Binding of Isaac Damage

Today The Great Ziggyny posted about restarting speedruns of the Binding of Isaac to get good items. I've watched some speedruns myself and saw this behaviour. It makes sense to me - starting with a good item can make a run substantially faster.

Seven character speed runs clock in at about 2 hours. That's 17 minutes per character. If you are targeting 35 of 220 items, as Ziggyny suggests, and each reset takes about 4-5 seconds, then you'd be spending an average of about 30 seconds per run to get a "good" item. The good item only has to increase the speed of your run by around 3% to make that a valuable trade. So resetting definitely seems right.

However, I was curious about how these items that increase damage work. Some items say "Damage Up" some say "All Stats Up" some do other things. I know that the base damage Isaac does with tears is 3.5. If I get a damage up item does that go to 4.5 - a nearly 30% increase?

The Rebirth wiki doesn't have a lot of good information about stats, but the wiki for the original game does. Assuming the same calculations are used in Rebirth, it turns out the answer is no, +1 damage doesn't mean going from 3.5 to 4.5. It means going from 3.5 to 5.2. That might strike you as weird and get you wondering what the damage formula is.

Well, it's 3.5 × (1 + 1.2 * Damage Bonus)^0.5. Bet you weren't expecting that! The formula for increasing your shot rate is similarly bizarre. If something gives +1 tears that goes into 16 - 6 × (1 + 1.3 * Tears Bonus)^0.5 to determine how many "frames" it takes to shoot. Since the original game was thirty frames per second, you can divide that into 30 to get shots per second. If tears goes negative, though, the formula changes, making negative tears even worse.

Also, when an item says "Damage Up" that sometimes but doesn't always mean +1 damage. It could mean +0.3, or +0.5. "Tears Up" seems to range from 0.16 to 0.7. Then there are items that provide a flat multiplier or otherwise modify damage or tears after that calculation is done.

With formulas, of course, we can make spreadsheets.

Taking a look at that, you'll see that not all items are created equal. The winner is Cricket's Head because, in addition to adding +1 Damage, it multiplies damage by 1.5. 20/20 literally just doubles your damage. The Magic Mushroom gives a much smaller boost to all stats than the halo but, like the Cricket's Head, has a 1.5 multiplier that makes it very good. One item on that list that was not on Ziggyny's list is the Odd Mushroom (thin). This actually reduces your damage, but it dramatically overcompensates with a massive increase to tears and comes in 6th on the overall damage increase. Four of the items on my list are curse room items rather than treasure room items, all of which rank among the more powerful damage increases.

Some of the damage increases are actually quite weak. Iron Bar, Odd Mushroom (large) and Stigmata only give 0.3 damage which only translates to a 17% damage increase. Remember that a 17% increase to damage doesn't mean a 17% faster run. You don't spend your entire game doing damage to enemies with tears. Pisces has a terrible tears increase making it add very little damage. Mutant Spider and The Inner Eye increase the delay between shots so much that the former barely adds to damage and the latter actually decreases it. I put in three lines for Money = Power to show the range of its effect - maximum, minimum and exceedingly reasonable.


The following list of items from Ziggyny's list didn't make it on my spreadsheet because I just didn't have the data to figure out what effect they have on DPS:

Chocolate Milk
Dr. Fetus
Ipecac
Monstro's Lung
PhD
Polyphemus
Proptosis
Tech.5
The Ludovico Technique

I'm quite certain that almost all of these deserve to be on the list, though. Even though I find Dr. Fetus' damage increase questionable, there is no question it's a huge asset for speedrunning since it allows you to bomb past nearly every room if it suits you to do so. I'm less convinced on PhD, but I have personally found it to be a great item, and depending on your pill pool it can be obscene.

Having played with the Inner Eye I'm not totally convinced that the delay calculation I found on the wiki was correct. It would have me shooting less than once a second and I don't think it was quite that slow. On the other hand, I'm also not convinced that it is very good - the firing rate was quite low.

What about items that don't add to damage or tears but that supply good damage anyway?

I'd suggest that the following items are all probably better than Iron Bar and down from the list, if they don't rival some of the higher items:

???'s Only Friend - A drivable companion similar to the Ludovico Technique, but with a choice of whether to use that or tears, with the possibility of using both when the stars align. I don't know how much damage this actually does, though.

Daddy Longlegs - Again, no information on how much damage this does, but having played with it this would probably be my number one choice of items if I had to pick. This hits your enemies regardless of range and obstacles and will one-shot non bosses pretty much every time. When you think of this as having one or two fewer enemies in every room, you can see how it makes a run much faster and much easier. The damage to bosses also seems awfully high as well.

Guillotine - This, according to the wiki, gives +1 damage and +0.16 tears in addition to the orbital, so that would make it +58% damage and put it high on the list.

Judas' Shadow - Not for me, because I'm bad, but Judas's Shadow has a ×2 damage multiplier. So if you get this and get yourself killed, you do massive damage for the rest of the game.

Then there are items that I'm not really sure about:


Leech - Not a huge amount of damage, but I found this to be a significant damage source for most bosses, and not bad for many enemy types.

Normal Babies - How much damage do these do? I'm not sure I know. I don't think they are very good though.

Tough Love - This item makes you fire teeth instead of tears about 10% of the time. Teeth do triple damage. Now that's not very good, but apparently the chance to fire a tooth goes up by about 10% per point of luck you get, so a couple of luck ups and this item goes from not very good to very good in a hurry. Still, you can't count on luck ups, so while this is potentially powerful, I probably wouldn't keep it.

So, as a proposed revision, I would strike Iron Bar, Mutant Spider, the Inner Eye and Pisces from the list, and add ???'s Only Friend, Daddy Longlegs, Guillotine and Judas' Shadow. I'd keep the large odd mushroom and stigmata because while they are lower on damage they both also provide heart container. Also, as noted, I would only add Judas' Shadow if I was actually good enough to speed run, which I am not, but which people doing speedruns presumably are. And then again, if you aren't good enough to count on winning after intentionally killing yourself to get the damage bonus, then you can probably use the extra life.

The thing about this list is that it's not just for speedruns, though. A typical game of Isaac for me takes over half an hour and I have probably about a 15-20% chance of winning, maybe less now that I've unlocked Sheol and the Cathedral. Maybe I should think about making sure I start with good items before investing that amount of time in getting smashed on the later levels. Really, though, I'd only do that if I was working on specific unlocks. For now I should stick with lousy items and get better at the game.