Scoring and Ranking

Reiy uses a two-stage scoring system: quotes are ranked for selection, then solutions are scored for winner determination and reward distribution.

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Quote ranking

Fisherman ranks quotes per intent to select the best response. Ranking depends on the quote type. Exact-in (fixed sell amount): Exact-out (fixed buy amount):

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Solve scoring

After a solution is submitted, Fisherman computes a score per intent and a total score for the allocation.

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Raw surplus

For each intent $I_i$ in the solution: $$\text{raw\_surplus}_i = p_i - \text{floor}_i$$ Where $p_i$ is the actual payout and $$\text{floor}_i = \max(m_i(f_i), \text{bm}_i)$$ is the higher of the user’s minimum and the protocol benchmark floor.

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Normalized score

$$\text{score}_i = \text{value}(\text{buy\_token}_i,\text{raw\_surplus}_i,\text{score\_time})$$ Normalization converts surplus into a protocol score unit (numéraire, e.g. USD-equivalent). When all surplus is in the same token, raw surplus may be used directly.

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Package score

$$\text{score}_j = \sum \text{score}_i \quad \text{for all intents in solver } P_j$$

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Allocation score

$$\text{total\_score} = \sum \text{score}_j \quad \text{for all solvers in the allocation}$$

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Winner selection

The allocation with the highest total score wins. Ties are broken alphabetically by solver endpoint ID.

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Score validity

At settlement the committed scores are checked against a tolerance: $$\begin{aligned} \text{actual\_score}_j &\ge \text{committed\_score}_j \times \frac{\text{score\_tolerance\_bps}}{10\,000} \\ \text{actual\_total\_score} &\ge \text{committed\_total\_score} \times \frac{\text{score\_tolerance\_bps}}{10\,000} \end{aligned}$$ A default tolerance of 9,500 bps (95%) is typical.

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Uniform surplus ratio (EPSR)

Intents in the same directed pair should receive equal proportional improvement above their floor. Core relation: $$\frac{p_i}{\text{floor}_i} \approx k_d$$ with the same $k_d$ for all intents in the pair.

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Fixed-point representation

$$K_{\text{SCALE}} = 1\,000\,000\,000$$ and $$k_d = \left\lfloor \frac{p_{\text{first}} \times K_{\text{SCALE}}} {\text{floor}_{\text{first}}} \right\rfloor$$

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Cross-multiplication check

For every subsequent intent: $$\left| p_i \times \text{floor}_{\text{first}} - p_{\text{first}} \times \text{floor}_i \right| \le \epsilon_{\text{bps}} \times \frac{ \text{floor}_{\text{first}} \times \text{floor}_i }{10\,000}$$ Typical $\epsilon_{\text{bps}}$ is 1–5 bps.

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Batch-level tolerance

At settlement: $$k_{\text{actual}} \ge k_{\text{committed}} \times \frac{k_{\text{tolerance\_bps}}}{10\,000}$$ A typical tolerance is 9,500 bps (95%).

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