diff --git a/plan/cbo_test.go b/plan/cbo_test.go
index efceb0ea0fb0..b07f900e6ef2 100644
--- a/plan/cbo_test.go
+++ b/plan/cbo_test.go
@@ -15,6 +15,7 @@ package plan_test
 
 import (
 	"fmt"
+	"time"
 
 	"github.com/juju/errors"
 	. "github.com/pingcap/check"
@@ -34,6 +35,32 @@ var _ = Suite(&testAnalyzeSuite{})
 type testAnalyzeSuite struct {
 }
 
+// CBOWithoutAnalyze tests the plan with stats that only have count info.
+func (s *testAnalyzeSuite) TestCBOWithoutAnalyze(c *C) {
+	defer testleak.AfterTest(c)()
+	store, dom, err := newStoreWithBootstrapWithStatsLease(10 * time.Millisecond)
+	c.Assert(err, IsNil)
+	testKit := testkit.NewTestKit(c, store)
+	defer func() {
+		dom.Close()
+		store.Close()
+	}()
+	testKit.MustExec("use test")
+	testKit.MustExec("drop table if exists t")
+	testKit.MustExec("create table t1 (a int)")
+	testKit.MustExec("create table t2 (a int)")
+	testKit.MustExec("insert into t1 values (1), (2), (3), (4), (5), (6)")
+	testKit.MustExec("insert into t2 values (1), (2), (3), (4), (5), (6)")
+	time.Sleep(1 * time.Second)
+	testKit.MustQuery("explain select * from t1, t2 where t1.a = t2.a").Check(testkit.Rows(
+		"TableScan_9   cop table:t1, range:(-inf,+inf), keep order:false 6",
+		"TableReader_10 HashLeftJoin_7  root data:TableScan_9 6",
+		"TableScan_11   cop table:t2, range:(-inf,+inf), keep order:false 6",
+		"TableReader_12 HashLeftJoin_7  root data:TableScan_11 6",
+		"HashLeftJoin_7  TableReader_10,TableReader_12 root inner join, small:TableReader_12, equal:[eq(test.t1.a, test.t2.a)] 7.499999999999999",
+	))
+}
+
 func constructInsertSQL(i, n int) string {
 	sql := "insert into t (a,b,c,e)values "
 	for j := 0; j < n; j++ {
@@ -307,3 +334,15 @@ func newStoreWithBootstrap() (kv.Storage, *domain.Domain, error) {
 	dom, err := tidb.BootstrapSession(store)
 	return store, dom, errors.Trace(err)
 }
+
+func newStoreWithBootstrapWithStatsLease(lease time.Duration) (kv.Storage, *domain.Domain, error) {
+	store, err := tikv.NewMockTikvStore()
+	if err != nil {
+		return nil, nil, errors.Trace(err)
+	}
+	tidb.SetSchemaLease(0)
+	tidb.SetStatsLease(lease)
+	domain.RunAutoAnalyze = false
+	dom, err := tidb.BootstrapSession(store)
+	return store, dom, errors.Trace(err)
+}
diff --git a/plan/new_physical_plan_builder.go b/plan/new_physical_plan_builder.go
index a0f59658849c..84ca0fc0d671 100644
--- a/plan/new_physical_plan_builder.go
+++ b/plan/new_physical_plan_builder.go
@@ -1040,6 +1040,7 @@ func (p *basePhysicalPlan) getChildrenPossibleProps(prop *requiredProp) [][]*req
 }
 
 func (p *PhysicalHashJoin) getChildrenPossibleProps(prop *requiredProp) [][]*requiredProp {
+	p.expectedCnt = prop.expectedCnt
 	if !prop.isEmpty() {
 		return nil
 	}
diff --git a/plan/stats.go b/plan/stats.go
index a81a69c634e2..e36c4b9cc3b9 100644
--- a/plan/stats.go
+++ b/plan/stats.go
@@ -74,7 +74,7 @@ func (p *DataSource) getStatsProfileByFilter(conds expression.CNFExprs) *statsPr
 	}
 	for i, col := range p.Columns {
 		hist, ok := p.statisticTable.Columns[col.ID]
-		if ok {
+		if ok && hist.NDV > 0 {
 			profile.cardinality[i] = float64(hist.NDV)
 		} else {
 			profile.cardinality[i] = profile.count * distinctFactor
@@ -242,7 +242,7 @@ func (p *LogicalJoin) prepareStatsProfile() *statsProfile {
 	}
 	leftKeyCardinality := getCardinality(leftKeys, p.children[0].Schema(), leftProfile)
 	rightKeyCardinality := getCardinality(rightKeys, p.children[1].Schema(), rightProfile)
-	count := (leftProfile.count * rightProfile.count / leftKeyCardinality / rightKeyCardinality) * math.Min(leftKeyCardinality, rightKeyCardinality)
+	count := leftProfile.count * rightProfile.count / math.Max(leftKeyCardinality, rightKeyCardinality)
 	if p.JoinType == LeftOuterJoin {
 		count = math.Max(count, leftProfile.count)
 	} else if p.JoinType == RightOuterJoin {