diff --git a/src/PrizePool.sol b/src/PrizePool.sol
index 4cb2971..bad9bd0 100644
--- a/src/PrizePool.sol
+++ b/src/PrizePool.sol
@@ -692,7 +692,7 @@ contract PrizePool is TieredLiquidityDistributor {
   /// @return The number of draws
   function getTierAccrualDurationInDraws(uint8 _tier) external view returns (uint24) {
     return
-      uint24(TierCalculationLib.estimatePrizeFrequencyInDraws(getTierOdds(_tier, numberOfTiers)));
+      TierCalculationLib.estimatePrizeFrequencyInDraws(getTierOdds(_tier, numberOfTiers), grandPrizePeriodDraws);
   }
 
   /// @notice The total amount of prize tokens that have been withdrawn as fees or prizes
@@ -1011,7 +1011,7 @@ contract PrizePool is TieredLiquidityDistributor {
     }
 
     SD59x18 tierOdds = getTierOdds(_tier, numberOfTiers);
-    uint24 startDrawIdInclusive = computeRangeStartDrawIdInclusive(lastAwardedDrawId_, uint24(TierCalculationLib.estimatePrizeFrequencyInDraws(tierOdds)));
+    uint24 startDrawIdInclusive = computeRangeStartDrawIdInclusive(lastAwardedDrawId_, TierCalculationLib.estimatePrizeFrequencyInDraws(tierOdds, grandPrizePeriodDraws));
 
     uint32 tierPrizeCount = uint32(TierCalculationLib.prizeCount(_tier));
 
diff --git a/src/libraries/TierCalculationLib.sol b/src/libraries/TierCalculationLib.sol
index 5dd7fb4..a614af3 100644
--- a/src/libraries/TierCalculationLib.sol
+++ b/src/libraries/TierCalculationLib.sol
@@ -27,10 +27,13 @@ library TierCalculationLib {
   }
 
   /// @notice Estimates the number of draws between a tier occurring.
+  /// @dev Limits the frequency to the grand prize period in draws.
   /// @param _tierOdds The odds for the tier to calculate the frequency of
+  /// @param _grandPrizePeriod The number of draws between grand prizes
   /// @return The estimated number of draws between the tier occurring
-  function estimatePrizeFrequencyInDraws(SD59x18 _tierOdds) internal pure returns (uint256) {
-    return uint256(convert(sd(1e18).div(_tierOdds).ceil()));
+  function estimatePrizeFrequencyInDraws(SD59x18 _tierOdds, uint24 _grandPrizePeriod) internal pure returns (uint24) {
+    uint256 _prizeFrequencyInDraws = uint256(convert(sd(1e18).div(_tierOdds).ceil()));
+    return _prizeFrequencyInDraws > _grandPrizePeriod ? _grandPrizePeriod : uint24(_prizeFrequencyInDraws);
   }
 
   /// @notice Computes the number of prizes for a given tier.
diff --git a/test/PrizePool.t.sol b/test/PrizePool.t.sol
index 100ab30..5932eac 100644
--- a/test/PrizePool.t.sol
+++ b/test/PrizePool.t.sol
@@ -377,7 +377,7 @@ contract PrizePoolTest is Test {
   }
 
   function testGetTierAccrualDurationInDraws() public {
-    assertEq(prizePool.getTierAccrualDurationInDraws(0), 366);
+    assertEq(prizePool.getTierAccrualDurationInDraws(0), 365);
   }
 
   function testContributePrizeTokens() public {
diff --git a/test/libraries/TierCalculationLib.t.sol b/test/libraries/TierCalculationLib.t.sol
index 24f9e95..ab3198e 100644
--- a/test/libraries/TierCalculationLib.t.sol
+++ b/test/libraries/TierCalculationLib.t.sol
@@ -32,19 +32,19 @@ contract TierCalculationLibTest is Test {
 
   function testEstimatePrizeFrequencyInDraws() public {
     assertEq(
-      TierCalculationLib.estimatePrizeFrequencyInDraws(TierCalculationLib.getTierOdds(0, 4, 365)),
-      366
+      TierCalculationLib.estimatePrizeFrequencyInDraws(TierCalculationLib.getTierOdds(0, 4, 365), 365),
+      365
     );
     assertEq(
-      TierCalculationLib.estimatePrizeFrequencyInDraws(TierCalculationLib.getTierOdds(1, 4, 365)),
+      TierCalculationLib.estimatePrizeFrequencyInDraws(TierCalculationLib.getTierOdds(1, 4, 365), 365),
       124
     );
     assertEq(
-      TierCalculationLib.estimatePrizeFrequencyInDraws(TierCalculationLib.getTierOdds(2, 4, 365)),
+      TierCalculationLib.estimatePrizeFrequencyInDraws(TierCalculationLib.getTierOdds(2, 4, 365), 365),
       31
     );
     assertEq(
-      TierCalculationLib.estimatePrizeFrequencyInDraws(TierCalculationLib.getTierOdds(3, 4, 365)),
+      TierCalculationLib.estimatePrizeFrequencyInDraws(TierCalculationLib.getTierOdds(3, 4, 365), 365),
       1
     );
   }