Two Santas Event Helper Analysis: Rudolph, Star Atop Christmas Tree and Christmas Lights
It’s the Christmas Event! The event brings 3 helpers – and with the Christmas theme the daemons are really colourful and bright. I especially like the art of Star Atop Christmas Tree. She looks like she is bursting with joy. The event, as usual, is a tower, and the helpers have their usual event limited effects.
Rudolph the Red Nosed
4 ★ Assist Divina
Stats
Max/MLB Attack: 7500/9195
Max/MLB HP: 7000/8583
Bond Effects
Base bond effect: Increases Attack
Red-Nose (lvl 80): Increases 5% all Divina team members’ Crit Rate. (Only take effect once to the team.)
Event Skill: Increase Event Points by 33% – 100%
Opinion
Rudoph has evolved! She first appeared as a Christmas event helper in December 2016, being another version of the puppeteer playing Chimera / Cerberus / Hydra, but dressed up and with a reindeer puppet. This version of Rudolph is completely different, without a hint of the original, based on the artwork. The daemon’s type has also changed, Rudy was a Phantasma, but now Rudolph is a Divina.
As an assist daemon Rudolph boosts all the Divina team mate’s Crit Rate by 5%, with the boost locked at level 80, which requires 5 copies / MLB. Like other team wide boosts from most other assist daemons, only one application of her boost can apply, so you can’t purchase multiple copies, level and seal and bond her to multiple daemons on the team to stack the boost.
5% Crit Rate boost which is type limited is not that fantastic. It seems to me like yet another version of Zombilina, Gretel and Candy House. Just with the boost applicable to Divina and affecting Crit Rate. Sure, 5% is more than 2% and 3%. But it is still type limited, not stackable, and requiring a large number of copies to unlock.
We have seen type passive crit rate boosts from Platina and Aurum Elf. The elves each boosted Divina Crit Rate 10% (together 20%). Titanium Elf (commonly used together with Plat and Aurum) innately boosted her OWN crit rate by 21% with another Elf on the team. In that team (Plat, Aurum, Titanium) Titanium would crit frequently spontaneously with the innate crit rate boosts, but to get the entire team to crit more reliably, players still needed crit rate boosters like Qilin, Katsushika Houkusai (and to a certain extent, Kong Ming). With the Crit Rate cap announced by Mitama to be at 85%, 5% from Rudolph really is of minimal significance.
Christmas Lights
4 ★ Assist Anima
Stats
Max/MLB Attack: 7500/9195
Max/MLB HP: 7000/8583
Bond Effects
Base bond effect: Increases Max HP
The light that illuminates the darkness (lvl 80): Normal attack targets have 25% chances of increasing 10% more DMG taken
Event Skill: Increase Skill DMG by 33% – 100%
Opinion
Christmas Lights provides a weaker a version of Mara’s second ability to whichever daemon he is bonded to.
Without having tested the daemon myself, I will assume:
- The debuff can stack
- The debuff period lasts 8s
- The daemon hits once every 2s
A very rough interpretation of the skill goes like this: over a period of 8s the daemon hits 4 times. And of those 4 hits, each as 25% chance of inflicting the debuff. Of course there is a chance of all the hits inflicting the debuff, and a chance of none of the hits inflicting a debuff, but overall the probabilities show that mostly 1 of the 4 hits inflicts a debuff. The size of the debuff is 10%. So that ability effectively equates to the targeted daemon receives 10% more DMG throughout the battle, with some variance for period of time when there are multiple debuffs, and when there are period of time when there are no debuffs.
The same math applies to Malefic: Thorn. Thorn’s output is 19.8%, which is better than the bond effect of Christmas Lights, but weaker than Mara’s.
For a passive ‘opponent takes % more DMG’, other daemons that provide such debuffs include: Hibiki [Sun Spear] 20%, Momiji Hime 18%, and Poor Devil 10%. Do note that the first 2 are limited to the battle’s final wave. The disadvantage of using these daemons is that they require a slot on the team or reserve to be of use. Christmas Lights can provide the debuff by being placed on a support daemon on the team.
The question at this point is how Christmas Light’s assist ability stacks with Mara and Thorn’s passives.
Mara’s original debuff is:
- Normal attacks have a 33% to increase targets damage taken by 20%.
Christmas Light’s debuff is
- Normal attack targets have 25% chances of increasing 10% more DMG taken.
If one simply adds the percentage of activation and percentage debuff you’d get:
- Normal attack have 58% chance of increasing 30% DMG taken.
That would give Mara with Christmas Tree bonded an effective debuff over time of 69.6%.
Unfortunately this type of treatment is wrong.
The correct math for the effective damage of Mara bonded with Christmas Lights would need to consider the chance of applying the debuffs separately on each of the hits.
Each of Mara’s hits would have a separate 33% chance of 20% debuff, and 25% of 10% debuff. There are hits where none of the debuffs take effect, and times when both debuffs take effect.
- Let buff 1 be Mara’s own 33% chance of 20% debuff
- Let buff 2 be Christmas Light’s 25% chance of 10% debuff
- P(buff 1 + buff 2) = 0.33 * 0.25 = 0.0825
- P(no buff at all) = 0.67* 0.75 = 0.5025
- P(buff 1 only) = 0.33 * 0.75 = 0.2475
- P(buff 2 only) = 0.67 * 0.25 = 0.1675
Average debuff from 1 hit =
- 0.0825 * 30 + 0.5025 * 0 + 0.2475 * 20 + 0.1675 * 10 = 9.1%
After 4 hits, the debuff stacks: 9.1% * 4 = 36.4%
Repeating the same math for Malefic Thorn with Christmas Light bonded, his effective debuff would increase from 19.8% after 4 hits to 29.8%.
The thing about Christmas Lights is that despite his debuff being poorer than that of Mara or Malefic: Thorn, his status as an assist daemon allows him to be bonded to multiple different daemons on the team, and then that’s where the debuff stacking adds up. With the game rules one can have a maximum of 2 copies of Mara / Thorn on the team (one of your own plus one borrowed from your ally). But you could bond 4 copies of Christmas Lights to each of your own team, and have your ally’s Mara have Christmas Light bonded also.
So this theoretical team with 2 Mara with Christmas Light bonded, Malefic Thorn with Christmas Light bonded, and 2 other daemons with Christmas Light bonded would give you an effective constant debuff against a single opponent after the first 8s (they must be all hitting the same opponent for 4 hits for the auto attacks to stack and for the math to work) of 36.4% + 36.4% + 29.8% + 10% + 10% = 122.6%.
This max debuff from Christmas Lights, 2 Mara and Thorn surpasses the debuff cap of the World Boss (75%). Unfortunately it is less significant on Conquests where the debuff cap is either much higher or non existent (one generally hits the game’s auto and skill damage caps before the debuff cap of 99,999 and 999,999 first when testing for the conquest debuff cap). So, one could possibly see a world boss team of: 2x Mara with Christmas Lights bonded along with 3 other daemons (Sola, Philo and Yoritomo come to mind) to inflict a debuff that maxes the World Boss mode’s debuff cap. Having Beelzebub [HW] would further boost the effect of the debuffing (more auto hits means more chances of the debuff to proc). Unfortunately Mara’s active skill (hits all targets) is of minimal use on a single target stage like the World Boss, resulting in rather inefficient orb usage on the team. Do also note that the current World Boss Kanato has a skill that cleanses the debuffs, so all the debuffs that stack nicely over 8s gets cleansed ever so frequently. World Boss attacks that interfere with your daemon’s auto attacks like stun and paralysis also reduce the effectiveness of the debuff stacking.
P.S. This is of course a theoretical team for full auto attack (no skill DMG), anyone with the actual cards available for testing please do so and post your results (videos would be nice too!) in the comments below. Realistically I don’t expect it to compete with the skill DMG based teams – skill DMG boosts are not capped (only diminishing returns when you have too much), and there are some really large skill boosts on daemons currently in the game’s meta right now.
Star Atop Christmas Tree
4 ★ Assist Anima
Stats
Max/MLB Attack: 7500/9195
Max/MLB HP: 7000/8583
Bond Effects
Base bond effect: Increases Skill DMG
Star of Glory (lvl 75): Increases 36% of Crit DMG.
Event Skill: Increase Drop Rate by 33% – 100%
Opinion
Despite absolutely loving the art on this daemon, I can’t help but be disappointed in her assist ability. 36% Crit DMG is precisely 1% Crit DMG more than Saigyo, released months ago, which was recently closely scrutinized in comparison with the more recently released Matsuo Basho.
1% more Crit DMG compared to Saigyo won’t change the result of the Saigyo vs Basho comparison. Basically Star is to Saigyo what Book of Five Rings is to Katsushika Houkusai. A slight improvement, but otherwise a copy-paste of the same skill.
Thanks for the reviews! Fun and informative as always
I disagree with this statement:
“A very rough interpretation of the skill goes like this: over a period of 8s the daemon hits 4 times. And of those 4 hits, each as 25% chance of inflicting the debuff. Of course there is a chance of all the hits inflicting the debuff, and a chance of none of the hits inflicting a debuff, but overall the probabilities show that mostly 1 of the 4 hits inflicts a debuff. The size of the debuff is 10%. So that ability effectively equates to the targeted daemon receives 10% more DMG throughout the battle, with some variance for period of time when there are multiple debuffs, and when there are period of time when there are no debuffs. ”
You’re looking for the probability of 4 straight failures here for the debuff to NOT be applied. That can be determined by multiplying the failure rate by itself four times (binomial probability comes into play here). That means the probability of NOT applying the debuff once every 4 attacks (8 seconds) is (.75 * .75 * .75 * .75) = .316 or 31.6%.
That means your success and failure rates are:
Success: 68.4% (at least one hit applies the debuff)
Failure: 31.6% (four straight attacks without a debuff)
You might be applying the debuff more often than not, but it’s far from a statistical guarantee. You do have a statistically significant failure rate.
Please read the paragraph you highlighted again. It is clearly mentioned:
1. “A very rough interpretation’
2. There are times when none of the debuffs proc, and there are times when multiple debuff proc.
3. But over time you get a 10% AVERAGE debuff, some times you get more debuff and sometimes you get less.
If you want to get into the full probabilities over 4 hits
P (0 debuff 0%) = (0.75^4) = 0.31640625
P (1 debuff 10%) = 4 * (0.75^3 * 0.25) = 0.421875
P (2 debuff 20%) = 6 * (0.75^2*0.25^2)=0.2109375
P (3 debuff 30%) = 4 * (0.75 * 0.25^3) = 0.046875
P (4 debuff 40%) = 0.25^4 = 0.00390625
Total probability = 1
Average debuff = P (0 Debuff) * 0 + P (1 debuff) *10 + P(2 debuff)*20 + P(3 debuff)*30 + P(4 debuff)*40
=0 + 0.421875*10 + 0.2109375*20+ 0.046875*30+ 0.00390625*40
=10
True, 10% average is not the same as 10% constant debuff. 10% constant debuff will give 10% average also. But with Mara, Thorn, X’mas Lights the debuff is variable, on-hit. But how else to do a comparison with this mechanic to the familiar situation with fixed debuffs? Most reasonable solution in my opinion is to take the average debuff over time for calculation. I think that is sufficiently clearly expressed in the write up.
How else would you express it in order to make a comparison?
I’m a numbers person, so I think a chart comparing the full probabilities for 0 – 4 debuffs for the related cards would be the most accurate comparison as we have enough of those types of cards now to compare them to themselves. The overall rate of failure for each card is, I think, fairly important too. Knowing that Christmas Tree Lights fails to refresh it’s debuff about once every three 8-second series compared to Mara’s 20% (once every five 8-second series) failure rate is valuable information.
The average debuff is good information too, but I think a general “sometimes it’s higher and sometimes it fails” is a little too broad.
Also, the more I look at this card, the more I think it might be excellent as an Endless Challenge option. The reliance on auto attack and lack of control could make an auto attack debuffer quite useful there.
I’m a numbers person too…and I think it’s best both of you (including my other card reviewer ;)) go read my previous review for Mara. I didn’t really read this review before it was posted but to me it’s much easier to show it how I did previously.
Your 31% failure point I don’t particularly like, but I agree with potentially having a table to show chances of given debuffs at any point in time. After my holiday perhaps I will make an article about the potential of these cards
I think for the majority of people just knowing that there 10% average debuff and that there are some caveats (first 8 seconds, stuns/other status effects, etc) is good enough for most people.
Everything else is just icing and us numbers people can figure that stuff out on our own anyway =) I appreciate the possible applications with double Mara + Christmas Lights team, and if you like Valsu, your idea of a chart with probabilities sounds interesting as well, if you decide to make it feel free to post the results here via Google Sheets or imgur or something =)
So which one i must exchange?
You can exchange any them if you need helpers for the event.
I see. How about the 5* knecht? I like zoff art, But he maybe not so good
20% more damage to the boss of whatever you’re running seems quite excellent to me, especially with only two copies (easily attainable). Stick him in your reserve and deal 20% more damage to the World Boss, for example. There are no restrictions as to type either, which means everybody benefits from doing more damage to the enemy.
He is useless for Endless Challenge, I suppose.
World boss can remove debuff itself, will it make knecht’s effect also disappear ?
The debuff applied from passive abilities do not show up as a status effect during the battle, and apply throughout the battle, regardless of cleansing.
In short, no.