diff --git a/go.sum b/go.sum
index c5c27bdca6c6c..17f64067a1eab 100644
--- a/go.sum
+++ b/go.sum
@@ -465,6 +465,7 @@ github.com/russross/blackfriday v1.5.2/go.mod h1:JO/DiYxRf+HjHt06OyowR9PTA263kcR
 github.com/russross/blackfriday/v2 v2.0.1/go.mod h1:+Rmxgy9KzJVeS9/2gXHxylqXiyQDYRxCVz55jmeOWTM=
 github.com/sasha-s/go-deadlock v0.2.0/go.mod h1:StQn567HiB1fF2yJ44N9au7wOhrPS3iZqiDbRupzT10=
 github.com/satori/go.uuid v1.2.0/go.mod h1:dA0hQrYB0VpLJoorglMZABFdXlWrHn1NEOzdhQKdks0=
+github.com/sergi/go-diff v1.0.1-0.20180205163309-da645544ed44 h1:tB9NOR21++IjLyVx3/PCPhWMwqGNCMQEH96A6dMZ/gc=
 github.com/sergi/go-diff v1.0.1-0.20180205163309-da645544ed44/go.mod h1:0CfEIISq7TuYL3j771MWULgwwjU+GofnZX9QAmXWZgo=
 github.com/shirou/gopsutil v2.19.10+incompatible/go.mod h1:5b4v6he4MtMOwMlS0TUMTu2PcXUg8+E1lC7eC3UO/RA=
 github.com/shirou/gopsutil v3.20.12+incompatible h1:6VEGkOXP/eP4o2Ilk8cSsX0PhOEfX6leqAnD+urrp9M=
diff --git a/statistics/histogram.go b/statistics/histogram.go
index d5a1a22742e1d..58df8dd1a22bc 100644
--- a/statistics/histogram.go
+++ b/statistics/histogram.go
@@ -23,6 +23,7 @@ import (
 	"unsafe"
 
 	"github.com/pingcap/errors"
+	"github.com/pingcap/failpoint"
 	"github.com/pingcap/parser/charset"
 	"github.com/pingcap/parser/model"
 	"github.com/pingcap/parser/mysql"
@@ -1233,15 +1234,20 @@ func (idx *Index) GetRowCount(sc *stmtctx.StatementContext, coll *HistColl, inde
 		if isSingleCol && lowIsNull {
 			totalCount += float64(idx.NullCount)
 		}
+		expBackoffSuccess := false
 		// Due to the limitation of calcFraction and convertDatumToScalar, the histogram actually won't estimate anything.
 		// If the first column's range is point.
 		if rangePosition := GetOrdinalOfRangeCond(sc, indexRange); rangePosition > 0 && idx.StatsVer == Version2 && coll != nil {
-			expBackoffSel, err := idx.expBackoffEstimation(sc, coll, indexRange)
+			var expBackoffSel float64
+			expBackoffSel, expBackoffSuccess, err = idx.expBackoffEstimation(sc, coll, indexRange)
 			if err != nil {
 				return 0, err
 			}
-			totalCount += expBackoffSel * idx.TotalRowCount()
-		} else {
+			if expBackoffSuccess {
+				totalCount += expBackoffSel * idx.TotalRowCount()
+			}
+		}
+		if !expBackoffSuccess {
 			totalCount += idx.BetweenRowCount(l, r)
 		}
 	}
@@ -1252,7 +1258,7 @@ func (idx *Index) GetRowCount(sc *stmtctx.StatementContext, coll *HistColl, inde
 }
 
 // expBackoffEstimation estimate the multi-col cases following the Exponential Backoff. See comment below for details.
-func (idx *Index) expBackoffEstimation(sc *stmtctx.StatementContext, coll *HistColl, indexRange *ranger.Range) (float64, error) {
+func (idx *Index) expBackoffEstimation(sc *stmtctx.StatementContext, coll *HistColl, indexRange *ranger.Range) (float64, bool, error) {
 	tmpRan := []*ranger.Range{
 		{
 			LowVal:  make([]types.Datum, 1),
@@ -1286,7 +1292,7 @@ func (idx *Index) expBackoffEstimation(sc *stmtctx.StatementContext, coll *HistC
 			continue
 		}
 		if err != nil {
-			return 0, err
+			return 0, false, err
 		}
 		singleColumnEstResults = append(singleColumnEstResults, count)
 	}
@@ -1299,14 +1305,20 @@ func (idx *Index) expBackoffEstimation(sc *stmtctx.StatementContext, coll *HistC
 	for i := 0; i < l && i < 4; i++ {
 		singleColumnEstResults[i] = singleColumnEstResults[i] / float64(coll.Count)
 	}
+	failpoint.Inject("cleanEstResults", func() {
+		singleColumnEstResults = singleColumnEstResults[:0]
+		l = 0
+	})
 	if l == 1 {
-		return singleColumnEstResults[0], nil
+		return singleColumnEstResults[0], true, nil
 	} else if l == 2 {
-		return singleColumnEstResults[0] * math.Sqrt(singleColumnEstResults[1]), nil
+		return singleColumnEstResults[0] * math.Sqrt(singleColumnEstResults[1]), true, nil
 	} else if l == 3 {
-		return singleColumnEstResults[0] * math.Sqrt(singleColumnEstResults[1]) * math.Sqrt(math.Sqrt(singleColumnEstResults[2])), nil
+		return singleColumnEstResults[0] * math.Sqrt(singleColumnEstResults[1]) * math.Sqrt(math.Sqrt(singleColumnEstResults[2])), true, nil
+	} else if l == 0 {
+		return 0, false, nil
 	}
-	return singleColumnEstResults[0] * math.Sqrt(singleColumnEstResults[1]) * math.Sqrt(math.Sqrt(singleColumnEstResults[2])) * math.Sqrt(math.Sqrt(math.Sqrt(singleColumnEstResults[3]))), nil
+	return singleColumnEstResults[0] * math.Sqrt(singleColumnEstResults[1]) * math.Sqrt(math.Sqrt(singleColumnEstResults[2])) * math.Sqrt(math.Sqrt(math.Sqrt(singleColumnEstResults[3]))), true, nil
 }
 
 type countByRangeFunc = func(*stmtctx.StatementContext, int64, []*ranger.Range) (float64, error)
diff --git a/statistics/integration_test.go b/statistics/integration_test.go
index 4d75569cdf41d..6bb4ae09dac36 100644
--- a/statistics/integration_test.go
+++ b/statistics/integration_test.go
@@ -14,6 +14,7 @@ package statistics_test
 
 import (
 	. "github.com/pingcap/check"
+	"github.com/pingcap/failpoint"
 	"github.com/pingcap/parser/model"
 	"github.com/pingcap/tidb/domain"
 	"github.com/pingcap/tidb/kv"
@@ -203,14 +204,23 @@ func (s *testIntegrationSuite) TestExpBackoffEstimation(c *C) {
 		output [][]string
 	)
 	s.testData.GetTestCases(c, &input, &output)
+	inputLen := len(input)
 	// The test cases are:
 	// Query a = 1, b = 1, c = 1, d >= 3 and d <= 5 separately. We got 5, 3, 2, 3.
 	// And then query and a = 1 and b = 1 and c = 1 and d >= 3 and d <= 5. It's result should follow the exp backoff,
 	// which is 2/5 * (3/5)^{1/2} * (3/5)*{1/4} * 1^{1/8} * 5 = 1.3634.
-	for i := 0; i < len(input); i++ {
+	for i := 0; i < inputLen-1; i++ {
 		s.testData.OnRecord(func() {
 			output[i] = s.testData.ConvertRowsToStrings(tk.MustQuery(input[i]).Rows())
 		})
 		tk.MustQuery(input[i]).Check(testkit.Rows(output[i]...))
 	}
+
+	// The last case is that no column is loaded and we get no stats at all.
+	c.Assert(failpoint.Enable("github.com/pingcap/tidb/statistics/cleanEstResults", `return(true)`), IsNil)
+	s.testData.OnRecord(func() {
+		output[inputLen-1] = s.testData.ConvertRowsToStrings(tk.MustQuery(input[inputLen-1]).Rows())
+	})
+	tk.MustQuery(input[inputLen-1]).Check(testkit.Rows(output[inputLen-1]...))
+	c.Assert(failpoint.Disable("github.com/pingcap/tidb/statistics/cleanEstResults"), IsNil)
 }
diff --git a/statistics/testdata/integration_suite_in.json b/statistics/testdata/integration_suite_in.json
index 733a1203f0c7c..61f4badc3bb72 100644
--- a/statistics/testdata/integration_suite_in.json
+++ b/statistics/testdata/integration_suite_in.json
@@ -6,6 +6,7 @@
       "explain select * from exp_backoff where b = 1",
       "explain select * from exp_backoff where c = 1",
       "explain select * from exp_backoff where d >= 3 and d <= 5",
+      "explain select * from exp_backoff where a = 1 and b = 1 and c = 1 and d >= 3 and d<= 5",
       "explain select * from exp_backoff where a = 1 and b = 1 and c = 1 and d >= 3 and d<= 5"
     ]
   }
diff --git a/statistics/testdata/integration_suite_out.json b/statistics/testdata/integration_suite_out.json
index f8b3d60714869..d5f6ff224a282 100644
--- a/statistics/testdata/integration_suite_out.json
+++ b/statistics/testdata/integration_suite_out.json
@@ -24,6 +24,10 @@
       [
         "IndexReader_6 1.36 root  index:IndexRangeScan_5",
         "└─IndexRangeScan_5 1.36 cop[tikv] table:exp_backoff, index:idx(a, b, c, d) range:[1 1 1 3,1 1 1 5], keep order:false"
+      ],
+      [
+        "IndexReader_6 0.00 root  index:IndexRangeScan_5",
+        "└─IndexRangeScan_5 0.00 cop[tikv] table:exp_backoff, index:idx(a, b, c, d) range:[1 1 1 3,1 1 1 5], keep order:false"
       ]
     ]
   }