Black Swans and Red Numbers

Camilo Villegas’ low opening round at the Phoenix Open on Thursday was so low that it has allowed him to hold on to the lead despite a 69 on Friday—not that two under is a bad score, but if Villegas wants to win the tournament 69 will probably have to be his worst round of the week. Robert Allenby, the Australian golfer who I have discussed here before (“‘Caddie Killer’ or Killed by Grooves?”), had what might be regarded as the good fortune to shoot his 69 on Thursday, and is moving up the leaderboard today. Allenby isn’t the only one, but I have discussed him before and he is from Australia, home of cyngus atratus, the black swan.

As it happens, black swans are not merely ornithological curiousities, but also furnish the title of a recent book called The Black Swan: The Impact of the Highly Improbable by a man with the improbable name of Nassim Nicholas Taleb, whose thinking has greatly influenced how I have thought about scoring in golf. (Like the segue?) Anyway, Villegas’ performance thus far in this tournament brings up an addendum to my post about match-play, “Match the Emperor,” where I argued that in a stroke-play tournament a double-bogey was much more hurtful to a golfer than an eagle was helpful, despite the fact that both were an equal distance (plus or minus two) from par. Learning why will also teach you why anybody who compares golf to life is an idiot—especially if they are handling your money.

In match-play, I said, a double-bogey is not as harmful as it is during stroke-play. The addendum I want to discuss now is that while there is an asymmetry during a single round, my suspicion is that asymmetry also lessens the more rounds there are. What that means is that a double-bogey during the six-round Q-School finals—the tournament that can get an aspiring tour player his “card,” exemption, for the following year’s tour—should be less harmful than a double-bogey during a regular (4-round) tour stop, which in turn should be less harmful than it might be on the LPGA or Champions (nee Senior) tour, where they often play only three-round tournaments. Before, I tried to say that the amateur tends to regard the double-bogey and the eagle as equivalent, because they look that way on the scorecard, but that the professional knows that this is not true. Now, I want to show how that asymmetry can vary depending on the circumstances—but that there is always some asymmetry, that the double-bogey is always more harmful than the eagle is helpful.

To illustrate the point, I’m going to draw on the work of Taleb, who hasn’t written anything about golf but has written a great deal about the finance industry, which has certain similarities to golf—perhaps not accidentally, since it’s arguable that both are Scottish. Taleb begins by noting that the discovery of black swans in Australia was a great surprise for Europeans—before that, a “black swan” was a mythical animal, like a unicorn. (Presumably, white swans had something of the same effect on the Aborigines, though probably the huge boats and guns were even more surprising.) Thinking about it later, the British philosopher John Stuart Mill, following on David Hume (a Scot!), wrote that “No amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion.” If all the swans so far have been white, that is, a single black swan in effect outweighs all of them.

What Taleb wants to argue is that are thus valuable exactly insofar as they are rare—if there are about equal numbers of white swans and black swans, then a single new one won’t really change things very much. Here’s where the financial angle comes in, though I’m not going to get very far into the details: the inference Taleb draws is that, precisely because “black swans” (or rare events) are so rare they can never be properly valued by a given market. If they could be, then they wouldn’t be rare. QED. That fact, he says, has certain consequences for correct strategy in the financial markets.

Because human beings are wired the way they are, Taleb says—the arguments here are involved and not really germane—we prefer to have small but continuing successes. Hard work, we say, pays off; it’s better to be ant than the grasshopper, and so on. But as Taleb points out, there is no difference between gaining one bean a day for fifty days and getting no beans for 49 days and then harvesting fifty on the fiftieth day—or, say, planting fifty beans on one day in order to get 100 beans fifty days later. All of these methods have the same result: you are plus fifty beans at the end. As human beings, though, we prefer the first strategy to the others: there’s a steady reward every day, and at some deep level—Taleb thinks it’s biological, but it doesn’t make a difference—that’s comforting.

To put it another way, we would prefer to continue counting white swans. Black swans are disturbing. As rare events, they can be analogized to the method of getting no beans and then getting a whole bunch all at once. There you are, counting white swans, when all of a sudden a black one shows up. That is not a comfortable situation for most human beings: the Australian birds were so disturbing they made two giants of European philosophy think about them at length. Who the hell cares? They’re birds. So what?

The “so what” is that, again, “black swans”—rare events—are always undervalued. So what Taleb says most investors would be better off doing is the strategy that he follows. The mechanics aren’t important, but suffice it to say that Taleb actually loses a bit of money every day. What Taleb says is that because he is waiting for a rare event, when it happens it will be so undervalued by the market that his returns will overwhelm his losses. That sounds more than a little insane, of course. Conversely, people who pursue the opposite strategy, making a bit of money every day, will appear like hardworking, solid leader-types.

Until they blow up.

There they are, in other words, industriously counting their white swans, which continuously and regularly show up every day without any trouble. And then, one day, a black swan shows up on some distant continent somewhere. Or maybe the Russian government decides to default on their bonds all of a sudden—which, foreshadowing the events of the last year, caused the hedge-fund Long Term Capital Management to collapse and nearly take the global financial system, or at least the American branch of same, with it. Or some jackasses fly into a building. Or shoot the nation’s leader. Or, on the other side, a member of some oppressed group becomes the nation’s leader. Or that sports team famous for never winning finally does. And so on.

Betting on the unexpected, in other words, is a lock—something unexpected is going to happen. It’s guaranteed, if by nothing else than by the human proclivity for white swans. There is, of course, one problem with this idea, which the experienced will have spotted a mile a way. It’s the same problem faced by poker players: sure, such a strategy will always work—with an unlimited bankroll. What Taleb wants to say is that there are ways to structure your bets to get around that problem, because there are many more bets available in Chicago, New York, or London or Tokyo than are available at a casino. And more importantly, while the odds of blowing up (going bankrupt) can be calculated fairly precisely in poker or any human game, just so are they incapable of being so calculated in real life. There are infinitely more possible outcomes in reality than there are in a game.

Any golfer who tried to follow Taleb’s advice, after all, would very quickly exit the game. You can’t, in other words, bogey every hole—and then shoot 99 under par on the last hole to win by two. The outcome has been artificially constrained: that is exactly what makes golf a game. There isn’t any way to shoot a quadruple albatross, say. In that sense, following what we could call the “white swan” strategy in golf—or, “avoid all double-bogies”— is very wise. But what Taleb wants us to see is that following that sort of strategy in real life (or at least, the capitalist version of it contained in the financial markets) wouldn’t just be imprudent, but suicidal: it’s the only strategy guaranteed to fail.

Many commentators have noted the golf scores of Bernie Madoff, the Ponzi schemer, demonstrate the point. National Public Radio (thanks, federal government!) asked Drew Baden, head of the physics department at the University of Maryland, to look at Madoff’s scores as reported to the USGA per his handicap, and Baden found “Madoff’s scores make a nice bell curve.” Baden says that Madoff’s scoring was even more consistent than Tiger Woods’—a man who, aside from anything else, has missed the cut at something like less than ten tournaments in his career. It’s arguable, in fact, that Tiger Woods is the most consistent golfer in the history of the world—the rare outlier, or black swan, of all those playing a white swan strategy, we might say—(!)—but according to his scores, Madoff was even more consistent. That’s astonishing because even a scratch golfer is expected to throw in a score of 85 once in a while. Madoff was not a scratch golfer—he was a 10—but only 3 rounds in 20 were more than two shots different from his usual score of 84. It’s absurd: almost certainly Madoff was cheating.

That’s interesting not intrinsically to be sure but because Madoff in his business life routinely reported the same steady rate of return every year to his investors, usually around ten per cent to fifteen per cent I understand. But as a number of financial people have observed, such consistent returns are no more so, and almost assuredly less so, than on a golf course. Investment funds never perform that way: they will have some years where they go up twenty-five percent and years where they might drop ten. Madoff’s “errors” thus also each mirror the other. The financial crimes are the same as the golf “crimes”—smart people, in either case, should have known better. Madoff’s investors—attracted by the steady rate of return—should have known such results were highly improbable, just because they seemed so probable. Taleb calls this the “Ludic fallacy”: thinking that reality can behave like controlled situations, like games. Or, to put it another way, Madoff’s investors mistook golf for life.

Getting back to reality, or at least that representation of it called the PGA Tour, Robert Allenby shot another 69 today. He made six birdies and four bogies. Two of the bogies came on par-fives though; making a six on a par-five is almost as bad as making a double-bogey, because it means giving up almost two shots to the field (mathematically it is probably something like 1.6 or something). Allenby ended up about where he was yesterday, but he got Linda Ronstadted by those now above him on the leaderboard, most of whom had four to six under rounds today. In that sense, a low round can be, in effect, a kind of unexpected black swan in a game that for the most part militates against wild swings of fortune. While you can’t have a super low hole that can right a bad round suddenly, you can have a super low round that can move you from 48th to sixth, as Hunter Mahan did today. This afternoon, to demonstrate the other side of the point, Camillo Villegas shot even par to drop from first to fifth.

Brandt Snedeker is your leader with a 66 after the third round, five under par. On the 14th, Snedeker saved a bogey with a thirty-two-foot putt, thus avoiding a double-bogey. It was the first bogey Snedeker made in 27 holes. He’s leading therefore because he has been the best at following the “white swan” strategy that golf demands. What would be great to know is if these players were consciously following these strategies: are the guys who are laying up on the par-fives making more birdies, or are the players all going for it and it just happens to have worked out for some and not for others? At the highest levels of the game, does strategic thinking make a difference, or not? My suspicion—since I think it does at the levels I have seen, which includes only one step removed from the tour—is that it does. It certainly does where most of us play, which is why the best advice to a golfer is always, “It’s just a game.” Golf isn’t as ridiculous.


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