Beyond the Odds: What Prediction Markets Miss

Four times a year, members of the Federal Open Market Committee (FOMC) submit their forecasts for the federal funds rate. The charts and tables are released shortly after the FOMC meeting. The Fed does not publish a single number. It publishes the dot plot. Each dot is one official's view. The dots scatter - sometimes tightly, sometimes widely - and the shape of that scatter is the actual signal. When the dots cluster, the committee is confident. When they spread, it is not.

These shapes are everywhere. Ask a friend where Bitcoin closes the year and listen carefully. They will not give you a single number. They will say something like, "I think mid-$80K, maybe $90K, but I wouldn't be shocked at $70K or $120K." That is a distribution. Two people can both say "I think Bitcoin ends near $85K." One might mean "definitely between $80K and $90K." The other might mean "probably $85K, but really anywhere from $60K to $120K." Same headline, different beliefs. The shape is what tells them apart.

Yet traders have to slice continuous beliefs into all-or-nothing positions. The binary contract, the default primitive across nearly every venue, compresses these nuanced probability distributions into discrete outcomes, limiting resolution to yes or no.

Most prediction markets accept beliefs only after they have been flattened: the forecaster with a rich distribution has to chop her curve into separate yes/no markets, place capital across isolated order books, and accept that her variance, skew, and tails are gone before the market sees them.

The result is less encouraging than the structure suggests. More than a third of the multi-market infrastructure on Polymarket has never been meaningfully used. Volume sits in a small number of venues, in a small number of events, and within those events, in a small number of contracts.

To be clear, binary markets have their uses. They are simple to build, easy to understand, and oracles can quickly verify binary outcomes - which is why they came first. But they are limited.

Binary markets force messy reality into an artificial yes/no frame and make prediction markets look more like gambling than forecasting. More importantly, binary outcomes throw away the most interesting primitives: prediction markets as reliable infofinance structures.

The Federal Reserve Board now publishes Kalshi-derived probability estimates alongside its own survey data. As the Michigan Journal of Economics noted, while sports markets will continue to drive revenue growth for Kalshi and Polymarket, their role as information-gathering marketplaces lies elsewhere: in markets where participants with dispersed knowledge are pricing outcomes that no single institution can predict alone. Those are the markets where the binary primitive becomes the bottleneck.

A continuous primitive allows a trader to post the belief she actually has, in the shape she actually holds it. Variance fits. Skew fits. Tails fit. Several protocols and researchers have been pushing in this direction, and the case has been developed in depth by functionSPACE research.

This piece argues four things.

First, the forecasting workflow that produces a tradeable view - whether at an institutional macro desk or in front of a Polymarket dashboard - generates a distributional mental object rather than a point estimate.

Second, the binary primitive compresses that distributional object in two specific ways. It discards everything except threshold positions, and bracket markets that try to recover dimensionality fragment liquidity into isolated pools.

Third, the compression problem shows up empirically. In a sample of 622 mutually exclusive bracket events on Polymarket, less than half price a coherent probability distribution.

Fourth, continuous market design changes the unit of trade from directional exposure to distributional accuracy, and it is the first structure that matches the actual shape of how both institutional analysts and prediction market traders reason about uncertainty.

Treating compression as a structural problem produced by binary architecture, rather than a design problem, is worth being precise about. It explains why both macro analysts and crypto-native traders cannot properly express their views.

A macro analyst pricing an FOMC decision is not generating a single probability. They are running a Bayesian update against a multi-source information set, and the output is a distribution before it is anything else.

For major macro events, the typical information set is wide: official data and release history; market-implied expectations from OIS, fed funds futures, the Treasury curve, options surface, and skew; economist consensus and dispersion; historical analogs; cross-asset signals; positioning and liquidity; and model-based nowcasts. Each input contributes a different signal, and the prior gets updated as data arrives.

P(outcome | data) ∝ P(data | outcome) × P(outcome)

Plain English: start with a prior, update it as new information lands, then ask whether the market is already pricing the updated probability correctly.

The other piece that matters is the distinction between probability and expected value. A trade is rarely "I think this outcome has 60% probability." The real question is:

E[trade] = Σ p_i × payoff_i - costs - risk penalties

An event with 45% probability can still be attractive if the payoff is asymmetric, and a 70% probability event can be a bad trade if everyone is already positioned. The analyst's edge is rarely in calling the modal outcome - it is in pricing the distribution and the payoff structure together.

This is what the binary primitive cannot carry. A binary market price reflects probability, but it also reflects liquidity, risk premia, constraints, hedging demand, and participant composition. The EV calculation that determines whether a trade is taken is constructed somewhere else (on a spreadsheet, in a model, in the analyst's head) before the position is sized.

The compression is both the strength and the weakness of binaries. The strength is that one number aggregates dispersed views into a single signal. The weakness is what gets lost: the shape of the distribution, the tails, the skew, the confidence levels, the scenario clustering, the path dependency, and the EV map. Splitting the question into 20 binaries does not recover what is lost. It just produces 20 compound signals instead of one.

A prediction market trader pricing an event runs the same kind of Bayesian update against a different information set. The output has the same shape: a distribution before it is anything else.

A common professional workflow: scan markets, flag the ones where the trader's internal price disagrees with the market price, then run an investigative loop. Why is the market at 80 if I think it is worth 20? The starting point is not a binary call. It is a price, with conviction, generated by a workflow that synthesises news, history, models, structural priors, and increasingly automated signals.

A useful concept that surfaces repeatedly is market sharpness. A sharp market has tight spreads, deep bids on both sides, and prices that move quickly with new information. Professional traders explicitly avoid sharp markets where they have no informational edge and concentrate on loose markets where their domain work creates asymmetric information. The binary price does not distinguish between the two. Both report a probability. One is doing genuine probability work; the other is doing liquidity work and reporting it as probability.

Two patterns appear consistently in how distributional views get compressed into binary positions.

The first is portfolio construction across multi-outcome markets. Take a market on total combined points in an NBA Finals game. A trader who expects something around 215 builds the position like a fantasy team: heavier YES bets in the buckets around her mode, thin bets reaching into the high-scoring range for the overtime case. The mental object is a probability distribution across the field; the instrument forces it to be expressed as a stitched-together collection of binary positions.

The second is the shift from reaction speed to reaction accuracy. In mature prediction markets, the edge has moved away from being fastest and toward being most correct. Government shutdown markets are a clean example: prices oscillate rapidly with each headline, and the durable edge sits in interpreting the headline correctly rather than trading it first. This interpretation work is exactly what the binary price discards.

There is also a real distinction between losing for the right reasons (the distribution was right, the outcome was unlucky) and losing for the wrong reasons (the distribution itself was wrong). The binary market resolves only on outcome. It cannot reward the trader who held an accurate distribution and got a low-probability tail draw, or punish the trader who held an inaccurate distribution and got lucky.

The compression at the final step is the same for both workflows. The next section breaks it down.

The framing in this section draws on observations from two profitable participants: Domer, an 18-year prediction market professional with over $4 million in lifetime trades, profiled by 60 Minutes; and Gaetan Dugas, a top-50 Kalshi trader with over $1.25 million in 2025 earnings.

We have established that the mental object forecasters form is a distribution, but the available expression on Polymarket and Kalshi is usually a binary contract: YES or NO at a particular strike or condition. That strike may be arbitrary from the perspective of the forecaster's belief, even if the market later determines a price for it. The translation from a continuous or multi-outcome distribution into isolated binary contracts discards information.

A good example is an AI benchmark market: "Will GPT-5 score above 90 on benchmark X?" One trader believes the model will probably score around 91, with a tight range between 89 and 93. Another believes the range is wider, from 75 to 98, but still assigns 60% probability to clearing 90. In the binary market, both views become the same YES trade, and the shape, the skew, and confidence levels are all gone.

This is the cleanest form of compression. Whatever the trader believes about the distribution beyond the threshold question, the binary instrument records the YES price and discards everything else.

Bracket markets attempt to recover the lost dimensionality by listing multiple binaries across a numerical range. In theory, this lets the forecaster express a distribution by trading multiple buckets. In practice, it does not work.

The core argument is that bracket markets fragment capital across isolated order books, each with its own liquidity, slippage, and resolution risk. The price in each bucket reflects local supply and demand for that specific binary, not the underlying distributional view. They also reintroduce the threshold problem at every boundary: a position priced at $0.02 can only move in 50% increments due to the $0.01 tick size, which makes tail brackets effectively un-tradeable at fine resolution.

A close look at bracket markets reveals a failure: the architecture does not function as a coherent distributional pricing mechanism. It is expected that when a bracket event lists multiple binary contracts whose outcomes are mutually exclusive and exhaustive (only one can win), the YES prices across those constituents should sum to one (because the outcomes can't happen together, the sum of all the "Yes" prices should add up to roughly 1 or 100%). However, this is hardly the case.

Take the OpenAI IPO Closing Market Cap market on Polymarket. The event has seven buckets covering market cap ranges at IPO close. It has accumulated $1.6 million in trading. When you add up what the market thinks the probability is for each bucket, the sum is 0.93. Seven cents of probability mass is just missing.

Where did it go? One of the seven buckets is sitting at the $0.01 minimum tick. The architecture cannot price anything below one percent, so beliefs about low-probability market cap outcomes get rounded to zero. The shape an analyst with a careful IPO valuation distribution would form - exactly the kind of distributional thinking Section 2 describes - has no place to express its tails.

We pulled all open multi-market events with three or more constituent markets across Crypto, Finance, Politics, and Weather categories via Polymarket's Gamma API, filtered to negRisk = true events (mutually exclusive cohort) with at least three priced open constituents. The snapshot was taken in early May 2026.

For each event, we computed the sum of YES prices across constituent markets and classified them into three bands: 0.98-1.02 (coherent), below 0.98 (missing tail mass), above 1.02 (overpriced). Final sample: 622 negRisk events with $3.1 billion in cumulative volume.

Less than half of bracket events price a coherent probability distribution: only 41.8% (260 events) have implied probabilities that sum within an acceptable range (0.98 to 1.02). Of the rest, 16.2% (101 events) have missing tail probabilities, while 42.0% (261 events) are overpriced, meaning their probabilities sum above 100%. By trading volume, the overpriced cohort is far larger at $753 million versus $47 million for the missing-probability group.

The second finding is that the missing-probability problem is almost entirely caused by Polymarket's $0.01 price floor. Because prices cannot go below 1 cent, markets where traders assign very low probabilities (say 0.3%) still have to display $0.01. Across many markets within one event, this rounding adds up. In 74.3% of events where probabilities summed too low, at least one market was stuck at exactly $0.01, and each affected event was missing roughly 8.5 cents of probability on average.

The third finding is that pricing errors shift in character as bracket size 'N' grows. Small brackets (3 to 5 markets) are the most accurate overall, with 57.3% pricing coherently, but they carry the highest missing-probability rate at 25.9%. Large brackets (11 to 20 markets) largely solve that problem, dropping the missing-probability rate to 11.6%, but 63.1% of them are overpriced instead. Adding more markets does not improve accuracy. It just trades one type of error for another.

Even in bracket events, which are specifically designed so probabilities add up to 100%, fewer than half actually do. The main cause is the 1-cent price floor, which forces the platform to round very small probabilities to zero, leaving part of the probability distribution unrepresented. Larger brackets do not fix this. Instead, they introduce the opposite problem, where prices add up to more than 100%, and the platform has no built-in mechanism to correct it.

These findings confirm that the compression problem is structural. Belief is a shape, and the person who thinks Bitcoin will close the year at probably $85K, but really anywhere from $60K to $120K, still cannot express that view cleanly.

If the binary primitive flattens what forecasters think, and bracket markets recover the appearance of dimensionality without the substance of it, the next question becomes: what kind of market correctly prices belief?

If the unit being traded is a curve rather than a token, the things that get compressed away stop getting compressed away.

In mathematics, a function space is exactly what it sounds like: a space whose points are functions. Each point is a whole curve, not a number, not a tuple of numbers, but an entire shape mapped onto a domain. You can do geometry in a function space. You can measure how close two curves are. You can add them, scale them, and project one onto another.

A probability distribution lives naturally in a function space. So does every Fed dot plot read as a kernel density, every implied volatility surface, every belief about an election result. They were always functions. The dot plot from Section 1 is, mathematically, a point in a function space. The friend's view on Bitcoin is another. The architecture either accepts those shapes or flattens them.

A continuous market is one that accepts them. The state of the market is itself a function: the current consensus distribution. Trades are vectors that move that function. A trader posts a probability density across the outcome range and pays collateral proportional to how much her belief deviates from the current consensus. Settlement is the integral of the realised outcome against the trader's submitted function.

First, the unit of trade changes. In a binary market, the trader earns based on whether the outcome lands in the contract's bucket. The reward is for being right at the level of bucket selection. In a continuous market, the trader earns based on how her submitted distribution compares to the realised outcome and the consensus distribution. The reward is for being right about the shape of the uncertainty, not just the location of the mode. A trader with a precise distribution that turns out to be correct earns more than a trader with a vague distribution centred on the same point.

Second, compression gets structurally eliminated. The instrument is no longer trying to approximate a continuous space using discrete primitives. Liquidity rests on a single shared pool rather than separate order books per bucket. Every trade deposits collateral into that one pool and contributes a complete distributional belief, which the protocol aggregates into a consensus probability density spanning the full outcome range. Because the pool backs the entire curve at once, a trader expressing tail conviction transacts against the shape of that consensus distribution rather than needing to find a willing seller in a thin, isolated order book.

A narrow belief costs different collateral than a wide one, even when both are centred on the same point. Posting mass where the consensus has none gets a stronger push for the same dollar. That is not a feature bolted onto a binary market. It is a different mechanism with different math.

None of this argues that continuous markets solve every problem in the prediction market space. Several things need to be true beyond the instrument design.

Liquidity formation is the first. A continuous market with no participants prices nothing, regardless of how expressive the structure is. Adhi's work on minimum viable liquidity (MVL) makes a credible argument that the bar for useful price signal in a continuous market is lower than in a binary one, because every position contributes to the shape of the consensus rather than fighting for depth in a single bucket. But that is an argument about the floor, not a guarantee of the ceiling.

Resolution quality matters too. A market can be continuous at entry and still become too discrete at settlement if the outcome is resolved through coarse bins or ambiguous rules. Continuous markets are powerful for prices, margins, scores, rates, totals, and other quantifiable outcomes. They are less useful when the underlying question is vague enough that the curve becomes false precision.

The interpretation layer matters as well. A market-implied distribution is not the same thing as the true probability distribution. Like an options-implied PDF, it reflects trader beliefs, risk preferences, hedging demand, inventory, and collateral constraints. Any serious use of the signal has to preserve that distinction.

For prediction markets to become part of financial infrastructure, their prices must be discoverable through standardised references. Institutional capital does not simply trade against bilateral quotes; it needs methodology-grade reference rates that can be marked, audited, reported, hedged, and embedded into wrappers such as structured notes, ETFs, and other products. Lauris' benchmark argument is useful here.

The reasonable critique is that a continuous probability market is just a binary market with extra math. The unit being traded is the real differentiator. Both the institutional analyst pricing an FOMC decision and the crypto-native trader pricing a Polymarket event hit the same compression at the same final step. The shape of belief is the same on both sides. The instrument is what flattens it.

• Polymarket Gamma API: public endpoint, used for event-level and market-level data on FOMC and CPI bracket events.
• CME FedWatch Tool: Fed funds futures-implied meeting-by-meeting probabilities. Used as reference for the analyst workflow description.
• Atlanta Fed Market Probability Tracker: SOFR futures and options-implied distributions over future three-month average rates.
• FactSet Earnings Insight: consensus aggregation for earnings forecasts, used as an analogue for sell-side aggregation.
• Kalshi public market data: cross-venue reference for binary macro contracts.
• functionSPACE binary events research: Polymarket multi-market structure analysis, used as the methodological baseline for Section 3.
• Practitioner observations: trader workflow section draws on public interviews from Domer and Gaetan Dugas; analyst section draws on feedback from Dmitry Klimenko.

Analyst. A sell-side or buy-side professional working at an institutional desk, whose forecasting workflow is anchored in formal infrastructure.

Trader. A crypto prediction market participant. Carries no implication that the participant is or is not professional; it refers to the workflow type.

Distributional view. The output of the forecasting workflow before it gets compressed into a tradeable position. Has at minimum a shape, a skew, and varying conviction across the distribution.

Compression. The loss of information when a distributional view is forced through an instrument with lower dimensionality than the underlying belief.

negRisk. Exactly one market resolves "YES". Election candidates and price brackets are typically negRisk.

Market sharpness. A property of the market state. A sharp market has tight spreads, deep two-sided liquidity, and prices that move quickly with new information.

Overpriced events. Events where the prices add up to more than 100%. This volume is concentrated in a handful of large multi-candidate events where no arbitrage force connects the separate order books (a single 2028 nomination market accounts for most of it). Because traders can buy into multiple buckets at once and nothing automatically keeps the totals at 100%, the combined prices can drift well above it.