Beta-Weighted Distribution

Yamata's optional beta function rewards both stake size AND timing, creating incentives for early market participation when enabled by the market creator.

How Beta Works

• Before Market Opens (t < tOpen): Maximum beta weight (betaOpen, typically 5.0)

• During Market Period (tOpen ≤ t ≤ tClose): Beta decreases linearly from betaOpen to 1.0

• At Market Close (t = tClose): Beta = 1.0 (no timing bonus)

Mathematical Formula

Numerical Example

Market Parameters:

• betaOpen: 5.0

• tOpen: Jan 1, 2025 00:00

• tClose: Jan 2, 2025 00:00

• tResolve: Jan 2, 2025 01:00

Commitments:

User	Time	Outcome	Amount	Beta	Weighted
Alice	Dec 31, 23:00	Germany	$20	5.0	$100
Bob	Jan 1, 00:00	France	$300	5.0	$1,500
Carol	Jan 1, 06:00	Germany	$50	4.0	$200
Dave	Jan 2, 00:00	Brazil	$100	1.0	$100

Resolution: Germany wins

Payout Calculation:

• Total losing stakes: $300 + $100 = $400

• Platform fees: $10

• Profits to distribute: $390

Winners' Share:

• Alice's share: 100/(100+200) × $390 = $130 profit + $20 stake = $150 total

• Carol's share: 200/(100+200) × $390 = $260 profit + $50 stake = $310 total

Notice: Alice committed less money but received a higher profit ratio due to earlier timing and higher beta weight.