diff --git a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/HardcodedGraphStatistics.scala b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/HardcodedGraphStatistics.scala
index c325e8d0ce6d6..f6d993f6a434a 100644
--- a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/HardcodedGraphStatistics.scala
+++ b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/HardcodedGraphStatistics.scala
@@ -27,10 +27,10 @@ case object HardcodedGraphStatistics extends HardcodedGraphStatisticsValues
 
 class HardcodedGraphStatisticsValues extends GraphStatistics {
   val NODES_CARDINALITY = Cardinality(10000)
-  val NODES_WITH_LABEL_SELECTIVITY = Selectivity(0.2)
+  val NODES_WITH_LABEL_SELECTIVITY = Selectivity.of(0.2).get
   val NODES_WITH_LABEL_CARDINALITY = NODES_CARDINALITY * NODES_WITH_LABEL_SELECTIVITY
   val RELATIONSHIPS_CARDINALITY = Cardinality(50000)
-  val INDEX_SELECTIVITY = Selectivity(.02)
+  val INDEX_SELECTIVITY = Selectivity.of(.02).get
 
   def indexSelectivity(label: LabelId, property: PropertyKeyId): Option[Selectivity] =
     Some(INDEX_SELECTIVITY)
diff --git a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/Metrics.scala b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/Metrics.scala
index c6ac07d9453a6..79b1e83b65fda 100644
--- a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/Metrics.scala
+++ b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/Metrics.scala
@@ -84,7 +84,7 @@ case class Cardinality(amount: Double) extends Ordered[Cardinality] {
   def *(that: Selectivity): Cardinality = amount * that.factor
   def +(that: Cardinality): Cardinality = amount + that.amount
   def *(that: Cardinality): Cardinality = amount * that.amount
-  def /(that: Cardinality): Option[Selectivity] = if (that.amount == 0) None else Some(amount / that.amount)
+  def /(that: Cardinality): Option[Selectivity] = if (that.amount == 0) None else Selectivity.of(amount / that.amount)
   def *(that: CostPerRow): Cost = amount * that.cost
   def *(that: Cost): Cost = amount * that.gummyBears
   def ^(a: Int): Cardinality = Math.pow(amount, a)
@@ -153,15 +153,14 @@ object Multiplier {
     Multiplier(Math.max(l.coefficient, r.coefficient))
 }
 
-case class Selectivity(factor: Double) extends Ordered[Selectivity] {
-  def -(other: Selectivity): Selectivity = factor - other.factor
-  def *(other: Selectivity): Selectivity = other.factor * factor
-  def *(other: Multiplier): Selectivity = factor * other.coefficient
-  def ^(a: Int): Selectivity = Math.pow(factor, a)
+case class Selectivity private(factor: Double) extends Ordered[Selectivity] {
+  assert(factor >= 0 && factor <= 1.0)
+  def *(other: Selectivity): Selectivity = Selectivity(other.factor * factor)
+  def ^(a: Int): Selectivity = Selectivity(Math.pow(factor, a))
   def negate: Selectivity = {
     val f = 1.0 - factor
     if (factor == 0 || f < 1)
-      f
+      Selectivity(f)
     else
       Selectivity.CLOSEST_TO_ONE
   }
@@ -170,13 +169,13 @@ case class Selectivity(factor: Double) extends Ordered[Selectivity] {
 }
 
 object Selectivity {
-  def of(value: Double): Option[Selectivity] = if (value.isInfinite || value.isNaN) None else Some(value)
+
+  def of(value: Double): Option[Selectivity] = if (value.isInfinite || value.isNaN || value < 0.0 || value > 1.0) None else Some(Selectivity(value))
 
   val ZERO = Selectivity(0.0d)
   val ONE = Selectivity(1.0d)
   val CLOSEST_TO_ONE = Selectivity(1 - 5.56e-17)    // we can get closer, but this is close enough
 
-  implicit def lift(amount: Double): Selectivity = Selectivity(amount)
 
   implicit def turnSeqIntoSingleSelectivity(p: Seq[Selectivity]): Selectivity =
     p.reduceOption(_ * _).getOrElse(Selectivity(1))
diff --git a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/StatisticsBackedCardinalityModel.scala b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/StatisticsBackedCardinalityModel.scala
index 152535046ad80..77cef6da4b815 100644
--- a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/StatisticsBackedCardinalityModel.scala
+++ b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/StatisticsBackedCardinalityModel.scala
@@ -49,7 +49,7 @@ class StatisticsBackedCardinalityModel(queryGraphCardinalityModel: QueryGraphCar
 
     // Distinct
     case projection: AggregatingQueryProjection if projection.aggregationExpressions.isEmpty =>
-      in * Selectivity(0.95)
+      in * Selectivity.of(0.95).get
 
     // Aggregates
     case _: AggregatingQueryProjection =>
diff --git a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/ExpressionSelectivityCalculator.scala b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/ExpressionSelectivityCalculator.scala
index d5a00191a7212..3814149df2bf1 100644
--- a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/ExpressionSelectivityCalculator.scala
+++ b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/ExpressionSelectivityCalculator.scala
@@ -40,7 +40,7 @@ case class ExpressionSelectivityCalculator(stats: GraphStatistics, combiner: Sel
 
     // WHERE false
     case False() =>
-      Selectivity(0)
+      Selectivity.of(0).get
 
     // WHERE x.prop IN [...]
     case In(Property(Identifier(name), propertyKey), Collection(expressions)) =>
@@ -104,15 +104,13 @@ case class ExpressionSelectivityCalculator(stats: GraphStatistics, combiner: Sel
             stats.indexSelectivity(labelId, propertyKeyId)
 
           case _ =>
-            Some(Selectivity(0))
+            Some(Selectivity.ZERO)
         }
     }
 
-    val expandedSelectivities = Stream.from(0).take(sizeHint).flatMap(_ => indexSelectivities)
+    val itemSelectivity = combiner.orTogetherSelectivities(indexSelectivities).getOrElse(DEFAULT_EQUALITY_SELECTIVITY)
+    val selectivity = combiner.orTogetherSelectivities(1.to(sizeHint).map(_ => itemSelectivity)).getOrElse(DEFAULT_EQUALITY_SELECTIVITY)
 
-    val selectivity: Option[Selectivity] = combiner.orTogetherSelectivities(expandedSelectivities)
-
-    selectivity.
-      getOrElse(DEFAULT_EQUALITY_SELECTIVITY * Multiplier(sizeHint)) // If no index exist, use default equality selectivity
+    selectivity
   }
 }
diff --git a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/SelectivityCombiner.scala b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/SelectivityCombiner.scala
index 1831e86288826..38830d0f6165a 100644
--- a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/SelectivityCombiner.scala
+++ b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/SelectivityCombiner.scala
@@ -49,7 +49,7 @@ case object IndependenceCombiner extends SelectivityCombiner {
   }
 
   private def fromBigDecimal(bigDecimal: math.BigDecimal): Selectivity = {
-    Selectivity(bigDecimal.doubleValue())
+    Selectivity.of(bigDecimal.doubleValue()).get
   }
 }
 
diff --git a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/AssumeIndependenceQueryGraphCardinalityModel.scala b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/AssumeIndependenceQueryGraphCardinalityModel.scala
index 969d8914876e4..1570a29539494 100644
--- a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/AssumeIndependenceQueryGraphCardinalityModel.scala
+++ b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/AssumeIndependenceQueryGraphCardinalityModel.scala
@@ -107,6 +107,6 @@ case class AssumeIndependenceQueryGraphCardinalityModel(stats: GraphStatistics,
 
     val selectivity = combiner.andTogetherSelectivities(expressionSelectivities ++ patternSelectivities.flatten)
 
-    (selectivity.getOrElse(Selectivity(1)), numberOfZeroZeroRels)
+    (selectivity.getOrElse(Selectivity.ONE), numberOfZeroZeroRels)
   }
 }
diff --git a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/PatternSelectivityCalculator.scala b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/PatternSelectivityCalculator.scala
index 9c80cea6058a7..06c2af6148c91 100644
--- a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/PatternSelectivityCalculator.scala
+++ b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/PatternSelectivityCalculator.scala
@@ -43,8 +43,7 @@ case class PatternSelectivityCalculator(stats: GraphStatistics, combiner: Select
   def apply(pattern: PatternRelationship, labels: Map[IdName, Set[LabelName]])
            (implicit semanticTable: SemanticTable, selections: Selections): Selectivity = {
     val allNodes = stats.nodesWithLabelCardinality(None)
-    val lhs = pattern.nodes._1
-    val rhs = pattern.nodes._2
+    val (lhs, rhs) = pattern.nodes
     val labelsOnLhs: Seq[TokenSpec[LabelId]] = mapToLabelTokenSpecs(selections.labelsOnNode(lhs) ++ labels.getOrElse(lhs, Set.empty))
     val labelsOnRhs: Seq[TokenSpec[LabelId]] = mapToLabelTokenSpecs(selections.labelsOnNode(rhs) ++ labels.getOrElse(rhs, Set.empty))
 
@@ -53,7 +52,7 @@ case class PatternSelectivityCalculator(stats: GraphStatistics, combiner: Select
 
     // If either side of our pattern is empty, it's all empty
     if (lhsCardinality == Cardinality.EMPTY || lhsCardinality == Cardinality.EMPTY)
-      Selectivity(1)
+      Selectivity.ONE
     else {
       val types: Seq[TokenSpec[RelTypeId]] = mapToRelTokenSpecs(pattern.types.toSet)
 
@@ -133,12 +132,12 @@ case class PatternSelectivityCalculator(stats: GraphStatistics, combiner: Select
 
   private def calculateLabelSelectivity(specs: Seq[TokenSpec[LabelId]]): Selectivity = {
     val selectivities = specs map {
-      case SpecifiedButUnknown() => Selectivity(0)
+      case SpecifiedButUnknown() => Selectivity.ONE
       case spec: TokenSpec[LabelId] =>
         stats.nodesWithLabelCardinality(spec.id) / stats.nodesWithLabelCardinality(None) getOrElse Selectivity.ZERO
     }
 
-    combiner.andTogetherSelectivities(selectivities).getOrElse(Selectivity(1))
+    combiner.andTogetherSelectivities(selectivities).getOrElse(Selectivity.ONE)
   }
 
   // These two methods should be one, but I failed to conjure up the proper Scala type magic to make it work
diff --git a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/GraphStatistics.scala b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/GraphStatistics.scala
index 26870788250b6..18b42952f69d4 100644
--- a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/GraphStatistics.scala
+++ b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/GraphStatistics.scala
@@ -23,13 +23,13 @@ import org.neo4j.cypher.internal.compiler.v2_2.planner.logical.{Cardinality, Sel
 import org.neo4j.cypher.internal.compiler.v2_2.{LabelId, PropertyKeyId, RelTypeId}
 
 object GraphStatistics {
-  val DEFAULT_RANGE_SELECTIVITY          = Selectivity(0.3)
-  val DEFAULT_PREDICATE_SELECTIVITY      = Selectivity(0.75)
-  val DEFAULT_EQUALITY_SELECTIVITY       = Selectivity(0.1)
+  val DEFAULT_RANGE_SELECTIVITY          = Selectivity.of(0.3).get
+  val DEFAULT_PREDICATE_SELECTIVITY      = Selectivity.of(0.75).get
+  val DEFAULT_EQUALITY_SELECTIVITY       = Selectivity.of(0.1).get
   val DEFAULT_NUMBER_OF_ID_LOOKUPS       = Cardinality(25)
   val DEFAULT_NUMBER_OF_INDEX_LOOKUPS    = Cardinality(25)
   val DEFAULT_LIMIT_CARDINALITY          = Cardinality(75)
-  val DEFAULT_REL_UNIQUENESS_SELECTIVITY = Selectivity(1.0 - 1 / 100 /*rel-cardinality*/)
+  val DEFAULT_REL_UNIQUENESS_SELECTIVITY = Selectivity.of(1.0 - 1.0 / 100 /*rel-cardinality*/).get
 }
 
 trait GraphStatistics {
diff --git a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/QueriedGraphStatistics.scala b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/QueriedGraphStatistics.scala
index 7990cea4a7846..ce93ecba13d84 100644
--- a/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/QueriedGraphStatistics.scala
+++ b/community/cypher/cypher-compiler-2.2/src/main/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/QueriedGraphStatistics.scala
@@ -100,9 +100,9 @@ class QueriedGraphStatistics(graph: GraphDatabaseService, queryContext: QueryCon
       }
 
       if (values.isEmpty)
-        Some(Selectivity(0)) // Avoids division by zero
+        Some(Selectivity.ZERO) // Avoids division by zero
       else
-        Some(Selectivity(1.0 / values.size))
+        Selectivity.of(1.0 / values.size)
     }
   }
 
diff --git a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/DbStructureGraphStatistics.scala b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/DbStructureGraphStatistics.scala
index 66c7f3854fb1f..4d49241bf5bb0 100644
--- a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/DbStructureGraphStatistics.scala
+++ b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/DbStructureGraphStatistics.scala
@@ -41,6 +41,6 @@ class DbStructureGraphStatistics(lookup: DbStructureLookup) extends GraphStatist
    */
   override def indexSelectivity( label: LabelId, property: PropertyKeyId ): Option[Selectivity] = {
     val result = lookup.indexSelectivity( label.id, property.id )
-    if (result.isNaN) None else Some(Selectivity(result))
+    Selectivity.of(result)
   }
 }
diff --git a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/MetricsTest.scala b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/MetricsTest.scala
index 3771381d2b9db..f0dd675ebb11d 100644
--- a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/MetricsTest.scala
+++ b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/MetricsTest.scala
@@ -24,15 +24,15 @@ import org.neo4j.cypher.internal.commons.CypherFunSuite
 class MetricsTest extends CypherFunSuite {
 
   test("negating a selectivity behaves as expected") {
-    Selectivity(.1).negate should not equal Selectivity.ONE
-    Selectivity(5.6e-17).negate should not equal Selectivity.ONE
-    Selectivity(1e-300).negate should not equal Selectivity.ONE
+    Selectivity.of(.1).get.negate should not equal Selectivity.ONE
+    Selectivity.of(5.6e-17).get.negate should not equal Selectivity.ONE
+    Selectivity.of(1e-300).get.negate should not equal Selectivity.ONE
 
     Selectivity.ZERO.negate should equal(Selectivity.ONE)
-    Selectivity(0).negate should equal(Selectivity.ONE)
+    Selectivity.ZERO.negate should equal(Selectivity.ONE)
 
     Selectivity.ONE.negate should equal(Selectivity.ZERO)
-    Selectivity(1).negate should equal(Selectivity.ZERO)
+    Selectivity.ONE.negate should equal(Selectivity.ZERO)
 
     Selectivity.CLOSEST_TO_ONE.negate should not equal Selectivity.ONE
   }
diff --git a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/StatisticsBackedCardinalityModelTest.scala b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/StatisticsBackedCardinalityModelTest.scala
index 4944606c2778a..322b5bae04300 100644
--- a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/StatisticsBackedCardinalityModelTest.scala
+++ b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/StatisticsBackedCardinalityModelTest.scala
@@ -89,7 +89,7 @@ class StatisticsBackedCardinalityModelTest extends CypherFunSuite with LogicalPl
 
   test("aggregations should never increase cardinality") {
     givenPattern("MATCH (a:Person)-[:REL]->() WITH a, count(*) as c MATCH (a)-[:REL]->()").
-      withGraphNodes(1).
+      withGraphNodes(allNodes).
       withLabel('Person -> .1).
       withRelationshipCardinality('Person -> 'REL -> 'Person -> .5).
       shouldHavePlannerQueryCardinality(produceCardinalityModel)(2.5)
diff --git a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/CardinalityTestHelper.scala b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/CardinalityTestHelper.scala
index b1efc41909887..336bf1fe7337e 100644
--- a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/CardinalityTestHelper.scala
+++ b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/CardinalityTestHelper.scala
@@ -41,9 +41,9 @@ trait CardinalityTestHelper extends QueryGraphProducer with CardinalityCustomMat
 
   def combiner: SelectivityCombiner = IndependenceCombiner
 
-  def not(number: Double) = Selectivity(number).negate.factor
-  def and(numbers: Double*) = combiner.andTogetherSelectivities(numbers.map(Selectivity.apply)).get.factor
-  def or(numbers: Double*) = combiner.orTogetherSelectivities(numbers.map(Selectivity.apply)).get.factor
+  def not(number: Double) = Selectivity.of(number).getOrElse(Selectivity.ONE).negate.factor
+  def and(numbers: Double*) = combiner.andTogetherSelectivities(numbers.map(Selectivity.of(_).getOrElse(Selectivity.ONE))).get.factor
+  def or(numbers: Double*) = combiner.orTogetherSelectivities(numbers.map(Selectivity.of(_).getOrElse(Selectivity.ONE))).get.factor
 
   def degree(above: Double, below: Double) = above / below
 
@@ -139,9 +139,9 @@ trait CardinalityTestHelper extends QueryGraphProducer with CardinalityCustomMat
           (labelName, propertyName) match {
             case (Some(lName), Some(pName)) =>
               val selectivity = knownIndexSelectivity.get((lName, pName))
-              selectivity.map(Selectivity.apply)
+              selectivity.map(Selectivity.of(_).getOrElse(Selectivity.ONE))
 
-            case _ => Some(Selectivity(0))
+            case _ => Some(Selectivity.ZERO)
           }
         }
 
diff --git a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/ExpressionSelectivityCalculatorTest.scala b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/ExpressionSelectivityCalculatorTest.scala
index cb5bf852987e1..c0822bd0e2420 100644
--- a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/ExpressionSelectivityCalculatorTest.scala
+++ b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/ExpressionSelectivityCalculatorTest.scala
@@ -39,7 +39,7 @@ class ExpressionSelectivityCalculatorTest extends CypherFunSuite with AstConstru
 
     val stats = mock[GraphStatistics]
     Mockito.when(stats.nodesWithLabelCardinality(None)).thenReturn(1000.0)
-    Mockito.when(stats.indexSelectivity(LabelId(0), PropertyKeyId(0))).thenReturn(Some(Selectivity(0.1d)))
+    Mockito.when(stats.indexSelectivity(LabelId(0), PropertyKeyId(0))).thenReturn(Selectivity.of(0.1d))
 
     val calculator = ExpressionSelectivityCalculator(stats, IndependenceCombiner)
 
diff --git a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/NodeCardinalityEstimatorTest.scala b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/NodeCardinalityEstimatorTest.scala
index e7868bf12b638..32554ed327f5a 100644
--- a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/NodeCardinalityEstimatorTest.scala
+++ b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/NodeCardinalityEstimatorTest.scala
@@ -44,8 +44,8 @@ class NodeCardinalityEstimatorTest extends CypherFunSuite with LogicalPlanningTe
   val hasAnimalOnA: Expression = HasLabels(ident("a"), Seq(LabelName("Animal")_))_
   val hasPersonOnB: Expression = HasLabels(ident("b"), Seq(LabelName("Person")_))_
 
-  val personSelectivity = Selectivity(0.5)
-  val animalSelectivity = Selectivity(0.1)
+  val personSelectivity = Selectivity.of(0.5).get
+  val animalSelectivity = Selectivity.of(0.1).get
 
   test("should estimate node labels") {
     when( selectivityEstimator.apply(hasPersonOnA ) ).thenReturn( personSelectivity )
@@ -106,8 +106,8 @@ class NodeCardinalityEstimatorTest extends CypherFunSuite with LogicalPlanningTe
     val pred1 = mock[Expression]
     val pred2 = mock[Expression]
 
-    when( selectivityEstimator.apply( pred1 ) ).thenReturn( Selectivity( 0.5d ) )
-    when( selectivityEstimator.apply( pred2 ) ).thenReturn( Selectivity( 0.25d ) )
+    when( selectivityEstimator.apply( pred1 ) ).thenReturn( Selectivity.of( 0.5d ).get )
+    when( selectivityEstimator.apply( pred2 ) ).thenReturn( Selectivity.of( 0.25d ).get )
 
     val qg = QueryGraph
       .empty
@@ -122,7 +122,7 @@ class NodeCardinalityEstimatorTest extends CypherFunSuite with LogicalPlanningTe
     val (estimates, used) = estimator(qg)
 
     estimates should equal(Map(
-      IdName("a") -> allNodes * Selectivity( 0.5d ),
+      IdName("a") -> allNodes * Selectivity.of( 0.5d ).get,
       IdName("b") -> allNodes
     ))
 
diff --git a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/SelectivityCombinerTest.scala b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/SelectivityCombinerTest.scala
index eed43b1888978..507db2a52de53 100644
--- a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/SelectivityCombinerTest.scala
+++ b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/SelectivityCombinerTest.scala
@@ -25,27 +25,27 @@ import org.neo4j.cypher.internal.compiler.v2_2.planner.logical.Selectivity
 class SelectivityCombinerTest extends CypherFunSuite {
 
   test("should not lose precision for intermediate numbers") {
-    val selectivities = Seq(Selectivity(1e-10), Selectivity(2e-10))
+    val selectivities = Seq(Selectivity.of(1e-10).get, Selectivity.of(2e-10).get)
 
-    IndependenceCombiner.orTogetherSelectivities(selectivities).get should not equal Selectivity(0)
+    IndependenceCombiner.orTogetherSelectivities(selectivities).get should not equal Selectivity.ZERO
   }
 
   test("should not lose precision for small numbers") {
-    val selectivities = Seq(Selectivity(1e-100), Selectivity(2e-100), Selectivity(1e-300))
+    val selectivities = Seq(Selectivity.of(1e-100).get, Selectivity.of(2e-100).get, Selectivity.of(1e-300).get)
 
-    IndependenceCombiner.orTogetherSelectivities(selectivities).get should not equal Selectivity(0)
+    IndependenceCombiner.orTogetherSelectivities(selectivities).get should not equal Selectivity.ZERO
   }
 
   test("ANDing together works as expected") {
-    val selectivities = Seq(Selectivity(.1), Selectivity(.2), Selectivity.ONE)
+    val selectivities = Seq(Selectivity.of(.1).get, Selectivity.of(.2).get, Selectivity.ONE)
 
-    IndependenceCombiner.andTogetherSelectivities(selectivities).get should equal(Selectivity(0.02))
+    IndependenceCombiner.andTogetherSelectivities(selectivities).get should equal(Selectivity.of(0.02).get)
   }
 
   test("ORing together works as expected") {
-    val selectivities = Seq(Selectivity(.1), Selectivity(.2))
+    val selectivities = Seq(Selectivity.of(.1).get, Selectivity.of(.2).get)
 
-    IndependenceCombiner.orTogetherSelectivities(selectivities).get should equal(Selectivity(0.28))
+    IndependenceCombiner.orTogetherSelectivities(selectivities).get should equal(Selectivity.of(0.28).get)
   }
 
 }
diff --git a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/AssumeIndependenceQueryGraphCardinalityModelTest.scala b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/AssumeIndependenceQueryGraphCardinalityModelTest.scala
index a93e2cf86ec3e..01a564d1b61d5 100644
--- a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/AssumeIndependenceQueryGraphCardinalityModelTest.scala
+++ b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/AssumeIndependenceQueryGraphCardinalityModelTest.scala
@@ -121,8 +121,8 @@ class AssumeIndependenceQueryGraphCardinalityModelTest extends RandomizedCardina
       "MATCH (a:A:B)-->()"
         -> {
         val maxRelCount = N * N * Asel * Bsel
-        val A_relSelectivity = A_STAR_STAR / maxRelCount
-        val B_relSelectivity = B_STAR_STAR / maxRelCount
+        val A_relSelectivity = math.min(A_STAR_STAR / maxRelCount, 1.0)
+        val B_relSelectivity = math.min(B_STAR_STAR / maxRelCount, 1.0)
         val relSelectivity = A_relSelectivity * B_relSelectivity
         A * B * relSelectivity
       },
@@ -132,7 +132,7 @@ class AssumeIndependenceQueryGraphCardinalityModelTest extends RandomizedCardina
         val patternNodeCrossProduct = N * N
         val labelSelectivity = Asel * Bsel
         val maxRelCount = patternNodeCrossProduct * labelSelectivity
-        val relSelectivity = (A_T1_B + A_T2_B) / maxRelCount - (A_T1_B / maxRelCount) * (A_T2_B / maxRelCount)
+        val relSelectivity = or(A_T1_B / maxRelCount, A_T2_B / maxRelCount)
         patternNodeCrossProduct * labelSelectivity * relSelectivity
       },
 
@@ -153,8 +153,8 @@ class AssumeIndependenceQueryGraphCardinalityModelTest extends RandomizedCardina
         val patternNodeCrossProduct = N * N
         val labelSelectivity = Asel * Dsel
         val maxRelCount = patternNodeCrossProduct * labelSelectivity
-        val relSelectivityT1 = (A_T1_STAR / maxRelCount) * (D_T1_STAR / maxRelCount)
-        val relSelectivityT2 = (A_T2_STAR / maxRelCount) * (D_T2_STAR / maxRelCount)
+        val relSelectivityT1 = and(A_T1_STAR / maxRelCount, D_T1_STAR / maxRelCount)
+        val relSelectivityT2 = and(A_T2_STAR / maxRelCount, D_T2_STAR / maxRelCount)
         val relSelectivity = or(relSelectivityT1, relSelectivityT2)
         patternNodeCrossProduct * labelSelectivity * relSelectivity
       },
@@ -168,8 +168,8 @@ class AssumeIndependenceQueryGraphCardinalityModelTest extends RandomizedCardina
         val patternNodeCrossProduct = N * N
         val labelSelectivity = Asel * Bsel * Csel * Dsel
         val maxRelCount = patternNodeCrossProduct * labelSelectivity
-        val relSelT1 = (A_T1_C / maxRelCount) * (A_T1_D / maxRelCount) * (B_T1_C / maxRelCount) * (B_T1_D / maxRelCount)
-        val relSelT2 = (A_T2_C / maxRelCount) * (A_T2_D / maxRelCount) * (B_T2_C / maxRelCount) * (B_T2_D / maxRelCount)
+        val relSelT1 = and(A_T1_C / maxRelCount, A_T1_D / maxRelCount, B_T1_C / maxRelCount, B_T1_D / maxRelCount)
+        val relSelT2 = and(A_T2_C / maxRelCount, A_T2_D / maxRelCount, B_T2_C / maxRelCount, B_T2_D / maxRelCount)
         val relSelectivity = or(relSelT1, relSelT2)
         patternNodeCrossProduct * labelSelectivity * relSelectivity
       },
diff --git a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/PatternSelectivityCalculatorTest.scala b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/PatternSelectivityCalculatorTest.scala
index 641468eb14b80..f5ddd49ea2012 100644
--- a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/PatternSelectivityCalculatorTest.scala
+++ b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/planner/logical/cardinality/assumeIndependence/PatternSelectivityCalculatorTest.scala
@@ -21,6 +21,8 @@ package org.neo4j.cypher.internal.compiler.v2_2.planner.logical.cardinality.assu
 
 import org.mockito.Matchers.any
 import org.mockito.Mockito._
+import org.mockito.invocation.InvocationOnMock
+import org.mockito.stubbing.Answer
 import org.neo4j.cypher.internal.commons.CypherFunSuite
 import org.neo4j.cypher.internal.compiler.v2_2.LabelId
 import org.neo4j.cypher.internal.compiler.v2_2.ast.{AstConstructionTestSupport, HasLabels, LabelName}
@@ -66,7 +68,7 @@ class PatternSelectivityCalculatorTest extends CypherFunSuite with LogicalPlanCo
     implicit val selections = Selections(Set(Predicate(Set[IdName]("a"), HasLabels(ident("a"), Seq(label))(pos))))
     val result = calculator.apply(relationship, Map(IdName("a") -> Set(label)))
 
-    result should equal(Selectivity(42))
+    result should equal(Selectivity.ONE)
   }
 
   test("handles variable length paths over 32 in length") {
@@ -83,6 +85,34 @@ class PatternSelectivityCalculatorTest extends CypherFunSuite with LogicalPlanCo
     implicit val selections = Selections(Set(Predicate(Set[IdName]("a"), HasLabels(ident("a"), Seq(label))(pos))))
     val result = calculator.apply(relationship, Map(IdName("a") -> Set(label)))
 
-    result should equal(Selectivity(Math.pow(3, 32)))
+    result should equal(Selectivity.ONE)
+  }
+
+  test("should not produce selectivities larger than 1.0") {
+    val stats: GraphStatistics = mock[GraphStatistics]
+    when(stats.nodesWithLabelCardinality(any())).thenAnswer(new Answer[Cardinality] {
+      override def answer(invocationOnMock: InvocationOnMock): Cardinality = {
+        val arg = invocationOnMock.getArguments()(0).asInstanceOf[Option[LabelId]]
+        arg match {
+          case None => Cardinality(10)
+          case Some(_) => Cardinality(1)
+        }
+      }
+    })
+    when(stats.cardinalityByLabelsAndRelationshipType(any(), any(), any())).thenReturn(Cardinality(42))
+
+    val calculator = PatternSelectivityCalculator(stats, IndependenceCombiner)
+    val relationship = PatternRelationship("r", ("a", "b"), Direction.OUTGOING, Seq.empty, SimplePatternLength)
+
+    val labels = new mutable.HashMap[String, LabelId]()
+    for (i <- 1 to 100) labels.put(i.toString, LabelId(i))
+    val labelNames = labels.keys.map(LabelName(_)(pos))
+    val predicates = labelNames.map(l => Predicate(Set[IdName]("a"), HasLabels(ident("a"), Seq(l))(pos))).toSet
+
+    implicit val semanticTable = new SemanticTable(resolvedLabelIds = labels)
+    implicit val selections = Selections(predicates)
+    val result = calculator.apply(relationship, Map.empty)
+
+    result should equal(Selectivity.ONE)
   }
 }
diff --git a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/GraphStatisticsSnapshotTest.scala b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/GraphStatisticsSnapshotTest.scala
index fcd1dac16b0a5..a38bb0058d09c 100644
--- a/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/GraphStatisticsSnapshotTest.scala
+++ b/community/cypher/cypher-compiler-2.2/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/GraphStatisticsSnapshotTest.scala
@@ -35,7 +35,7 @@ class GraphStatisticsSnapshotTest extends CypherFunSuite {
       Cardinality(relTypeId.fold(5000)(_.id * 10) * FACTOR)
 
     def indexSelectivity(label: LabelId, property: PropertyKeyId): Option[Selectivity] =
-      Some(1.0 / ((property.id + 1) * FACTOR))
+      Selectivity.of(1.0 / ((property.id + 1) * FACTOR))
   }
 
   test("records queries and its observed values") {
diff --git a/community/cypher/cypher/CHANGES.txt b/community/cypher/cypher/CHANGES.txt
index 7187ba0585893..6e397254e5519 100644
--- a/community/cypher/cypher/CHANGES.txt
+++ b/community/cypher/cypher/CHANGES.txt
@@ -1,5 +1,6 @@
 2.2.6
 -----
+o Fixes #5336 - Properly handle matching on multiple labels
 o Fixes #5195 - USING INDEX hints breaks some queries
 
 2.2.5
diff --git a/community/cypher/cypher/src/test/scala/org/neo4j/cypher/MatchAcceptanceTest.scala b/community/cypher/cypher/src/test/scala/org/neo4j/cypher/MatchAcceptanceTest.scala
index 95e5930b8a054..0259344ca011a 100644
--- a/community/cypher/cypher/src/test/scala/org/neo4j/cypher/MatchAcceptanceTest.scala
+++ b/community/cypher/cypher/src/test/scala/org/neo4j/cypher/MatchAcceptanceTest.scala
@@ -2282,4 +2282,17 @@ return b
       Map("p" -> PathImpl(b, r2, a, r1, b)))
   }
 
+  test("should be able to match on nodes with MANY labels") {
+    //given
+    val start = createLabeledNode('A' to 'M' map(_.toString):_* )
+    val end = createLabeledNode('U' to 'Z' map(_.toString):_* )
+    relate(start, end, "REL")
+
+    //when
+    val result = executeWithAllPlanners("match (n:A:B:C:D:E:F:G:H:I:J:K:L:M)-[:REL]->(m:Z:Y:X:W:V:U) return n,m")
+
+    //then
+    result.toList should equal(List(Map("n" -> start, "m" -> end)))
+  }
+
 }
diff --git a/community/cypher/cypher/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/QueriedGraphStatisticsTest.scala b/community/cypher/cypher/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/QueriedGraphStatisticsTest.scala
index 33eba5ad40df2..8aae03f92e350 100644
--- a/community/cypher/cypher/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/QueriedGraphStatisticsTest.scala
+++ b/community/cypher/cypher/src/test/scala/org/neo4j/cypher/internal/compiler/v2_2/spi/QueriedGraphStatisticsTest.scala
@@ -104,7 +104,7 @@ class QueriedGraphStatisticsTest extends CypherFunSuite with GraphDatabaseTestSu
       val xLabel = LabelId(qtx.getLabelId("X"))
       val pkId = PropertyKeyId(qtx.getPropertyKeyId("age"))
 
-      stats.indexSelectivity(xLabel, pkId) should equal(Some(Selectivity(1.0/3.0)))
+      stats.indexSelectivity(xLabel, pkId) should equal(Selectivity.of(1.0/3.0))
     }
   }
 
@@ -116,7 +116,7 @@ class QueriedGraphStatisticsTest extends CypherFunSuite with GraphDatabaseTestSu
       val xLabel = LabelId(qtx.getLabelId("X"))
       val pkId = PropertyKeyId(qtx.getPropertyKeyId("age"))
 
-      stats.indexSelectivity(xLabel, pkId) should equal(Some(Selectivity(1.0/4.0)))
+      stats.indexSelectivity(xLabel, pkId) should equal(Selectivity.of(1.0/4.0))
     }
   }