Black Kat Farming Sep 2014: BK & Spookat appearance rates, and Book of Dark Ritual drop rate 😸 Cheshireccat's Classes

The September 2014 Kataclysm is over. As I did after the May 2014 Kataclysm I will now publish my research to benefit the SK community!
I created a spreadsheet to track the various data points from September 2014.
http://i.imgur.com/CUGvZUL.png
I have a second spreadsheet which combines all of the data from May and September.
http://i.imgur.com/Ka8hJSk.png
Here you will see a graph which interprets the Book drop per BK probability curve from my data. It includes the standard error of my sample data--the true probability should be somewhere between the two error curves. There is also a hypothetical curve; it shows what the book drops might look like if the drop rate were 0.5%--the percentage that most people assume is the correct one.
http://i.imgur.com/PBTZqyX.png
- Spookats:Run Alone in the Dark has two more Spookats (on average) than Weight of Darkness. This is likely due to WoD's poison theme; zombies sometimes spawn in lieu of Spookats.
- BK:Run In 423 runs, a total of 101 BKs appeared. Taking into account the confidence interval, the BK-per-Candlestick-Run is somewhere between 21.80% and 25.95%. That comes out to 1:4.6 and 1:3.9 runs.
- This DOES NOT mean you should find a BK every four runs. I myself had 19 runs in a row without finding a BK. This is an average, describing what will happen over time if you make enough runs.
- BK:Spookats There are an average of 20.94 Spookats-per-Candlestick-Run. 101 BKs appeared in 423 runs. Multiplying the average Spookats-per-Candlestick by the number of runs gives an appearance rate of 1:87.7 BK:Spookats. Applying the standard of error gives us a range of 0.62% to 1.66%, or 1:160.3 to 1:60.4.
- This does not take into account themed Spookat spawn rates, only total Spookat spawn rates.I was not aware of the themed spawn requirement when beginning my research. Next Katastrophe's research will focus on the BK-per-themed Spookats to more accurately answer this question.
- Book of Dark Rituals:Book drop chances Each person in the party had a chance of obtaining a Book of Dark Rituals. There were 1389 total Book chances (see methodology) and 5 Books were found. Since it is so difficult to find BKs and the Books are so rare it is hard to get an accurate prediction. Nevertheless we can calculate a standard error from this data--the average Book drop rate is between 0.20% and 0.52%, or 1:501.8 to 1:192.1 Book chances.
- Note: This does not mean that you cannot get a Book outside of this range. I know players who have not received a Book with 400 chances, and someone who received a Book on his second chance. My data is for the average Book drop rate.
- The three contributors (Cheshireccat, Flawedknight, Vtmoon) all received books no higher than 368. If the book drop % is at the upper bound of my standard error that could put the the 90+% book range at 440+. 370+ would be 74%, possibly explaining this phenomenon.
- At our current average, you are 97%+ likely to have earned a book by your 968th Book chance. If you haven't found a Book by then you must have done something to offend the Dark God RNG ("Lord RNG, deliverer of triumph and misery, bless us with your favor and protect us from your ire"). I suggest you visit Punch and make offerings to the Dark God in the hopes he changes his mind.
- Books were found after the party members went solo from the group, on alts, and on alts after rejoining the main party. It appears from these first-hand accounts there are no systems in place to increase or decrease book drops. I FIRMLY believe OOO would not bother building in any such blocks or party trickery to this--it costs dev time and server resources that a small game developer wouldn't waste. See http://forums.spiralknights.com/en/node/104787#comment-948173
- Almost all of the data was recorded on Elite, using the D19 "Alone in the Dark" or D24 "Weight of Darkness" missions.
- Flawedknight contributed the 78 WoD and 265 AitD numbers from 9/14. He ran on Normal.
His result is in line with the Elite data, suggesting that there is no difference between Normal and Elite (though this is not statistically proven). He also contributed one of the books from 9/14.
- Flawedknight contributed the 78 WoD and 265 AitD numbers from 9/14. He ran on Normal.
- There were a varying number of people in each party, but always at least three.
- When a Black Kat was found some members of each party would use the "go solo" trick for extra token drop and Book chances.
- The data from the two missions were kept separate. You can view them on the spreadsheet.
- The data from the two events were kept separate. You can view them on the spreadsheet.
- The Book drop rate and BK appearance rates were calculated with combined data from the two missions from both events. This precludes the assumption that the Book drop chance is equal for both missions (at two different T3 depths) and has not changed between events.
- If you wish to see the data and conclusions for May alone, please refer to my previous Cheshireccat's Classes Black Kat post.
- If you wish to see the data and conclusions for September alone, please refer to the linked image at the top of this post.
- To better understand the math behind the confidence interval and the ranges I provide, feel free to research "binomial proportion confidence interval."
- Mewkats found: 1
- Love Puppies found: 2
- Rock Jellies found: more than 8
- Rare drops from Mewkats/Love Puppies: 0
- Anger after a week of hardcore farming and no book: brobdingnagian.
- Happiness when I found a book: equal to receiving a new puppy. There may have been dancing involved.
- Record more data on themed Spookat numbers in AitD.
- Find more books!!! :D
A heartfelt THANK YOU to FlawedKnight and VTmoon for their contributions to this data!
Thank you as well for reading! I hope this info helps you out!
Until next Kataclysm... see you in Haven!
--Cheshireccat
PS: I highly suggest you save the linked image files. You never know when a third-party host may change something and break the links.
PPS: I like pudding.

I highly suggest you save the linked image files. You never know when a third-party host may change something and break the links.
oh, by the way, your 4. link is broken :P.

See? Save these images--you never know when someone will make a mistake when copying the URL :P
Fixed. Thanks!
--Cheshireccat
Can confirm that Alone in the Dark will net you some serious Kats
Found this little devil on my 2nd run through the place.

I'll just sneak my Black Kat FAQ from last time in here.
(I would ammend that WOD seems to lean slightly more to the zombie side, so AID has a marginal advantage).

I just took AP Stats this year and I don't want to think about that class anymore. Kinda done with it (even though it was rather easy). I don't want to hear about confidence intervals or standard error anymore. But either way, it's still super helpful, I'll take this stuff into account.

Thanks for all the amazing statistics! Really helps shed some light on the elusive books.
This year it looks like OOO made a few changes, most notably that you can no longer join in on someone else's Kat find and still find pages. I hope they didn't do anything else.

UPDATED:
Ran 99 runs, all doing 9-2 Alone in the Dark
Kats Found: 19
Books Found: 0
Longest Kat Streak: 2
Longest Dry Streak: 14
Rare Monsters:
Rock Jellies: 3
Mewkats: 1
Love Puppies: 1
Rare Drops: Ghostly Aura
Eternal Orbs Found: 8
Sparks of Life Found: 4

After a few days of runs, here's what i have:
165 runs, 40 kats
longest dry streak was 17
longest kat streak was 4
I've seen someone get 1000 pages with no book, another found book after 300 pages, and another found book after 15 pages XD
Also Weight of Darkness can be much easier than Alone in the Dark, as poison>shock. As someone with chaos, 10 seconds of shock hurts a lot.
edit: updated run and kat counts

Day 1; Session Time: 2 hours, 32 minutes (152 minutes)
Runs: 45 (43 Solo, 2 Dual)
Black Kats Encountered: 7...
Book Drops: 0
Location: Alone in the Dark (1st Level), as if it really mattered- same rates for WoD anyway.
Notes: Brought MSI VH, average run time pertain to 3.38 minutes; may differ ~24 seconds / ~.24 minutes in error.
Primarily solo. Run times when 2+ appear shorter when you don't have to put down a damn key to lower the gate.
Day 2 & 3; Session Time: 2 hours, 45 minutes (165 minutes)
Runs: 45 (39 Solo, 6 Dual)
Black Kats Encountered: 5...
Book Drops: Obviously 0
Location: Weight of Darkness (1st Level), comparison to AitD
Notes: Screw Grimalkins, screw seizures. MSI VH, average run time pertain to 3.68 minutes; may differ ~56 seconds in error due to sidetracking (Briefly staying in Haven, making pet food).
Dress like a Black Kat and beg the almighty dark overlord Margrel to bless you with his bad luck and cursed divinity.
^Oxymorons much

I'm rather tired of having people claiming AitD is better than WoD. So here's why there is no difference. This is copied and pasted from my other comment. I'm not trying to discredit Cheshire, whom i recognize put a LOT of time and effort into this. I only want to make people think twice about what they read.
Cheshire's results for spawnrates of Kats in AitD comes out to be 21.8%, with 66/303 kats per run. His results for WoD comes out to be nearly 30%, which I believe to be a little high, likely because he did fewer WoD runs.
I have completed 351 runs on WoD, and found 77 Kats. Thats 21.8%, which is almost exactly the same as Cheshire's AitD results. On the other hand, it is much lower than his WoD results, which leads me to wonder if his data suffers from too few samples. If his results for BK spawn rates are so far off, his findings for the total number of regular Kats may be as well. (I haven't been collecting info on the regular kat spawns.)
Basically:
BK's are no more likely to spawn on AitD as WoD
The "2 more kats on AitD" theory is likely false. If you are willing to believe his results, then you should also be willing to believe it when he says WoD spawns BK's 30% of the time, while AitD has a 22% chance.
Edit:
Cheshire also hypothesizes the reason for fewer Kats on WoD is due to there being a possibility of a Kat being replaced by a zombie, but I have never seen this occur. Once again I have no definitive proof that this isn't true, but I know the Kat spawns very well and not once have they been replaced by a zombie.
Thanks for posting this. I especially like how you included confidence intervals, to get at the uncertainty in the conclusions. Frequently when I talk about collecting data, players say, "Why? We already know the results." The answer is that we need more data to narrow down the uncertainty.