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Why predicting distributions beats predicting yes/no.

The Fundamental Difference

Binary Markets

“Will Bitcoin be above $100,000 on December 31?” Options: Yes or No Payout: Yes = $1, No = $1

Continuous Markets (Skepsis)

“What will Bitcoin’s price be on December 31?” Options: Any range within the market bounds Payout: $1 per share if outcome lands in your range

Visual Comparison

Binary: One Data Point

Question: "BTC > $100K by Dec 31?"

Yes: 45% ████████████████████░░░░░░░░░░░░░░░░░░░░
No:  55% ████████████████████████████░░░░░░░░░░░░

Information: "Market thinks ~45% chance of crossing $100K"
Unknown: Will it be $100,001 or $500,000? Both are "Yes"

Continuous: Full Distribution

Question: "Where will BTC be on Dec 31?"

$80K-$85K:   3%  ██
$85K-$90K:   8%  ████
$90K-$95K:   15% ████████
$95K-$100K:  22% ████████████
$100K-$105K: 25% ██████████████  ← Mode (most likely)
$105K-$110K: 15% ████████
$110K-$120K: 9%  █████
$120K+:      3%  ██

Information: Full probability landscape
- Expected value visible
- Uncertainty visible
- Tail risks visible

Information Density

What Binary Markets Tell You

A single binary market at 45% “Yes” tells you:
  • There’s a 45% chance of crossing the threshold
  • That’s it

What Continuous Markets Tell You

A continuous distribution tells you:
  • Expected value: Where the market thinks it’ll land
  • Confidence: is the distribution narrow (confident) or wide (uncertain)?
  • Skew: is the market more bullish or bearish?
  • Tail risk: what’s the chance of extreme outcomes?
  • Mode vs Mean: most likely outcome vs average expected outcome

Edge Cases: Where Binary Fails

The “Almost Right” Problem

Binary market: “Will BTC hit $100K?”
ScenarioBTC PriceBetResult
A$99,999YesLOSE
B$100,001YesWIN
You were right about BTC being “around $100K” in both cases. Binary punishes you in Scenario A. Continuous market: “Where will BTC be?”
ScenarioBTC PriceRange BetResult
A$99,99998K98K-102KWIN
B$100,00198K98K-102KWIN
Your actual belief (around $100K) is captured and rewarded.

The “Precision Penalty” Problem

Binary framing forces false precision:
"Will GPT-5 launch before June 1, 2025?"

You think: "Probably April-August 2025"
Binary forces: Pick June 1 as the cutoff

If GPT-5 launches June 15:
- You were basically right (summer 2025)
- Binary says: WRONG
Continuous market:
"When will GPT-5 launch?"

Your bet: April-August 2025 range
GPT-5 launches June 15
Result: WIN (exactly as you predicted)

The “Missing Nuance” Problem

Binary: “Will it rain tomorrow?”
  • Doesn’t capture: How much rain?
  • Drizzle and monsoon both = “Yes”
  • No way to express “probably light rain”
Continuous: “How much rainfall tomorrow?”
  • 0.0-0.1 inches: 30%
  • 0.1-0.5 inches: 45% ← You bet here
  • 0.5-1.0 inches: 20%
  • 1.0+ inches: 5%
Your prediction matches your actual belief.

Capital Efficiency

Binary: Multiple Markets Needed

To express “BTC will be between 95K95K-105K,” you need:
Market 1: "BTC > $95K?" → Buy Yes
Market 2: "BTC > $105K?" → Buy No

Two transactions
Two sets of fees
Two positions to track
Capital spread across markets

Continuous: One Market

Range: $95K-$105K
One transaction
One fee
One position
Capital concentrated
Result: Same belief, half the friction.

Price Discovery

Binary Markets: Threshold Games

In binary markets, traders fight over the threshold:
"BTC > $100K?"
Currently: 48% Yes

Trader A thinks BTC will be $102K → Buys Yes
Trader B thinks BTC will be $98K → Buys No
Trader C thinks BTC will be $150K → Buys Yes (same as A!)

The market can't distinguish A and C's very different views.

Continuous Markets: Full Spectrum

"Where will BTC be?"

Trader A (thinks $102K) → Bets $100K-$105K
Trader B (thinks $98K) → Bets $95K-$100K  
Trader C (thinks $150K) → Bets $140K-$160K

Each view has its own odds
Market shows full range of beliefs
Much richer information

When Binary Markets Work

Binary isn’t always wrong. They work well when:

1. The Question is Naturally Binary

  • “Will [candidate] win the election?” (1st or not 1st)
  • “Will [company] go bankrupt?” (exists or doesn’t)
  • “Will [law] pass?” (passes or doesn’t)

2. Threshold is Meaningful

  • “Will inflation be above 3%?” (policy threshold)
  • “Will [movie] make $100M opening?” (industry benchmark)

3. Extremes Don’t Matter

  • “Will [team] make playoffs?” (whether they dominate or barely qualify doesn’t change the outcome)

When Continuous Markets Excel

1. Magnitude Matters

  • Price predictions (How high? How low?)
  • Measurements (How much? How many?)
  • Timing (When exactly?)

2. Uncertainty is Important

  • Is the market confident or uncertain?
  • What are the tail risks?
  • What’s the range of likely outcomes?

3. Nuance Adds Value

  • Weather (temperatures, rainfall amounts)
  • Economic indicators (inflation rate, unemployment)
  • Performance metrics (revenue, users, etc.)

The Hybrid Future

At Skepsis, we believe continuous markets can handle most prediction needs. But we’re also exploring:

Derived Binary Markets

From a continuous market, you can derive any binary question:
Continuous: "Where will BTC be Dec 31?"

Derived binaries (from same underlying):
- "BTC > $100K?" → Sum of probability above $100K
- "BTC > $90K?" → Sum of probability above $90K
- "BTC between $95K-$105K?" → Sum of that range
One continuous market = infinite binary markets

Summary

AspectBinaryContinuous
InformationSingle probabilityFull distribution
ExpressivenessThreshold onlyAny range
Edge casesPunishes “almost right”Rewards accuracy
Capital efficiencyMultiple marketsOne market
Price discoveryLimitedRich
NuanceNonePreserved
Best forNaturally binary eventsNumerical outcomes

Try the Difference

Experience continuous markets yourself:
Make a continuous prediction: Launch Skepsis →

Next Steps

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