Recently I've been playing a lot of The Bazaar, and thinking about burn. Burn is a common form of damage over time in video games generally, so hopefully this analysis generalizes.

We'll define burn here as a number which stacks when applied, and on every tick it applies damage equal to the current stacks size, then reduces the stack by one.

Damage from Burn

The first question on my mind: when I add a burn, how much damage does it do?

If we assume 5 stacks of burn, the damage would be 5 + 4 + 3 + 2 + 1 = 15. This type of operation is known as an arithmetic series. Using this formula, we can calculate the damage from burn for any number of stacks.

Above we can see how damage scales super-linearly as we apply more burn.

This is helpful to know if you're only applying burn once.

Incremental Damage from New Burn

The whole point of burn is that it stacks, however. So let's take a look at new damage from additional burn applied over some existing amount of burn.

Interestingly, the burn damage increases linearly, such that the damage from new burn is equal to current burn.

That's a very helpful heuristic for understanding burn damage!

Burn Saturation

So far we've avoided thinking about Max HP. 100 Burn will deal 5,050 damage, but not if the enemy's Max HP is 1,000!

Let's take a look at what happens to the incremental damage with a max of 1,000.

As you can see above, the damage drops to 0 once you hit a saturation point. This means that the burn damage will not increase further even if you apply more burn.

Here I've plotted burn saturation vs max HP, so you can see the relationship between the two.

Beyond Saturation

Thinking in terms of burn saturation has a significant limitation: it doesn't account for the fact faster is better.

Once we've reached the saturation point, incremental burn will speed up the time to kill the enemy.

As you can see, the survival time drops off quite quickly as you pass the saturation point, and flattens out after that.

Conclusions

• Low burn is low damage, but burn damage increases super-linearly.
• Burn applied late in the fight is much less impactful than burn applied early in the fight.
• Reaching the saturation point is important, and going beyond is very valuable initially, but falls off.
• This means burst is crucial for maximizing burn damage.

Hopefully this gave you some additional insights into burn!