feat(metrics): publish margin of error on every delta — #2495, #2524

The metrics card had one volume threshold doing two jobs.
recMetricsLowVolume = 20 is a DISPLAY floor — below that a skip rate is
anecdote — but the card then presented deltas as though it were also a
DECISION floor. Those differ by an order of magnitude: detecting the ~13pp
differences that matter needs ~133 plays per arm for 80% power at a=0.05.

So Discover's taste-matched (59 plays) and random-unheard (70) both rendered
as full-confidence rows with a bold delta beside them, and that comparison
sits at p ~ 0.06. The card said "signal"; the arithmetic said "maybe". It
produced a recommendation the data didn't support, and any reader with the
same numbers would have made the same call.

Deltas now carry a 95% margin of error and a `distinguishable` flag, computed
server-side so both clients read the same arithmetic instead of each
re-deriving it. Skip rate is a two-proportion difference; completion is
Welch, which needs a variance — hence completion_sqsum in the query. It is
the sum of squares rather than stddev_samp on purpose: raw source rows are
merged into surface families in Go, and sums of squares combine across groups
exactly whereas standard deviations cannot.

recMetricsLowVolume is untouched. "Too thin to show" and "too thin to act on"
are different questions.

Web renders an indistinguishable delta as dimmed and prefixed "≈", with the
range on hover and a legend explaining the glyph. Colour is withheld unless
the delta clears its margin — colouring noise red is what made the old card
misleading. Breakdown rows go through the same path; those are the thinnest
samples on screen and where the old card misled most.

Also fixes the admin trends view, which had the same problem worse: its
"Latest skip"/"Latest completion" columns are one WEEK while the adjacent
Plays column is the whole window. I misread exactly that and briefly
concluded Deep cuts was the worst surface, from ~17 plays in a single week —
over 180 days it is one of the best. Headers now name their period and the
skip cell carries that week's play count.

#2524: resolveArtist now recognises a duplicate-MBID unique violation as the
expected condition it is, matching resolveAlbum. Two rows mapping to one
MusicBrainz artist is a merge candidate, not a fault; without the branch it
logged a generic warning plus a Postgres ERROR line on every scan, which
teaches an operator to ignore database errors.

web/src/routes/settings/+page.svelte

@@ -12,7 +12,7 @@
     createRecommendationMetricsQuery,
     type RecommendationMetrics,
     type SurfaceIntent,
-    type SurfaceMetric
+    type MetricDelta
   } from '$lib/api/metrics';
   import { theme, setTheme, type ThemePreference } from '$lib/stores/theme.svelte';
   import { player, setCrossfade } from '$lib/player/store.svelte';
@@ -45,20 +45,39 @@
     return `${(v * 100).toFixed(0)}%`;
   }
 
-  // Delta in percentage points vs the baseline, signed ("+12" / "−5").
-  function deltaPts(value: number, baseline: number): string {
-    const pts = Math.round((value - baseline) * 100);
-    return pts > 0 ? `+${pts}` : `${pts}`;
+  // Deltas come from the server with their margin of error (#2495). The client
+  // no longer subtracts rates itself: the margin needs the sample sizes and
+  // variances, and having both clients re-derive it invites them to disagree.
+  //
+  // A delta that isn't distinguishable from zero is prefixed "≈" and dimmed.
+  // That is the point of this whole change — the card used to render a −12 on
+  // 59 plays exactly as boldly as a −6 on 400, and the first of those is noise.
+  function deltaText(d: MetricDelta | undefined): string {
+    if (!d) return '';
+    const pts = Math.round(d.delta_pp);
+    const signed = pts > 0 ? `+${pts}` : `${pts}`;
+    return d.distinguishable ? signed : `≈${signed}`;
   }
 
-  // A surface's skip delta is "worse" when it skips more than the
-  // baseline; completion delta is "worse" when it completes less.
-  function skipDeltaClass(m: SurfaceMetric, baseline: SurfaceMetric): string {
-    return m.skip_rate > baseline.skip_rate ? 'text-danger' : 'text-text-secondary';
+  function deltaTitle(d: MetricDelta | undefined): string | undefined {
+    if (!d) return undefined;
+    const range = `${d.delta_pp.toFixed(1)} ± ${d.margin_pp.toFixed(1)} points vs baseline`;
+    return d.distinguishable
+      ? `${range} (95% confidence)`
+      : `${range} — not distinguishable from zero at 95% confidence, so read this as no measured difference.`;
   }
 
-  function completionDeltaClass(m: SurfaceMetric, baseline: SurfaceMetric): string {
-    return m.avg_completion < baseline.avg_completion ? 'text-danger' : 'text-text-secondary';
+  // A skip delta is "worse" above the baseline; a completion delta is "worse"
+  // below it. Neither gets a colour unless it's distinguishable — colouring
+  // noise red is what made the old card misleading.
+  function skipDeltaClass(d: MetricDelta | undefined): string {
+    if (!d?.distinguishable) return 'text-text-secondary opacity-60';
+    return d.delta_pp > 0 ? 'text-danger' : 'text-text-secondary';
+  }
+
+  function completionDeltaClass(d: MetricDelta | undefined): string {
+    if (!d?.distinguishable) return 'text-text-secondary opacity-60';
+    return d.delta_pp < 0 ? 'text-danger' : 'text-text-secondary';
   }
 
   // Pick-kind breakdowns are collapsed by default (#1270): with every
@@ -384,18 +403,16 @@
                   <td class="py-1 text-right tabular-nums">{m.plays}</td>
                   <td class="py-1 text-right tabular-nums">
                     {pct(m.skip_rate)}
-                    {#if baseline}
-                      <span class="ml-1 text-xs {skipDeltaClass(m, baseline)}">
-                        {deltaPts(m.skip_rate, baseline.skip_rate)}
-                      </span>
+                    {#if m.skip_delta}
+                      <span class="ml-1 text-xs {skipDeltaClass(m.skip_delta)}"
+                            title={deltaTitle(m.skip_delta)}>{deltaText(m.skip_delta)}</span>
                     {/if}
                   </td>
                   <td class="py-1 text-right tabular-nums">
                     {pct(m.avg_completion)}
-                    {#if baseline}
-                      <span class="ml-1 text-xs {completionDeltaClass(m, baseline)}">
-                        {deltaPts(m.avg_completion, baseline.avg_completion)}
-                      </span>
+                    {#if m.completion_delta}
+                      <span class="ml-1 text-xs {completionDeltaClass(m.completion_delta)}"
+                            title={deltaTitle(m.completion_delta)}>{deltaText(m.completion_delta)}</span>
                     {/if}
                   </td>
                 </tr>
@@ -420,18 +437,16 @@
                       <td class="py-1 text-right text-xs tabular-nums">{b.plays}</td>
                       <td class="py-1 text-right text-xs tabular-nums">
                         {pct(b.skip_rate)}
-                        {#if baseline}
-                          <span class="ml-1 {skipDeltaClass(b, baseline)}">
-                            {deltaPts(b.skip_rate, baseline.skip_rate)}
-                          </span>
+                        {#if b.skip_delta}
+                          <span class="ml-1 {skipDeltaClass(b.skip_delta)}"
+                                title={deltaTitle(b.skip_delta)}>{deltaText(b.skip_delta)}</span>
                         {/if}
                       </td>
                       <td class="py-1 text-right text-xs tabular-nums">
                         {pct(b.avg_completion)}
-                        {#if baseline}
-                          <span class="ml-1 {completionDeltaClass(b, baseline)}">
-                            {deltaPts(b.avg_completion, baseline.avg_completion)}
-                          </span>
+                        {#if b.completion_delta}
+                          <span class="ml-1 {completionDeltaClass(b.completion_delta)}"
+                                title={deltaTitle(b.completion_delta)}>{deltaText(b.completion_delta)}</span>
                         {/if}
                       </td>
                     </tr>
@@ -442,6 +457,12 @@
           </table>
         </div>
       {/each}
+      <p class="text-xs text-text-secondary">
+        Deltas compare each surface with your manual plays. A delta marked
+        <span class="opacity-60">≈</span> is smaller than its own margin of error at this
+        sample size — it can't be told apart from no difference, however big it looks.
+        Hover any delta for its range.
+      </p>
     {:else}
       <p class="text-sm text-text-secondary">
         No plays recorded yet. Play something from For You, Discover, or a mix.

web/src/routes/settings/settings.test.ts

@@ -241,6 +241,71 @@ describe('Settings page — Recommendation metrics card', () => {
     expect(screen.queryByText(/Taste picks/)).not.toBeInTheDocument();
   });
 
+  // #2495: the card used to render a delta computed client-side with no notion
+  // of uncertainty, so a -12 on 59 plays looked exactly as solid as a -6 on 400.
+  // Deltas now arrive from the server with a margin, and an indistinguishable
+  // one is marked with "≈" and dimmed rather than coloured.
+  test('a delta smaller than its margin is marked as indistinguishable', async () => {
+    setupPage();
+    metricsMock.data = {
+      window_days: 30,
+      baseline: metric('manual', 'Manual library plays', { plays: 400, skip_rate: 0.27 }),
+      groups: [
+        {
+          intent: 'discovery',
+          label: 'Discovery mixes',
+          surfaces: [
+            metric('discover', 'Discover', {
+              plays: 59,
+              skip_rate: 0.153,
+              // 13.3pp gap, but the margin at n=59 is wider than the gap.
+              skip_delta: { delta_pp: -13.3, margin_pp: 14.5, distinguishable: false },
+              completion_delta: { delta_pp: 28.0, margin_pp: 12.1, distinguishable: true }
+            })
+          ]
+        }
+      ]
+    };
+    render(SettingsPage);
+    await waitFor(() => expect(screen.getByText('Discover')).toBeInTheDocument());
+
+    // The indistinguishable skip delta is prefixed and explained on hover.
+    const skip = screen.getByText('≈-13');
+    expect(skip).toBeInTheDocument();
+    expect(skip).toHaveAttribute('title', expect.stringContaining('not distinguishable from zero'));
+    // It must NOT be coloured as a real regression/improvement.
+    expect(skip.className).toContain('opacity-60');
+
+    // The completion delta clears its margin, so it renders plainly.
+    const completion = screen.getByText('+28');
+    expect(completion).toBeInTheDocument();
+    expect(completion.className).not.toContain('opacity-60');
+
+    // And the legend explains the glyph rather than leaving it a mystery.
+    expect(screen.getByText(/smaller than its own margin of error/i)).toBeInTheDocument();
+  });
+
+  // A delta is omitted entirely when the samples are too thin for a margin to
+  // mean anything — the server decides that, and the cell must simply show the
+  // rate rather than a bare "0".
+  test('a surface with no delta shows its rate and nothing else', async () => {
+    setupPage();
+    metricsMock.data = {
+      window_days: 30,
+      baseline: metric('manual', 'Manual library plays', { plays: 400 }),
+      groups: [
+        {
+          intent: 'go_to',
+          label: 'Go-to surfaces',
+          surfaces: [metric('radio', 'Radio', { plays: 1, skip_rate: 0 })]
+        }
+      ]
+    };
+    render(SettingsPage);
+    await waitFor(() => expect(screen.getByText('Radio')).toBeInTheDocument());
+    expect(screen.queryByText(/≈/)).not.toBeInTheDocument();
+  });
+
   test('surfaces without a breakdown render no toggle and no sub-rows', async () => {
     setupPage();
     metricsMock.data = {