Blessing Frequency - 1 Year Analysis (w/ 8x 3D Pie & 2D Bar Charts)

[Ravi-Sama]

We've had a little over a year of blessings now, on both HH and Nu.  1 year & 3 weeks, or 55 weeks.  It makes sense to analyze it, to see if there's any irregularities, or trends.  

Are they truly random?

All of the pie charts are HH and Nu's blessings combined, to help see the bigger picture.  55 weeks * 4 blessings = 220 blessings total.  There's some outliers unique to HH and Nu, that I'll point out.  I'll spare you from having to see all of the regular charts, there's 9 of them.  Forgive my liberal use of color @DvDivXXX 🙏🏽.  I think it's justified, and helps in this context, for rarities, elements, hair, and eye colors.

Out of the 6 attributes that can be blessed, Elements have been blessed least often (14 HH, 9 Nu, 23 total), ~60% below the 36.7 avg (220 blessings / 6 attributes), and Poses/Zodiac are most often blessed (42-44 times) 12.6-16.5% above avg.  Edit: elements didn't exist for the first 15 weeks of blessings, so it's close to it's own 26.7 avg (160/6).

Specific elements are blessed least often compared to the rest of the attributes.  Only 23 times, compared to the avg of 36.7.

Edit: Since elements didn't exist for the first 15 weeks, that's closer to the avg of 26.7. (55 weeks - 15 weeks = 40 weeks * 4 blessings = 160 blessings / 6 attributes)

Dominatrix, Exhibitionist, and Physical were blessed most often (4 times each).  Perhaps uncoincidentally, the sensual element has never been blessed on either HH or Nu.  Eccentric was also never blessed on Nu.  It should've happened at least 3 times on average.  It's not as if sensual girls haven't been blessed at all, but whenever they were blessed, it was due to some other attribute, besides the sensual element.

The range of percentages that each attribute is blessed, is pretty even, and unbiased.  A 35% blessing is most common (50 times).  I expected to see that a 40% blessing occurred less often, and it did (39 times), but it's still close enough to the avg of 44 (220 blessings / 5 percentages), that it could be random.  Nothing fishy to see here.

Nose dive, doggy style, and splitting bamboo are the most often blessed positions (5x M6s).  Dolphin and Suspended congress were never blessed on HH (3x M6s).  It seems like Charm had a slight advantage here.  There's 12 of them, so the avg should be ~3 (36.7/12).  Nose dive is double the avg, but I think it could still be random.  There's only 1 nose dive M6, Druiada Titania.

Gemini, Sagittarius, and Virgo were blessed the most often (4x M6s, there's no Sagittarius M6).  Libra and Leo were never blessed on HH (3x M6s).  Capricorn and Pisces were never blessed on Nu (3x M6s).  The most common mythic zodiac sign is Aries, w/ 5x M6s, and they were blessed 3 times, which is avg. Once on HH, and twice on Nu.  There's 12 zodiac signs, so the avg should be ~3 (36.7/12).  I feel like an Astrologist.

Golden, Brown, and Silver hair were blessed the most (4-6 times).  Grey, Pink, and Unknown hair were never blessed.  There's 17 hair colors, ignoring unknown, so each should've been blessed at least twice on avg (36.7/17).
*Looks at Bunna, Golden Lupa, and Royal Housemaid*

Purple eyes were blessed the most (5 times), which favored Matcha.  Blue, green, pink, and silver eyes, were also blessed often (4 times), which benefits 13x other mythic girls.  Black eyes were blessed the least (once), only really affecting Stellaluna.  Orange eyes were never blessed on HH, excluding the L5s Ryoko and Vespa.  Golden and Black eyes were never blessed on Nutaku, which excludes the 3x M6s Bunna, Golden Lupa, Succubus Abraël, and another 6x L5s.  There's 12 eye colors, excluding unknown, so the avg should be ~3 (36.7/12), and it seems very close to that.

Rare girls were blessed about twice as often (6 HH, 5 Nu, 11 total) as legendary girls (3 HH, 2 Nu, 5 total).  That makes me feel better about maxing my R5s.  Whenever all legendary girls are blessed, we tend to make a lot of progress in the Pantheon.  In a year, it only happened thrice on HH, and twice on Nutaku, when it should've been 3.67 times on avg for both (36.7/5/2).  I'd say Nutaku is overdue for another legendary blessed week.  (I play on HH, so that's an unbiased statement).

My conclusion is that the frequency of blessing percentages, eye colors, zodiac signs, positions and elements seem random, and unmanipulated.  The sensual element was never blessed, neither on HH, nor Nu.  Eccentric was also never blessed on Nutaku.  At first I thought this wasn't random, but now I understand that elements had 15 weeks less time, so it does appear random. 

However, the blessing frequency of the hair colors, and rarities show signs of manipulation, and might not be completely random. 

The hair colors grey and pink, which would benefit Bunna & Golden Lupa, were never blessed, neither on HH, nor Nu.  Bunna's first MDR occurred during the first blessing week (July 23rd, 2021).  Perhaps, that would've made Bunna super broken.  I finally recently acquired Bunna, like 11 others on the forum, so it'd be a shame if there was some "soft-ban" curse upon her dual grey and pink hair colors, and if that's just an illusory advantage, w/o a real possibility.  There's 17 hair colors, ignoring unknown, so each should've been blessed at least twice on avg (36.7/17).  Is it a coincidence that Bunna's hair colors went unblessed for a year? *shrugs*

This also leads me to believe that dual eye colors are better than dual hair colors, b/c they're blessed about once more on avg per year, (Eyes @ 3.67 vs Hair @ 2.15 avg frequency).  I have 60 girls w/ dual hair, but just 29 w/ dual eye colors, making them rarer, so this would make sense.  There's also only 1x M6 girl w/ dual eye colors atm, Succubus Abraël.

Rare girls were blessed (11) twice as often as legendary (5) girls, 49.8% above the 7.34 avg, and that speaks for itself.

Thanks to @zoopokemon for recording the weekly blessings.  I only play on HH.  Otherwise, I wouldn't know Nutaku's blessings.
Shout out to @EpicBacon for requesting the pie charts.  I hope they were satisfactory.

Edited August 1, 2022 by Ravi-Sama

[zoopokemon]

53 minutes ago, Ravi-Sama said:

Elements have been blessed least often (14 HH, 9 Nu, 23 total), ~60% below the 36.7 avg (220 blessings / 6 attributes)

Remember Elements didn't exist for the first 15 weeks worth of blessings, so it only has an expected value of 26.7 not 36.7.

[Ravi-Sama]

Just now, zoopokemon said:

Remember Elements didn't exist for the first 15 weeks worth of blessings, so it only has an expected value of 26.7 not 36.7.

I don't remember that, thanks for pointing it out.  Does that explain sensual never blessed?

[Rarum]

Sensual has been blessed on the test server. I seem to remember two times personally. But I've left no actual record of the blessings there. Since timings matter here, I started playing there on Jan 4, 2022.

[DvDivXXX]

@Ravi-SamaThanks a ton for this huge post, looking forward to dissect those pie charts (I agree with @EpicBacon they're easier to read for laypersons than the kind of abstract art dotted lines Rarum produces, or the long and plain spreadsheets most often used). And thanks for pinging me! I was looking forward to this as well.  

[EpicBacon]

9 minutes ago, DvDivXXX said:

@Ravi-SamaThanks a ton for this huge post, looking forward to dissect those pie charts (I agree with @EpicBacon they're easier to read for laypersons than the kind of abstract art dotted lines Rarum produces, or the long and plain spreadsheets most often used). And thanks for pinging me! I was looking forward to this as well.  

Indeed, I like data, but when people start using scatter plots and floating points I kind of start to tune out.
Kind of suprised we havent seen more Venn diagrams to be honest.

Just give me a good ol pie chart, witch turns out. its actually really good for this type of data.

[Ravi-Sama]

11 hours ago, EpicBacon said:

Indeed, I like data, but when people start using scatter plots and floating points I kind of start to tune out.
Kind of suprised we havent seen more Venn diagrams to be honest.
Just give me a good ol pie chart, witch turns out. its actually really good for this type of data.

I've made venn diagrams and webs before, but don't do them as often, b/c they take way more effort.  I haven't figured out a way to automate it yet, so I had to manually think of all of the connections and similarities between the girls.  I did it for Succubus Abraël, last May.  It was still fun to make.

On 5/3/2022 at 1:55 PM, Ravi-Sama said:

I put some thought into which groups of mythic girls have attributes and blessings that overlap, to see which sets of girls might all get blessed together one week.  Succubus Abraël fits into many groups, most notably blue eyes (5 girls), pink hair (4 girls), and golden eyes (3 girls).  She sadly doesn't have anything in common w/ my Undercover Valentina, except that Physical and Voyeur both affect critical hit chance.

High Mage Arcana has blue hair and eyes, so her hair matches Valentina, and her eyes match Abraël.  Arcana can be the bridge between the two, creating the possibility of at least two of my M6 girls getting blessed at once.  I already have 24 affection for Arcana, so I'll only need 4 SP boosters, and will definitely aim to get her on August 23rd, when she revives.  New Year Estelle would work too, and I have 28 affection, but I have no idea when she'll return, b/c she was one of the first mythic girls to be revived only ~8 months after her introduction.

[EpicBacon]

3 hours ago, Ravi-Sama said:

I've made venn diagrams and webs before, but don't do them as often, b/c they take way more effort.  I haven't figured out a way to automate it yet, so I had to manually think of all of the connections and similarities between the girls.  I did it for Succubus Abraël, last May.  It was still fun to make.

I actually like Venn Diagrams; once i started to understand how they work they are really cool.
Never been a fan of bubble charts tho, but its more of a personal preference.

It's going to be interesting to see how the blessings comes along, if they will balance out when a larger sample size is accumilated

[Rarum]

16 hours ago, DvDivXXX said:

they're easier to read for laypersons than the kind of abstract art dotted lines Rarum produces, or the long and plain spreadsheets most often used

Okay, I guess I'll derail this a bit. I often produce charts that convey some information over time, and pie charts are horrible at that. You'd have to have a series of them, and if the total also gets larger over time, the way to convey this would be with increasing the total area of the pie chart. I at least wouldn't intuitively know how to even read a series of pie charts of varying sizes.

In data visualization it's even best practice to avoid pie charts (humans being better at gauging lengths than areas or something). But it gets "sin-worthy" when you add a 3D component. I mostly looked at the raw numbers in these graphics personally, which to me signifies a failure for the visualization.

[EpicBacon]

3 hours ago, Rarum said:

Okay, I guess I'll derail this a bit. I often produce charts that convey some information over time, and pie charts are horrible at that. You'd have to have a series of them, and if the total also gets larger over time, the way to convey this would be with increasing the total area of the pie chart. I at least wouldn't intuitively know how to even read a series of pie charts of varying sizes.

In data visualization it's even best practice to avoid pie charts (humans being better at gauging lengths than areas or something). But it gets "sin-worthy" when you add a 3D component. I mostly looked at the raw numbers in these graphics personally, which to me signifies a failure for the visualization.

There is nothing stopping you to make your own analysis about the data using whatever type of graph you want.
And I don't mean this in any condescending way, I just happen to like pie graphs, I don't do detailed analysis of data, I don't know what is the most "efficient"
or what is the best representable way to display data.

[DvDivXXX]

@Rarum Thanks for the clarification and link (that was a good read). I tend to be very cautious of biases and misinformation, and I had already read and watched debunks of misleading graphs like the ones shown in the blog you linked to. It's clear that using a 3D pie chart with the right angle, and with the "picks up a slice" effect it's easy to make a small share look as big if not bigger than those with higher numbers. This reminds me of the graphs that shows you columns but cropped to hide the x axis, then  zoom in, so that the 29 column appears twice as big as the 25 column, stuff like that. You're right that this kind of thing should be avoided, especially sources using them deliberately for their agenda. I think we'd all agree it's not what Ravi did here, even if the pie chart format does twist our perception by itself (for instance the two 7 slices up front in the Rarity pie look HUGE compared to the ones shrunk down by perspective, even the 11 one).

I understand and share Bacon's hunger for relatively easy to read, intuitive graphs, though. 2D columns would probably have been clearer and better show the proportions in this case. Unfortunately, for the type of graphs you tend to do, I don't know what could help me read them. I get that showing the evolution of multiple data streams over time in relation to each other kind of requires a bunch of lines that can intersect. It's just that in most of your graphs there are so many and they cross paths so often that it ends up looking abstract to me. For many things that kind of graph works well and is super clear to show trends, but usually when there are only a few lines and they take mostly different paths. I'm not sure which other format would be clearer to read for your league graphs, if any. But I know it's really hard for me to decipher the ones you post, regardless of my jokes about them looking like abstract art. I'd love to be able to look closer into your data. Anyway, please don't take this the wrong way, I'm just sharing my experience and view (literally) on graphs. You're clearly able to read and analyze your graphs and use your data to great effect in league, so it's not you, it's me. ^^

[Ravi-Sama]

7 hours ago, Rarum said:

In data visualization it's even best practice to avoid pie charts (humans being better at gauging lengths than areas or something). But it gets "sin-worthy" when you add a 3D component. I mostly looked at the raw numbers in these graphics personally, which to me signifies a failure for the visualization.

Okay, in an effort not to sin w/ pie charts, here's some bar charts.  The pie charts were requested, and I think they're fun & look cool.  I also paid attention to the numbers, even w/o the charts, so my interpretation didn't change.  I still think hair and rarity seem suspicious.  The rest could be random.

3 hours ago, EpicBacon said:

There is nothing stopping you to make your own analysis about the data using whatever type of graph you want.
And I don't mean this in any condescending way, I just happen to like pie graphs, I don't do detailed analysis of data, I don't know what is the most "efficient"
or what is the best representable way to display data.

I can do it quick.  I have the tables already.

1 hour ago, DvDivXXX said:

...You're right that this kind of thing should be avoided, especially sources using them deliberately for their agenda. I think we'd all agree it's not what Ravi did here, even if the pie chart format does twist our perception by itself (for instance the two 7 slices up front in the Rarity pie look HUGE compared to the ones shrunk down by perspective, even the 11 one).

Yep, not trying to distort the data.  I don't have an agenda,... except maybe to vent about Bunna's grey/pink hair never blessed.  It still could be random I suppose, b/c 220 blessings isn't a huge sample size, even though it took a year.  I'll *put on my tinfoil hat* anyway, b/c it's both of Bunna's hair colors, and they weren't blessed on either HH or Nu.  Also, they removed Royal Housemaid's pink hair, and replaced it w/ unknown for no reason, so I know they like to meddle w/ this kind of thing, ...hair color rant over.

[lepidocter]

Ok, istograms. They are the best ones. The only defenders of phallocracy in a world dominated by cheating pie charts.

Look those viril bars towering toward the skies. Pures and prouds, unbreakable pillars of exquisite assertion.

[EpicBacon]

11 minutes ago, Ravi-Sama said:

Okay, in an effort not to sin w/ pie charts, here's some bar charts.  

You should have made then 3d, just to passive-agressively jab Rarum.

If anyone didn't get that, that was a joke
Calm your tits folks

[Ravi-Sama]

1 minute ago, EpicBacon said:

You should have made then 3d, just to passive-agressively jab Rarum.

If anyone didn't get that, that was a joke
Calm your tits folks

Lol, nah, I wouldn't have done that.  I get his point.  It's interesting how flawed human perception is, when comparing length vs. area.

Anyway, this thread was about blessings, not the charts used to interpret them.

[F-L-K]

find it stupid that "mythic" is even more blessed than "legendary"....

[DvDivXXX]

6 minutes ago, F-L-K said:

find it stupid that "mythic" is even more blessed than "legendary"....

Well, from day one of the blessings' introduction, many of us argued there simply shouldn't be a mythic blessing. It makes no sense to buff all the girls who are already the strongest by default. Our feedback was forwarded... So. ^^ I'm afraid it's there to stay.

[EpicBacon]

13 minutes ago, DvDivXXX said:

Well, from day one of the blessings' introduction, many of us argued there simply shouldn't be a mythic blessing. It makes no sense to buff all the girls who are already the strongest by default. Our feedback was forwarded... So. ^^ I'm afraid it's there to stay.

Well, the mythics are only 14.23% stronger then the highest legendaries (25->28.56) so it's not that big of an increase.
That basically means that any blessing that affect a top tier legend is going to make it better then an unbless mythic.
(I belive the lowest blessing buff is 20%)

Now I am all for making more girls viable, unfortunaly with the current system we have right now; I do not have any excess resources to do anything with it.
Having a blessing just for mythic girls tho; yeah.. probably a bit of an overkill.

[Attirm]

On 8/1/2022 at 12:56 AM, Ravi-Sama said:

Dominatrix, Exhibitionist, and Physical were blessed most often (4 times each).  Perhaps uncoincidentally, the sensual element has never been blessed on either HH or Nu.  Eccentric was also never blessed on Nu.  It should've happened at least 3 times on average.  It's not as if sensual girls haven't been blessed at all, but whenever they were blessed, it was due to some other attribute, besides the sensual element.

Just running some quick estimates of the probabilities, this looks like it's well within the expected range of random results. Presuming each element has an equal 1 in 8 chance, then after 23 elemental blessings there is about a 33% chance that at least one element wouldn't have come up for blessing yet. 

Edited August 11, 2022 by Attirm

[Ravi-Sama]

1 minute ago, Attirm said:

Just running some quick estimates of the probabilities, this looks like it's well within the expected range of random results. Presuming each element has an equal 1 in 8 chance, then after 23 elemental blessings there is about a 33% chance that at least one element wouldn't have come up for blessing yet. 

Yeah, I figured that, after being reminded that elements didn't exist for the first 15 weeks.  Also, that sensual was blessed before on the test server.  Check if it's likely for grey, and pink hair to go unblessed on both HH and Nu for 55 weeks.

[Attirm]

2 minutes ago, Ravi-Sama said:

Yeah, I figured that, after being reminded that elements didn't exist for the first 15 weeks.  Also, that sensual was blessed before on the test server.  Check if it's likely for grey, and pink hair to go unblessed on both HH and Nu for 55 weeks.

A little more complex, so I just did a quick Monte Carlo on this one. I ran 100,000 simulations of 38 blessings with 17 possible hair colors, and on average 1.7 colors were unrepresented at the end of each trial. So we're pretty much exactly where we'd expect to be if things were perfectly fair and random. 

[Ravi-Sama]

21 minutes ago, Attirm said:

A little more complex, so I just did a quick Monte Carlo on this one. I ran 100,000 simulations of 38 blessings with 17 possible hair colors, and on average 1.7 colors were unrepresented at the end of each trial. So we're pretty much exactly where we'd expect to be if things were perfectly fair and random. 

Alright, that's good news.  *Removes Tinfoil Hat*

[DvDivXXX]

What seems pretty insane to me is that, even though apparently her double hair color has yet to come into play for that, I'm still under the impression that Bunna has got to be one of the most often blessed mythics so far. It would be nice if we could make a chart for the most frequently blessed girls or something. But since zoo's spreadsheet (and your charts derived from it) only archive the blessings and not their results, that would require crosschecking the girls' attributes with past blessings, which sounds like a ton of work (unless it can be done automatically without burning anyone's CPU ^^).

On top of that, even though it's a small number of girls, both hair and eye colors have been changed multiple times, and are still getting changed occasionally (like a couple of girls going from Dark to Black for their hair like yesterday?). Who knows, by the time pink and grey get blessed, maybe Bunna's hair will have been changed to fuchsia and silver... ^^

[Ravi-Sama]

16 minutes ago, DvDivXXX said:

What seems pretty insane to me is that, even though apparently her double hair color has yet to come into play for that, I'm still under the impression that Bunna has got to be one of the most often blessed mythics so far. It would be nice if we could make a chart for the most frequently blessed girls or something. But since zoo's spreadsheet (and your charts derived from it) only archive the blessings and not their results, that would require crosschecking the girls' attributes with past blessings, which sounds like a ton of work (unless it can be done automatically without burning anyone's CPU ^^).

On top of that, even though it's a small number of girls, both hair and eye colors have been changed multiple times, and are still getting changed occasionally (like a couple of girls going from Dark to Black for their hair like yesterday?). Who knows, by the time pink and grey get blessed, maybe Bunna's hair will have been changed to fuchsia and silver... ^^

I thought about it.  Maybe I'll do it later.  I also wanted to figure out the odds of each particular blessing appearing, plus 20-40%, and the potential total power of the teams they'd make.  Also, I ran out of reactions again. lol

[Liliat]

Il y a 6 heures, DvDivXXX a dit :

What seems pretty insane to me is that, even though apparently her double hair color has yet to come into play for that, I'm still under the impression that Bunna has got to be one of the most often blessed mythics so far.

Really? She was my first Mythic, and I have the feeling that she's never blessed. I don't remember using her a lot (Except maybe in the first few weeks? But I only had 7 Mythics or less then).

Just a feeling though. Not actual data.