feat: show sensitivity bracket around required average

After the binary search converges, also simulate predicted rating at
required±1 average. Display the three rows in the modal so the user can
see how sharp the requirement is — e.g. whether averaging 1 point lower
costs them 1 point of predicted rating or 5.

public/css/players.css

@@ -360,3 +360,24 @@
     gap: 12px;
     align-items: flex-start;
 }
+
+.target-rating-result .sensitivity {
+    margin-top: 12px;
+    padding-top: 12px;
+    border-top: 1px dashed var(--border);
+}
+
+.target-rating-result .sensitivity-heading {
+    font-size: 0.9em;
+    color: var(--text-muted);
+    margin-bottom: 4px;
+}
+
+.target-rating-result .sensitivity-row {
+    font-variant-numeric: tabular-nums;
+    padding-left: 12px;
+}
+
+.target-rating-result .sensitivity-row.is-target {
+    font-weight: 600;
+}

public/js/players.js

@@ -647,6 +647,10 @@ async function calculateTargetRating(event) {
         mutedLine.textContent = 'Across ' + data.rounds + ' synthetic rounds before the next PDGA update.';
         summary.appendChild(mutedLine);
 
+        if (data.sensitivity) {
+            renderSensitivity(data.sensitivity, summary);
+        }
+
         if (data.warning) {
             _targetResultMsg(summary, 'warning', data.warning);
         }
@@ -666,6 +670,30 @@ function closeTargetRatingModal(event) {
     document.getElementById('target-rating-modal').style.display = 'none';
 }
 
+function renderSensitivity(sensitivity, container) {
+    const wrapper = document.createElement('div');
+    wrapper.className = 'sensitivity';
+
+    const heading = document.createElement('div');
+    heading.className = 'sensitivity-heading';
+    heading.textContent = 'Sensitivity:';
+    wrapper.appendChild(heading);
+
+    const rows = [
+        { row: sensitivity.lower, isTarget: false },
+        { row: sensitivity.target, isTarget: true },
+        { row: sensitivity.upper, isTarget: false }
+    ];
+    for (const { row, isTarget } of rows) {
+        const line = document.createElement('div');
+        line.className = 'sensitivity-row' + (isTarget ? ' is-target' : '');
+        line.textContent = 'Average ' + row.average + ' → predicted ' + row.predicted + (isTarget ? ' (target)' : '');
+        wrapper.appendChild(line);
+    }
+
+    container.appendChild(wrapper);
+}
+
 function renderNoHistoryPrompt(pdgaNumber, container) {
     const wrapper = document.createElement('div');
     wrapper.className = 'no-history-prompt';

src/routes/players.js

@@ -495,7 +495,8 @@ router.post('/api/calculate-target-rating/:pdgaNumber', async (req, res) => {
       requiredAverage: result.requiredAverage,
       predictedRating: result.simulatedPredicted,
       warning: result.warning,
-      iterations: result.iterations
+      iterations: result.iterations,
+      sensitivity: result.sensitivity
     });
   } catch (err) {
     logger.error(`Target rating calc failed for PDGA ${pdgaNum}: ${err.message}`);

src/services/target-rating-calculator.js

@@ -58,6 +58,14 @@ function calculateRequiredAverage(roundRatings, targetRating, numRounds) {
     warning = 'Could not converge precisely; result is approximate.';
   }
 
+  const lowerAvg = Math.max(400, Math.round((requiredAverage - 1) * 10) / 10);
+  const upperAvg = Math.min(1200, Math.round((requiredAverage + 1) * 10) / 10);
+  const sensitivity = {
+    lower: { average: lowerAvg, predicted: simulate(lowerAvg) },
+    target: { average: requiredAverage, predicted: simulatedPredicted },
+    upper: { average: upperAvg, predicted: simulate(upperAvg) }
+  };
+
   logger.debug(`Target rating calc: target=${targetRating} rounds=${numRounds} → avg=${requiredAverage} (iterations=${iterations}, simulated=${simulatedPredicted})`);
 
   return {
@@ -65,7 +73,8 @@ function calculateRequiredAverage(roundRatings, targetRating, numRounds) {
     currentPredicted,
     simulatedPredicted,
     iterations,
-    warning
+    warning,
+    sensitivity
   };
 }