Notes on Statistics Done Wrong

Statistics Done Wrong
Alex Reinhart

https://www.statisticsdonewrong.com/


P Values

  • Measure of ‘surprise’. The smaller the p the larger the ‘surprise’. P values work by assuming that there is no difference between the 2 samples. If you want to show a drug works you counterintuitively show that “the data is inconsistent with the drug not working”
  • P values say nothing about the magnitude of the effect. A small p can reveal a massive effect or a tiny effect with great certainty (say if you collected massive data). Statistical significance does not mean practical significance! Similarly, statistical insignificance does not mean zero and is simply the best evidence-based on the trial data you studied.
  • Neyman-Pearson uses p-values in a conceptually different way. They estimate an acceptable false positive rate called ‘alpha’. Statistical significance allows us to reject the null hypothesis for the established alpha or false positive rate. This rate is informed by the experimenter’s understanding of the procedure.

Confidence Intervals

  • These are preferable to p-values since they provide a point estimate and a measure of uncertainty and if they can be supplied instead of just p-values they should.
  • They are less common in the literature perhaps b/c they can be very wide

Statistical Power

  • The probability that a study of a given amount of data is capable of showing statistical significance. For example, how many coin flips do you need to be 95% sure that your experiment can reveal a biased coin that is 60% weighted towards heads? Statistical power is a function of :
    • The size of the effect; a smaller effect requires more data
    • Sample size; more data means the study has higher statistical power
    • Measurement error; more subjective measurements have less power
  • Many studies are underpowered because there is not enough data. This often occurs because it is expensive/risky (ie drug studies) or unethical (studies on animals)
  • While an antidote for multiple comparison problems can be to require lower p values, the trade-off is that studies will become underpowered
  • The concept of power is often forgotten because it is not taught in intro stats and is not readily intuitive. Again, confidence intervals which are wide can reveal a lack of statistical power again supporting their use over p values.
  • Truth inflation or type M error (‘magnitude’) is the effect of there being many experimenters ‘competing’ to publish extreme results.
  • Small samples have more variance; be careful to draw conclusions from them since they are more likely to be underpowered
    • Rural states have counties with both the lowest AND highest kidney cancer rates; this is likely due to small populations, not a real effect. The same is true for test scores in smaller schools; we may interpret them to be ‘better’ based on test scores but this is because their average extremes are higher than the average extremes of bigger schools!
    • Remedies for this include shrinkage. Weighting the average from a small sample with a weighted average from a larger population (ie weighting a small county with a higher weighted national average). This will, unfortunately, bias truly abnormal cases too much towards normal. The best remedy is to try to find a larger sample (ie use congressional districts instead of counties). Shrinkage is a good technique in measuring average product reviews (products with few reviews are shrunk towards a generic version of the product).

Pseudoreplication

  • Using additional measurements that are highly dependent on highly correlated to previous data. This form of replication doesn’t allow you to generalize inferences.
  • If you cannot eliminate hidden sources of correlation between variables you must try to statistically adjust for confounding factors.

Base rate fallacy

  • A low p-value is often touted as evidence of significance but significance also depends on the base rate. Consider Bayesian examples like mammogram testing. If mammograms have a false positive rate of 5% and a 90% chance of accurately identifying cancer then if you test 1000 people and 50 of them test positive then it is still quite unlikely that most of those people have cancer. Why? Because the base rate is a mere 1%. Only 10 people in that sample have cancer and we expect 9 of them to be accurately identified but more than 50 will test positive! When testing for conditions with very low base rates false-positive rates will swamp true positive rates.
  • An extreme example of these false discovery rates you are looking for an effect which definitely does not exist, no matter how low you set your p threshold we know your so-called significant results are still false positives, and you are bound to record significance results with a large enough sample.
  • Combatting false discovery rates with multiple comparisons is challenging but important since you expect many false discoveries. Tips include:
    • Remember p < .05 doesn’t mean there’s a 5% chance your result is false
    • When making multiple comparisons using a procedure such as Bonferroni or Benjamin-Hochberg will make your required p values much more conservative by accounting for the number of tests
    • Be aware of stat techniques specific to your field for testing data
    • Have an idea of base rates to estimate how prevalent false positives are likely to be

Confounding variables

  1. Correlation is not causation
  • Because you do not know if there is a confounding variable. If you create a model that predicts heart attack rates based on weight, exercise, and diet it’s tempting to say that if you change one of them x% that the heart attack rate will change by y%. However, that is not what you tested. You didn’t change the variables in a real experiment and measure the outcomes. It is not clear that a confounding variable is actually influencing the heart attack rate.
  • Also, to say a variable changes all else equal is a fantasy. In reality, it is unusual for single variables to change in a vacuum.
  1. Simpsons Paradox
  • When a trend in the data disappears when the data is divided into natural groups. It tends to occur in observational studies with biased samples thus obscuring a confounding variable.
  • Examples:
    • Berkeley admission bias against women in 1973. In aggregate, women looked discriminated against but at the department level, the opposite was true. The bias occurred bc women applied in higher numbers to competitive, underfunded departments. The bias happened earlier in the process: women were systematically pushed towards these fields
    • Penicillin appeared to improve outcomes for meningitis cases in the UK. At a closer look, the sample was biased since it was only administered to children who were not rushed to the hospital so they were the milder cases. Isolating the sample to those who visited a general practitioner first we find that penicillin, in fact, seemed to correlate with worse outcomes (there are theories about the breakdown of the contagion causing shock but there aren’t experiments for testing if penicillin actually causes meningitis patients to die)
    • Looking at aggregate data United flights are delayed more frequently than Continental. But at individual airports, the trend reverses. The aggregate data doesn’t account for the fact that United flys out of more airports with bad weather.

Notes on How Not to Be Wrong: The Power of Mathematical Thinking

How Not to Be Wrong: The Power of Mathematical Thinking
by Jordan Ellenburg


  • Math gives you tools to extend your common sense of reasoning and logic. He uses the analogy of Ironman’s suit.
  • Competitions including war are often decided by small edges. Being 5% better at x or y can decide the outcome over a long enough game. (Similar to my experience with boardgames. A more efficient engine in a game of 7 Wonders or Settlers can save you actions; like reducing the cost of capturing winning victory points.)
  • Zooming in on points of a curve they look and can be approximated by lines. Trajectories are curves influenced by gravity but objects appear to move in straight lines. Using lines to approximate curves is the basis of calculus and even the derivation of pi as the area of a circle (Archimedes did this by iteratively computing the edges of a circumscribed circle as a polygon. Imagine an octagon, then a polygon with 64 sides, and so forth until it looks like a circle. You can then use trigonometry to compute the area of the triangles you keep creating until the sum of all the area approximates the area of the circle)
    • Critics of this method like Zeno highlighted the uncomfortable paradox of constantly halving something until you get nowhere. Comically, the skeptic Diogenes countered Zeno by simply walking across the room to make the point that motion is indeed possible!
  • The law of large numbers explains why South Dakota can have the highest rate of brain cancer and North Dakota the smallest. They both have small populations. Be careful when comparing quantities from 2 very different sample sizes. Small samples are more volatile. If you flip 10 coins, your odds of getting 8 heads is unlikely but real. But flip 1000 coins it’s nearly impossible to get 800 heads.

Data mining 

“The more chances you give yourself to be surprised the higher your threshold for surprise had better be.”

“A significance test is a scientific instrument and like any other instrument, it has a certain degree of precision. If you make the test more sensitive by increasing the size of the studies population, for example, you enable yourself to see ever-smaller effects. That’s the power of the method but also the danger”

  • An underpowered study has the opposite problem. You dismiss an effect that your method was too weak to see. A good example is the original 1985 hot hand studies. They rejected the idea of a hot hand but it turns out the methods they used rejected a hot hand even on data sets that were generated by simulations that deliberately baked in a hot hand! In fact, their methods failed to notice even the effects of good vs bad defenses which we know influences offensive shooting percentages.
    • The final verdict is there may be some hot hand effect but it is too difficult to detect because if it exists it is very small. In fact, players who think they are hot take harder shots and perform worse so it’s best for them to not believe in the effect since it will be more than offset by an unjustifiably confident shot selection.

The Bayesian examples in the book are great.

  • In a Bayesian framework how much you believe something after you see the evidence depends not just on what the evidence shows but much you believed it to begin with. Posterior probabilities still depend on the strength of your priors.
  • On conspiracy theories: “If you do happen to find yourself partially believing a crazy theory, don’t worry — probably the evidence you encounter will be inconsistent with it, driving down your degree of belief in the craziness until your beliefs come in line with everyone else’s. Unless, that is, the crazy theory is designed to survive the winnowing process. That’s how conspiracy theories work”.

Tradeoffs and cost of perfection

  • Stigler type arguments that optimal decisions often leave a margin for error. Getting to the airport early enough to have a 100% chance of making the flight is probably so conservative it’s wasteful (depends on your utility curve but almost certainly wasteful to be 100% certain vs say 95%). When you read a story about social security overpaying people bc they were actually dead, it turns out that mistake represents less than 1 basis point of payments. In other words, they do a great job not making this mistake and the cost of being 100% compliant may simply not be cost-effective to be worthwhile.

St Petersburg and the role of expected utility

  • Fran Lebowitz utility curve of money: she would drive a cab each month until she could eat and pay rent. Afterwards, she would write. In other words, she had a linear utility curve which flattened abruptly. If you raise her taxes she works more as opposed to someone with a logarithmic curve who is at the point of indifference between work and leisure
  • Ellsburg Paradox highlights the limitations of utility theories. It highlights the difference between what Rumsfeld called “known unknowns” or what mathematics refers to as risk vs “unkown unknowns” or uncertainty. Utility theory may help with uncertainty but formal math is less useful.

Regression to the mean explains many phenomena that are usually attributed to another reason.

  • Examples, best-performing companies (competition attribution), musician/writer sophomore slump, RB after signing a big contract, dietary fiber speeding or slowing digestion, Scared Straight juvenile detention program, diet effects when people are at their peak weights. When something is at an extreme we should expect reversion simply bc of math and therefore be very careful of attributing to an intervention.

Correlations between variables reduce the information content of the variable.

  • You try to identify criminals by foot and hand size you are choosing highly correlated variables.
  • Strong correlations lie behind how we compress images and music files. A green pixel is probably next to a green pixel.

Notes From Lessons of History

The Lessons of History
by Will and Ariel Durant


Geography

  • As technology evolves, the influence of geography is diminished
  • The prosperity of civilizations is closely tied to geography notably rivers and coasts
  • Ultimately, humans create culture, not the earth

Biological lessons of history

  • Life is competition
  • We rely on the protection of our tribes and may cooperate within its confines but this is adaptive behavior in service of a wider competitive landscape. Until a group is as large as a state it will “continue to act like individuals and families in the hunting stage”
  • Life is selection
  • Nature knows nothing of our egalitarian ideals or Bill of Rights. “Freedom and equality are sworn enemies”. If people are free, relative advantages will grow nearly geometrically. Inequality is inborn, we can only aspire to ideals such as equal access to education and justice.
  • Natural selection benefits from the diversity and range of natural ability as it is the basis of evolution.
  • Life must breed; birth rates shape history
  • Nature cares only about the species, not the individual. Diversity and large “litters” are the fertile grounds that natural selection needs as fuel. Nature’s check on overpopulation is famine, pestilence, war.
  • Higher birth rates can give rise to stronger tribal powers while progression into a higher standard of livings and industry appears to slow the birth rates as the tribe advances.
  • To track the future of ideas, it may be instructive to watch birth rates; weakened ties to ethnicity or tribalism can leave the incumbent group vulnerable (Caesar and Augustus were aware of this and sought to penalize birth control; Italy’s ethnicity diluted over time making the empire vulnerable to its neighbors)
  • On race: “A knowledge of history may teach us that civilization is a cooperative product, that nearly all peoples have contributed to it; it is it common heritage and debt; and the civilized soul will reveal itself in treating every man or woman, however lonely, as a representative of one of these creative and contributory groups.”

Government

  • Monarchy has been the historical norm while democracies have been ‘hectic interludes’
    • Roman democracy crumbled under class wars giving way to Pax Romana, a 200 year succession of benevolent dictators until the murder of Caesar. This period was followed by disgraceful monarchs including Caligula before giving way to the greatest succession of monarchs ever, the last being Marcus Aurelius. Some of these monarchs had no heirs and promoted by merit until Aurelius died. Afterward his son Commodus ruled when no heir was named.
    • Monarchy has a mixed record, typically at its worst is when it is determined by blood and accompanying incompetence
  • Most modern, complex governments  are oligarchies — ruled by a minority
    • Aristocracy by birth
    • Theocracy by religion
    • Democracy by wealth
  • Plato reduced the cycle to monarchy->aristocracy->democracy->dictatorship. Repeat. This was based on Greece and repeated with the Romans. Democracies are overthrown or conquered as envy amongst the majority tires of the ‘sham’ of having a vote and uses the state to seize wealth. Other oligarchies fall when they wield their great power to narrowly or incompetently.
  • The US democracy started from a wider base and in unity against British rule. Rural land-owning enhanced the sense and dedication to freedom, while geographic isolation created a national sense of freedom. These conditions have given way as land as sparse and cities have grown “Every advance in the complexity of the economy puts an added premium upon superior ability and intensifies the concentration of wealth and [power]”
  • Democracy is a difficult form of gov’t since effective mob rule requires widespread intelligence to avoid manipulation by ‘the forces that mold public opinion’.
  • Democracy, however, has done the most good and it can maintain its promise only if it affords equal opportunity for education [my own thought is this will always be uneven, and the unevenness grows with population size. For a small population, it is reasonable that the average access to education can be even]
  • “If a race or class war divides us into hostile camps, changing political argument into blind hate, one side…may overturn the hustings with the rule of the sword. If our economy of freedom fails to distribute wealth as ably as it has created it, the road to dictatorship will be open to any man who can persuasively promise security to all”

History and War

  • Competition via war is often for the same reasons as competition amongst individuals however while individuals are restrained by law and morals a state ‘acknowledges no substantial restraint either because it is strong enough to defy any interference…or because there is no superstate to offer its basic protection, and no international law or moral code wielding effective force’
  • Religious wars in the 16th century and the wars of the French Revolution were battles between aristocracies leaving the masses to maintain mutual respect for their foreign counterparts while wars of the 20th century in accordance with technology and ‘means of indoctrination’ made war all-consuming ‘struggles between people’ and completely destroying centuries of labor and property.
  • He presents the general case for the inevitability of war — competitive human nature, envy, beliefs so fundamentally different that cannot be settled by negotiation. Perhaps and only if we were united against aliens could we imagine our species not warring with each other. The opposing view is that the imperative to avoid large scale war because of the destructive power of current technology will prevail over any disagreements over ways to organize our lives and economies.

Progress

  • Are we the ‘same trousered apes’ merely armed with increased tech, locomotion, and knowledge but weighed down by the persistent features which moor us to our primitive ancestors? Progress is defined not by happiness or similar measure but to the degree in which we may control our environment. By this standard, as evidenced by our increased adaptability and lifespans we have made tremendous progress. While subject to lapses and regressions, the avergae human has been the beneficary of an accumulated history and knowledge which has been succeeds in being recorded and transmitted to subsequent generations so that they may continue to build on this heritage from its most advanced point.

Mauboussin on Making Better Comparisons

Michael Mauboussin Guide to Making Better Comparisons (Link)


Comparing via analogies (steps and common mistakes)

  1. Select the source for analogy
    • Common pitfall at this stage: Undersampling due to availability bias
  2. Map the source to target to make inferences usually looking for similarities
    • A common pitfall at this stage: mistaking correlation for causality
      • Consider the first attempts at flight were people putting feathers on their arms, not studying lift
      • Confusing a star performer with talent in a volatile field
  3. Adjust for differences between source and target
    • Tversky showed we place more emphasis on similarity than differences
    • The framing problem: We are influenced by which differences and similarities we are prodded to focus on (ie framing)
  4. Learn by the success or failure of the analogy
    • Pitfalls in heuristics and intuition
      • Intuition works great in chess since it is a form of pattern recognition, but works poorly in investing where outcomes are non-linear
      • Recency bias influences sample
      • Choice-supportive or confirmation bias taps into our need to be consistent; we create stories after the fact to validate our decisions
      • Hyperbolic discount rates prevail when we study inter-temporal decision making
        • Stress is good response for crisis because it focuses on immediate needs; chronic stress causes decisions to be short-sighted
    • Using poor reference points in comparison
      • 2 companies in different industries can be more similar than their peers within their own industry; this shows how we can conflate attributes with what is actually driving value
      • Not recognizing that widely varied values can be justifiable. For example, 2 companies with the same earnings growth can trade at justifiably different valuations if underlying returns on invested capital are very different
      • Anchoring bias
      • When I went to Capital Camp, Mauboussin discussed T Theory. The top row of a category have more in common with each other than the average in the category. This articulates how I think about investors! Warren Buffet, Annie Duke, and Sam Hinkie have more in common with each other than other people in the same category.

So how to get better?

Instead of relying on analogies drawn from memory we can use “similarity-based” forecasting.

  • Inputs
    1. A wide sample for the reference class rather than 1 or 2 examples from memory
      • Additional refinement by weighting the results of the most similar samples more heavily
        • Ways to quantify the similarity
          • “nearest neighbor” algorithm (requires identifying relevant axes for the dimensions)
          • “connectionist” technique for weighting features by similarities and differences
    2. A statistical “base rate” drawn from the outcomes of varied reference classes

Contrarian Examples from How I Built This

Allen Cheng writes the best book and content summaries on the web. He wrote this post summarizing what he learned from 50 episodes of Guy Raz’s How I Built This podcast.

Many of the businesses were built on ideas that seemed polarizing or crazy at the time. Pulling directly from Allen, these are the ones that jumped at me:

  • Airbnb: idea of staying in someone’s house was crazy
  • Sam Adams: American beer at the time were watered down lagers. Didn’t want to compete with Budweiser.
  • Southwest: Violated all the “rules” of airlines. Discount airline (some tickets cost $10), no frills, direct routes between second tier airports. Focused not on market share but profitability.
  • Jose Andres: Did crazy things in the kitchen at El Bulli with Ferran Adria. “Don’t take things for granted. You have to discover things for yourself. If you only follow the teachings of people before you, you are only following others.” Also was part of the tapas sharing-food movement in the US – “just move your plate 20 inches to indicate sharing.”
  • Patagonia: “If you want to understand an entrepreneur, understand a juvenile delinquent.” If you can’t win at a sport, invent your own sport that you can be best in. Don’t go head to head against Coca-Cola, they’ll kill you. Do it differently. Figure out something that no one else has thought about.
  • Melissa & Doug: In the digital age, they went retro, building physical toys that gave parents nostalgia. “Don’t go with the tide. If we copy every good model out there, we’re going to be mediocre by definition.”
  • Warby Parker: Got a lot of feedback of glasses being weird to buy online, people wanted to touch them. They offered free shipping and returns for home trial program.
    • Price was believed to be signal of quality. Would be absurd to consumers that a comparable product was sold at 10% of price. $100 presents a psychological barrier, so they priced at $95 so it looks deliberate (as opposed to $99)
    • Conventional wisdom was to either build a brand or ecommerce site, not both. They wanted to build a vertically integrated brand.
  • Zumba: Novel in how much fun people had while exercising. Make it easy so your mom can do it. Don’t use microphone or it’ll interrupt the music – cue visually.
  • Drybar: Gave blowouts at $40, in between the expensive $100+ salons that would guilt you into cutting hair, and the discount Supercuts experience (classic Blue Ocean).
  • Honest Tea: Saw there was a sweetness gap, between unsweetened and super sweet. Also made its tea by brewing, not by powder. People who liked the tea were loyal since other teas tasted so different. But distributors for Snapple etc. rejected them thinking there wasn’t a market for it.
  • Zappos: Seemed like classic bad dotcom idea – no one wanted to buy shoes without trying them out. But footwear was a $40B industry in US, and mail order was fastest segment of shoes.
  • Kate Spade: Felt handbags at the time were too complicated, wanted simple architectural shapes.
  • Lyft: In 2012, saw Uber with elite black cars picking up on demand. Thought, we should do this for personal vehicles. Getting into a stranger’s car was absurd at the time (like Airbnb) and regulation was heavy. Even as they gained traction, other companies were waiting to see how the regulatory problems would be resolved.
  • Beyond Meat: All an animal is doing is taking in plant matter and water and creating protein and lipids. Why can’t we do this too outside the animal? Wasn’t a big hit among investors until Kleiner Perkins got involved.
  • Crate & Barrel: European furniture was expensive and out of reach of young couples. In addition to their direct-from-factory purchase model, a few trends grew the market – jet travel to Europe, food culture (eg Julia Childs), and America was getting wealthier.
  • Atari: Home arcade machines were completely novel. Toy vendors didn’t think people were willing to pay much for them.
  • Stripe: Around the time of founding in 2010, payments seemed like a relatively solved problem. From the consumer side, payments (eg to Amazon) were already frictionless, investors thought Paypal would take care of developer ease.
    • Also, Stripe targeted developers rather than businesses through a salesforce, which was of unclear value to investors and competitors. Stripe assumed that targeting developers would let Stripe grow with its customers (as did happen with customers Lyft and Shopify).
  • Betterment: Starting a fintech company required wading through regulation, something many tech entrepreneurs were unwilling to do. Around 2008, faced some criticism around starting a financial company around the time of the recession, but they believed it was the best time, given the confusion around what to do with money then.

Matt Levine on shareholder value

Matt Levine discusses:

  • Traditional and progressive views of the role of corporations
  • How a narrow desire to raise shareholder value keeps frauds from capitalizing on investors who appeal to higher causes.
  • Compartmentalizing your job from your personhood as a necessary convenience

https://www.bloomberg.com/view/articles/2018-09-27/shareholder-value-could-be-worse



Primacy of Corporate profits

Friedman, along with Michael Jensen and William Meckling, is probably the person most associated with the theory that—as his famous article put it—“The Social Responsibility of Business Is to Increase its Profits.” In this theory, managers of a corporation have a singular duty to the shareholders to maximize their economic return as far as possible (while complying with the law), and if managers pursue any other objective—treating workers well or being good environmental stewards or standing up for what they believe in—at the expense of shareholder value, then they are misbehaving. Of course, there is plenty of room to argue that pursuing those other objectives actually enhances shareholder value. And there is much to be said for Friedman’s view—which is also after all Adam Smith’s view—that by focusing on economic profits, a company will maximize the amount of social good that it does, simply because the normal way to maximize profits is to figure out what people want and then sell it to them.

Including More Stakeholders

It is popular, these days, to criticize that view. The corporation is a political construct, embedded in a society; it has many stakeholders whose interests it needs to consider, not just shareholders. You see this criticism everywhere, from attacks on stock buybacks to Elizabeth Warren’s call for “accountable capitalism.” In its more extreme form, you can see shareholder-profit-maximizing corporations compared to science-fiction robot villains, or to psychopaths: If you value only profit and nothing else, then there is something inhuman about you.

Compartmentalizing

That probably overstates matters. If you come to work and focus on maximizing the profits of your company, that probably doesn’t mean that you’re a psychopath. It probably just means that you have a job. You compartmentalize things a bit; your work does not contain the entirety of your personhood; it’s a thing that you do because you need to make a living. In this sense, a company whose philosophy is “we will sell products that people want for more than it costs us to make them so that we can make a profit and increase our share price” is rather psychologically healthy. That is a good goal to work on during business hours Monday through Friday, and then leave. It is a modest, reasonable, businesslike goal. Obviously there are large contested margins, and you shouldn’t do psychopathic things to pursue that goal, and some people do and that’s bad, but for the most part “shareholder value” is the sort of mission that inspires people more or less the right amount. If you go around murdering people to maximize shareholder value then, yes, you are a psychopath, but most people aren’t.

The Difficulty of Accounting for Intentions

But there are other goals. Those goals are bigger, and you can wrap your whole personhood up in them, and you can believe that those goals are so important that they can justify anything. If Facebook’s goal is to maximize revenue by selling targeted ads to clothing companies, and you find out that it has features that enable genocide, then you shut down those features because the ads just aren’t worth it. If Facebook is about the “noble mission” of “connecting people,” then the tradeoffs are murkier. If “Facebook is truly the only company that’s singularly about people,” then … what even … how do you measure how about-people it is being? If you’re the singular company whose focus is people, then whatever you do is sort of necessarily good; your end is so vague and noble that it can justify any means. And for all that Facebook’s meddling with Instagram and WhatsApp seems to be driven by straightforward ad-revenue-maximization considerations, it’s worth saying that Facebook isn’t really answerable to shareholders and that its explicit ideology rejects shareholder value as a goal. “Facebook was not originally created to be a company,” Mark Zuckerberg wrote when it went public. “It was built to accomplish a social mission.” Okay!

Grand Visions Can Be Weaponzied, But Shareholder Value? Not So Much.

I am late to it, but I just finished reading John Carreyrou’s “Bad Blood,” the story of the fraud at Theranos Inc. and his work to uncover it. Theranos—in Carreyrou’s view, and the view of federal prosecutors—issued tens of thousandsof blood-test results to real patients using technology that it knew didn’t work, endangering those patients’ lives. There are a lot of passages in the book about Theranos founder Elizabeth Holmes inspiring and cajoling her employees to work harder, to get with the mission, to override their moral objections to faking the technology and push ahead. None of those passages mention shareholder value or profit maximization. They mention Holmes’s vision of revolutionizing health care to save lives and treat cancer patients. If you want to inspire people to do terrible things, it is very useful to sell them on a grand vision, a higher purpose, a noble mission. Shareholder value is nobody’s idea of an inspiring mission. That’s what’s good about it!”

How much to wager when you have edge? (Hint: median not mean outcomes!)

Link: Rational Decision-Making under Uncertainty: Observed Betting Patterns on a Biased Coin


  • Optimal bet size as a fraction of bankroll is 2p-1 where p is the probability of winning1. You will recognize this as the edge per trial reported as a percent. So a 60% coin has 20% expected return or edge
  • The formula is a solution to a proportional betting system which implicitly assumes the gambler has log utility of wealth

Imagine tossing a 60% coin 100x and starting with a $25 bankroll

Arithmetic Mean Land

The mean of one flip is 20% positive expectancy

Optimal bet size is 20% of bankroll since you have .20 expectancy per toss

Increase in wealth per toss betting a Kelly fraction: 20% of bankroll x .20 expectancy = 4%

Expected (mean) value of game after 100 flips betting 20% of your wealth each time

$25 * (1+.04) ^ 100 = $1,262

Median Land

The median of one flip betting a Kelly fraction is (1.2^.60 * .8^.40 – 1) or 2%

Median value of game after 100 flips betting 20% of your wealth each time

25 * (1.2^60) * (.8^40) = $187.25!

Things to note

  • The median outcome by definition is the increase in utility since Kelly betting implicitly assumes the gambler has log utility
  • After 100 flips, the median outcome is only about 1/10 of the mean outcome! The median outcome gives an idea of how much to discount the mean payoff. If your utility function is not a log function (ie does quadrupling your wealth make you twice as happy) then a different Kelly fraction should be used

Refactored “When the Culture War Comes for the Kids”

This is a 10:1 compression and refactoring of George Packer’s When the Culture War Comes for the Kids


There is a deep sense of inequality prevailing in America. 

The parents on the fortunate ledge 0f this chasm gaze down, vertigo stuns them. Far below they see a dim world of processed food, obesity, divorce, addiction, online-education scams, stagnant wages, outsourcing, rising morbidity rates—and they pledge to do whatever they can to keep their children from falling…By kindergarten, the children of elite professionals are already a full two years ahead of middle-class children, and the achievement gap is almost unbridgeable.

The need for equality and the role of merit.

The claim of democracy doesn’t negate meritocracy, but they’re in tension. One values equality and openness, the other achievement and security. Neither can answer every need. To lose sight of either makes life poorer. The essential task is to bring meritocracy and democracy into a relation where they can coexist and even flourish.

In 2014 the front line of social advocacy hardened

This new mood was progressive but not hopeful…At the heart of the new progressivism was indignation, sometimes rage, about ongoing injustice against groups of Americans who had always been relegated to the outskirts of power and dignity…Over time the new mood took on the substance and hard edges of a radically egalitarian ideology…its biggest influence came in realms more inchoate than policy: the private spaces where we think and imagine and talk and write, and the public spaces where institutions shape the contours of our culture and guard its perimeter…You could almost believe they spoke for a majority—but you would be wrong…The new progressivism was a limited, mainly elite phenomenon.

“For better or worse, it’s all identity now.”

The battleground of the new progressivism is identity…progressive politics meant thinking in groups. In politics, identity is an appeal to authority—the moral authority of the oppressed: I am what I am, which explains my view and makes it the truth. The politics of identity starts out with the universal principles of equality, dignity, and freedom, but in practice it becomes an end in itself—often a dead end, a trap from which there’s no easy escape and maybe no desire for escape. Instead of equality, it sets up a new hierarchy that inverts the old, discredited one—a new moral caste system that ranks people by the oppression of their group identity. It makes race, which is a dubious and sinister social construct, an essence that defines individuals regardless of agency or circumstance—as when Representative Ayanna Pressley said, “We don’t need any more brown faces that don’t want to be a brown voice; we don’t need black faces that don’t want to be a black voice.”

De Blasio’s schools chancellor, Richard Carranza, has answered critics of the diversity initiative by calling them out for racism…Carranza has mandated anti-bias training…One training slide was titled “White Supremacy Culture.” It included “Perfectionism,” “Individualism,” “Objectivity,” and “Worship of the Written Word” among the white-supremacist values that need to be disrupted.

Witchhunt?

At times the new progressivism, for all its up-to-the-minuteness, carries a whiff of the 17th century, with heresy hunts and denunciations of sin and displays of self-mortification. The atmosphere of mental constriction in progressive milieus, the self-censorship and fear of public shaming, the intolerance of dissent—these are qualities of an illiberal politics.

[In Jared Dillian’s Daily Dirtnap, he recounts “I’m not sure if you heard about the spectacle at the Des Moines Register, but here goes. Guy goes to a football game and holds up a sign asking for beer money over Venmo. He gets some money. He gets more money. Then more money. He has $1 million! He donates it to a children’s hospital. Reporter at the Des Moines Register digs up old racist tweets from him when he was 16. The guy who saved the children. Outrage mob forms, digs up old racist and homophobic tweets on the reporter. Pandemonium ensues. Thousands of people canceling subscriptions from the newspaper. Newspaper editors stonewalling. Now death threats. This is where we are. Every day is worse than the last. Tomorrow will be worse than today. Yesterday was worse than the day before. This will continue for the next 20-30 years.”]

[Dave Chappelle, in his Netflix special Sticks and Stones, calls out the prevailing ‘cancel culture’: “If you do anything wrong in your life and I find out about it, I’m gonna try to take everything away from you!”]

It struck me that this would punish kids whom the movement was supposed to protect…

In the name of equality, disadvantaged kids were likelier to falter and disappear behind a mist of togetherness and self-deception. Banishing tests seemed like a way to let everyone off the hook. This was the price of dismissing meritocracy.

The middle-school scramble subjected 10- and 11-year-olds to the dictates of meritocracy and democracy at the same time: a furiously competitive contest and a heavy-handed ideology. The two systems don’t coexist so much as drive children simultaneously toward opposite extremes, realms that are equally inhospitable to the delicate, complex organism of a child’s mind.. Wokeness prettifies the success race, making contestants feel better about the heartless world into which they’re pushing their children. Constantly checking your privilege is one way of not having to give it up.

Our goal shouldn’t be to tell children what to think. The point is to teach them how to think so they can grow up to find their own answers.

There is no answer to this

I can imagine the retort—the rebuke to everything I’ve written here: Your privilege has spared them. There’s no answer to that—which is why it’s a potent weapon—except to say that identity alone should neither uphold nor invalidate an idea

“The legacy of racism, together with a false meritocracy in America today that keeps children trapped where they are, is the root cause of the inequalities in the city’s schools. But calling out racism and getting rid of objective standards won’t create real equality or close the achievement gap, and might have the perverse effect of making it worse by driving out families of all races who cling to an idea of education based on real merit. If integration is a necessary condition for equality, it isn’t sufficient. Equality is too important to be left to an ideology that rejects universal values.

 

 

Tradeoffs in tax policy

Excerpts from Howard Mark’s memo: It’s All Very Taxing

The concept of “paying a fair share” is nebulous at best. It’s very contentious because everyone has a horse in the race. Mark’s memo is my favorite reference for the complexities and competing goals when designing tax policy.

Mark’s published the memo in November 2011 so the specifics are outdated but this doesn’t negate the reasoning. In fact, the changes actually highlight how our tax code evolves to punish or incentivize certain behavior.


Intro

We have a progressive system of taxation, meaning that higher earners don’t merely pay more in terms of dollars; they generally pay a higher percentage of their incomes in taxes. Most people agree that this is fair. But is it? Why should success be penalized through greater taxation? And if the tax rate for those who earn more should be higher, how much higher?

Under the U.S. system, people in higher income brackets pay tax at higher rates. In large part, the question of fairness primarily surrounds whether the higher rates are high enough. Talk about “the eye of the beholder.” There’s evidence on both sides of this debate: The top 1% of U.S. taxpayers pay 38% of all individual federal taxes.

A breakdown of the numbers

The top 10% pay 70% of all taxes, the top 25% pay 86%, and the top 50% pay 97%. The bottom 50% of all taxpayers paying only 3% of the total.

About half of Americans pay no federal income tax, and almost 25% pay no federal taxes at all. The average federal income tax rate for the top 1% of Americans is 23% (and for the top half it’s 14%), while the average rate for the bottom half is 3%.

They pay at lower rates than they used to and it seems progressivity has declined. . . . the effective federal tax rate, including payroll taxes, for the wealthiest 0.01 percent of earners fell to 31.5 percent in 2005, from 42.9 percent in 1979 [for a decline of 26.6%], according to data from the Congressional Budget Office. Over the same time, effective rates for taxpayers in the center of the range fell to 14.2 percent, a decrease of just 4 percentage points [or 22.0%]. (The New York Times, September 21, 2011). Total revenues from income taxes have declined in the U.S. – they “are at a historic low. of 15.3 percent of the gross domestic product, compared with a postwar average of 18.5. percent” (Financial Times, September 25) – and they’ve declined more for top earners. than for the rest. This is because of both specific rate cuts that have been enacted and the fact that the rates applied to dividends and capital gains – which clearly flow more to people in the upper-income brackets – have declined relative to the rates on salaries and wages.

  • On average, higher earners absolutely do pay a higher percentage than those who earn less.
  • But the decision as to whether the differential is just right, too little or too great is highly subjective and certainly a valid topic for debate.

A non-exhaustive list of trade-offs to consider

  • Are some forms of income more desirable to society and thus deserving of taxation at lower rates?

A discussion about investment vs wage income

    • Long-term capital gains are taxed at reduced rates because of a judgment that long-term investment in things like securities, companies and real estate is beneficial for the economy and should be encouraged. Right now, the top tax rate on long-term investment profit is less than half that on short-term gains and ordinary income.
    • What about interest? Why are dividends taxed at preferential rates and interest at ordinary rates? The explanation may lie in the fact that interest is deductible for corporations, while dividends aren’t. Interest is paid out of pretax income, while in theory dividends are paid out of after-tax income – although the existence of corporate deductions and credits means dividends may, in fact, be paid out of income that hasn’t been taxed by the U.S. Alternatively, the difference in tax treatment may be the result of a desire to encourage investment in “risky” equities rather than “safe” debt. But some companies’ dividends are no doubt safer than some other companies’ interest payments, so this distinction is questionable. If the goal is to encourage risk-bearing, is dividend versus interest the right criterion?
    • While on the subject of gains from investments, it’s interesting to note that, not long ago, dividends were included with interest under the rubric “unearned income.” And it was taxed more heavily than wages.
    • But now things have turned 180 degrees, and returns on capital are taxed at lower rates than wages. It’s worth noting that the Democrats – commonly considered the party of labor – controlled the government for much of the period 1928 to 1980, when earned income was favored. On the other hand, the Republicans – the party of those with capital to invest – have been in control more of the time since 1980, and the taxation of returns on capital has declined in relative terms. The definition of virtuous income that should be encouraged through lower taxes clearly is subjective, impermanent and subject to change with the winds of politics.
  • Should we encourage certain expenditures by making them deductible from taxable income?

The drafters called them deductions: provisions that reduce the net income on which taxes are levied. Critics call them loopholes, suggesting there’s something underhanded
about those provisions. And politicians use the laudatory-sounding term tax incentives to describe tax code provisions that reduce tax revenues in order to encourage certain
behavior. It all depends on your point of view.

Interest on mortgages

    • For as long as I can remember, interest on home mortgages has been treated as a desirable expenditure that should be encouraged. Because homeownership is considered part of the American dream, the tax code subsidizes it by reducing the after-tax cost for those who borrow to buy homes (and are able to itemize rather than take the standard deduction). While everything else may be arguable, certainly this seems fair. But is it? Are homeowners more virtuous than renters? If mortgage interest is deductible but rent isn’t, we’re requiring renters to subsidize owners. Is that appropriate?
    • On average, homeowners are from the middle and upper-income brackets. Is it fair that poorer renters provide a benefit for richer owners?
    • And is it desirable that those able to buy more expensive homes should get more of a subsidy than those consigned to cheaper ones?
    • As with the taxation of dividends, judgments on these matters change over time. Until 1987, there was no limit on the amount of mortgage interest that could be deducted. If you could afford to own ten homes with multiple million-dollar mortgages on each one, taxpayers would collectively share the cost by reducing your income taxes due. Today interest is deductible on only a maximum of $1.1 million of debt, and only on first and second mortgages, and only on a primary residence and a second home. So the tax treatment of owners of many homes and more expensive homes has become less generous. But it’s still better than that of renters. Is that proper?

Charitable deductions

    • As I travel the world visiting with clients, I see that two things about the U.S. are quite uncommon: (a) Americans give a lot of money to charity and (b) donations to charity are deductible in calculating taxable income. Everyone tells me the latter is the main reason for the former. In particular, these things are part of the explanation for the existence of the
      many private, non-state-supported colleges and universities in the U.S.
    • Part of this is true because legislators decided at some point to subsidize non-profits by encouraging contributions through the tax code. That’s certainly understandable. And yet, changes were made in recent years to limit upper-bracket taxpayers’ use of deductions in order to ensure that they pay some minimum tax rate. What about the unevenness of the subsidy?
      • The cost of giving $1 to charity is reduced by the amount of taxes it saves the donor, which is equal to $1 times the person’s tax rate. So today, speaking simplistically, it costs a top-bracket taxpayer 65 cents to give a dollar to charity, while it costs a bottom-bracket taxpayer 85 cents. Is that fair? Should the bigger earner receive a greater reward for a dollar of philanthropy than someone who can afford it less easily?
      • And should those who aren’t inclined to give to charity be required to subsidize those who are?

State and local deductions (SALT)

    • Deductibility on the federal tax return somewhat evens out the burden and ensures that (a) the states get first crack at taxing income and (b) the federal government can only tax
      what’s left, in line with federalist principles.
    • This raises a number of questions. Is the deductibility of state and local taxes fair? As with other deductions, the key question is “fair to whom?” Some people pay more state
      and local taxes than others, meaning they get greater deductions than others. As a result, while a person with a given income who lives in a high-tax state pays higher total taxes,
      he or she pays less federal tax than someone in a low-tax state. Is that fair?
    • Should the federal government subsidize spending on the part of high-tax states? That is, should residents in low-tax states bear part of the expenses of high-tax states?
    • While the source of an exemption rather than a deduction, what about interest on “municipal bonds” issued by states, counties, cities and local agencies. This is exempt from federal taxation, under the legal doctrine that the federal government mustn’t tax the operations of the states. But here again, we’re talking about a federal benefit (in the form of a lower cost of capital) for the biggest-spending local governments and their citizens, and a tax break for people who lend to them.

Property and sales taxes

    • Property taxes deductible without limitation. Thus the owner of a mansion – or ten mansions – receives more of a tax benefit than a low-income earner. And it’s another subsidy for homeowners versus renters. Is this right, or should it be changed?
    • Sales tax used to be deductible, too (meaning the buyer of a Rolls Royce got assistance from the federal government). Now it’s not. More fair?

The biggest exclusions of all: employer-provided health care and the deferral of taxation of contributions to pension plans

    • In both cases, those receiving these employer-paid benefits enjoy a substantial benefit not shared by those not fortunate enough to participate. For instance, is it fair that many better-paid workers get thousands of dollars a year in untaxed health-care benefits, while other workers enjoy no such subsidy?
  • Just think of how complicated the argument is on “fair” ways to raise taxesThere’s an argument that for the deficit solution to be equitable, all citizens should contribute to it. Though some government spending benefits all citizens alike, such as national defense, national parks and the administration of justice, much spending disproportionately benefits lower earners, in the form of public education and transportation (which are supported by the federal government), unemployment insurance, food stamps, Medicare and Medicaid, etc. Thus the effect of the coming spending cuts will fall more heavily on the poor. Some argue that since they receive less in benefits and are therefore less likely to experience their loss, the wealthy should share the burden of reducing the deficit through increased tax payments.
  • Keeping taxes low in general
    • Reduce wastefulness
    • Laffer curve
    • Encourage growth

Notes from The Rebel Allocator

The Rebel Allocator
by Jacob L. Taylor


Summary

Using a Socratic device, the author creates a Buffet/Munger composite doppelganger named Mr X to help guide Nick, a young left-leaning journalist turned investor. Nick is disillusioned by the business world from his seat at Big Rock, a cartoon of a private equity firm whose short-term, scorched earth practices give capitalism a bad name. Through his regular lessons, Nick learns the principles of sound capital allocation and sees them applied within billionaire Mr X’s nationwide burger chain. The book covers a broad array of ideas that underpin business and strategy, while its narrative structure makes the lessons more enjoyable and practical than the dry texts that typically teach these topics.

The Profit Constraint

Apply this: revenue – profit = expenses aka pay yourself first.

  • Yarak: “hungry but not weakened”
    • A bird in this state is the purest expression of its genetic capabilities.

3 Key qualities in employees

Integrity, intelligent, energy

  • 2 out of 3 will do so long as you have integrity!

A compass for what to focus on

4 hours a day spent on something that will make other things easier or unnecessary

Zero-based budgeting

Every year budget items are subject to a ‘delight’ test. If the expense doesn’t delight the customer it’s non-strategic and subject to trimming. Don’t paint the (unseen) fourth wall.

Effect of compounding improvement

365 days of 1% improvement is 37x return

Iron Law of Economic Survival

Cost, price, value triangle (straws model introduced in ch 19)

  1. Cost is true economic cost not accounting cost.
  2. Price can be based on lifetime revenue.
  3. Value is subjective,context dependent, and variable.
  • Trade-off between profit (price minus cost) and brand (value minus price).
  • By flying under the radar with lower profits you may be able to store brand in your customer’s mind.
    • Profit would alert competitors and regulators! Brand is poorly measured.
    • Me: Interesting to think of underpriced companies as those storing economic value in their brand which exists in the customer mind.
    • Net promoter score surveys compare the percent of people who are superfans vs those who are ambivalent or detractors

Customers don’t want a quarter-inch drill bit they want a quarter-inch hole

A business should consider its competition broadly with the criteria of who else fills the need. (ie Southwest airlines early on was competing with Greyhound for short trips).

Understand your edge

​Franchise model allows parent company to do what it does best: source ingredients, craft customer experience, marketing. The franchisee is really in the real estate business. (in the 4 seasons model this is same). Real estate unlevered returns are close to inflation while the fictional McDonald’s is closer to 12%

Effective capital allocation requires evaluating all options

Mr X looking at an empty plot poses the question, how many ways could we build a restaurant?

Student answers buy a plot, hire a construction crew and build one. But there are more strategies:

  1. Buy land and erect building later
  2. Buy land and wait
  3. Buy competitors store and convert
  4. Buy public stock
  5. Buyback your own stock
  6. Just waiting
  • Your next best option is your opportunity cost. Important to not define menu too narrowly
  • If you were trying to improve the experience of traveling across the country one option is to fly faster. This will cost substantial additional fuel and maintenance. Installing TVs on the planes may provide a better ratio of benefit to cost to the consumer.

2 kidneys for a reason

Tradeoff between efficiency and survival: virtue of cash and less leverage

Trees don’t grow to the sky

There are feedback loops which lead to mean reversion

The virtues of efficient capital allocation

“Good capital allocation means doing more with less to create happier customers. The pressure to continually deliver value is one of the wonders of the free market. Roll up all of those customers into society at large. When you are able to provide value for the least required cost, you free up resources that can go toward adding value somewhere else.

Imagine that inside you are all of these different locks. Each lock represents one of your wants or desires. You have a lock for food, a lock for shelter, a lock for water, a lock for the opposite sex. Now imagine that each capital allocation project creates one key. Ideally, the entrepreneur knows the lock their key will fit beforehand. A restaurant provides you food, a hotel gives you shelter, shoes protect your feet. The role of business is to use the least amount Of resources to create the key that fits a certain lock. Doing a proper job spares resources to create more keys for other locks. In this sense, profit should be celebrated as a signal that an entrepreneur provided value while consuming the least amount of resources to do so. When all of society’s businesses are properly allocating capital, more locks get keys, and we’re all better off.

That’s all technology really is: the means for us to turn more locks using fewer and cheaper keys.”

When simple models outperform experts

Simple models thrive when:

  • Problem is ill-structured and complex.
  • The information is incomplete, ambiguous, and changing.
  • The goals are ill-defined, shifting, or competing.
  • The stress is high, due to time constraints and/or high stakes.