feat: surface juror-balanced scores and AI calibration advisory

Adds a shared juror-balancing utility (z-score normalization per juror,
rescaled back onto the raw 1-10 scale) and wires it into:

- Admin reports page: Top-10 project table now shows "Raw Avg" and
  "Balanced" columns side by side, and the summary stats row shows a
  balanced-average tile. Sort defaults to balanced so harsh and lenient
  graders no longer skew the ranking.
- Ranking dashboard: each project row shows a green/amber balanced-score
  chip next to the raw average when the two differ by ≥0.05, making it
  obvious when juror calibration moved a project's effective ranking.

Also adds AI Juror Calibration Advisory — a mutation that takes
anonymized per-juror stats, calls OpenAI, and produces a plain-language
explanation of the cohort's grading patterns plus per-juror severity
(normal / notable / outlier) with a one-sentence narrative. The advisory
describes the statistical balance that already runs; it does not
introduce a new weighting layer. Rendered as a panel in the Juror
Consistency tab when a specific round is selected.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src/app/(admin)/admin/reports/page.tsx

@@ -45,7 +45,11 @@ import {
   Trophy,
   ArrowRight,
   Hash,
+  Sparkles,
+  Loader2,
+  AlertTriangle,
 } from 'lucide-react'
+import { toast } from 'sonner'
 import { formatDateOnly } from '@/lib/utils'
 import {
   ScoreDistributionChart,
@@ -271,6 +275,12 @@ function ReportsOverview() {
                 const evaluated = projectRankings.filter(p => p.averageScore !== null)
                 const scores = evaluated.map(p => p.averageScore as number)
                 const avgScore = scores.length ? scores.reduce((a, b) => a + b, 0) / scores.length : 0
+                const balancedScores = projectRankings
+                  .map(p => p.balancedScore)
+                  .filter((s): s is number => s != null)
+                const avgBalanced = balancedScores.length
+                  ? balancedScores.reduce((a, b) => a + b, 0) / balancedScores.length
+                  : null
                 const minScore = scores.length ? Math.min(...scores) : 0
                 const maxScore = scores.length ? Math.max(...scores) : 0
                 const evalPercent = projectRankings.length ? Math.round((evaluated.length / projectRankings.length) * 100) : 0
@@ -281,14 +291,28 @@ function ReportsOverview() {
 
                 return (
                   <>
-                    <div className="grid grid-cols-2 gap-3 sm:grid-cols-4">
+                    <div className="grid grid-cols-2 gap-3 sm:grid-cols-5">
                       <div className="rounded-lg border p-3 text-center">
                         <p className="text-xs text-muted-foreground">Total Projects</p>
                         <p className="text-xl font-bold tabular-nums">{projectRankings.length}</p>
                       </div>
-                      <div className="rounded-lg border p-3 text-center">
-                        <p className="text-xs text-muted-foreground">Avg Score</p>
-                        <p className="text-xl font-bold tabular-nums">{avgScore ? avgScore.toFixed(1) : '-'}</p>
+                      <div
+                        className="rounded-lg border p-3 text-center"
+                        title="Unweighted mean of all submitted juror scores"
+                      >
+                        <p className="text-xs text-muted-foreground">Raw Avg</p>
+                        <p className="text-xl font-bold tabular-nums text-muted-foreground">
+                          {avgScore ? avgScore.toFixed(1) : '-'}
+                        </p>
+                      </div>
+                      <div
+                        className="rounded-lg border p-3 text-center"
+                        title="Juror-balanced average: per-juror z-score normalization rescaled to the 1–10 range"
+                      >
+                        <p className="text-xs text-muted-foreground">Balanced Avg</p>
+                        <p className="text-xl font-bold tabular-nums">
+                          {avgBalanced == null ? '-' : avgBalanced.toFixed(1)}
+                        </p>
                       </div>
                       <div className="rounded-lg border p-3 text-center">
                         <p className="text-xs text-muted-foreground">Evaluated</p>
@@ -319,7 +343,7 @@ function ReportsOverview() {
                     {/* Top 10 ranked table */}
                     <div>
                       <p className="text-sm font-medium text-muted-foreground mb-2 flex items-center gap-1.5">
-                        <Trophy className="h-3.5 w-3.5" /> Top 10 by Average Score
+                        <Trophy className="h-3.5 w-3.5" /> Top 10 by Balanced Score
                       </p>
                       <div className="rounded-lg border">
                         <Table>
@@ -328,7 +352,18 @@ function ReportsOverview() {
                               <TableHead className="w-10">#</TableHead>
                               <TableHead>Project</TableHead>
                               <TableHead className="hidden sm:table-cell">Team</TableHead>
-                              <TableHead className="text-right">Avg</TableHead>
+                              <TableHead
+                                className="text-right"
+                                title="Raw average of juror scores — uncorrected for per-juror harshness"
+                              >
+                                Raw Avg
+                              </TableHead>
+                              <TableHead
+                                className="text-right"
+                                title="Juror-balanced average: each juror's contribution is z-score normalized against their own grading distribution, then rescaled to the 1–10 range. Harsh and lenient jurors contribute on equal footing."
+                              >
+                                Balanced
+                              </TableHead>
                               <TableHead className="text-right">Evals</TableHead>
                               <TableHead>Status</TableHead>
                             </TableRow>
@@ -345,9 +380,12 @@ function ReportsOverview() {
                                 <TableCell className="hidden sm:table-cell text-muted-foreground">
                                   {p.teamName || '-'}
                                 </TableCell>
-                                <TableCell className="text-right tabular-nums">
+                                <TableCell className="text-right tabular-nums text-muted-foreground">
                                   {p.averageScore === null ? '-' : p.averageScore.toFixed(2)}
                                 </TableCell>
+                                <TableCell className="text-right tabular-nums font-semibold">
+                                  {p.balancedScore == null ? '-' : p.balancedScore.toFixed(2)}
+                                </TableCell>
                                 <TableCell className="text-right tabular-nums">{p.evaluationCount}</TableCell>
                                 <TableCell>
                                   <Badge variant="outline">{formatStatusLabel(p.status)}</Badge>
@@ -870,10 +908,150 @@ function JurorConsistencyTab() {
           }}
         />
       )}
+
+      {queryInput.roundId && (
+        <JurorCalibrationPanel roundId={queryInput.roundId} />
+      )}
     </div>
   )
 }
 
+function JurorCalibrationPanel({ roundId }: { roundId: string }) {
+  const mutation = trpc.analytics.generateJurorCalibration.useMutation({
+    onError: (err) => toast.error(`Calibration analysis failed: ${err.message}`),
+  })
+  const result = mutation.data
+
+  const severityStyle: Record<string, string> = {
+    outlier: 'bg-red-50 text-red-700 border-red-200',
+    notable: 'bg-amber-50 text-amber-700 border-amber-200',
+    normal: 'bg-muted text-muted-foreground',
+  }
+
+  return (
+    <Card>
+      <CardHeader>
+        <div className="flex flex-wrap items-start justify-between gap-3">
+          <div>
+            <CardTitle className="flex items-center gap-2">
+              <Sparkles className="h-5 w-5 text-[#de0f1e]" />
+              AI Juror Calibration Advisory
+            </CardTitle>
+            <CardDescription>
+              Plain-language explanation of the per-juror score balancing already applied to rankings.
+              Describes, does not prescribe — the math runs regardless.
+            </CardDescription>
+          </div>
+          <Button
+            onClick={() => mutation.mutate({ roundId })}
+            disabled={mutation.isPending}
+            className="gap-2"
+          >
+            {mutation.isPending ? <Loader2 className="h-4 w-4 animate-spin" /> : <Sparkles className="h-4 w-4" />}
+            {mutation.isPending ? 'Analyzing…' : result ? 'Regenerate' : 'Analyze jurors'}
+          </Button>
+        </div>
+      </CardHeader>
+      <CardContent className="space-y-5">
+        {!result && !mutation.isPending && (
+          <p className="text-sm text-muted-foreground">
+            Run the analysis to see per-juror grading patterns, cohort stats, and the calibration
+            narrative for the selected round.
+          </p>
+        )}
+
+        {result && (
+          <>
+            <div className="grid grid-cols-2 gap-3 sm:grid-cols-4">
+              <div className="rounded-lg border p-3 text-center">
+                <p className="text-xs text-muted-foreground">Cohort Mean</p>
+                <p className="text-xl font-bold tabular-nums">{result.cohortMean.toFixed(2)}</p>
+              </div>
+              <div className="rounded-lg border p-3 text-center">
+                <p className="text-xs text-muted-foreground">Cohort Stddev</p>
+                <p className="text-xl font-bold tabular-nums">{result.cohortStddev.toFixed(2)}</p>
+              </div>
+              <div className="rounded-lg border p-3 text-center">
+                <p className="text-xs text-muted-foreground">Evaluations</p>
+                <p className="text-xl font-bold tabular-nums">{result.totalEvaluations}</p>
+              </div>
+              <div className="rounded-lg border p-3 text-center">
+                <p className="text-xs text-muted-foreground">Jurors</p>
+                <p className="text-xl font-bold tabular-nums">{result.totalJurors}</p>
+              </div>
+            </div>
+
+            <div className="rounded-lg border bg-muted/30 p-4">
+              <p className="text-sm leading-relaxed">{result.overallSummary}</p>
+              {result.keyTakeaways.length > 0 && (
+                <ul className="mt-3 space-y-1.5 text-sm">
+                  {result.keyTakeaways.map((t, i) => (
+                    <li key={i} className="flex items-start gap-2">
+                      <ArrowRight className="mt-1 h-3.5 w-3.5 flex-shrink-0 text-muted-foreground" />
+                      <span>{t}</span>
+                    </li>
+                  ))}
+                </ul>
+              )}
+            </div>
+
+            <div className="rounded-lg border">
+              <Table>
+                <TableHeader>
+                  <TableRow>
+                    <TableHead>Juror</TableHead>
+                    <TableHead className="text-right">Evals</TableHead>
+                    <TableHead className="text-right">Mean</TableHead>
+                    <TableHead className="text-right">Δ Cohort</TableHead>
+                    <TableHead className="text-right" title="Juror's stddev / cohort stddev">
+                      Influence
+                    </TableHead>
+                    <TableHead>Severity</TableHead>
+                    <TableHead>Notes</TableHead>
+                  </TableRow>
+                </TableHeader>
+                <TableBody>
+                  {result.jurors.map((j) => (
+                    <TableRow key={j.userId}>
+                      <TableCell className="font-medium">{j.name}</TableCell>
+                      <TableCell className="text-right tabular-nums">{j.evaluationCount}</TableCell>
+                      <TableCell className="text-right tabular-nums">{j.rawMean.toFixed(2)}</TableCell>
+                      <TableCell
+                        className={`text-right tabular-nums ${
+                          j.deltaFromCohort < -0.5 ? 'text-red-600' : j.deltaFromCohort > 0.5 ? 'text-emerald-600' : ''
+                        }`}
+                      >
+                        {j.deltaFromCohort > 0 ? '+' : ''}
+                        {j.deltaFromCohort.toFixed(2)}
+                      </TableCell>
+                      <TableCell className="text-right tabular-nums">
+                        {j.effectiveInfluence == null ? '-' : j.effectiveInfluence.toFixed(2)}
+                      </TableCell>
+                      <TableCell>
+                        <Badge variant="outline" className={severityStyle[j.severity]}>
+                          {j.severity === 'outlier' && <AlertTriangle className="mr-1 h-3 w-3" />}
+                          {j.severity}
+                        </Badge>
+                      </TableCell>
+                      <TableCell className="max-w-md text-sm text-muted-foreground">
+                        {j.summary}
+                      </TableCell>
+                    </TableRow>
+                  ))}
+                </TableBody>
+              </Table>
+            </div>
+
+            <p className="text-xs text-muted-foreground">
+              Generated {result.generatedAt.toLocaleString()} · {result.tokensUsed} tokens · model {result.model}
+            </p>
+          </>
+        )}
+      </CardContent>
+    </Card>
+  )
+}
+
 function DiversityTab() {
   const [selectedValue, setSelectedValue] = useState<string | null>(null)