From 0.9≠90% to the Beginning: Reimagining Polymarket's Pricing Truth

Source: Movermaker Chinese

Labeling Polymarket as a speculative platform is a serious misconception. Its core functionality is to aggregate humanity's collective judgment on future events, dynamically compressing and securitizing it into a tradable financial asset. Therefore, to truly understand its pricing system, we must look beyond the surface-level intuition of "0.9 US dollars representing a 90% probability."

This article will start from a simple question that you will definitely ask when trading, revealing to you the rigorous pricing logic behind Polymarket and why this logic is sound.

1. Polymarket's Two Pillars: The "Math" and "Money" Hard Constraints

To understand Polymarket, you don't need to delve into complex models from the start; you just need to understand two "hard rules" that make it function.

Pillar One: The Math Hard Constraint (Probability Must Equal 100%)

Firstly, every market on Polymarket is mathematically a "complete and mutually exclusive" event.

Complete: Implies that all possible outcomes have been listed.

Mutually Exclusive: Implies that two outcomes cannot occur simultaneously.

In the simplest binary market (e.g., "Will Event A Occur?"), there are only two outcomes: {Yes} or {No}.

Based on the basic probability axiom, the sum of the probabilities of all possible outcomes must equal 1 (i.e., 100%). Thus, we have the first inviolable mathematical constraint: P(Yes) + P(No) = 1

This equation serves as the mathematical anchor for all subsequent analysis.

Pillar Two: The Money Hard Constraint (Price Must ≈ 1 US Dollar)

Mathematical axioms are just theoretical; Polymarket's strength lies in enforcing this constraint in reality through financial engineering.

This mechanism is the "1 Dollar Redemption Guarantee".

1. Creating "Complete Shares" You cannot only buy "Yes" or only buy "No".

To participate in a market, you must:

Deposit Collateral: You deposit 1 USDC into the smart contract. Receive a "Suite": The contract will immediately mint and issue a complete set of outcome tokens to you, namely: 1 USDC → 1 unit of A-Token (Yes) + 1 unit of B-Token (No)

2. "Winner Takes All" Settlement During contract expiration settlement, as the events are mutually exclusive ("Yes" and "No" only one can win), the value of this set of shares is strictly pegged:

When the oracle determines the result as "A": Your A-Token (Yes) is now worth 1 dollar, which can be redeemed for 1 USDC. Your B-Token (No) becomes worthless. (If the result is B, the reverse is true).

3. "No Arbitrage" Price Anchoring The most critical impact of this mechanism is:

At the moment of final event settlement, a complete set of {A-Token, B-Token} share combination unmistakably and conclusively equals 1 dollar in total value.

Since we know that this set of shares is guaranteed to be worth 1 dollar in the future, its market price today must be infinitely close to 1 dollar. If the price deviates, arbitrageurs will immediately intervene and force the price back:

Scenario 1: Price Sum Below 1 (e.g., $0.95) If A-Token is selling at $0.60 and B-Token is selling at $0.35, the total price is $0.95.

An arbitrageur will immediately spend $0.95 to buy a complete set of shares in the market, and hold them until expiration. Upon expiration, this set of shares can be redeemed for 1 dollar. The arbitrageur, by buying at a price of 95 cents, has purchased a $1 "risk-free bond," locking in a risk-free return of approximately (1−0.95)/0.95≈5.26% (assuming the platform and USDC are risk-free). This buying pressure will drive the price back up to $1.

Scenario 2: Price Sum Above 1 (e.g., $1.05) If A-Token is selling at $0.70 and B-Token is selling at $0.35, the total price is $1.05.

An arbitrageur will immediately deposit 1 USDC, mint a new {A, B} share set, and promptly sell it on the market for $1.05. They have instantly cashed out $1.05 with a cost of $1, making a profit of $0.05 out of thin air. This selling pressure will drive the price back down to $1.

This bidirectional arbitrage pressure forces the market price to form a strong equilibrium, which we refer to as a financial-level anchoring relationship: V(A) + V(B) ≈ $1

Now we have two "hard constraints" from different fields:

Mathematical constraint: P(A) + P(B) = 1

Financial constraint: V(A) + V(B) ≈ $1

Polymarket's pricing system is built on these two cornerstones. Next, we will explore how these two constraints are combined and ultimately derive the core logic of "price equals probability."

2. Why Sell 90% Probability for $0.9?

In the previous chapter, we established two "hard constraints":

Mathematical constraint: The probabilities of an event's "yes" and "no" outcomes must sum to 1. P(A) + P(B) = 1

Financial constraint: The token prices of an event's "yes" and "no" outcomes must sum to approximately $1. V(A) + V(B) ≈ $1

2.1 Price Equals Probability: An Intuitive Derivation

When you put these two constraints side by side, Polymarket's core logic becomes evident: the structures of the two formulas correspond entirely.

This strongly implies that the price of a token V(A) is the market's best estimate of the probability P(A) of that event occurring.

Why must this equation hold true? We can understand it from the perspective of "fair value."

What is "Fair Value"?

Suppose an event (A) has a 90% probability of occurring and a 10% probability of not occurring. The future cash flow of your A-Token (yes) is:

With a 90% chance, it is worth $1.

With a 10% chance, it is worth $0.

So, what is the reasonable "fair value" (or "expected value" EV) of this "lottery" today?

EV(A) = (90% * $1) + (10% * $0) = $0.9

*The fair value is $0.9. In a rational market, the price will always tend toward its fair value.

If Price < Fair Value: Suppose the market price V(A) is only 0.8. Professional traders would see this as a "discounted sale opportunity," and they would buy in large quantities until the price is pushed up to 0.9.

If Price > Fair Value: Suppose the market price V(A) is 0.95. Traders would view this as a "premium sale opportunity," and they would sell in large quantities until the price is pushed down to 0.9.

Therefore, persistent arbitrage pressure in the market will force the price V(A) to anchor around its expected value P(A). V(A) ≈ P(A)

2.2 An Important Adjustment: Price = Probability - "Risk Premium"

Now, we must introduce a crucial adjustment. You will often find a scenario where a poll shows a 95% probability of an event occurring, but the price on Polymarket may only stabilize at $0.9.

Does this mean the market is "wrong"?

No. This is actually the market acting "right" because it's pricing in the risk.

In financial engineering, we must differentiate between two concepts:

True Probability (P): The "God's-eye view" objective probability of an event occurring (e.g., a 95% poll).

Risk-Neutral Probability (Q): The price at which the financial market (like Polymarket) actually trades.

In the real world, investors are risk-averse. They hold a token not only to bear the risk of the event itself but also a range of platform-specific risks:

Will the Oracle fail? Will the smart contract be exploited? Will USDC break its peg? Will the platform face regulatory crackdown?

To bear these additional and un-hedgeable risks, investors will demand a "discount" as compensation, known in finance as a "risk premium."

Therefore, a more accurate pricing formula is: V(A) = Q(A)-λ

where Q(A) is the event's risk-neutral probability, and λ (Lambda) is a composite risk discount (or "risk fee"), representing the market's compensation requirement for all the structural risks mentioned above.

When you see a price of 0.9 USD on Polymarket, the professional information it conveys is: "Market participants are willing to bet real money on the event's risk-neutral probability, and this price has already been downward adjusted (discounted) for all perceivable platform and event risks."

This is the fundamental difference between Polymarket and polls: Polls reflect "opinion," while Polymarket prices "risk."

3. How is the Price Formed?

In the preceding sections, we established two cornerstones:

Mathematically, the probabilities must add up to 1.

Financially, the prices must add up to approximately 1 USD.

Now, let's get into the action. How did we arrive at that $0.9 price you see on your screen? And what is keeping it from deviating?

3.1 Price Formation

The most common mistake beginners make is to imagine Polymarket as an AMM like Uniswap, thinking the price is calculated based on a fixed mathematical formula (e.g., X*Y = K).

This is incorrect.

At the core of Polymarket is a Central Limit Order Book (CLOB), which operates just like Binance, Nasdaq, or any stock exchange.

The $0.9 you see is the real-time transaction price formed by the "highest bidder" and the "lowest asker" in the market coming together. The price is "discovered" by all participants, not "calculated" by the platform.

Polymarket's system combines "speed" and "security":

Lightning-fast (off-chain matching): You place orders, adjust prices, cancel orders... all of this is done instantly and for free on a centralized server.

Absolute Security (On-Chain Settlement): Only after your order is executed, the final settlement information is sent to the blockchain, ensuring the security of your assets.

What does this mean for a market maker?

It means "no slippage." They place a $0.8 buy order, and the execution price is $0.8. This allows them to stabilize their earnings by placing a $0.8 buy order and a $0.81 sell order, just like in the real stock market, to consistently earn the $0.01 spread.

3.2 Why is the price always "good" and "stable"?

You might ask: If everyone freely places orders, what if no one places orders? Wouldn't the price go haywire?

This is the most ingenious incentive design of Polymarket, which has two layers:

Incentive 1: Return "Profit Fee" to "Market Makers"

Polymarket does not charge transaction fees, but after market settlement, it takes a "performance fee" (e.g., k%) from your net profit.

Key point: This money does not go to Polymarket! The platform returns the majority of this fee directly to those who "provide liquidity" in this market (i.e., place orders). This incentivizes professional players to flock in and provide you with stable and deep quotes.

Incentive 2: "Quadratic Scoring" (forcing you to aim for the best price)

The platform's reward distribution method is not "evenly distributed" but uses a "quadratic scoring" terror weapon.

In plain language, the better price you offer (smaller bid-ask spread), the more your reward will exponentially increase.

For example: In a market with a qualifying spread of 4 cents. Player A offers a 2-cent spread and receives a score of 0.25. Player B offers a 1-cent spread (only twice as good as A), but receives a score of 0.5625 (2.25 times that of A!). (This is a simplified formula: Score ∝ (...)^2)

This non-linear incentive compels all market makers to "desperately push the price towards the most reasonable midpoint."

What does this mean for newcomers?

It means that as a regular user, you can always enjoy the extremely narrow bid-ask spread and very low transaction costs brought about by the competition of professional players.