Glossary / Betting math / Implied sum
A ParlayAPI glossary entry

Implied sum

The implied sum is the sum of implied probabilities across all sides of a market. On a single book it exceeds 1.0 by the vig. Computed across different books' best prices, an implied sum below 1.0 is the mathematical signature of an arbitrage opportunity.

Worked example

# Best available price on each side, different books
        Book A:  Team X  +105   ->  48.8%
        Book B:  Team Y  +110   ->  47.6%
        implied sum = 48.8% + 47.6% = 96.4%   # < 100%
        # Staking both sides in proportion locks ~3.6% regardless of result

On one book the implied sum measures how expensive the market is (see overround). Across books it measures how far the market disagrees with itself - the disagreement arbitrage and middling monetize.

Where it shows up in ParlayAPI

The arb scanner continuously computes cross-book implied sums from the aggregated feed and surfaces markets where the sum drops below 1.0. You can reproduce it from the raw odds endpoints: take the best price per side across books, convert to implied probability, and sum.

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