Expected Value
Previous Next “The weight of evidence for an extraordinary claim must be proportioned to its strangeness.”"
"Pierre-Simon, marquis de Laplacewas a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. “The curious mind embraces science; the gifted and sensitive, the arts; the practical, business; the leftover becomes an economist.”
Nassim Nicholas Talebis a Lebanese-American essayist, mathematical statistician, former option trader, risk analyst, and aphorist[1] whose work concerns problems of randomness, probability, and uncertainty. "Let your dreams outgrow the shoes of your expectations.""
Ryunosuke Satorois regarded as the "Father of the Japanese short story" and Japan's premier literary award, the Akutagawa Prize, is named after him. "When one's expectations are reduced to zero, one really appreciates everything one does have"
Stephen Hawkingwas an English theoretical physicist, cosmologist, and author who, at the time of his death, was director of research at the Centre for Theoretical Cosmology at the University of Cambridge. "A simple lifestyle can make you happy and high expectations can disappoint a lot."
Koena Mitra is an Indian actress and model who appears in Bollywood films. "I am happy with what comes, I don't have expectations of any stature."
Leon Russell"I am happy with what comes, I don't have expectations of any stature." was an American musician and songwriter who was involved with numerous bestselling records during his 60-year career that spanned multiple genres including rock-and-roll, country, gospel, bluegrass, rhythm and blues, southern rock, blues rock, folk, surf and the Tulsa Sound. Sergey Brin "I had no dreams of such economic success. You should have fun and not be so weighed down by expectations."
Sergey Brinis an American business magnate, computer scientist, and internet entrepreneur. He co-founded Google with Larry Page. Brin was the president of Google's parent company, Alphabet Inc., until stepping down from the role on December 3, 2019. "Never idealize others. They will never live up to your expectations." also known as "Dr. Love",
Leo Buscagliawas an American author, motivational speaker, and a professor in the Department of Special Education at the University of Southern California. "We don't want people to have expectations of us, but then we have expectations of everybody else."
Lauryn Hillis an American rapper, singer, songwriter, and actress. She is often regarded as one of the greatest rappers of all time, as well as being one of the most influential musicians of her generation. "As far as expectations go, you can never work for expectations. You have to work against them."
Kajol Devgan, aka Kajolis an Indian actress. Described in the media as one of the most successful actresses of Hindi cinema,[2] she is the recipient of numerous accolades, including six Filmfare Awards, among which she shares the record for most Best Actress wins with her late aunt Nutan. "There is hardly any activity, any enterprise, which is started out with such tremendous hopes and expectations, and yet which fails so regularly, as love."
Erich Fromm was a German social psychologist, psychoanalyst, sociologist.st, humanistic philosopher, and democratic socialist. A German Jew, he fled the Nazi regime and settled in the US. "Expectation is the root of all heartbreak".
William Shakespearewas an English playwright, considered by many to be the finest writer in modern history. "Statistics is the grammar of science."
Karl Pearsonwas an English mathematician and biostatistician. He has been credited with establishing the discipline of mathematical statistics. "He uses statistics as a drunken man uses lamp posts - for support rather than for illumination."
Andrew Langwas a Scottish poet, novelist, literary critic, and contributor to the field of anthropology. He is best known as a collector of folk and fairy tales. Previous Next Expected Value
Mention some recent scientific finding and watch everyone's ears perk up. I know, because I taught about Marine Mammals every Saturday afternoon for 10 years at K-dock on Pier39 where San Francisco's famous California Sea Lions haul out.
I'd stake out a spot on the viewing stands right in front of the docks where they were busy sleeping, barking, play-fighting, and generally being Sea-Lions. With several pairs of binoculars, a spotting scope, a few picture-books of The Marine Mammal Center's operations in Sausalito along with a few pelts and bones to touch, many visitors would stop to take a look, inevitably leading to more questions about them.
It's among the busiest and most popular of San Francisco's many tourist venues. On any given Saturday I could count on over 500 contacts with a curious public. While I'd stress science and the natural history of the pinnipeds, seals sea-lions and walrus, I'd occasionally have to quote a few statistics.
Which, even in the fresh air and sunshine of San Francisco Bay, threatened to put them to sleep. Because If there's a topic or college class that, statistically speaking, puts more students to sleep than any other it's got to be Statistics. Mention anything that even has the word statistics in it, other than sports, and most people's eyes start slamming shut.
But everything I know, am able to pass on to these curious visitors, came to be known after some scientist cared enough to devise an experimental design with some cogent statistical test pointing the way to the truth. Or "the best information we have for now" as scientists put it.
And at the heart of every statistical test or prediction is a thing called "The Expected Value";
"In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable."
I almost put myself to sleep reading that definition. So I get it. Statistics get tediously boring quite fast.
Yet the truth is inescapable; questions I get while teaching in the field, the ones I can answer with confidence at any rate, are asked and subsequently answered with an "expected value" validating them both. Because no good result can come from an invalid question, and no answer can be generated with confidence without a good question having paved the way.
All good questions, it's "expected values" to the rescue every time.
Yet a stark irony comes with that reality, learned once and for all when I was getting my Masters degree in Statistics. The most important lesson we learned while seeking out those 'expected values" was to avoid "expectations". As a statistical consultant, the worst thing we could do was "expect" any knowledge, prowess, or assumption about the problem, the data, or our clients
So the "expected value" at the heart of anything we discover about the natural world is seemingly contradicted by any "expectations" that such insight can solve our problems.
Confused? Welcome to the club. So were we. But not anymore. Because I've learned how and why they are very different things.
Expected values come from data, while expectations come with us before we ever lay our eyes on a speck of experimentally derived evidence. The former comes from hard-won knowledge, the latter is a mere artifact of our human cognitive machinery.
We were required to take 10 hours of 'statistical consulting", then work another 10 hours as a "statistical consultant" in Florida State University's Statistical Consulting Center to graduate. As a State capital and the home of Florida A&M University as well as FSU, Tallahassee is a great place to host such a center. That we were hopping busy neatly underscores its excellent placement.
It was there, after a series of time-consuming sessions with a ranking member of the State of Florida Attorney General's office, that a path to learning that lesson first-hand came my way.
"Estoppel" is an equitable doctrine in the law, a bar that prevents one from asserting a claim or right that contradicts what one has said or done before, or what has already been legally established as true. It can be used as a bar to the re-litigation of issues or as an affirmative defense.
His group had devised a pre-indictment ratings-system for use by the Florida Department of Law Enforcement. The scale they used ran from minus-5 to positive-5, labeled as "weak precedent" to "strong precedent" based on past case-law. Referred to as a Likert Scale, it's fairly standard practice in such applications.
So I couldn't figure out why this client kept coming back. They wanted a final estimate of the likelihood the case for indictment could be supported by "collateral estoppel", a specialized issue-barring concept. I'd set up a spread-sheet for him that would programmatically take care of the statistical computations.
After some thoughtful questioning about their methodology, I learned that as principal investigator he was expected to present and defend the results of the survey to the Attorney General himself. He felt he couldn't, which presented an insurmountable problem when the result is, as in this case, the "expected value" or "average score".
I recall the moment the light bulb went-off inside my head. While writing out the simple computational algorithm on the nearby blackboard, again, I caught his eye for a moment and saw his deep concentration on this simple bit of arithmetic. Glancing at his notes, the real problem became apparent. He didn't know how to add positive and negative numbers.
Raised to be tactful, I couldn't point out that it was basic math he should have learned way back in the 6th grade. So, adding one more step demonstrated how the average scores were calculated in the spreadsheet I built them. I explained it verbally, in his terms, as…
"minusing a minus turns it into a plus."
And I never saw him again. Apparently, he was able to carry the statistical-ball himself from then on. It was inconceivable to me that someone who had attained a Bachelors Degree, then a Law Degree from two well-regarded colleges could not know such a simple thing. That after over 20 years of formal education this could have slipped though his training unnoticed.
Yet it had. Reputed to be a brilliant litigator, and a truly interesting conversationalist as it turns out, he was well-schooled in literature, writing, history, communications, and the law. But not basic arithmetic.
How it is that the multitude of complex thoughts that went through my mind at the same time from nearly 40 years ago can seem like yesterday still amazes me.
I recall feeling incredulity. A bit of sad judgement along with its twin, prideful superiority. Humor. Empathy. And more than a bit of chagrin, all at the same time.
Looking back, I recognize now that he was far more in touch with the basic theme of "Great Expectations" than me, Charles Dickens most sophisticated novel about "desire and self-improvement". Its subliminal moral message, that love loyalty and conscience are more significant than wealth social status and class was directly on point here.
I'd been afforded an opportunity to learn several great lessons in life at once;
One of my Professors had schooled us on this; anecdotally. You see, he was living outside of town in an RFD, a rural fire district. Just not Mayberry RFD, as featured in the 1970's TV show of the same name starring Andy Griffith.
Since north Florida is ecologically dominated by the Pine-Palmetto fire-climax community its many National and State Forests operated under the auspices of the National Wildfire Coordinating Group. Providing national leadership to enable interoperable locally operated and managed wilderness fire operations, they oversaw those RFD's by coordinating federal, state, local, tribal, and territorial partners.
As a volunteer Dispatcher for his district north of town, he discovered his own expectations made him a less than stellar performer in getting their all-volunteer fire-fighting crews mobilized. Trained to ask routine questions like "What's your phone number?" and "What's your mailing address?", he quickly learned that the to seemingly easy questions formed during training-sessions in a conference room might not be so easy to answer for someone calling from inside a kitchen that was on fire!
So he assembled some probing followup-questions for the Dispatchers when they couldn't get a good location from the harried callers. Questions like "Who's your closest neighbor?" and "How long does it take to drive to your home from Tallahassee?" helped them pinpoint the location when used in conjunction with some maps be assembled to augment the Dispatcher's fire-location resources.
He taught us that to be useful to our clients we had to learn how to recognize our own expectations about them before we even met them.
By previewing their research, data they might have sent us, or even the literature in journals chronicling their specialty, we could turn three sessions into one. Help them understand the statistics used in a way they could defend to others on their own. And even prevent embarrassing yet natural gaps in their knowledge about applied mathematics from becoming common knowledge among their cohorts.
He was a wise man, utterly dedicated to his craft, and a great teacher. I've since applied my statistical mentor's #NoExpectations approach when leading groups into "The Great Outdoors" as a Field-Guide.
Having learned to inform the group what they can expect to see without fueling their expectations, it seems as if everyone has benefited.
Knowing what to expect can be truly useful information. But planting an expectation about an upcoming foray into the wilderness does nothing but set people up for disappointment. And that's where the value of the "expected value" lies. Instructing others to "expect without expectation" might, at first blush, seem like conflicting advice.
But the two concepts are like oil and water, an intellectual emulsion, so to speak. Adjacently arrayed top-to-bottom while never meeting.
To inform others while being open to learning something new oneself can be expected to be valuable without any expectations of extracting that value simply by recognizing it. So, values can be valuable, if they're the right ones, while many ostensible valuables turn out to have no value at all.
Such blatant contradiction can seem confusing, much like expectations. But even confusion has value if we can just learn how to expect that there can be something valuable hidden deep inside it.