Math and Spawn Rates

[Snagglepuss]

I've noticed that we have some mathematically oriented minds on the forums (Tecmos, Loraen, Koros, Ele, etc). It seems like every few weeks someone is asking about what is normal for a spawn rate as far as what is a good run or bad run of variance and to what extent.

I've played a enough poker to understand things like risk of ruin and how variance can be your best friend or your worse enemy. Many older players at the table will always say to a bad beat, "I'd rather be a lucky player than a good player..." From the point of view of a professional poker player, you should look at each table siting as the piece of one big game that never ends. This way, your actions that have positive expected value will pay off over time...

Now, what I want to know concerns spawn rates. I was camping a mob that "according the wiki" had a 5% chance to pop on a standard outdoor timer. Being static, I had no reason to worry about any other variables or PHs. The bugger was killed immediately as he spawned, then I would reset my timer. Between two people, we camped the mob 29 hours straight this weekend to no avail. I guess we saw around 265 to 270 spawns.

Obviously, this is a run of bad luck, but what I'm interested in knowing is how bad. If you normally distributed its chance to pop, what would be considered outside one standard deviation? Also, should I look at this knowing the old gambler's fallacy and interpret my chances of camping a mob as "one big camp." It's hard to tell yourself after a 12 hour session that he's got to pop within the hour, but we all know fortunes have been lost from the words, "I can't keep getting these cards. One more hand; I know I'll get some good cards soon!" All actions are independent of the outcome, correct? Every chance is 5%, even if you have gotten no pops 267 times in a row? Wouldn't that be as unlikely as getting 12 pops in a row though? Still 5%...

Could someone explain some math or statistics about how long a camp like that could take and still be within the realm of "reasonable bad luck"?

[Vayder]

If the spawn chance is really 5% and you were killing the correct PHer you're results are literally right around 1 in a million (1.13 in a million rounded).

This is far more likely than getting the named to pop 12 times in a row however (which is around 24 in a quadrillion chances).

[Itap]

Reminds me of raster camp in lguk. I remember helping a friend do it back in 2001 and we sat down there for around 36 hours straight before he popped.

[Ele]

Sounds like a pained soul thread. That camp leaves plenty of time to ponder the deeper things in life.

You've already addressed the biggest mistake I've seen people make about these kinds of camps, which is the gambler's fallacy. "Just one more spawn, I've been here forever, it has to happen soon!" Each and every spawn is an independent event (in most cases) that has no bearing on the what the last place holder was. It was 5% last time, it is 5% this time.

With a 5% chance to occur, there is a 95% chance that it does not occur.

[Itap]

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

"Just one more spawn, I've been here forever, it has to happen soon!"

Lol, I think this is just what people to say to keep themselves from slipping into senility.


What hurts more is when soandso goes in there and gets spawn within an hour.

[zanderklocke]

I sort of just posted this on another thread, but I'm wondering where people pull most of their data from spawn rate percentages to drop rate percentages. I'm not a computer wizard, so I'm not sure if people have readily available access to source code somewhere? Or, is this proprietary information, and I'm just being naive?

[jerok88]

The math is: 95%^267, which is .000000112% chance of it not spawning every single time. 1/.000000112 = this happens once every 886,742 times.

[Briscoe]

Assuming everything is "working as intended," I tend to think that 5% is a bit too optimistic of a reported spawn rate. If we assume instead a 1% spawn rate, then the chances of 270 consecutive placeholders is 1 in 15, which is five orders of magnitude more likely to occur than 1 in 1 million (which is indeed the right number, as calculated by Vayder above).

[Handull]

One important thing to look at is how long this server has been running for.

Flip a coin 8 times, you'd expect to get at least one heads and one tails (ie you won't likely see a streak of 8 of the same outcome). Flip a coin 1000 times, you have a pretty good shot of at some point over that 1000 to see a streak of 8 heads or 8 tails in a row.

If you ask people to imagine they flipped a coin 20 times and to make up the results (asking someone to make a randomized distribution), most people will avoid longer streaks of the same result, even though statistically they aren't unlikely.

The last thing to consider is that the people who get the bad luck of not getting a spawn over X hours will likely be more vocal about their failure than the person who just found the mob up randomly, or got a spawn in only a short period of time. So just by browsing the forums it would sound like tons of people have this bad luck, but there are just as many who have good luck and don't post about it.

And like Ele said, each spawn is an independent event. Though don't give up, cause then you'll never get it.

[zanderklocke]

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

One important thing to look at is how long this server has been running for.

Flip a coin 8 times, you'd expect to get at least one heads and one tails (ie you won't likely see a streak of 8 of the same outcome). Flip a coin 1000 times, you have a pretty good shot of at some point over that 1000 to see a streak of 8 heads or 8 tails in a row.

If you ask people to imagine they flipped a coin 20 times and to make up the results (asking someone to make a randomized distribution), most people will avoid longer streaks of the same result, even though statistically they aren't unlikely.

The last thing to consider is that the people who get the bad luck of not getting a spawn over X hours will likely be more vocal about their failure than the person who just found the mob up randomly, or got a spawn in only a short period of time. So just by browsing the forums it would sound like tons of people have this bad luck, but there are just as many who have good luck and don't post about it.

And like Ele said, each spawn is an independent event. Though don't give up, cause then you'll never get it.

Posts like this are such a great read. That was excellent.