diff --git a/public/app/features/trails/MetricSelectScene.tsx b/public/app/features/trails/MetricSelectScene.tsx
index 995a012db44..4912cfc1e6c 100644
--- a/public/app/features/trails/MetricSelectScene.tsx
+++ b/public/app/features/trails/MetricSelectScene.tsx
@@ -1,5 +1,4 @@
 import { css } from '@emotion/css';
-import leven from 'leven';
 import { debounce } from 'lodash';
 import React, { useCallback } from 'react';
 
@@ -29,6 +28,7 @@ import { MetricCategoryCascader } from './MetricCategory/MetricCategoryCascader'
 import { MetricScene } from './MetricScene';
 import { SelectMetricAction } from './SelectMetricAction';
 import { hideEmptyPreviews } from './hideEmptyPreviews';
+import { sortRelatedMetrics } from './relatedMetrics';
 import { getVariablesWithMetricConstant, trailDS, VAR_DATASOURCE, VAR_FILTERS_EXPR, VAR_METRIC_NAMES } from './shared';
 import { getColorByIndex, getTrailFor } from './utils';
 
@@ -431,22 +431,6 @@ function getCardPanelFor(metric: string) {
     .build();
 }
 
-// Computes the Levenshtein distance between two strings, twice, once for the first half and once for the whole string.
-function sortRelatedMetrics(metricList: string[], metric: string) {
-  return metricList.sort((aValue, bValue) => {
-    const aSplit = aValue.split('_');
-    const aHalf = aSplit.slice(0, aSplit.length / 2).join('_');
-
-    const bSplit = bValue.split('_');
-    const bHalf = bSplit.slice(0, bSplit.length / 2).join('_');
-
-    return (
-      (leven(aHalf, metric!) || 0 + (leven(aValue, metric!) || 0)) -
-      (leven(bHalf, metric!) || 0 + (leven(bValue, metric!) || 0))
-    );
-  });
-}
-
 function getStyles(theme: GrafanaTheme2) {
   return {
     container: css({
diff --git a/public/app/features/trails/relatedMetrics.ts b/public/app/features/trails/relatedMetrics.ts
new file mode 100644
index 00000000000..9aaf24745e1
--- /dev/null
+++ b/public/app/features/trails/relatedMetrics.ts
@@ -0,0 +1,42 @@
+import leven from 'leven';
+
+export function sortRelatedMetrics(metricList: string[], metric: string) {
+  return metricList.sort((aValue, bValue) => {
+    const a = getLevenDistances(aValue, metric);
+    const b = getLevenDistances(bValue, metric);
+
+    return a.halfLeven + a.wholeLeven - (b.halfLeven + b.wholeLeven);
+  });
+}
+
+type LevenDistances = { halfLeven: number; wholeLeven: number };
+type TargetToLevenDistances = Map<string, LevenDistances>;
+
+const metricToTargetLevenDistances = new Map<string, TargetToLevenDistances>();
+
+// Provides the Levenshtein distance between a metric to be sorted
+// and a targetMetric compared to which all other metrics are being sorted
+// There are two distances: once for the first half and once for the whole string.
+// This operation is not expected to be symmetric; order of parameters matters
+// since only `metric` is split.
+function getLevenDistances(metric: string, targetMetric: string) {
+  let targetToDistances: TargetToLevenDistances | undefined = metricToTargetLevenDistances.get(metric);
+  if (!targetToDistances) {
+    targetToDistances = new Map<string, LevenDistances>();
+    metricToTargetLevenDistances.set(metric, targetToDistances);
+  }
+
+  let distances: LevenDistances | undefined = targetToDistances.get(targetMetric);
+  if (!distances) {
+    const metricSplit = metric.split('_');
+    const metricHalf = metricSplit.slice(0, metricSplit.length / 2).join('_');
+
+    const halfLeven = leven(metricHalf, targetMetric!) || 0;
+    const wholeLeven = leven(metric, targetMetric!) || 0;
+
+    distances = { halfLeven, wholeLeven };
+    targetToDistances.set(targetMetric, distances);
+  }
+
+  return distances;
+}