Variance (and Skips)

[loramin]

I have what I hope will be a simple question about variance. I noticed that the wiki didn't have a page on how variance works, so I tried to make one ... and then realized that I didn't know either (or at least I was unclear about the exact details).

Let's take Lodi (18 hour respawn, 1 hour variance, two potential skips) as an example.

If Lodi was killed at 6:00 PM on Monday, then Lodi could appear anywhere from 17 hours from then (11:00 AM Tuesday) to to 19 hours from then (1:00 PM Tuesday). I think I have that much corect.

But then what if he skips that window: does the 17-19 hours for the next window start from the beginning or end of the first skipped window? Or could it start from anywhere in that time, making the subsequent window a potentially four hour period?

[Legidias]

AFAIK it adds +1 hour variance on it (due to him possibly spawning / skipping at any point during the window), so the next would be 16-20 hours from the theoretical middle point.

[d3r14k]

https://i.imgur.com/CegHYmm.png

[loramin]

So then if Lodi was killed at 6PM Monday, and he skips his first two windows, his window on the third (and guaranteed spawn) would be from 3PM Thursday to 9PM Thursday (because each skip added two hours, and the "window center" remains the original kill time)?

[BurtMacklinFBI]

correct

[Wallicker]

Yes, but the statistics of him spawning in the first or last 30mins well...

[Wallicker]

100% in the last 30 if it’s 3rd window before REEEEE

[loramin]

Thanks for the help all!

I think I understand now, but in fact my example was wrong: if I Lodi is killed ay 6pm on a Monday and skips his first two windows, it seems like his third window should actually be: 9:00 PM (Wednesday) - 3:00 AM (Thursday).

It's all broken down here for future reference: http://wiki.project1999.com/Variance

P.S.

Yes, but the statistics of him spawning in the first or last 30mins well...

It seems to me the spawns should be concentrated in the middle of the window after skips occur.

Think of it this way: if Lodi is killed at 6pm on a Monday and skips two windows, the only way he could possibly spawn at 9:00 PM Wednesday is if he "spawned" (but not really) at exactly 11:000 AM Tuesday, and then exactly 4:00 AM Wednesday.

But if he spawns at midnight Wednesday, there's many other ways that could happen (eg. he could have spawned at 11:00 AM Tuesday, then 6:00 PM Wednesday, or, 12:00 AM Tuesday then 6:00 PM Wednesday, or ...)

Since there's more possible non-spawn "spawn times" that can lead to times in the middle of the window, it seems like he should be more likely to spawn then.

[Dugface]

It'd be interesting to know - what are the chances of him spawning or skipping in the different windows.

i.e. is it a 1/3 chance of him spawning in the 1st window, a 1/3 or 1/2 in the 2nd window, etc.?

[Thomacles]

Ok, come on now. I know some of you math geeks can do this. Come up with the algebraic expression on the calculation. If they could do it on live for the Party Machine quest, surly one of you can come up with the Lodi spawn ;)

[loramin]

I'm probably the wrong person to answer this, as I've failed multiple math classes in my life, but I think the simplest way to explain it is that the probability doubles (or halves, depending on your point of view) when the mob skips.

Let's say Lodi was killed at 8:00 PM, and so now has a window of 1:00 - 3:00 PM the next day. He skips that window. If you just assume he was going to spawn at 2:00 PM (ie. exactly 16 hours after his death, no variance) then his new window would be 18 hours forward/6 hours back, ie. 7:00-9:00 AM.

Within that window I believe Lodi has roughly twice the chance of spawning as he does in his "extended" window, ie. the full possible window, ie. 6:00-10:00 AM. So from 6:00-7:00 AM he has roughly half the chance of spawning as he does between 7:00-8:00 AM.

But I don't that's actually right, that's too simple. I think it's more like the extreme ends (eg. 6:01 AM and 9:59 AM) have the absolute lowest chance, and as you get closer and closer to 8:00 AM the chances continue to improve, until they peak at 8:00 AM. If you graphed it , I think you'd basically see a half circle (or at least half oval), which touches the x-axis at 6:00 and 10:00 AM, and reaches its highest point at 8:00 AM.

But again, I've failed (and later passed ... but still, I initially failed) Algebra 2, Trigonometry, and Calculus, so I wouldn't even have bothered answering if anyone else had.

[eezl]

That makes sense to me Loramin, and that's how I've always viewed such spawns. Now, can people confirm that Stormfeather can skip x3?!

[Rang]

I never once saw Lodi pop in the “extended window” so I don’t think it’s real.

[Dugface]

The logic is correct Loramin, but I have my doubts that Lodizal is actually programmed that way. We need data from the Lodizal addicts please. Jailen and Ragu probably get most FTEs. Please supply a graph.Thanks

[CodyF86]

It would look like a sine wave...I think or:

https://imgur.com/W02vqGG.png

[Jibartik]

lol at the understanding variance can be difficult pic on the wiki

[loramin]

lol at the understanding variance can be difficult pic on the wiki

:D (although I can't take any credit, it was all d3r14k)

[TomisFeline]

it is a bell curve when multiple repeat windows are in question (assuming equal chance for every moment within the window).

the middle of the original window has the highest probability of overlap, given multiple expanding windows.

consider, even if the first windows non spawn happens at an extreme end, the next spawn chance could still be the center of the original window.

[TomisFeline]

to illustrate some of this with numbers,

let's assume mob can spawn every minute within an hour.

example 1
first spawn
1/60 chance boom you hit the last minute of that hour.
second spawn
you have again a 1/60 chance to hit the last minute of the (now larger) extended window

example 2
now if on the first spawn chance you hit anywhere at all 60/60 = 100%
on the second spawn chance you have a 1/60 chance of hitting the middle of the original window.

so comparing the two:
example 1
1/60 x 1/60 to hit the end of the window after two spawns
example 2
60/60 * 1/60 to hit the middle of the window after two spawns

[Frumplevernvern]

It's a uniform-sum distribution aka Irwin-Hall distirbution (https://en.wikipedia.org/wiki/Irwin%E2%80%93Hall_distribution) with the caveat that it won't skip more than twice (stops at n=3).

For example, this is what it looks like after 2 skips (https://www.wolframalpha.com/input/?i=uniform+sum+distribution,+n+%3D+3,+min+%3D+-1,+max+%3D+1).

Stormfeather works the same way but with a max of 3 possible skips.

Probability of skipping seems to be roughly 50% based on my sample of ~100 spawns but I'd be interested if someone actually has hard numbers for this.

[elwing]

Yes, that would be correct if the rng output was flat... But I fear eq rng is relatively flawed and I wouldn't be sutprised if it were top and bottom heavy...