diff --git a/docs/changelog/144562.yaml b/docs/changelog/144562.yaml
new file mode 100644
index 0000000000000..fa0931ae3b134
--- /dev/null
+++ b/docs/changelog/144562.yaml
@@ -0,0 +1,5 @@
+area: Search
+issues: []
+pr: 144562
+summary: Adjust the formula for "adaptive replica selection"
+type: bug
diff --git a/server/src/main/java/org/elasticsearch/node/ResponseCollectorService.java b/server/src/main/java/org/elasticsearch/node/ResponseCollectorService.java
index 633cd07265170..933e98ea3c1e2 100644
--- a/server/src/main/java/org/elasticsearch/node/ResponseCollectorService.java
+++ b/server/src/main/java/org/elasticsearch/node/ResponseCollectorService.java
@@ -17,6 +17,7 @@
 import org.elasticsearch.common.io.stream.StreamInput;
 import org.elasticsearch.common.io.stream.StreamOutput;
 import org.elasticsearch.common.io.stream.Writeable;
+import org.elasticsearch.common.util.FeatureFlag;
 import org.elasticsearch.common.util.Maps;
 import org.elasticsearch.common.util.concurrent.ConcurrentCollections;
 
@@ -38,6 +39,8 @@ public final class ResponseCollectorService implements ClusterStateListener {
      */
     public static final double ALPHA = 0.3;
 
+    public static final FeatureFlag ARS_FORMULA_ADJUSTMENT_FEATURE_FLAG = new FeatureFlag("ars_formula_adjustment");
+
     private final ConcurrentMap<String, NodeStatistics> nodeIdToStats = ConcurrentCollections.newConcurrentMap();
 
     public ResponseCollectorService(ClusterService clusterService) {
@@ -172,8 +175,12 @@ private double innerRank(long outstandingRequests) {
             // defines service time as the inverse of service rate (muBarS).
             double muBarSInverse = serviceTime / FACTOR;
 
-            // The final formula
-            return rS - muBarSInverse + Math.pow(qHatS, queueAdjustmentFactor) * muBarSInverse;
+            double innerRank = Math.pow(qHatS, queueAdjustmentFactor) * muBarSInverse;
+            // When the feature flag is enabled, the rS - muBarSInverse term is dropped.
+            if (ARS_FORMULA_ADJUSTMENT_FEATURE_FLAG.isEnabled() == false) {
+                innerRank += rS - muBarSInverse;
+            }
+            return innerRank;
         }
 
         public double rank(long outstandingRequests) {
diff --git a/server/src/test/java/org/elasticsearch/action/admin/cluster/node/stats/ComputedNodeStatsTests.java b/server/src/test/java/org/elasticsearch/action/admin/cluster/node/stats/ComputedNodeStatsTests.java
index dc61e42398551..77dcdd3318edf 100644
--- a/server/src/test/java/org/elasticsearch/action/admin/cluster/node/stats/ComputedNodeStatsTests.java
+++ b/server/src/test/java/org/elasticsearch/action/admin/cluster/node/stats/ComputedNodeStatsTests.java
@@ -9,6 +9,7 @@
 
 package org.elasticsearch.action.admin.cluster.node.stats;
 
+import org.elasticsearch.node.ResponseCollectorService;
 import org.elasticsearch.node.ResponseCollectorService.ComputedNodeStats;
 import org.elasticsearch.test.ESTestCase;
 
@@ -19,13 +20,26 @@
  */
 public class ComputedNodeStatsTests extends ESTestCase {
 
+    private static final boolean ARS_ADJUSTMENT = ResponseCollectorService.ARS_FORMULA_ADJUSTMENT_FEATURE_FLAG.isEnabled();
+
     public void testBasicInvariants() {
-        // When queue size estimate is 0, the rank should equal response time.
-        ComputedNodeStats stats = createStats(0, 150, 100);
-        assertThat(stats.rank(0), equalTo(150.0));
+        if (ARS_ADJUSTMENT) {
+            // With the adjustment, rank = qHatS^3 * muBarSInverse.
+            // When queueSize=0 and outstandingRequests=0: qHatS = 1, so rank = muBarSInverse = serviceTime.
+            ComputedNodeStats stats = createStats(0, 150, 100);
+            assertThat(stats.rank(0), equalTo(100.0));
+
+            stats = createStats(0, 20, 19);
+            assertThat(stats.rank(0), equalTo(19.0));
+        } else {
+            // Without the adjustment, rank = rS - muBarSInverse + qHatS^3 * muBarSInverse.
+            // When queueSize=0 and outstandingRequests=0: qHatS = 1, so rank = rS.
+            ComputedNodeStats stats = createStats(0, 150, 100);
+            assertThat(stats.rank(0), equalTo(150.0));
 
-        stats = createStats(0, 20, 19);
-        assertThat(stats.rank(0), equalTo(20.0));
+            stats = createStats(0, 20, 19);
+            assertThat(stats.rank(0), equalTo(20.0));
+        }
     }
 
     public void testParameterScaling() {
@@ -38,14 +52,16 @@ public void testParameterScaling() {
         second = createStats(1, 200, 200);
         assertTrue(first.rank(3) < second.rank(3));
 
-        // A larger response time should always result in a larger rank.
-        first = createStats(2, 150, 100);
-        second = createStats(2, 200, 100);
-        assertTrue(first.rank(1) < second.rank(1));
+        if (ARS_ADJUSTMENT == false) {
+            // A larger response time should always result in a larger rank (only when the response time term is included).
+            first = createStats(2, 150, 100);
+            second = createStats(2, 200, 100);
+            assertTrue(first.rank(1) < second.rank(1));
 
-        first = createStats(2, 150, 150);
-        second = createStats(2, 200, 150);
-        assertTrue(first.rank(1) < second.rank(1));
+            first = createStats(2, 150, 150);
+            second = createStats(2, 200, 150);
+            assertTrue(first.rank(1) < second.rank(1));
+        }
 
         // More queued requests should always result in a larger rank.
         first = createStats(2, 150, 100);
diff --git a/server/src/test/java/org/elasticsearch/node/ResponseCollectorServiceTests.java b/server/src/test/java/org/elasticsearch/node/ResponseCollectorServiceTests.java
index acfaabaf3910c..ca8b64d930d6a 100644
--- a/server/src/test/java/org/elasticsearch/node/ResponseCollectorServiceTests.java
+++ b/server/src/test/java/org/elasticsearch/node/ResponseCollectorServiceTests.java
@@ -139,4 +139,21 @@ public void testNodeRemoval() throws Exception {
         assertTrue(nodeStats.containsKey("node1"));
         assertFalse(nodeStats.containsKey("node2"));
     }
+
+    public void testArsFormulaAdjustmentFeatureFlag() {
+        // 100ms response time, 10ms service time
+        collector.addNodeStatistics("node1", 1, 100 * 1_000_000L, 10 * 1_000_000L);
+        double rank = collector.getAllNodeStatistics().get("node1").rank(1);
+
+        if (ResponseCollectorService.ARS_FORMULA_ADJUSTMENT_FEATURE_FLAG.isEnabled()) {
+            // With the adjustment enabled, the response time component (rS - muBarSInverse) is dropped,
+            // so rank should equal just the queue-based term: qHatS^3 * muBarSInverse
+            // qHatS = 1 + 1*1 + 1 = 3, muBarSInverse = 10ms, so rank = 27 * 10 = 270
+            assertThat(rank, equalTo(270.0));
+        } else {
+            // Without the adjustment, rank = (rS - muBarSInverse) + qHatS^3 * muBarSInverse
+            // = (100 - 10) + 270 = 360
+            assertThat(rank, equalTo(360.0));
+        }
+    }
 }