouls, offsides and free kicks diminish significantly as close matches draw to a close.’ This is the ‘omission’ bias, and we all tend to suffer from it – we prefer to let bad things happen than to take a chance on doing the right thing and risk carrying the can. If a referee intervenes in a game near the end, it looks like he’s deciding the outcome. That’s going to make some people mad.

Moskowitz and Wertheim describe a classic sporting example of what can happen when an official tries to overcome his or her omission bias. At the 2009 US Open a brave/foolhardy tennis line judge called a foot-fault against Serena Williams at the climax of her semi-final against Kim Clijsters. Subsequent replays showed the call was correct. But it provoked outrage. Line judges rarely call foot-faults, since they don’t want to look conspicuous. What was this one doing interposing herself at such a crucial moment in the match and helping to decide the outcome? Just doing her job? Come on – she was making a spectacle of herself. After she had been foot-faulted, Williams turned on the official and screamed at her: ‘You better be fucking right! You don’t fucking know me! … If I could, I would take this fucking ball and shove it down your fucking throat!’ This outburst meant Williams was docked a point, which cost her the match. The crowd went crazy. John McEnroe commentating on television, agreed: ‘You can’t call that there. Not at that point in the match.’ So it turns out it didn’t matter that the line judge was fucking right; she was still run out of town.

As Moskowitz and Wertheim show, most officials have internalised these sorts of lesson. They don’t like to interpose themselves at crucial moments, when people can say: it was the goddam ump! They don’t even like to make calls at any point in a game when their decision will stand out. So, for instance, in baseball, when an umpire has made three consecutive calls against the pitcher, meaning one more ‘ball’ (a pitch called outside the strike-zone) will give the batter a free walk to first base, he usually shies away from making the call. Better to call a strike, so it doesn’t look like the umpire has dominated that little period of play. This has important implications. It’s a truism of baseball coaching that when hitters are at 3-0 (three balls, no strikes) they shouldn’t swing at the next pitch. Don’t waste a dominant position. Make the pitcher, who is under all the pressure, get it over the plate. But in fact the umpire, who’s really the one under pressure, will probably see the ball as going over the plate regardless of whether it is or not. So the truism is false – you’re better off swinging. This lesson can be applied to many areas of life. Say you’re going to a job interview. You know you’re the outstanding candidate, so you decide to play it safe. But if you really are the outstanding candidate, the umpires are unlikely to want to strike you out on the basis of a single interview. So you might as well swing for the fences …