Muffled Movement is expected to provide 50% movement noise reduction. However, the magnitude of reduction is unexpectedly higher under the following circumstances:
<ol>
<li>When you take the perk, you have Illusion perk Kindred Mage and are not a vampire. (KindredMage adds its +10 bonus to the 0.5 base magnitude of spell PerkMuffledMovement, yielding 1050% noise reduction.)</li>
<li>When you take the perk, you are a vampire. (The "Champion of the Night" 25% Illusion boost, which comes from perk VampireSkillsPerk, affects spell PerkMuffledMovement.)</li>
<li>When you take the perk, you have an active Fortify Illusion alchemy effect. (The IllusionPowerMod entry in perk AlchemySkillBoosts affects spell PerkMuffledMovement.)</li>
</ol>
In all cases, the enhanced magnitude sticks until you remove the perk.
The above behavior technically also applies to Silence (which does 100% reduction), but reduction higher than 100% makes no difference so it doesn't matter.
The root cause is that magic effect PerkMuffleConstantSelf has its Magic Skill field set to 'Illusion', which allows it to satisfy the entry point conditions within KindredMage, VampireSpellsPerk, and AlchemySkillsBoosts. The Magic Skill field of PerkMuffleConstantSelf should probably be set to 'NONE' in order to fix this issue, or else the entry point conditions on the perks should be tightened up.
In similar fashion, the Restoration perk Recovery is supposed to provide 25% and 50% bonus magicka regen at ranks 1 and 2, respectively, but these magnitudes are increased by any active Fortify Restoration alchemy effect on you at the moment you take each rank. The new magnitude sticks for the duration of the perk. In this case, it's the RestorationPowerMod entry in AlchemySkillBoosts that is getting applied to spells PerkMagickaRecovery1 and PerkMagickaRecovery2 because the underlying magic effect, PerkMagickaRecovery, has its Magic Skill field set to 'Restoration'. Setting it to 'NONE' should fix the issue, or else the entry point conditions within AlchemySkillBoosts should be tightened up.