Variance (and Skips)

[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:

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[Jibartik]

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

[loramin]

Originally Posted by Jibartik [You must be logged in to view images. Log in or Register.]

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

[You must be logged in to view images. Log in or Register.] (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 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.

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.