Monthly Archives: October 2008

Notes for “The Drunkard’s Walk: How Randomness Rules our Lives”

Unnecessary Disclaimer: The following is not intended to be a detailed summary of the book in question but instead merely an exposition of the high points as I saw them through the reading of the text. No attempt has been made to create a connected narrative. Readers who want one of THOSE should obtain the book. It should be noted that the facts are the sole property of the author. The poor wit is the sole property of me.

So now we begin…

Evolution is apparently no guarantee of success at even the simplest of tasks. When faced with a light which randomly blinks red or green, humans are regularly out performed by rats. If the light blinks green 75% of the time, rats and lower mammals will choose the food dispensing button linked to the green light every time, guaranteeing themselves success 75% of the time. Humans who take the exact same test tend to believe that they can perceive a pattern in the blinking of the lights and their attempts to outsmart the randomness results in a success rate of around 60%.

Humans are also easily fooled by the patterns of randomness in their daily lives. One example given is a group of Air Force pilots in training during World War II. Their flight instructor stated emphatically that his brutal methods of roundly and publicly criticizing his trainees when they did poorly was much more effective than praising them when they did well. His reasoning went something like this: When his pilots did well, if he praised them then the next time they went out they did much more poorly than the previous flight. If, on the other hand, he simply criticized them when they did terribly then their next flights were invariably better. What the instructor failed to realize was that the good and bad flights were merely statistical outliers. So if a trainee had an exceptionally good flight then chances are good that no matter what feedback he was given he would have a worse flight the next time. The same holds for the opposite case. This phenomenon is known as “Regression to the Mean”. As a general rule, exceptional outcomes are typically followed by more average ones.

The author is also obviously a big fan of sports and gives us several pleasant statistical tidbits from the sporting world:
* The odds that a player with Roger Maris’ career home run stats will break Ruth’s homerun record in any given year: 1/32. [So you Mantle fans can sit down a shush for a while]
* From a statistical viewpoint, the 7-game playoff series in many sports is woefully insufficient. If two teams A and B have a probability of winning 55% and 45% of their head-to-head games respectively then the inferior team will still win a 7-game series 40% of the time. You’d need a series of 269 games to really prove anything. Think your teams aren’t that closely matched? If the teams compete at 66% and 33% then the inferior team still wins 20% of the time and 23 games would be required to determine the true champion.
* Justin Wolfers analyzed the outcomes of 70,000 college basketball games and found that when compared against the point spread there was a significant surplus of games that ended just below the predicted point spread at the expense of those that ended just above the point spread.

The Greeks had no proper concept of the laws of probability and this may have at least partially had to do with the fact that they had no dice. Instead they have astragali, the heel-bones of sheep. To the Greeks, the result of every throw of the astragali was the direct will of the gods themselves. This belief persists in the NFL where every touchdown reception is still the direct result of divine intervention. [at least if the touchdown celebrations are to be taken at face value]

DNA evidence in the courtroom can identify a crime suspect with a probability of error of 1:1 Million to 1:1 Billion. What is not typically talked about is the fact that the incidence of laboratory error is 1%.

This author, like so many before him treats us to an exposition of the “Monty Hall Problem.” The issue goes something like this. You’ve given three doors with three prizes. Behind one is a brand new car and behind 2 are goats. You pick your door, it doesn’t matter which one and in response Monty opens one of the remaining two doors revealing a goat. So now there is one door with a goat and one door with a car. To make your chances of winning as high as possible, do you stay with your original door or do you switch? As it turns out, if you stay with your original door your chances of winning are 1/3. If you switch, however, your odds are an even 50/50. This result, to say the least, is TERRIBLY unintuitive. To make it clearer though, it’s useful to extend the example to 100 doors with 99 goats and 1 car. Just as before, you pick your one door and in response Monty opens up 98 doors revealing 98 goats. Now you’re left with your original door and the one tantalizing door that remains unopened. So do you switch in this situation? Hopefully the answer now is a “damn right you do.”

Geralamo Cordano (died 1576) was one of the founders of probability theory though like so many never really lived to see his work used or popularized. The technical bits of his work aren’t all that interesting but his life in general was an odd one. His mother was unwed at the time of his birth so she tried to abort him using an evil brew of wormwood, burned barleycorn and tamarisk root. This obviously failed making Garalamo a pretty lucky fellow (or his mother a pretty shitty pharmacologist). He died a pauper after his own son testified against him in some uninteresting civil matter or other just to get himself a plum job as a torturer with the inquisition.

In 1995, the German lottery pulled 6 balls from a set of 49 as it always does each week. This would not normally be news except that the result was exactly the same as one week in 1986. The chances that a lottery of this sort will pull the same numbers twice in this time period: 28%.

Blaise Pascal gave up mathematics and went into religious seclusion near the end of his life, presumably after pondering an enigma termed “Pascal’s Wager”. It runs something like this. Assume there is no God. In that event the best you can do is to live a life of debauchery and then you die and it’s over. Contrarily, assume there IS a God. If you live a pious life then you have gained an infinite reward of an eternity in heaven. If you don’t, then all you got, again, was a brief life of pleasure. So, if one assumes there’s a 50% chance that God exists, the risk that he does NOT exist is dwarfed by the INFINITE reward you can receive if he DOES exist. Therefore, you should just assume that he does and thus at least take a shot at your life of bliss for all eternity. It’s obvious from Pascal’s behavior after this revelation which path he chose…

In 1992 the Virginia State Lottery offered a prize of $27,000,000. The lottery is configured to 6 random numbers from a pot of 44, a mere 7,000,000 possibilities. An investment group in Melbourne Australia got the bright idea to buy 7,000,000 tickets, one with each number combination. After a massive logistical nightmare, 1.4 million tickets filled out by hand, the group was almost too late. They managed to only get 5,000,000 of the numbers submitted in time but none the less did win the prize and collect the jackpot.

Joseph Jagger took his statistical prowess to Monte Carlo in 1873 to turn himself a tidy profit. He and six assistants took careful note of the outcomes on six roulette wheels over a 2-week period. At the end of that time, it was found that one of the wheels had a distinct bias towards certain numbers. A few days later exited with the equivalent of five million dollars in winnings. He was eventually foiled when the casino noticed his turn of luck and began reconfiguring the wheels at the end of each night.

The Greeks had far too much time on their hands it seems. Zeno, yet another Greek philosopher, postulated that you can never actually go anywhere. His logic runs this way. In order to travel 1 meter, you must first travel half a meter. Before you can travel half a meter though, you must first travel a quarter of a meter and so on. Therefore, to travel any distance at all requires you to travel an infinite number of finite distances which would of course take an infinite amount of time. Zeno, it seems, was married to the Red Queen. You’ve got to run TERRIBLY fast just to stay where you are! The Greeks had far too much time on their hands it seems. [This Geeky Greek sandwich is known as ‘Zenos Paradox’]

Bernoulli originated the idea that in order to obtain a good estimate of something’s true value you must first obtain a large sample of data for analysis. Unfortunately, in practice his original formulae are a bit off and often require the ENTIRE dataset to be obtained before any certainty is obtained. [U.S. political polls under the original Bernoulli mathematics would require polling 80% of the houses in the country]. This concept is known as the Law of Large Numbers.

On the other side of the fence, Kahneman and Tversky coined the ironic Law of Small Numbers to describe the tendency of the human population to assign inappropriate significance to vanishingly small data samples.

People pay respect and homage to numbers when clearly they shouldn’t. One large example given was the business of rating wines. When asked about the system the editor of Wine and Spirits Magazine was quoted as saying, “On many levels the rating system is completely nonsensical.” His colleague at the Wine Enthusiast is no more enthusiastic as he states simply, “The deeper you get into this system the more misguided and misleading it is.” Apparently even at the aesthetic level things are no better. When subjects are presented with five bottles of wine whose contents are identical but have different labels and prices ranging from $10 to $90 they will invariably state that the $90 wine is significantly better. In a similar test, most can’t tell a red wine from a white wine that has food coloring added. Perhaps most damning of all, when wine experts were presented with three wines, two of which were identical, half the time they could not even determine which wine was which.

The human mind is very poor at detecting randomness even when it encounters it. In a string of 1,000,000 random 1s and 0s, for example, one should expect to find strings of hundreds of 0s or 1s in a row. Recently, Apple’s iPod received hoards of complaints about its shuffle feature. Customers complained that sometimes the same song was played twice in a row; statistically, a very normal occurrence even in large libraries. Apple has since revised their shuffle algorithm to be LESS random so that it’ll appear MORE random.

People have a fundamental and deep-seated problem with randomness because it messes with our need to be in control. Ellen Langer did a study with nursing home retirees. In one group the retirees were allowed to arrange their own rooms and pick a plant to take care of. In the other it was all done for them and they had no say in the arrangement of their rooms. After 18 months the mortality rate in the group that had no control over their rooms was DOUBLE that of those that got to pick their own room layouts. [This is a stunning conclusion but one that lends itself to sample-space bias. Sicker individuals are going to a priori be placed in the no-control group so this could be a total red herring.]

The idea of Confirmation Bias also tends to skew our view of events. If a situation arises about which we have pre-conceived notions then we will tend to fit the facts to meet our theory rather than viewing them with complete rationality. David L Rosenhan demonstrated exactly that when he sent 10 people, 5 of them doctors, into a psychiatric ward. He told them all to act completely normally but to claim only that they were hearing voices that were not there. All 10 were admitted to the hospital. After being admitted, the subjects dropped the pretence of insanity and went about their normal activities while in the mental ward. Despite the fact that the participants were acting perfectly normally the doctor’s notes for the patients reflected obvious psychosis. Every simple everyday action the subjects performed pointed at some mental condition or other. The subjects were eventually released from the hospital after an average of 19 days.

It’s not just enthusiastic wine enthusiasts who can’t make qualitative judgments on a consistent basis. In a recent music experiment 14,341 participants were given the chance to download 48 songs by bands they had never heard of. The test subjects were divided into 9 different groups. The first 8 groups could see the average rating of each song by previous downloaders and how many times it had been downloaded but only for subjects in their group. So what you ended up with was 8 distinct music microcosms that had no connection to each other. The 9th group rated the songs but they couldn’t see the ratings of anyone else. Ostensibly this was the group that was totally unbiased by the influence of other participants so these ratings were more akin to true musical quality. Unsurprisingly, the 9 groups differed wildly on their ratings for the 48 songs. One song in particular was a #1 smash in one group but a #40 bomb in another. The control group ranked it at #29. Apparently what happens is that some songs jump out to an early and random lead and this results in their popularity. The pop music charts have little to do with the actual quality of music it seems.

Our author also relates one anecdote that jives perfectly with my notion that Bill Gates is just a normal schmuck like the rest of us who happened to just get lucky. The story goes somewhat similarly to this. Back in the day IBM came to Gates and said they needed an OS for their new personal computer. Gates initially balked at the idea and sent them to someone else. Well, the someone else apparently didn’t impress IBM much so they came back to Gates. Gates in the mean time had heard of a bit of software that might do the trick so he brought it up to IBM. After what must have been a comical bit of shrugging and “what do we do now” Gates obtained the software for $50,000 from this unnamed source, modified it slightly and then licensed it to IBM. The rest, it seems, is history. Gates didn’t do anything special. He just happened to be a software nexus of sorts. I gotta get me a nexus.

Vodka, it seems, is a masterfully marketed product. Despite the fact that it’s intended to be non-distinctive and neutral every vodka out there seems to make some weird claim to be unique. Ironically, when the New York Times put 21 vodkas to a blind taste test, the winner was the bartender’s cheapest, Smirnoff.

Publishing too is no stranger to the laws of luck. When the Sunday Times of London took the first chapter from two winners of the prestigious Mann-Booker prize for fiction and submitted them to publishers, not only did the publishers not recognize the pieces, 19 out of the 20 publishers rejected the books for publication. Gotta get lucky in this world I guess. Or maybe just verbose…

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