Ninja Snowman Assassin Encounter Rate

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Ninja Snowman Assassin Encounter Rate

Postby weas » Tue Jul 09, 2013 11:20 pm

I used FaxNet to try and spade the encounter rate on ninja snowman assassins. faxnet_5.zip contains session logs of 43 accounts running at least 100 turns at +5% combat rate. faxnet_25.zip contains 43 accounts running 100 turns at +25% combat rate.

I have no analysis ability so I am just dumping the data here. Hopefully this is a big enough sample size, and I didn't fuck anything up.
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Re: Ninja Snowman Assassin Encounter Rate

Postby blisterguy » Tue Jul 09, 2013 11:21 pm

Awesome, thanks Weas! I know some people who have been working on it already, so I've shove this new info down their pie-holes.
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Re: Ninja Snowman Assassin Encounter Rate

Postby Darzil » Wed Jul 10, 2013 9:19 am

Great stuff. I'm seeing the following : (Corrected after conflating two datasets stupidly)

Guaranteed Assassin on turns 11, 21 and 31.
Steadily increasing rate from around 10% at turn 1 to 100% at turn 60 at +25% combat.
Steadily increasing rate from around 5% at turn 1 to 100% at turn 66 at +5% combat.
It is possible the Guaranteed Assassins overwrite semi-rare, as there are no semi-rares on turns 11, 21 or 31.

Most files have 101 encounters. In several there are only 100, and it is the first encounter that is missing or malformed, so guaranteed assassins do not line up unless you account for this.
Something odd happened on LFM fax, there are 106 encounters, and they don't line up right, so have excluded it.
Observered rate excludes semi-rare.

Image of 5% rate :
AssassinRate5.gif
AssassinRate5.gif (54.1 KiB) Viewed 4610 times

Image of 25% rate :
AssassinRate25.gif
AssassinRate25.gif (53.98 KiB) Viewed 4610 times

Spreadsheet (zipped as .xls not allowed) :
Ninja Assassins.zip
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Last edited by Darzil on Wed Jul 10, 2013 10:33 am, edited 1 time in total.
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Re: Ninja Snowman Assassin Encounter Rate

Postby Draco Cracona » Wed Jul 10, 2013 10:17 am

That is excellent to know- thank you muchly, Weas! Disagrees with my current formula slightly (chance = (0.125+wombatMod*0.01/10)*(1+advCount/10), but that's based on small samples) if the +25% cap is 66 (current formula I've been running with has cap at 57 for +25%), and has a lower base rate. Darzil, a few questions- are the guaranteed assassins on 11, 21 and 31 there in the +5% data as well? What's the +5% cap, and how much lower than the 25% one is it at the start? What's the total numbers of assassins encountered by T66 for the +25%, and by the cap on the +5%?
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Re: Ninja Snowman Assassin Encounter Rate

Postby Darzil » Wed Jul 10, 2013 10:21 am

Oopsie, accidentally put the two together in one. Will revise.

To address the questions:

Guaranteed adventures are in both datasets at 11, 21 and 31.
Cap at 5% is at least 66, as 65 missed assassin.
Cap at 25% is at least 60, as 59 missed assassin.

Assassins by turn 10 : 44 at 5% (of 42 samples), 85 at 25% (of 43 samples)
Assassins by turn 20 : 179 at 5% (of 42 samples), 247 at 25% (of 43 samples)
Assassins by turn 30 : 364 at 5% (of 42 samples), 479 at 25% (of 43 samples)
Assassins by turn 40 : 619 at 5% (of 42 samples), 766 at 25% (of 43 samples)
Assassins by turn 50 : 898 at 5% (of 42 samples), 1084 at 25% (of 43 samples)
Assassins by turn 60 : 1249 at 5% (of 42 samples), 1477 at 25% (of 43 samples)

A pretty rough calculation shows that the average time to get 3 assassins, assuming the observed rates, and assuming they are accurate (which won't be true), would be around 15-16 turns at 5%, and 11 turns at 25%.

I can also now understand why I used to think the cap for 3 assassins was around 21 or so. By 21 you are guaranteed to have 2 assassins, and even at 5% would have expected to meet another three, at 25% another five.
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Re: Ninja Snowman Assassin Encounter Rate

Postby Draco Cracona » Wed Jul 10, 2013 12:48 pm

Okay, some thoughts after trying to fit these two to the same formula:

I can't get a continuous function that fits roughly 6% and 10% starting assassin chance with caps of 60 and 66. My best guess, currently:

(0.05 + combatMod/5)+(floor((Adv)/6)*6*0.015).

I got to the first term, 0.05 + combatMod/5, by looking at the turn 1 information. You've got about 5% and 10% respectively, so the only thing that fits, really, is a 5% base and +1% per 5lb of combat modifiers. I originally had this base rate multiplied by the turns spent, but that just wouldn't fit. After moving the combat modifier term out, I still couldn't get it to fit until I moved the base out as well.

The second term just came from trying to fit the two caps together; the two datasets called for roughly similar multipliers for the adventureCount, but they weren't quite the same, so I looked over the graphs and noticed that it could easily be based on the floor of the adv/5 or similar, and so running with that roughly fits.

EDIT: Fixed MC results, by adding the guaranteed assassins in.

MC results:

+5%:

Avg assassins over 60 adv: 29.91 [expected: 29.73]
Avg length of time for 3 assassins: 14.39

+25%:

Avg assassins over 60 adv: 32.18 [expected: 34.34]
Avg length of time for 3 assassins: 12.76

+25% numbers are still slightly too low, but 5% numbers sound about right. Thoughts? Suggestions?
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Re: Ninja Snowman Assassin Encounter Rate

Postby Darzil » Wed Jul 10, 2013 2:16 pm

Try this :

% Chance = Combat Rate / 2 + Adventures spent in zone * 1.5

Remember, KOL counts adventures with 0 being the first, not 1 as most players do.

So this gives :

5% hits cap at Kol adventure 65 = 66th turn in zone
25% hit cap at Kol adventure 59 = 60th turn in zone

The prediction becomes expected turns for 3 assassins at 5% is 16 turns, at 25% is 11 turns.

At 60 adventures you'd expect around 30 at 5%, and 36 at 25%.

The positive is that it's a nice simple relationship, and hits the caps perfectly. The negative is that it matches the 5% line much better than the 25% line on Weas' data.

Spreadsheet with this line plotted on it :
Ninja Assassins.zip
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Re: Ninja Snowman Assassin Encounter Rate

Postby Draco Cracona » Wed Jul 10, 2013 2:39 pm

Darzil wrote:Try this :

% Chance = Combat Rate / 2 + Adventures spent in zone * 1.5

Remember, KOL counts adventures with 0 being the first, not 1 as most players do.

So this gives :

5% hits cap at Kol adventure 65 = 66th turn in zone
25% hit cap at Kol adventure 59 = 60th turn in zone

The prediction becomes expected turns for 3 assassins at 5% is 16 turns, at 25% is 11 turns.

At 60 adventures you'd expect around 30 at 5%, and 36 at 25%.

The positive is that it's a nice simple relationship, and hits the caps perfectly. The negative is that it matches the 5% line much better than the 25% line on Weas' data.

Spreadsheet with this line plotted on it :
Ninja Assassins.zip


That's pretty similar to mine (mine scales on a stepwise adv*1.5%)- I didn't look at that kind of size deviation from the T1 numbers (2.5% seems quite low compared to 5%). I'd try running the simulation with that when I get back in later :)
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Re: Ninja Snowman Assassin Encounter Rate

Postby Draco Cracona » Wed Jul 10, 2013 3:20 pm

Ah, bollocks. Just realized that what's been put forward as 60, 66, 11, 21 and 31 for caps/guaranteed assassins are actually not quite the numbers I should have been using. Or, more accurately, I need to go from adv 1 to adv 60 inclusive, not 0-59. That actually improves the numbers slightly.

Some slightly more updated numbers:

5+combatMod/5+floor(adv/6)*6*1.5 (my first equation, changed to match Darzil's):

+25%:
33.09 assassins in first 60;
13.07 turns for 3 assassins.

+5%:
30.80 assassins in first 60 adv
14.57 turns for first three assassins.

combatMod/2+adv*1.5:

+25%:

36.6 assassins in the first 60 adv
11.25 turns for first three assassins.

+5%:

30.9 assassins in the first 60 adv
14.59 turns for first three assassins.

Looks like having a 5% base rate with an extra 1% per +5% combat and a stepwise function fits slightly better, but do we have an average number of turns for the first three assassins? I'm bad at messing with complex spreadsheets for that kind of stuff, and those numbers would be handy for determining which is the better hypothesis.
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Re: Ninja Snowman Assassin Encounter Rate

Postby Darzil » Wed Jul 10, 2013 4:05 pm

My personal view, not having a significant statistical education, but instead an engineering one, is that we lack the quantity of data needed to accurately determine an equation, but we may have enough data to be useful.

The slope is pretty clear, and doesn't look to be based on the +combat rate. It is very close to 1.5% per adventure already spent in the zone.

The bonus given by the combat rate is clearly not the full combat rate. We don't have graphs that start at 5% and 25% and hit 100% at encounters 65 and 51, which we would if the full values counted. Halving this gives us graphs at 2.5% and 12.5% start, which hit 100% at encounters 66 and 60. This is consistent with our top values, and our 5% data, but doesn't fit the 25% data that well. However, to fit the 25% data well we'd have to change our slope calculation.

Given that the confidence about any given data point is pretty low, I'm not seeing in Weas' data a strong step function that is needed to justify a floor(adv/6)*6 term. Of course, you have access to more data than I.

What we can say is that chance of assassin increases linearly, with guarantees at 11, 21 and 31. Combat rate does have an effect on the assassin rate, but it is somewhat reduced. 5% combat gives around 16 adventures, which given only skills and ballroom song set, is the number that will need to be compared with the turns taken at +15% non-combat in the extreme slope. Each 5% above that saves 1 - 1.5 turns. So fax + 2 copies saves around 13 turns with 5% combat rate, or 8 turns with 25% combat rate, over normal assassin hunting. The practical cap is around 21 turns, as it is highly unlikely to avoid getting any assassin in the other 19 turns (around 2% chance at 5% combat rate, 0.3% chance at 25% combat rate), though the physical cap is 31 turns.
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Re: Ninja Snowman Assassin Encounter Rate

Postby Draco Cracona » Wed Jul 10, 2013 4:16 pm

Yeah, we're low on data, I'll agree there. We've got similar enough equations anyway :)
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Re: Ninja Snowman Assassin Encounter Rate

Postby IstariAsuka » Wed Jul 10, 2013 11:43 pm

Just fiddling around with best fit lines in excel. Linear fit is very, very strong in both cases, combat modifier obviously must just shift the line, without affecting the slope at all. With that in mind, the following attempts to reconcile the non-slope component of the two best-fit lines into a single formula involving the combat rate.

RATE = .015*ADV + COMBAT/(365-5*COMBAT)

It's a little funny, but it gives very good numbers. 365 is the number that results in the least deviation from best-fit equation components while being a round number still. Any number in that vicinity will give similar results, however. This equation gives the chance of an assassin on turn 60/66 at 25%/5% (respectively) as ~98.92% and ~98.97%, and >100% the turn after in both cases. This is close enough to 100% that the data never showing a failed assassin on these turns is around 50/50.

of course you could also do:
RATE = .015*ADV + COMBAT/215 - 0.01

As is obvious just to fit the data directly, but the trailing 0.01 seems unlikely to be in a real jick equation.
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Re: Ninja Snowman Assassin Encounter Rate

Postby Draco Cracona » Thu Jul 11, 2013 12:53 pm

Okay, some numbers:

Darth's com/(365-5*com):

+25%:

35.44 assassins in first 60.
11.83 turns for the first 3 assassins.
1.86 assassins expected in the first 10 turns.

+5%:

30.34 assassins in first 60 adv,
15.02 adv for first 3 assassins.
0.97 assassins in first 10 adv.

Darzil's com/2:

+25%:

36.6 assassins in first 60 adv.
11.25 turns for first three assassins.
2.07 [blinks. That's high...] assassins in first 10 adv.

+5%:
30.92 assassins in first 60 adv.
14.58 turns for first 3 assassins.
1.08 assassins in first 10 adv.

My 5%+com/5:

+25%:

33.08 assassins in first 60 adv.
13.06 adv expected for first three assassins.
1.45 assassins expected in first 10 adv.

+5%:

30.79 assassins expected in first 60 adv.
14.57 turns expected for the first 3 assassins.
1.05 assassins expected in first 10 adv.

--

Okay, so Darzil's or Darth's is better, based on a seen rate of ~2 assassins per first 10 adv. Pretty similar numbers either way, though
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