Here is a question that sounds simple: how much uncertainty does a coin flip contain?
The standard answer is one bit. Heads or tails, fifty-fifty, log₂(2) = 1. This is the textbook definition of entropy, the information-theoretic measure of uncertainty—assuming a fair coin, and that “outcome” means only heads or tails. It is clean, mathematical, and wrong—or rather, incomplete in a way that matters enormously once you try to apply it to anything real.
Entropy depends on what you are measuring. If you only care about heads or tails, the coin has one bit of entropy. But what if you also care about the angle the coin makes with magnetic north when it lands? Divide the compass into four quadrants, and you have eight possible outcomes (heads-north, heads-east, heads-south, heads-west, tails-north...). If those eight outcomes are roughly equally likely, the entropy is log₂(8) = 3 bits.
The physical coin hasn’t changed. The entropy has tripled. We didn’t discover more uncertainty in the coin; we changed the description—the outcome space we are using to measure it. What changed is the question being asked.
This is the physicist Christoph Adami’s crucial point: entropy is not a property of the object. It is a property of the relationship between an observer and an object, mediated by what the observer is trying to predict and what they already know. Change the observer’s question, change the entropy. Change what the observer already knows, change the entropy again.
Now consider “edge” in investing—the claimed ability to predict returns better than the market. It is often discussed as if it were a substance, something you have or don’t have, like a secret or a skill. But if Adami is right, this framing is confused from the start.
What kind of problem is this?
These debates about edge, efficiency, alpha—they treat these as intrinsic properties. “Does this manager have edge?” “Is the market efficient?” The debates never resolve, and the reason they never resolve is that the terms are underspecified. They are asking about the coin without specifying the measurement.
That is not a disagreement problem. It is a precision problem. And the discipline that has spent decades developing precise language for knowledge, uncertainty, and observation is information theory.
So let’s borrow.
This is the multi-model move: recognize the shape of a problem, find the discipline that has thought rigorously about that shape, and import its frameworks deliberately rather than reinventing them from scratch.
The edge debate has been asking the wrong question. “Does this manager have edge?” is like asking “Does this coin have entropy?” The answer is: edge about what? Measured by what signals? Conditional on what baseline? A manager might have edge about one target and none about another. The question isn’t yes or no. It’s relative to what.
Adami’s framework makes this precise. Any statement about information requires three specifications: the target (what you are trying to predict), the observer (whose uncertainty we are measuring), and the conditioning set (what you already know). Without all three, “information” is meaningless—and so is “edge.”
Let’s make that concrete.
What “Edge” Actually Means
Edge is not a property of the investor. It is a property of the relationship between the investor’s signals and the future, conditional on what is already priced.
This requires three specifications:
The target. What are you trying to predict? The direction of the S&P 500 over the next month? The relative performance of two stocks? The timing of a volatility spike? These are different targets with different entropy profiles. A signal that is informative about one may be useless for another.
The observer. Whose uncertainty are we measuring? Your signals, your models, your information set. Two investors looking at the same market face different uncertainties because they are equipped with different measurement apparatus.
The baseline. What do you already know—or more precisely, what does the market already know? Information theory measures the reduction in uncertainty from a signal, relative to some prior state. If the market has already incorporated a piece of news into prices, that news carries zero additional information for trading purposes, no matter how true or important it is.
Edge, then, is conditional mutual information: the information your signals carry about your target, given what is already reflected in prices. It is not “being right.” It is being right about something the market doesn’t already know, on a question that actually determines your returns.
The Measurement Problem
This reframes the usual debates about market efficiency. The Efficient Market Hypothesis is often stated as “you can’t beat the market” or “prices reflect all available information.” But information theory shows these formulations are imprecise. Information about what? Available to whom? Reflected how completely?
A market can be highly efficient for one target and inefficient for another. The S&P 500’s level tomorrow is probably hard to predict—too many sophisticated observers have already incorporated their views. But the relative value of two small-cap industrial companies with limited analyst coverage? The timing of a volatility regime shift that most participants aren’t even trying to forecast? These are different questions with different entropy profiles.
The physicist’s way of saying this: the market has no single “temperature.” Different observers, measuring different things, experience different levels of noise. What looks like perfect efficiency from one vantage point may look like exploitable structure from another—not because one observer is smarter, but because they are asking a different question.
This explains why the alpha debate never resolves. Value investors point to decades of factor returns and say edge exists. Efficient-market theorists point to the difficulty of beating benchmarks after fees and say it doesn’t. They may both be pointing at real effects—but interpreting those effects depends on the target and on your model of risk premia. The value factor may carry information about long-horizon returns that short-term price movements don’t reflect; or it may be compensation for bearing certain risks. The day-to-day direction of the market may be genuinely unpredictable. These aren’t necessarily contradictory findings; they are measurements of different things.
Conditioning Is Everything
The deepest implication is about the baseline. In information theory, the value of a signal depends entirely on what you are conditioning on—what you already know.
Consider two analysts who both predict that a company will beat earnings estimates. Analyst A made the prediction based on channel checks, supply chain data, and proprietary surveys. Analyst B made the same prediction by reading the company’s own guidance more carefully than most. Both are “right” if the company beats. But their edge profiles are completely different.
If the market has already incorporated the guidance—if prices reflect the information Analyst B used—then B has zero edge despite being correct. The information was already in the conditioning set. Analyst A, using signals the market hasn’t processed, may have genuine conditional information.
This is why “being right” is insufficient. The relevant question is never “do I know something true?” It’s “do I know something true that isn’t already priced, about a target that determines my returns, on a horizon where it matters?”
The formula for edge isn’t knowledge. It’s conditional knowledge.
The Target Isn’t Reality
But there’s a further subtlety. What exactly is the target you are trying to predict?
The naive answer is “reality”—future earnings, future growth, whether the technology works. But this misses something important. Markets don’t price reality directly. They price a kind of aggregate belief state—beliefs about reality, weighted by capital and risk tolerance, shaped by constraints. This isn’t the same as what people “think” in some survey sense. It is what gets expressed when money moves under real-world frictions: leverage limits, funding conditions, regulatory constraints, mandate restrictions. The pricing state includes not just what investors believe, but what they are able and willing to do given their constraints.
This means the true target is future consensus: the belief-and-constraint state the market will hold at your horizon, as reflected in prices. Edge is information about where that state is going, conditional on where it is now.
An investor who correctly forecasts earnings but can’t say how or when the market will reprice that information has a weaker claim to edge than one who understands the dynamics of belief revision—even if the latter’s fundamental views are less sophisticated. And an investor who ignores constraints—who says “the fundamentals are obvious, the market must reprice”—is missing half the mechanism. Markets can “know” something and still not price it, because constraints prevent the capital from flowing.
This explains a common frustration: “I was right, but I lost money.” You were right about reality. But you weren’t right about consensus. The market didn’t move to your view on your timeline, and in the interim, prices went against you. Being right about fundamentals is necessary but not sufficient. You need a view on fundamentals and a view on how the belief-and-constraint state will evolve.
At long horizons, fundamentals matter more—reality has more opportunities to force belief updating. Earnings arrive, defaults occur, technologies either work or don’t. But even then, you are not escaping consensus; you are betting that consensus will be forced to converge toward reality. That’s still a prediction about beliefs, not just about the world.
What follows from all this? Two things. Evaluating your own edge requires specifying all three components: target, observer, baseline. Vague claims like “I understand this company better than the market” are meaningless until you say what you are predicting, what signals you are using, and what you think is already priced. And edge is not conserved across questions—a signal that is highly informative for one target may be noise for another. It is common to transfer confidence across domains, assuming that insight into one question implies insight into related questions. Information theory says no. Each target has its own entropy, its own conditioning set, its own edge calculation.
The Observer’s Toolkit
Adami’s framework suggests a practical discipline. Before claiming to know anything predictively, you need to answer three prior questions—and these questions often go unasked.
The first is: what exactly am I trying to predict? Not “things will go well” but something precise enough to be wrong about. In investing, that might mean “the stock will outperform its sector by more than 5% over the next six months.” In medicine, “this treatment will reduce symptoms within two weeks.” In strategy, “this initiative will increase retention by Q3.” Precision forces you to confront the actual target. Vague predictions can’t be evaluated, which is why they are so popular.
The second is: what do I know that could inform this prediction? This means listing the signals, being specific about what you are actually measuring. In investing: channel checks, model outputs, management read, macro view. In medicine: test results, patient history, clinical markers. In any domain: what are your measurements? If you can’t name them, you are not reasoning; you are vibing.
The third is the hard one: what is already known? In investing, this means what’s priced. In other domains, it means the baseline expectation—what would a well-informed observer already predict? The value of your signal depends entirely on what it adds beyond that baseline. Lots of information is technically available but not yet incorporated into the consensus view, because attention is limited and processing is costly. That gap is where genuine predictive advantage lives.
If you can’t answer these three questions, you don’t know whether you have information. You have a feeling, a thesis, a view. These are not the same thing.
The coin flip looks simple. One bit of entropy, everyone agrees. But the moment you try to predict something real—a market, a diagnosis, a strategy’s success—the entropy depends on who is asking, what they are asking, and what they already know. Information is in the eye of the beholder.
The discipline is in asking: which eye, looking at what, through what measuring device?
References & Further Reading
What is Information?: Christoph Adami
The Model Thinker: What You Need to Know to Make Data Work for You: Scott E. Page
A Mathematical Theory of Communication: Claude Shannon
The Efficient Market Hypothesis and Its Critics: Burton Malkiel