The first on-chain market where you stake a full probability distribution — not a binary yes/no. Your precision is your edge.
The Problem
Ask "Will tomorrow's ERCOT peak price top $100/MWh?" and you're forced into yes or no. But you know far more than that.
You think the peak will clear around $104/MWh. The line is fixed at $100 with a ~5% house edge baked in. You can't say how confident you are or where you think it truly peaks.
Submit the distribution you actually believe. The closer your distribution to the realized outcome, the higher your payout. Your confidence (σ) matters just as much as your direction (μ).
Your Edge
In a binary market, you either picked the right side or you didn't. In an estimation market, being a little right still pays — and being very precise pays a lot.
| What you can express | Binary | Parabola |
|---|---|---|
| You believe: the peak lands around $104/MWh, probably $90–$118 | ||
| Direction (over/under) | ✓ yes/no | ✓ |
| How sure you are | ✗ ignored | ✓ |
| "Likely between $90–$118" | ✗ no market | ✓ |
| "Crowd is too uncertain" | ✗ no market | ✓ |
| Your edge captured | Partial | Full |
N($104, σ=7) and the crowd is at N($92, σ=15), you're implicitly saying the peak lands between $90–$118 with 95% probability. The crowd says only 51%. That gap — on a range no utility tariff even offers — is pure captured value. You earn for being right about the range, not just the side.
You think the outcome will be extreme — but you don't know which direction. Bet a wide distribution. Binary markets have no way to express this.
You agree with consensus on direction but think the crowd is overconfident. Bet a tighter σ — lower collateral, higher payout per dollar if you're right.
"It'll definitely land somewhere in this range." Express a narrow distribution centered on that range. There's no binary equivalent.
You think the consensus is sleeping on a tail outcome. Submit a distribution with heavier tails than the crowd to capture the underpriced extreme scenarios.
Under the log scoring rule, your score after outcome x is log Q(x). Taking expectations under the true distribution P*:
This shows log scoring is strictly proper: the unique best strategy is to report your true belief. Ordinary fixed-payoff binary bets do not automatically have this property — they reward being directionally right, not reporting a calibrated probability. A binary contract can be made proper (e.g. via log-score or Brier-score payoffs), but a standard over/under payout is not one of those.
Power example: KL(N(104,7) ‖ N(92,15)) = log(15/7) + (49+144)/450 − ½ ≈ 0.69 — a single number capturing both the mean shift and the tighter certainty.
How It Works
ERCOT/PJM/CAISO power prices, grid demand, cooling-degree days, carbon, GPU-compute costs — any outcome with a numeric realization.
Choose μ (where you expect the outcome) and σ (how certain you are). More conviction → tighter σ → less collateral.
Your distribution is an on-chain transaction. The AMM quotes you immediately against the current crowd distribution.
A proper scoring rule pays proportional to how close your distribution was to the realized outcome. Precision compounds.
Perpetual Estimation Markets
Distribution perps let you hold a long or short position on how the crowd's collective estimate evolves over time — a perpetual on crowd belief itself.
The AMM maintains a market-implied distribution relative to an oracle reference. Traders express views over the whole distribution — not a single binary event. Funding is based on a signed, statewise discrepancy (log-density ratios), so you are rewarded when the market distribution moves toward the one you supplied.
A binary market asks only: "Will the ERCOT evening peak exceed $100/MWh on Thursday?" That collapses your entire view of the grid into a single threshold probability. Suppose you believe the peak will land around $78/MWh — but with a fat right tail toward the $5,000 scarcity cap if a heat wave hits. A distribution market lets you express both: the expected level and the shape of that tail. You get rewarded for being right about the whole distribution of power prices — not just which side of an arbitrary line they land on.
Developer API
A full algorithmic-trading API sits behind the pilot: normalized market data, sandboxed backtesting, a strategy engine, and risk-checked execution — across a 4-layer architecture. Wire up a bot, or just text it your trades in plain English.
→ "buy 10 ERCOT-PEAK"
→ "short $5k of BTC if it breaks 90000"
→ "how's my balance?" · "close my power position"
4 layers — Data · Research/Backtesting · Strategy · Execution/Risk. Circuit breakers, buying-power & leverage caps enforced before every trade. Paper-trade first; live brokers are opt-in.
Early Access
Parabola is live on Solana devnet. Join the waitlist to get early access.