Original Title: "How Polymarket Uses 'Mechanisms' to Forge 'Probabilities'"
Original Source: Movermaker Chinese
Classifying Polymarket as a speculative platform is a serious misunderstanding. Its core function is to compress and securitize the collective human judgment of future events into a tradable financial asset in real-time. Therefore, to truly understand its pricing system, we must go beyond the superficial intuition of "0.9 dollars represents a 90% probability."
This article will start from a simple question that you will definitely ask when trading, revealing the rigorous pricing logic behind Polymarket and why this logic is unbreakable.
1. The Two Pillars of Polymarket: The Hard Constraints of "Mathematics" and "Money"
To understand Polymarket, you don't need to delve into complex models from the start; you just need to grasp two "hard rules" that allow it to operate.
Pillar One: The Hard Constraint of Mathematics (Probabilities Must = 100%)
First, every market on Polymarket is mathematically a "complete and mutually exclusive" event.
Complete: This means all possible outcomes are listed.
Mutually Exclusive: This means two outcomes cannot occur simultaneously.
In the simplest binary market (for example: "Will event A occur?"), there are only two outcomes: {Yes} or {No}.
According to basic probability axioms, the sum of the probabilities of all possible outcomes must equal 1 (i.e., 100%). Therefore, we have our first inviolable mathematical constraint: P(Yes) + P(No) = 1
This equation serves as the mathematical anchor for all subsequent analysis.
Pillar Two: The Hard Constraint of Money (Prices Must ≈ 1 Dollar)
Mathematical axioms are just theory; Polymarket's advantage lies in its enforcement of this constraint in reality through financial engineering.
This mechanism is the "1 Dollar Payout Guarantee."
- Creating a "Complete Share" You cannot just buy "Yes" or just buy "No."
To participate in a market, you must:
Deposit collateral: You deposit 1 USDC into the smart contract. Receive a "set": The contract will immediately mint and issue a complete set of outcome tokens to you, namely: 1 USDC → 1 A-Token (Yes) + 1 B-Token (No)
- "Winner Takes All" Settlement At the time of contract settlement, since the events are mutually exclusive (only one of "Yes" and "No" can win), the value of this set of shares is strictly locked:
When the oracle determines the result to be "A": your A-Token (Yes) is now worth 1 dollar and can be redeemed for 1 USDC. Your B-Token (No) is worth zero. (If the result is B, then vice versa).
- "No Arbitrage" Price Anchoring The most critical impact of this mechanism is:
At the moment of final settlement of the event, the total value of a complete {A-Token, B-Token} share combination is undoubtedly equal to 1 dollar.
Since we know this set of shares is guaranteed to be worth 1 dollar in the future, its market price today must be very close to 1 dollar. If the price deviates, arbitrageurs will immediately appear to force the price back:
Scenario 1: The sum of prices is below 1 (e.g., $0.95) If A-Token sells for $0.60 and B-Token sells for $0.35, the total price is $0.95.
Arbitrageurs will immediately spend $0.95 in the market to buy a complete set of shares and hold them until maturity. Upon maturity, this set of shares can be redeemed for $1. Arbitrageurs have purchased a $1 "safe bond" for 95 cents, locking in a (1−0.95)/0.95≈5.26% risk-free return (assuming the platform and USDC are risk-free). This buying pressure will push the price back up to $1.
Scenario 2: The sum of prices is above 1 (e.g., $1.05) If A-Token sells for $0.70 and B-Token sells for $0.35, the total price is $1.05.
Arbitrageurs will immediately deposit 1 USDC, mint a new {A, B} share set, and then sell it in the market for $1.05. They instantaneously cash out $1.05 at a cost of $1, making a profit of $0.05. This selling pressure will push the price back down to $1.
This two-way arbitrage pressure forces the market price to form a strong equilibrium, which we call a financial anchoring relationship: V(A) + V(B)≈$1
Now we have two "hard constraints" from different domains:
Mathematical Constraint: P(A) + P(B) = 1
Financial Constraint: V(A) + V(B) ≈ $1
Polymarket's pricing system is built on these two pillars. Next, we will explore how these two constraints combine and ultimately derive the core logic of "price equals probability."
2. Why Does a 90% Probability Sell for $0.9?
In the previous chapter, we established two "hard constraints":
Mathematical Constraint: The probabilities of "Yes" and "No" for an event must sum to 1. P(A) + P(B) = 1
Financial Constraint: The prices of "Yes" and "No" tokens for an event must sum to approximately 1 dollar. V(A) + V(B) ≈ $1
2.1 Price Equals Probability: An Intuitive Derivation
When you place these two constraints side by side, the core logic of Polymarket becomes evident: the structure of the two formulas corresponds perfectly.
This strongly suggests that: the price of a token V(A) is the best estimate of the market's probability P(A) of that event occurring.
Why must this equation hold? We can understand it from the perspective of "fair value."
What is "Fair Value"?
Assume an event (A) has a 90% probability of occurring and a 10% probability of not occurring. The future cash flow of the A-Token (Yes) you hold is:
There is a 90% chance it is worth 1 dollar.
There is a 10% chance it is worth 0 dollars.
So, what is the reasonable "fair value" (or "expected value" EV) of this "lottery ticket" today?
EV(A) = (90% * $1) + (10% * $0) = $0.9
*The fair value is $0.9. In a rational market, prices will always tend to their fair value.
If Price < Fair Value: Assume the market price V(A) is only 0.8. Professional traders will see this as a "discounted probability" and will buy heavily until the price is pushed up to 0.9.
If Price > Fair Value: Assume the market price V(A) sells for 0.95. Traders will see this as a "premium probability" and will sell heavily until the price is pushed down to 0.9.
Thus, the continuous arbitrage pressure in the market will force the price V(A) to remain anchored near its expected value P(A). V(A) ≈ P(A)
2.2 An Important Correction: Price = Probability - "Risk Premium"
Now, we must introduce a professional correction. You will often find that a poll shows a 95% probability of an event occurring, but the price on Polymarket may stabilize at only 0.9 dollars.
Does this mean the market is "wrong"?
No. This precisely reflects that the market is "correct" because it is pricing in risk.
In financial engineering, we must distinguish between two concepts:
True Probability (P): The objective likelihood of occurrence from a "God's-eye view" (e.g., the 95% from polls).
Risk-Neutral Probability (Q): The price actually traded in financial markets (like Polymarket).
In the real world, investors are risk-averse. They hold a token and must bear not only the risk of the event itself but also a series of structural risks associated with the platform:
Will the oracle make a mistake? Will the smart contract be hacked? Will USDC depeg? Will the platform face regulatory crackdowns?
To bear these additional, unhedgeable risks, investors will demand a "discount" as compensation, which is financially referred to as a "risk premium."
Therefore, a more precise pricing formula is: V(A) = Q(A) - λ
Where Q(A) is the risk-neutral probability of the event, and λ (Lambda) is a composite risk discount (or "risk premium") that represents the market's compensation requirement for all the aforementioned structural risks.
When you see a price of 0.9 dollars on Polymarket, the professional information it conveys is: "Market participants are willing to bet real money on the risk-neutral probability of this event occurring, and this price has been adjusted downward (deducted) for all perceivable platform and event risks."
This is the fundamental difference between Polymarket and polls: polls reflect "opinions," while Polymarket prices reflect "risks."
3. How Are Prices Formed?
Earlier, we established two pillars:
Mathematically, the sum of probabilities must equal 1.
Financially, the sum of prices must be approximately 1 dollar.
Now, we enter the practical aspect. How is the price of $0.9 that you see on the screen formed? And what prevents it from deviating?
3.1 Formation of Prices
The most common mistake beginners make is to imagine Polymarket as an AMM like Uniswap, thinking that prices are calculated according to a fixed mathematical formula (like X*Y = K).
This is incorrect.
The core of Polymarket is a "Central Limit Order Book" (CLOB), which operates exactly 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 seller" in the market. Prices are "discovered" by all participants, not "calculated" by the platform.
Polymarket's system combines "speed" and "security":
Lightning Fast (Off-chain Matching): You submit orders, modify prices, cancel orders… all of this is done instantly and for free on a centralized server.
Absolutely Secure (On-chain Settlement): Only after your order is executed is the final settlement information sent to the blockchain, ensuring the safety of your assets.
What does this mean for market makers?
This means "no slippage." They place buy orders at $0.8, and the transaction price is $0.8. This allows them to earn a stable profit of $0.01 by placing a buy order at $0.8 and a sell order at $0.81, just like in a real stock market.
3.2 Why Can Prices Always Be Both "Good" and "Stable"?
You might ask: If it all relies on everyone placing orders freely, what if no one places orders? Wouldn't the prices get chaotic?
This is where Polymarket's ingenious incentive design comes in, which has two layers:
Incentive One: Return "Performance Fees" to "Market Makers"
Polymarket does not charge trading fees, but it will take a percentage (e.g., k%) of your net profit as a "performance fee" after the market settles.
Key point: This money does not go to Polymarket! The platform returns the vast majority of this fee directly to those market makers who "provide liquidity" (i.e., place orders) in this market. This incentivizes professional players to flock in and provide you with stable and deep quotes.
Incentive Two: "Quadratic Scoring" (Forcing You to Offer the Best Price)
The way the platform returns rewards is not through "equal distribution," but rather by using a terrifying weapon of "quadratic scoring."
In simple terms: the better the price you provide (the smaller the bid-ask spread), the more your reward will increase "exponentially."
For example: In a market with a qualified spread of 4 cents, Player A offers a 2-cent spread and scores 0.25. Player B offers a 1-cent spread (only twice as good as A), but he scores 0.5625 (which is 2.25 times A's score!). (This is a simplified formula: Score ∝ (…)^2)
This nonlinear incentive forces all market makers to "strive to push prices toward the most reasonable midpoint."
What does this mean for beginners?
It means that as an ordinary user, you can always enjoy the extremely narrow bid-ask spreads and very low trading costs brought about by the competition among professional players.
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