Fat Tails in Value

March 24, 2026

The previous piece defined alignment as a property of goals that can jump discontinuously at thresholds. I want to develop what that implies.

1. Value Is Discontinuous

Line up every possible outcome of a pursuit, ordered from worst to best. Plot the value of each outcome. The resulting curve is not smooth. It is mostly flat with discontinuous jumps at certain thresholds.

LeBron James vs the 10th best NBA player. The gap in ability is small. Both are elite. Both have invested tens of thousands of hours. But the difference in value (endorsements, cultural influence, earnings, legacy) is not small. It is discontinuous. LeBron is not 10x better. He is perhaps 1000x more valuable.

This pattern repeats everywhere. Making a national team vs almost making it. Getting hired at a top company vs a good one. Being the person who built the thing vs one of the people who worked on something similar. At each of these thresholds, a small difference in outcome produces a massive difference in value.

The fat tail that matters is not in probability. It is in value. A small number of outcomes contain almost all the value. The top 1% of outcomes in most pursuits are worth more than the other 99% combined. This is the structural feature of the world worth noticing.

2. Low Probability

The goals that produce the largest jumps in value tend to have low probability of success. This is almost tautological: if they were easy, everyone would do them, and the discontinuity would not exist.

Qualifying for a national team, getting hired at a frontier lab, building something that reaches escape velocity. These are goals where most attempts fail. The probability of success for any individual attempt is low.

But the value, properly considered, can still be favorable. The value at the discontinuity is so large relative to the cost of the attempt that even a low probability of reaching it can make the bet worthwhile.

I want to be precise about this claim. I am asserting that in many (not all) domains, the ratio of value to probability at the top of the distribution exceeds the ratio in the middle. This is not obviously true in every case. It depends on the specific domain, the specific threshold, and how you measure value. But in the domains I care about (athletics, technology, career capital), I believe the pattern holds.

3. Why the Top Is Underpriced

Most people do not avoid high-value, low-probability goals because they have done the calculation and found it wanting. They avoid them for several reasons, most of which have nothing to do with the math.

Fear of failure. This is the largest factor. People are afraid of failing. Not in the abstract, but concretely: the rejection, the embarrassment, the feeling of having tried and not made it. This fear causes people to select away from goals where failure is likely, regardless of what success would be worth.

Information asymmetry. Many people do not know the top exists, or do not know how to access it. If you have never been exposed to people who work at frontier labs or compete at national levels, those goals do not enter your queue. You cannot pursue what you cannot see.

Resource constraints. Some people genuinely cannot afford to fail repeatedly. If a single failed attempt has real consequences (financial, familial, logistical), the low-probability bet is not viable even if the ratio is favorable. This is a real constraint, not a psychological one.

Social norms. People are funneled toward conventional paths by the expectations of parents, peers, institutions. These paths tend to cluster in the middle of the distribution, not because the middle is optimal, but because it is legible and socially endorsed.

The net effect is that fewer people pursue high-value, low-probability goals than the value warrants. The top is not literally uncontested, but it is less contested than it should be given the value at stake.

4. The Middle Is Overpriced

The corollary: if people avoid the top, where do they go? They crowd into goals where the probability of success is higher (maybe 25-30%), the value is mid-to-high, and the whole thing feels attainable.

This is where competition becomes disproportionate to value. Mid-tier internships, varsity-level athletics, “good but not great” positions. These goals attract enormous volumes of applicants because they sit in the sweet spot of feeling achievable while still signaling ambition. The result is that the competition-to-value ratio in the middle is often worse than at the top.

Consider the internship market. The compensation difference between a top-tier and mid-tier tech internship can be 5-10x. The difference in competitiveness is not 5-10x. It is comparable, sometimes even inverted. A mid-tier position can receive thousands of applications from candidates who self-selected out of the top tier due to fear, not due to inability. The middle absorbs the demand that fear deflected from the top.

5. The Bottom Is Honest

The bottom of the distribution (low value, high probability) is not overcrowded the way the middle is. If you genuinely enjoy the work or it is right for your situation, these positions are fine. They are priced roughly in proportion to their value.

Nobody is fighting over them because they do not signal ambition in the way the middle does. The middle is where people go to avoid the fear of failing at the top while also avoiding the perceived shame of being at the bottom. It is a compromise driven by psychology and social pressure, not by value.

The bottom, at least, is honest about what it is.

6. The Structure

The top is underpriced. The middle is overpriced. The bottom is honest.

This is a claim about the relationship between value, competition, and psychology across the distribution of outcomes. It follows from two observations: value is discontinuous at thresholds, and multiple forces (fear, information asymmetry, resource constraints, social norms) systematically push people away from the highest-value goals and into the middle.

I have not yet addressed how to act on this. There are at least two questions that follow:

• Taking Asymmetric Bets: Given that the top is underpriced, how do you actually capture that value? The mechanism involves volume, low opportunity cost per bet, and a tolerance for repeated failure.
• The Psychology of Failure: Fear of failure is the largest factor pushing people away from the top. What does it actually take to act in the presence of that fear?