Damage penalty

Damage penalty is the amount of lost points for suffering damage in a daily run. Its formula is defined as follows:

$$DamagePenalty = \left\lceil \left(1.0 - \exp(HitsTaken \times \frac{\log 0.8}{12})\right) \times (ExplorationBonus \times 0.8) \right\rceil$$

Caveats
Being tied to the exploration bonus, it means that getting hit once in the whole run bears different weights depending on how much you kill and explore:
 * getting hit once (1st floor, 1st room) and quitting the run: (10 exp. bonus) -1 damage penalty
 * getting hit once (1st floor, 1st room) and completing a full run: (20,000 exp. bonus) -295 damage penalty
 * an "average" run: (25 hits, 15k exp. bonus) -4,462 damage penalty
 * an "explore plenty, walk on spikes, eat bullets, dodge into enemies" run: (80 hits, 15k exp. bonus) -9,580 damage penalty

The same hit will come with a progressively heftier price the more rooms you explore and clear, and the more enemies you kill. In short, it doesn't matter when you get hit - it's already too late.

Some kind of hits count as twice the damage, ie: when getting hit by a Champion, walking on Spikes or otherwise losing a full heart by harm.

Exceptions
Not all forms of damage will add to the damage penalty, there are, in fact, many exceptions:
 * **Curse Rooms**, which will only raise the Damage penalty indirectly by adding points to the Exploration bonus
 * Using IV Bag, Razor Blade, a Blood Donation Machine, donating hearts to a Devil Beggar doesn't count as damage, but it will cost the player Schwag points for losing Red Hearts

Sacrifice Rooms
Using a Sacrifice Room has a complex cost, starting with 1 hit per half a heart - meaning 2 hits per pop in most cases (no Wafer, no Percs, etc). A full teleport comes with at least 24 hits (or 12 if the damage can be halved somehow); however, teleporting does not raise your damage penalty as much as previously thought, because reaching the Dark Room via teleport doesn't add points to your exploration bonus, only to the stage bonus. Reaching The Lamb by exploring, though, does.