by Nate Silver
* Contrast this with football, in which a great offensive line can make an All-Pro out of a mediocre running back, or basketball, in which the synergy between a point guard and a power forward can make them more than the sum of their parts.
* Although Bill Pecota hit just .249 for his career overall, he hit .303 in games against the Tigers.
* That works out to about $1.9 million per team per season.
* In the model that I use to forecast the outcome of U.S. House elections, for instance, I combine quantitative information like polls with the qualitative ratings from experts like the Cook Political Report. If Cook says a particular race is a toss-up, I code that as a 0. If they put the race in the Lean Democrat category, I code that as a +1, and so forth. Combining this information produces a better forecast than either type of information taken alone.
* Loft bears some physical resemblance to Rainn Wilson, the actor who plays Schrute.
* As we will see in chapter 8, it is not so easy to characterize Laplace along this spectrum. He was an eclectic thinker and was instrumental in the development of probability theory, motivated in part by his conviction that human beings were unlikely to live up to the perfection he saw in nature.
* That was not the Weather Service’s final move. In 1940, with an eye toward assisting the Civil Aeronautics Administration and the bourgeoning industry of manned flight, the Congress migrated it to the Department of Commerce, where it resides today.
* Unfortunately, although forecasters have gotten much better at figuring out where a hurricane will hit, they haven’t really gotten any better at predicting how powerful it will be when it does. The reason is that the forces that govern the intensity of a storm occur at much smaller scales than the ones that determine its track. This means they require a much finer lattice, and even the Bluefire is not yet up to the task.
* A poorly calibrated forecast can sometimes be detected more quickly. If you said there was a 100 percent chance of an outcome occurring and it didn’t, or a 0 percent chance and it did, we do not need any more data to conclude that your forecast was wrong.
* News accounts often refer to the Richter scale, named after the Caltech seismologist Charles Richter. In fact, a different and more accurate scale—the moment magnitude scale, developed at Caltech in the late 1970s—is in more common use among seismologists today. The moment magnitude scale is designed to be comparable to the Richter scale—both scales are logarithmic, and a magnitude 8.0 earthquake is a very serious one under either definition. But they are not calculated in quite the same way. The earthquake magnitudes described in this chapter generally refer to the moment magnitude scale.
* Seismologists use the term “earthquake swarm” to refer to a series of small earthquakes.
* The Japanese word kamikaze originally meant “divine wind,” referring to typhoons in 1274 and 1281 that had helped to disperse a Mongol invasion.
* The Haitian earthquake of 2010 was an exception to the pattern geographically, but not in how poverty and lax building standards contribute to immense death and destruction.
* Recall that the magnitude scale is already logarithmic, so this is what’s technically known as a double-logarithmic plot.
* If you feed a computer a string of coin tosses (a random mix of 1’s and 0’s representing heads and tails), and then test out statistical parameters to try to fit a pattern-matching model, eventually it will think it can call 60 percent or 70 percent or (if you include enough variables) 100 percent of coin flips correctly. All this is artificial, of course; over the long run, it will call exactly 50 percent of coin flips correctly, no more and no less.
* The political scientist Roger Pielke Jr., who was brought in to consult on the disaster, alerted me to this story.
* The 95 percent prediction interval—the standard that political polls use—is even larger: 9.1 percentage points, equivalent to a margin of error of plus or minus 4.6 points.
* The substantive variables fall into about a dozen major categories: growth (as measured by GDP and its components), jobs, inflation, interest rates, wages and income, consumer confidence, industrial production, sales and consumer spending, asset prices (like stocks and homes), commodity prices (like oil futures), and measures of fiscal policy and government spending. As you can see, this already gives you plenty to work with, so there is little need to resort to four hundred variables.
* This may be in part because the economic data from before World War II is quite incomplete.
* The root-mean squared error for the forecasts in these years was 1.1 points of GDP, versus 2.3 points for the years 1968–85.
* In contrast, consider India, where much of the population is either vegetarian or Muslim—two groups that do not consume any pork. (Even in the United States or Great Britain, you’re unlikely to find pork on the menu at an authentic Indian restaurant.) Although India meets the other two conditions, it has very rarely been the source for the flu.
* If you had assumed that the global population would continue to grow at a rate of 2.1 percent per year, the rate that it did in 1968 when Ehrlich published his book, global population would project to almost nine billion by 2012, considerably above its actual figure of seven billion.
* New York, for instance, does not allow you to file a police report online, while San Francisco does, as I found out when my rental car was broken into there in a reporting trip for this book. San Francisco is doing a better job of helping citizens and visitors to report and prevent crimes. But perversely, this makes its reported crime rate higher.
* A vaccine typically contains a small and very weak microorganism that is derived from the bug that it is hoping to prevent—just enough for you to develop some immunity to it without becoming sick.
* The title of this chapter is inspired by a line from the poem “The Road to Wisdom,” by the Danish mathematician Piet Hein: “to err and err and err again, but less and less and less.”
* This assumes that the Lakers would beat the Indiana Pacers, the Eastern Conference champions, in the NBA Finals, against whom they’d be heavily favored. Voulgaris could have hedged his bet again if he wanted to mitigate that slim risk.
* The number of possible combinations is calculated as 45,000 times 44,999 divided by two, which is 1,012,477,500.
* One difference is that the negative findings are probably kept in a file drawer rather than being published (about 90 percent of the papers published in academic journals today document positive findings rather than negative ones). However, that does not mask the problem of false positives in the findings that do make it to publication.
* Or more properly, the odds you would set as a betting line so as to be indifferent between either side of the bet. Most Bayesians do require that priors avoid what is called a Dutch book, where the odds are incoherent. If you establish a set of prior probabilities on each of the thirty teams winning the NBA championship, they have to add up to 100 percent exactly since this represents an exhaustive set of possibilities.
* It has been found that because 95 percent confidence in a statistical test is Fisher’s traditional dividing line between “signficiant” and “insignificant,” researchers are much more likely to report findings that statistical tests classify as 95.1 percent certain than those they classify as 94.9 percent certain—a practice that seems more superstitious than scientific.
* Although bear in mind that one of the conclusions of this book is that people are overconfident; we probably have too many beliefs that tend toward the 0 percent or 100 percent end of the spectrum.
* And that they don’t hold priors that they believe to be exactly 100 percent true or exactly 0 percent true; these will not and cannot change under Bayes’s theorem.
* Winning percentage, as I use the term here, refers to the number of points that each side scores out of the possible total, where one point is awarded for winning a game and half a point is awarded for a draw. If you play ten games, winning five, drawing three, and losing two, you have a wi
nning percentage of 65 percent.
* Rooks are typically evaluated by computers (and humans) as being about 60 percent more valuable than bishops, other things being equal.
* Promotion in chess refers to what happens when a pawn reaches the opponent’s eighth rank. It can be exchanged for a bishop, knight, rook or (as is almost always most advantageous) a second queen.
* In practice, this position is not winning, because chess employs a rule that automatically calls the game a draw if no pieces have been captured and no pawns have been advanced after fifty consecutive moves.
* A more recent analysis of the second game, conducted in 2007 with a computer that surpasses both Fritz and Deep Blue in skill, suggests that Kasparov may not have been able to draw the position if Deep Blue had played the exact right sequence of moves. Still, Kasparov may well have drawn the game had he played it out in 1997.
* Skynet was the evil computer in the Terminator series. It gets very mad when you confuse it with HAL 9000.
* Moneymaker has made “only” about $110,000 per year from poker tournaments since his World Series win, before accounting for his substantial entry fees into tournaments.
* The $5 and $10 increments refer to the obligatory bets, called blind bets, that rotate around the table and force the action. No-limit refers to the fact that players may bet any amount up to the amount sitting in front of them in chips, on any betting round. However, the betting in a no-limit hold ’em game is constrained by the amount that the lesser of the two players has before the hand begins. If you start the hand with $500 in chips and are playing against Bill Gates who has $500,000,000, the most you are putting at risk is $500; any bets that Gates makes above that amount are considered void. So he can’t force you to round up an additional $499,999,500 in chips just so that you might call his bluff.
* Occasionally a player might call rather than raise with a hand like a pair of aces for purposes of deception.
* Ivey’s hand was A 2 while Dwan’s was 7 6. The flop was J 3 5 and the turn was the 4, making Ivey a 5-high straight and Dwan a 7-high straight.
* Whereas the very best players deliberately insert some randomness into their play to make it harder to read their hands, the worst ones may play randomly because they don’t know what the right play is to begin with.
* My analysis of the players was weighted by the number of hands that each player was dealt. In poker, a very large proportion of the total hands are dealt to a very small percentage of the total players, those who play the game every day rather than once every month or every year. In fact, the online poker environment is a hyperbolized version of the 80-20 rule: about 80 percent of the hands in the database were dealt to just 2 percent of the total players. Since you are much more likely to encounter a player from the 2 percent of prolific players than if you selected at random from all players who had played even one hand, the analysis would create an unrealistic impression of the economy of a poker table if not conducted in this way.
* Online players often also “multitable,” meaning play in more than one game at once, which further multiplies their win rate. This is physically impossible (or at least disallowed) in a brick-and-mortar casino.
* While computer programs like Billings’s have become quite good at limit hold ’em, they are not yet very good at the more strategically challenging game of no-limit hold ’em.
* Meditation helps people achieve this, in part, by encouraging focus on posture and breathing—things that are within our control but which we normally take for granted.
* Some of it also represents market making: certain investment firms, like a well-stocked 7-Eleven, hold a lot of inventory and can be counted on to be open for business when no one else is, hoping to make a few pennies at a time for their trouble.
* One could imagine that a small fudge factor might be allowed if our probability estimates were close but not exactly the same, since there is some inconvenience associated with betting.
* I met Santorum for my New York Times story on the Iowa vote count dispute after the initial tally had shown Romney ahead. Santorum remembered my bet and jokingly asserted that the bet was my motivation for tracking him down. It may have provided some additional incentive.
* Because it is so cheap to bet on Intrade, but it is receiving an increasing amount of media attention and can generate more favorable press coverage for a campaign, it could conceivably be in the interest of a candidate or a “super PAC” to buy shares as a cheap form of advertising.
* This experiment re-creates a famous experiment by the Princeton economist Burton Malkiel, who had his class flip coins to generate these random charts, and then showed them to a technical analyst who insisted that he buy the stocks immediately.
* In rock-paper-scissors, the equilibrium strategy is to pick at random between rock, paper, and scissors. This strategy ensures that, over the long run, you cannot possibly lose. Unfortunately, it also ensures that you cannot possibly win. No matter how long you play, the expected return from the strategy is zero.
If you think your opponent is behaving predictably, of course, you can deviate from this strategy and try to outguess him. Perhaps like Bart Simpson, your opponent always plays rock. In this case, you should always play paper. The catch is that in trying to out-guess your opponent, your own strategy will become predictable. Once Bart realizes that you’re always playing paper, he can beat you anytime he wants by switching to scissors.
Much technical trading in the stock market probably obeys this sort of cat-and-mouse dynamic, with technical traders simply trying to outguess other technical traders. However, the patterns they are trading on can dissipate or even reverse themselves once other investors become aware of them. The result is a lot of money being passed around from trader to trader, but the pile slowly growing smaller as it is eaten away by transaction costs.
* Although this is technologically feasible, it will not make your flight attendant happy.
* Take, for instance, the oft-cited statistic that the stock market returns 7 percent annually after dividends and inflation. This is just a historical average. Reliable stock market data only goes back 120 years or so—not all that much data if you really want to know about the long run. Statistical tests suggest that the true long-run return—what we might expect over the next 120 years—could be anywhere from 3 percent to 10 percent instead of 7 percent. The answer to what economists call the “equity premium puzzle”—why stocks have returned so much more money than bonds in a way that is disproportionate to the risks they entail—may simply be that the returns stocks achieved in the twentieth century were anomalous, and the true long-run return is not as high as 7 percent.
* This is no surprise given how poor most of us—including most of us who invest for a living—are at estimating probabilities. The few who are good at it have the potential to clean up. However, most options traders receive a poor return, and it is a very risky activity on the whole.
* As Nassim Nicholas Taleb detailed in The Black Swan and as Fama also discussed in his thesis, the movement of stock prices does not follow a gentle bell-curve distribution. Instead, stock-price movements are characterized by very occasional but very large swings up or down. The distribution of stock-market crashes can also be modeled fairly well by a power-law distribution, which is the same function that governs the frequency of earthquakes.
* Senator Tim Wirth of Colorado later told PBS’s Frontline that he and his colleagues had deliberately opened the windows in the hearing room the previous evening to prevent the air-conditioning from functioning effectively.
* As I discuss in chapter 6, the concept of “statistical significance” is very often problematic in practice. But to my knowledge there does not exist a community of “obesity skeptics” who cite statistics like these to justify a diet of Big Macs and Fritos.
* In this sense, the term climate change may be inferior to the more specific term global warming. Climate change creates the impression that any potential change in our
environment—warming or cooling, more precipitation or less—is potentially consistent with the theory. In fact, some of these phenomena (like cooler temperatures) would contradict the predictions made by the theory under most circumstances.
* There is an alternative-energy lobby as well, although it is quite a bit smaller, spending about $30 million per year.
* Armstrong is an expert at the Heartland Institute, a conservative think tank that has opposed efforts to curb greenhouse emissions.