feat: formula-based ranking with optional AI, configurable score/pass-rate weights

Add scoreWeight and passRateWeight (0-10) to evaluation config for
configurable composite score formula. When ranking criteria text is
empty, triggerAutoRank uses pure formula ranking (no LLM calls).
When criteria text is present, AI-assisted ranking runs as before.

- Add FORMULA to RankingMode enum with migration
- Extract fetchCategoryProjects helper, add formulaRank service
- Update computeCompositeScore to accept configurable weights
- Add score/pass-rate weight sliders to ranking dashboard UI
- Mode-aware button labels (Calculator/formula vs Sparkles/AI)

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

src/server/routers/ranking.ts

@@ -6,6 +6,7 @@ import {
   parseRankingCriteria,
   executeAIRanking,
   quickRank as aiQuickRank,
+  formulaRank,
   fetchAndRankCategory,
   type ParsedRankingRule,
 } from '../services/ai-ranking'
@@ -269,14 +270,8 @@ export const rankingRouter = router({
       })
 
       const config = (round.configJson as EvaluationConfig | null) ?? ({} as EvaluationConfig)
-      const criteriaText = config?.rankingCriteria ?? null
-
-      if (!criteriaText) {
-        throw new TRPCError({
-          code: 'BAD_REQUEST',
-          message: 'No ranking criteria configured for this round. Add criteria in round settings first.',
-        })
-      }
+      const criteriaText = config?.rankingCriteria?.trim() || null
+      const isFormulaMode = !criteriaText
 
       // Create a RUNNING snapshot so all admins see the in-progress indicator
       const snapshot = await ctx.prisma.rankingSnapshot.create({
@@ -284,26 +279,46 @@ export const rankingRouter = router({
           roundId,
           triggeredById: ctx.user.id,
           triggerType: 'MANUAL',
-          criteriaText,
+          criteriaText: criteriaText ?? '',
           parsedRulesJson: {} as Prisma.InputJsonValue,
-          mode: 'QUICK',
+          mode: isFormulaMode ? 'FORMULA' : 'QUICK',
           status: 'RUNNING',
         },
       })
 
       try {
-        const result = await aiQuickRank(criteriaText, roundId, ctx.prisma, ctx.user.id)
+        let startup: { rankedProjects: unknown[] }
+        let concept: { rankedProjects: unknown[] }
+        let parsedRulesWithWeights: Prisma.InputJsonValue
+
+        if (isFormulaMode) {
+          // Formula-only: no LLM, pure math ranking
+          const result = await formulaRank(roundId, ctx.prisma)
+          startup = result.startup
+          concept = result.concept
+          const criteriaWeights = config.criteriaWeights ?? undefined
+          parsedRulesWithWeights = {
+            rules: [],
+            weights: criteriaWeights,
+            scoreWeight: config.scoreWeight ?? 5,
+            passRateWeight: config.passRateWeight ?? 5,
+          } as unknown as Prisma.InputJsonValue
+        } else {
+          // AI-assisted: parse criteria + rank with LLM
+          const result = await aiQuickRank(criteriaText, roundId, ctx.prisma, ctx.user.id)
+          startup = result.startup
+          concept = result.concept
+          const criteriaWeights = config.criteriaWeights ?? undefined
+          parsedRulesWithWeights = { rules: result.parsedRules, weights: criteriaWeights } as unknown as Prisma.InputJsonValue
+        }
 
-        // Embed weights alongside rules for audit
-        const criteriaWeights = config.criteriaWeights ?? undefined
-        const parsedRulesWithWeights = { rules: result.parsedRules, weights: criteriaWeights } as unknown as Prisma.InputJsonValue
         await ctx.prisma.rankingSnapshot.update({
           where: { id: snapshot.id },
           data: {
             status: 'COMPLETED',
             parsedRulesJson: parsedRulesWithWeights,
-            startupRankingJson: result.startup.rankedProjects as unknown as Prisma.InputJsonValue,
-            conceptRankingJson: result.concept.rankedProjects as unknown as Prisma.InputJsonValue,
+            startupRankingJson: startup.rankedProjects as unknown as Prisma.InputJsonValue,
+            conceptRankingJson: concept.rankedProjects as unknown as Prisma.InputJsonValue,
           },
         })
 
@@ -313,12 +328,12 @@ export const rankingRouter = router({
           action: 'RANKING_MANUAL_TRIGGERED',
           entityType: 'RankingSnapshot',
           entityId: snapshot.id,
-          detailsJson: { roundId },
+          detailsJson: { roundId, mode: isFormulaMode ? 'FORMULA' : 'AI' },
           ipAddress: ctx.ip,
           userAgent: ctx.userAgent,
         })
 
-        return { snapshotId: snapshot.id, startup: result.startup, concept: result.concept }
+        return { snapshotId: snapshot.id, startup, concept }
       } catch (err) {
         // Mark snapshot as FAILED so the indicator clears
         await ctx.prisma.rankingSnapshot.update({