Number Crunch – Calculating EHP in 5E

There are a lot of ways to be tanky in 5E, whether its strapping on plate armour, focussing on Dexterity and neatly dodging away from attacks, or even being a howling Barbarian that simply soaks up the damage.

Making direct comparisons between all of these different archetypes is tough, however. Is higher AC worth a lower Dexterity save? Should you prioritize boosting your HP or grab a feat for heavier armour?

Well, after a bit of work I think I’ve produced something that at least has a decent go at working out how effective various tanking builds will be.

It’s a formula that takes into account your AC, Saving Throws and Resistances, as well as the kinds of attacks your enemies are likely to be making, and spits out a number that represents your Effective HP (EHP) – essentially a measure of how much damage needs to be thrown at you before you go down.

Below is the EHP spreadsheet set up for my now-dead Level 4 Barbarian mentioned in an earlier blogpost, with the assumption that she is always Raging in combat and that her advantage on Dexterity Saves in equivalent to a +2 bonus. As you can see, despite being on the small side she was pretty incredible at tanking damage.

Meanwhile, the sheet below provides the stats for Sir Dollo, a human Fighter of the same level clad in splint mail, wielding a shield and sword with the ‘Protection’ fighting style. As you can see, despite being more of a traditional full-tank, the Fighter actually absorbs much less damage than the Barbarian.

You can download the spreadsheet for generating EHP values here, or you can view it as a Google Doc here – though if you want to actually understand what it means I strongly recommend reading the rest of the post.

Highly Effective

To give a little bit of background on why I think EHP is a worthwhile thing to calculate, I should probably start by explaining that I spent several years playing the incredible – if life-consuming – spaceships and spreadsheets MMO EVE Online.

In EVE, nobody will ever ask how much raw HP a ship has, because it’s a completely meaningless stat. It’s meaningless because of the emphasis the combat places on resistances – a percentage amount that reduces incoming damage.  Instead, what actually matters is the amount of Effective HP you have, which determines how much raw damage you can take before exploding.

For example, one ship could have 1,000 HP and 50% resistances across the board, while another has only 500 HP but resists 90% of damage. The first ship ignores half the damage dealt to it, effectively doubling the amount of attacks needed to kill it and giving it 2,000 EHP. The second can shrug off 90% of the damage done to it,  giving 5,000 EHP.

This means that despite having lower base HP, the second ship is clearly much tougher to kill.

Ideally, we’d calculate things the same way when it came to D&D. After all, simply having a huge raw HP value doesn’t mean a thing if you’re easy to hit.

However, while calculating EHP in EVE is relatively easy, it’s rather tough to do something similar in D&D. If you want to be at all realistic you don’t just need to take account of being resistant to various damage types, you need to work out the impact of your AC and your various saving throws too.

After a night hammering away at Excel I believe I have managed to come up with a reasonable model for working out EHP in D&D 5E. However, it does come with rather a long list of assumptions.

Assuming Command

The formula used to build my spreadsheet relied on the following assumptions:

  • 75% of damage is physical, divided evenly between bludgeoning, slashing and piercing
  • 25% of damage is elemental, divided evenly between all ten elements
  • Characters are being attacked by creatures with attack bonuses and spell DCs that follow the DMG guidelines for a creature with a CR equal to character level – 2
  • 80% of attacks are made against AC
  • 10% of attacks require a Dexterity Save
  • 5% of attacks require a Wisdom Save
  • 5% of attacks require a Constitution Save
  • A negligible amount of attacks require a Charisma, Strength or Intelligence Save

On a very basic level, this means that a character’s EHP is equal to their Base HP, multiplied by a factor that accounts for their resistances, multiplied by how likely they are to dodge an attack. For example, a character with 50 HP, no resistances and a 50% chance of dodging an attack would have 100 EHP. If they had a 75% chance of dodging an attack they would have 200 EHP.

If we want to create the ideal character – one that is resistant to all forms of damage, can only be hit by an enemy rolling a 20 and can only fail a save by rolling a 1 – has 40 times more EHP than baseline HP. That 50 HP character from earlier would be able to soak up 2,000 raw damage before going down.

In full, the formula works out looking something like this:

CodeCogsEqn

Is this formula completely accurate? Probably not – I’m not 100% happy with ignoring half of the saving throws, there’s no real way to account for some feats and I need to work out some way to account for regeneration or self-healing, which would give Fighters, Paladins and Clerics a boost.

But hopefully it’s close enough to guide you in making the best choices when it comes to tanking.

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