Given that you have enough mana, Mana Shield is a 60% reduction, which equates to a 2.5 effective HP multiplier against all types of damage.
This means you need to have enough mana so Mana Shield can block damage until you’re out of HP for maximum effectiveness. Less mana is insufficient, more is useless. In theory, this breaking point is reached when you have mana equal to 60% of your HP.
BUT
You want to have enough mana to cast our abilities – Manta is 125, Stone Gaze is 200. Mystic Snake is 170 but it will usually return with more mana, so we won’t count it.
Mana Shield is calculated BEFORE damage reductions. To block the same amount of damage, with every point of armor you get, you will lose less HP, but the Mana Shield will use the same amount of mana. This means that in the late game you’re going to need much more mana to sustain the shield.
Magical damage is easier to calculate as your spell resistance will always be 25%, although we all know there are many ways for your team to increase it (Rubick, Pipe) or for the enemy team to decrease it (Veil, Elder Titan), so it’s situational as well.
A few simple tests showed the following results (with HP = Mana):
At 20 armor, your mana ends when your HP is at around 20%
At 25 armor, your mana ends when your HP is at around 27%
At 30 armor, your mana ends when your HP is at around 35%
At 25% magic resistance, it’s the opposite – your HP ends when your mana is at around 33%
Yet, you’re also going to lifesteal in the late game, so you gain more HP and you need more mana to sustain the shield.
In conclusion, if you are playing against plenty of physical damage and you have high armor, you need a mana pool a bit higher than your HP pool, usually achieved with stat items like Skadi and the mana talent.