Resistance calculation — from 101 to perfection — of Dragon Quest of the Stars

Resistance is crucial; it REALLY matters, in Dragon Quest of the Stars(DQS), in particular in battles with super-strong bosses. Here's how to work out resistance.

Notice: This article is based on the Japanese version of the DQS. I can't play the worldwide version, which can not be played (nor downloaded) in Japan. So

• forgive glitches in terminology, and
• exact specification may differ from the worldwide version.

I'd appreciate your feedback. I'll check a thread at Dragon's Den (woodus.com).

Resistence calculation is done for each attribute separately. Below we suppose we focus on one attribute.

Resistance is not addition. NEVER EVER. "20% from foods, 30% from the armor, so 20+30=50%" is wrong. You'll be affected by 0.8×0.7=56%, so the resistance is 44%.

Sit back, I'll show it you again in slow motion. It's easy, and you'll soon get it.

Food, helmet, emblem... Do not think of each as an "xx% resistance", but as a "filter that passes yy%". Put differently, it's a filter whose transparency is yy%. In the above example, food penetrates 80%, and the armor lets 70% in. (Note: In the real world, a filter's performance is often expressed by how much it blocks, not by how much it passes.)

What you want in the end is to know by how many percents a character is affected. You can forget how much each filter prevented. What really matters is the harm that passes the food and that passes the armor; it's the 80% of the 70%, so 0.8×0.7=56% is the final amount.

This holds both for probability, for example sleep, and for HP damage.

It's multiplication, so the order doesn't matter. Absolutely. (In fact, basically. There's a corner case, which will be told later.)

What's handy to know

Case study: Alike? Quite different!

Suppose you'll get snooze casted repeatedly. Higher resistance is nice, undoubtedy.
But, both Lv1 (50% res) and Lv10 (60% res) "sleep guard: middle" by an "awakening ring" don't make much difference. Anyway the resistance is too inadequate. You'll nap and sleep and slumber. (If snooze is not often, it's not necessarily bad.)

The story changes completely if you equip two awakening rings. Two Lv1 rings let 25% in. By preparing a latte (60% res) too, it finally results in a passes-10% filter = 90% res. What if you hone two rings to Lv10? They already make a passes-16% filter = 84% resistance. It's well worth investigating, and you can spare foods for other attributes.

Case study: Get the figure, and it's secure.

Many Japanese DQS players were shocked when Doe...oh-oh, I should avoid a spoiler. Ahem, a certain villain throws debris of earth type three times, when entering the last HP gauge. A naked charater will be fed with about 300 points of damage from each throw. It's not rare that one character gets hit twice — its probability is 5/8 †, — so even if they parry, you may miss the condition of the no-death quest completion. The gauge-breaker attacker risks death without resistance. ‡ You reckon it's a bit difficult to achieve a no-death victory unless all characters have 20% resistance. It's not absolutely impossible, though.

It's clumsy to calculate? Spend one minute to work it out; it'll be much easier than to go over a same quest many times.

† The easiest way is to calculate the probability that each of three throws hits three different characters. Let the first throw goes to Alice. The second goes to someone else, by the probability 3/4. Call him Bob. The third doesn't fall upon Alice nor Bob by 2/4. Thus the possibility in question is 3/8. That means the risk that someone gets hit twice or three is 5/8 - more than a half!

‡ It's a bit more difficult to figure out how often the gauge-breaker X will be sent two or three throws. The first two throws comes to X and the last to someone else by the probability . Same for the "1st and 3rd" and "2nd and 3rd". All three throws hit X by . Adds up all, and it makes 10/64 ≈ 1/6.5. If that happens, I'm sorry. That's life, after all.

Cases where addition is roughly ok

Resistance is not addition, but!! There arecases where addition is not bad. It's when the total sum (of the resistance, not the filter rate) is small. Its upper limit is some 30 or 40%. Let's have a look.

• 1% resistance ×2 is a passes- filter, so 1.99% res. There!
• 10% res ×2 -> passes -> 19% res. Okay.
• 30% res + 10% res. It'll penetrate 0.7×0.9 = 0.63, so 37% res. Don't blame me.
• 30% res and 20% res, what about this? After a microsecond crunch, you see it's 44% resistance. Now the error is somewhat itchy.

For those interested, I'll explain with math formulae. You can skip them.

Suppose you have three items with x, y, and z resistance. The coefficient they make is

.

If you ignore R, the resistance is x + y + z, simply being addition. But how can it be justified to forget R? Recall we are thinking the case where x, y, and z are small. For example 1% = 0.01. Than the terms included in R are very small, e.g. xy is 1/10000 or so. If x = y = z = 0.3, R = 0.27, and it has to be taken into account.

Intermediate: Food in multiplayer. Emblem bonuses.

The food in mutliplayer games is anomalous. (Remember we are considering some one attribute.) A special rule is applied:

1. First, take the maximal resistance item (only one), and count it regularly.
2. Any items with the same attribute are counted as 20% of the max one. (Surprising? But it's true.)
3. Add them all. (Addition, not multiplication.)

Sources: [1][2] (Japanese)

For example "Strawberry slime icecream" has 25% sizz-resistance in the Japanese DQS. (Any other food has lower sizz-resistance.) So when there's two strawberry-slime-icecreams, and one tofu-hamburg (20% sizz-res), the total resistance is 25+5+5 = 35%.

This means the best practice is basically "to bring one high-resistance food and any other cheaper ones." Of course there's other points to consider. When each of all 4 participants brings a strawberry-slime-icecream, you'll get the bonus of additional 25% zap-resistance. A tofu-hamburg gives +20 defense, etc.

Emblem bonus is already shown in the game screen. As you can see, the "bonus" parts of the four emblems are combined together for each attribute. The basic parts are treated independently.

"Any breath resistance" of emblem bonus is summed independently from resistances of each sepcific kind of breaths.

You probably know Paladin's skill "戦友の盾" in Japanese (I guess it corresponds to "forbearance" in other DQ installments.) benefits from shields' emblem bonuses that's "valid when parried".

Technical details

Motivation: If you have much sleep resistance, sometimes you see cases where sleep-attacks always become "invalid!". But this can never happen if resistance is multiplication. How can that be possible?

The actual resistance calculation in the DQS app is guessed to be done by the following procedure:

1. Sort all elements from the one with the highest resistance to the lowest.
2. When there's no item with resistance, the character has a 100%-transparent filter. Take this as the initial value.
3. Multiply the current transparency by the transparency of the highest remaining resistance item.
4. In step 3, re-express the result in percent, and round to the nearest integer. (More precisely, round half down, i.e. 0.5 becomes 0.)
5. "Minus 1% guarantee": In step 4, it can happen the transparency doesn't lower, staying the same as the previous one. (For example, one starts from 5% transparency, and next takes a passes-by 95% element; the result is still 5%.) In that case, and only in that case, the transparency is decreased by one percent.
6. Go back to step 3, until all multiplication is done.

This algorithm was first proposed by the twitter user "碧@星ドラ" (@cobalt_dq) in this tweet in Sep 2017 (in Japanese.) It is considered to be correct, satisfying numerous tests. For example this study (in Japanese) by "Yuonero" found no contradiction.

I myself have an experience of "invalid!" seal in the following combination: "Seal guard" Lv9 (98%) of the helm, sage's vocation bonus (5%), and an emblem (5%). This is an example of "-1% guarantee", coming from the last two.