To see what is in front of one’s nose needs a constant struggle.
—George Orwell. “In Front of Your Nose”
Tribune, 22 March 1946
Who says country clubs are irony-free? When I walked into Medinah Country Club’s caddie shack on the first day of the big member-guest tournament, the Medinah Classic, Caddyshack, that vicious class-based satire of country club stupid was on the television. These days, far from being patterned after Caddyshack’s Judge Smails (a pompous blowhard), most country club members are capable of reciting the lines of the movie nearly verbatim. Not only that—they’ve internalized the central message of the film, the one indicated by the “snobs against the slobs” tagline on the movie poster: the moral that, as another 1970s cinematic feat put it, the way to proceed through life is to “trust your feelings.” Like a lot of films of the 1970s—Animal House, written by the same team, is another example—Caddyshack’s basic idea is don’t trust rationality: i.e., “the Man.” Yet, as the phenomena of country club members who’ve memorized Caddyshack demonstrates, that signification has now become so utterly conventional that even the Man doesn’t trust the Man’s methods—which is how, just like O.J. Simpson’s jury, the contestants in this year’s Medinah Classic were prepared to ignore probabilistic evidence that somebody was getting away with murder.
That’s a pretty abrupt jump-cut in style, to be sure, particularly in regards to a sensitive subject like spousal abuse and murder. Yet, to get caught up in the (admittedly horrific) details of the Simpson case is to miss the trees for the forest—at least according to a short 2010 piece in the New York Times entitled “Chances Are,” by the Schurman Professor of Applied Mathematics at Cornell University, Steven Strogatz.
The professor begins by observing that the prosecution spent the first ten days of the six-month long trial establishing that O.J. Simpson abused his wife, Nicole. From there, as Strogatz says, prosecutors like Marcia Clark and Christopher Darden introduced statistical evidence that showed that abused women who are murdered are usually killed by their abusers. Thus, as Strogatz says, the “prosecution’s argument was that a pattern of spousal abuse reflected a motive to kill.” Unfortunately however the prosecution did not highlight a crucial point about their case: Nicole Brown Simpson was dead.
That, you might think, ought to be obvious in a murder trial, but because the prosecution did not underline the fact that Nicole was dead the defense, led on this issue by famed trial lawyer Alan Dershowitz, could (and did) argue that “even if the allegations of domestic violence were true, they were irrelevant.” As Dershowitz would later write, the defense claimed that “‘an infinitesimal percentage—certainly fewer than 1 of 2,500—of men who slap or beat their domestic partners go on to murder them.’” Ergo, even if battered women do tend to be murdered by their batterers, that didn’t mean that this battered woman (Nicole Brown Simpson) was murdered by her batterer, O.J. Simpson.
In a narrow sense, of course, Dershowitz’s claim is true: most abused women, like most women generally, are not murdered. So it is absolutely true that very, very few abusers are also murderers. But as Strogatz says, the defense’s argument was a very slippery one.
It’s true in other words that, as Strogatz says, “both sides were asking the jury to consider the probability that a man murdered his ex-wife, given that he previously battered her.” But to a mathematician like Strogatz, or his statistician colleague I.J. Good—who first tackled this point publicly—this is the wrong question to ask.
“The real question,” Strogatz writes, is: “What’s the probability that a man murdered his ex-wife, given that he previously battered her and she was murdered?” That’s the question that applied in the Simpson case: Nicole Simpson had been murdered. If the prosecution had asked the right question in turn, the answer to it—that is, the real question, not the poorly-asked or outright fraudulent questions put by both sides at Simpson’s trial—would have been revealed to be about 90 percent.
To run through the math used by Strogatz quickly (but still capture the basic points): of a sample of 100,000 battered American women, we could expect about 5 of them to be murdered by random strangers any given year, while we could also expect about 40 of them to be murdered by their batterers. So of the 45 battered women murdered each year per 100,000 battered women, about 90 percent of them are murdered by their batterers.
In a very real sense then, the prosecution lost its case against O.J. because it did not present its probabilistic evidence correctly. Interviewed years later for the PBS program, Frontline, Robert Ball, a lawyer for one of the jurors on the Simpson case, Brenda Moran, said that according to his client, the jury thought that for the prosecution “to place so much stock in the notion that because [O.J.] engaged in domestic violence that he must have killed her, created such a chasm in the logic [that] it cast doubt on the credibility of their case.” Or as one of the prosecutors, William Hodgman, said after the trial, the jury “didn’t understand why the prosecution spent all that time proving up the history of domestic violence,” because they “felt it had nothing to do with the murder case.” In that sense, Hodgman admitted, the prosecution failed because they failed to close the loop in the jury’s understanding—they didn’t make the point that Strogatz, and Good before him, say is crucial to understanding the probabilities here: the fact that Nicole Brown Simpson had been murdered.
I don’t know, of course, to what degree distrust of scientific or rational thought played in the jury’s ultimate decision—certainly, as has been discovered in recent years, it is the case that crime laboratories have often been accused of “massaging” the evidence, particularly when it comes to African-American defendants. As Spencer Hsu reported in the Washington Post, for instance, just in April of this year the “Justice Department and FBI … formally acknowledged that nearly every examiner in an elite FBI forensic unit gave flawed testimony in almost all trials in which they offered evidence.” Yet, while it’s obviously true that bad scientific thought—i.e., “thought” that isn’t scientific at all—ought to be quashed, it’s also I think true that there is a pattern of distrust of that kind of thinking that is not limited to jurors in Los Angeles County, as I discovered this weekend at the Medinah Classic.
The Classic is a member-guest tournament, and member-guests are golf tournaments consisting of two-man teams made up by a country club member and his guest. They are held by country clubs around the world, played according to differing formats but usually dependent upon each golfer’s handicap index: the number assigned by the United States Golf Association’s computer after the golfer pays a fee and inputs his scores into the USGA’s computer system. (It’s similar to the way that carrying weights allows horses of different sizes to race each other, or how different weight classes allows boxing or wrestling to be fair.) Medinah’s member-guest tournament is, nationally, one of the biggest because of the number of participants: around 300 golfers every year, divided into three flights according to handicap index (i.e. ability). Since Medinah has three golf courses, it can easily accommodate so many players—but what it can’t do, however, is adequately police the tournament’s entrants, as the golfers I caddied for discovered.
Our tournament began with the member shooting an amazing 30, after handicap adjustment, on the front nine of Medinah’s Course Three, the site of three U.S. Opens, two PGA Championships, numerous Western Opens (back when they were called Western Opens) and a Ryder Cup. A score of 30 for nine holes, on any golf course, is pretty strong—but how much more so on a brute like that course, and how much more so again in the worst of the Classic’s three flights? I thought so, and said so to the golfers I was caddieing for after our opening round. They were kind of down about the day’s ending—especially the guest, who had scored an eight on our last hole of the day. Despite that I told my guys that on the strength the member’s opening 30, if we weren’t just outright winning the thing we were top three. As it turned out, I was correct—but despite the amazing showing we had on the tournament’s first day, we would soon discover that there was no way we could catch the leading team.
In a handicapped tournament like the Classic, what matters isn’t so much what any golfer scores, but what he scores in relation to the handicap index. Thus, the member half of our member-guest team hadn’t actually shot a 30 on the front side of Medinah’s Course 3—which certainly would have been a record for an amateur tournament, and I think a record for any tournament at Medinah ever—but instead had shot a 30 considering the shots his handicap allowed. His score, to use the parlance, wasn’t gross but rather net: my golfer had shot an effective six under par according to the tournament rules.
Naturally, such an amazing score might raise questions: particularly when it’s shot as part of the flight reserved for the worst players. Yet my player has a ready explanation for why he was able to shoot a low number (in the mid 40s) and yet still have a legitimate handicap: he has a legitimate handicap—a congenital deformity in one of his ankles. The deformation is not enough to prevent him from playing, but as he plays—and his pain medications wear off—he usually tires, which is to say that he can very often shoot respectable scores in the first nine holes, and horrific scores on the second nine holes. His actual handicap, in other words, causes his golf handicap index to be askew slightly from reality.
Thus, he is like the legendary Sir Gawain, who according to Arthurian legend tripled his strength at noon but faded as the sun set—a situation that the handicap system is ill-designed to handle. Handicap indexes presume roughly the same ability at the beginning of a round as at the end, so in this Medinah member’s case his index understates his ability at the beginning of his round while wildly overstating it at the end. In a sense then it could perhaps be complained that this member benefits from the handicap system unfairly—unless you happen to consider that the man walks in nearly constant pain every day of his life. If that’s “gaming the system” it’s a hell of a way to do it: getting a literal handicap to pad your golf handicap would obviously be absurd.
Still, the very question suggests the great danger of handicapping systems, which is one reason why people have gone to the trouble of investigating whether there are ways to determine whether someone is taking advantage of the handicap system—without using telepathy or some other kind of magic to determine the golfer’s real intent. The most important of the people who have investigated the question is Dean L. Knuth—the former Senior Director of Handicapping for the United States Golf Association, a man whose nickname is the “Pope of Slope.” In that capacity Mr. Knuth developed the modern handicapping system—and a way to calculate the odds of a person of a given handicap shooting a particular score.
In this case, my information is that the team that ended up winning our flight—and won the first round—had a guest player who represented himself as possessing a handicap index of 23 when the tournament began. For those who aren’t aware, a 23 is a player who does not expect to play better than a score of ninety during a round of golf, when the usual par for most courses is 72. (In other words, a 23 isn’t a very good player.) Yet this same golfer shot a gross 79 during his second round for what would have been a net 56: a ridiculous number.
Knuth’s calculations reflect that: they judge that the odds of someone shooting a score so far below his handicap to be on the order of several tens of thousands to one, especially in tournament conditions. In other words, while my player’s handicap wasn’t a straightforward depiction of his real ability, it did adequately capture his total worth as a golfer. This other player’s handicap though sure appeared to many, including one of the assistant professionals who went out to watch him play, to be highly suspect.
That assistant professional, who is a five handicap himself, said that after watching this guest play he would hesitate to play him straight up, much less giving the fellow ten or more shots: the man not only was hitting his shots crisply, but also hit shots that even professionals fear, like trying to get a ball to stop on a downslope. So for the gentleman to claim to be a 23 handicap seemed, to this assistant professional, to be incredibly, monumentally, improbable. Observation then seems to confirm what Dean Knuth’s probability tables would suggest: the man was playing with an improper handicap.
What happened as the tournament went along also appears to indicate that at least Medinah’s head professional was aware that the man’s reported handicap index wasn’t legitimate: after the first round, in which that player shot a similarly suspect score as his second round 79 (I couldn’t discover what it was precisely), his handicap was adjusted downwards, and after that second round 79 more shots got knocked off his initial index. Yet although there was a lot of complaining on the part of fellow competitors, no one was willing to take any kind of serious action.
Presumably, this inaction was on a theory similar to the legal system’s presumption of innocence: maybe the man just really had “found his swing” or “practiced really hard” or gotten a particularly good lesson just before arriving at Medinah’s gates. But to my mind, such a presumption ignores, like the O.J. jury did, the really salient issue: in the Simpson case, that Nicole was dead; in the Classic, the fact that this team was leading the tournament. That was the crucial piece of data: it wasn’t just that this team could be leading the tournament, it was that they were leading the tournament—just in the same way that, while you couldn’t use statistics to predict whether O.J. Simpson would murder his ex-wife Nicole, you certainly can use statistics to say that O.J. probably murdered Nicole once Nicole was murdered.
The fact in other words that this team of golfers was winning the tournament was itself evidence they were cheating—why would anyone cheat if they weren’t going to win as a result? That doesn’t mean, to be sure, that winning constitutes conclusive evidence of fraud—just as probabilistic evidence doesn’t mean that O.J. must have killed Nicole—but it does indicate the need for further investigation, and suggests what presumption an investigation ought to pursue. Particularly by the amount of the lead: by the end of the second day, that team was leading by more than twenty shots over the next competitors.
Somehow however it seems that Americans have lost the ability to see the obvious. Perhaps that’s through the influence of films from the 1970s like Caddyshack or Star Wars: both films, interestingly, feature scenes where one of the good guys puts on a blindfold in order to “get in touch” with some cosmic quality that lies far outside the visible spectrum. (The original Caddyshack script actually cites the Star Wars scene.) But it is not necessary to blame just those films themselves: as Thomas Frank says in his book The Conquest of Cool, one of America’s outstanding myths represents the world as a conflict between all that is “tepid, mechanical, and uniform” versus the possibility of a “joyous and even a glorious cultural flowering.” In the story told by cultural products like Caddyshack, it’s by casting aside rational methods—like Luke Skywalker casting aside his targeting computer in the trench of the Death Star—that we are all going to be saved. (Or, as Rodney Dangerfield’s character puts it at the end of Caddyshack, “We’re all going to get laid!”) That, I suppose, might be true—but perhaps not for the reasons advertised.
After all, once we’ve put on the blindfold, how can we be expected to see?