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What does randomness look like?

empiricalzeal.com

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Re: What does randomness look like?

#11
Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot.

And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss, what people think should happen is that if they kill that boss X times, they should see it drop once.

But the reality was of course that loot was very non-uniform. Some pieces we saw lots of times, and other pieces very rarely, despite them having the same drop chance. And the players who wanted those pieces that happened to be rare for our guild, got very, very angry.

We saw the same things on the official message boards, players were furious after having spent a year killing the same raid boss once a week, and never seeing a certain piece drop for them. But simple math shows that with million of players, tens of thousands of raiding guilds, some of those will see very streaky results.

These days in World of Warcraft, boss monsters drop tokens instead, and when you have X tokens, you can exchange that for a piece of armour, or a weapon, guaranteed. And noone complains about the random loot anymore.

Re: What does randomness look like?

#12
post #9

Very interesting! So, the basic point being made is that if you know that a set of events are random and independent and you know their mean value, then you can predict their spread? (or aggregation) edit: Hmm...another question that comes to mind: is the converse true? If the spread of values of these events do not match the poisson distribution, then can we presume them to be nonrandom? Or nonindependent? Or both?

The Poisson distribution is just one random number distribution; there are several others for situations where the events are correlated, or have other properties. Half the fun of probability is figuring out which distribution is the right one to apply to the question at hand. So if your measurements don't match up to Poisson, it doesn't mean they're not random - they could just be interdependent.

So yes, for a Poisson process, the spread (standard deviation) is equal to the square root of the mean; as the number of events gets large, the Poisson distribution approaches the normal distribution, but the relationship between the standard deviation and the mean continues to hold.

Re: What does randomness look like?

#13
Regarding the bomb plot at the very bottom. Examining the number of bombs dropped in each square and comparing it to the Poisson distribution, it appears that the distribution of the bombs is random.

But looking at the plot on the map, it appears that the higher incidence of bombs is focused on a specific region. The Poisson distribution doesn't account for the fact that a lot of the squares with a high incidence of bombs are adjacent to each other. From my layman's understanding, it appears that the bombs were in fact targeted on a specific area, but that there was a random offset from this area regarding where the bombs actually landed. Because of this, you'd see randomness in the distribution. But the distribution of bombs wasn't really perfectly random.

Is the author deliberately avoiding this point, or is there something I've misunderstood?

Re: What does randomness look like?

#14

Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot. And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss…

This is actually an important lesson for game designers. Real randomness is very frustrating for players! Games should be designed to not be random. For example, there's an expansion to The Settlers of Catan that lets you use cards instead of dice to ensure a nice smooth distribution of resources... I think it's a lot more fun!

Re: What does randomness look like?

#15

Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot. And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss…

Yeah,

And you know, it is always possible in those situations that there is a broken pseudo-random number generator involved. But of course, that's really hard to tell too because real randomness is so unrandom seeming.

Re: What does randomness look like?

#16
post #13

Regarding the bomb plot at the very bottom. Examining the number of bombs dropped in each square and comparing it to the Poisson distribution, it appears that the distribution of the bombs is random. But looking at the plot on the map, it appears that the higher incidence of bombs is focused on a specific region. The Poisson distribution doesn't account for the fact that a lot of the squares with a high incidence of…

I believe the table at the end deals with a subsection of the 3d graph, but I could be wrong.

Re: What does randomness look like?

#17

Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot. And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss…

These days in World of Warcraft, boss monsters drop tokens instead, and when you have X tokens, you can exchange that for a piece of armour, or a weapon, guaranteed. And noone complains about the random loot anymore.

This bit is not correct. All of the most desirable items (except darkmoon trinkets and tier sets) drop directly from raid bosses, and people still complain about the outcomes of random loot.

Re: What does randomness look like?

#18
post #13

Regarding the bomb plot at the very bottom. Examining the number of bombs dropped in each square and comparing it to the Poisson distribution, it appears that the distribution of the bombs is random. But looking at the plot on the map, it appears that the higher incidence of bombs is focused on a specific region. The Poisson distribution doesn't account for the fact that a lot of the squares with a high incidence of…

If you read the linked post its clearer whats going on: http://madvis.blogspot.ie/2010/09/flying-bombs-on-london-sum...

The poisson analysis is only done on a subset of the area thats in the 3d plots: "Clarke's analysis was focused on the central area of higher density here and with finer geographic coordinates. Within that area his analysis found no evidence of clustering that cannot be accounted for by a Poisson process."

Re: What does randomness look like?

#19

Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot. And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss…

On the other hand, sometimes it turns out the players are right when they suspect something is biased against them.

In Everquest when you cast a spell, there was a chance the spell would fizzle.

Occasionally, someone would get a streak of fizzles. Many argued this was just the normal streakiness you expect when you are do repeated independent trials. Some insisted that fizzles streaks were more common than you'd expect based on that model.

Finally, a statistician who also played EQ spend some time gathering data, and determined that fizzling was not independent. Your fizzle chance was an increasing function of the length of your current fizzle streak, up to a cap.

Things like that give a game character.

Re: What does randomness look like?

#20

Back in the day I was in a raiding guild in World of Warcraft. And back then, each boss monster in a raid dungeon had a loot table, and when you killed it, your raid got a few pieces of random loot. And I don't know how many times I, and the other guy in the guild who understood statistics, had to explain to the others that random doesn't mean uniform. If a certain piece of armour has a 1/X chance to drop from a boss…

A market would also fix this, in effect averaging over the entire population. Given players' anger at pieces not dropping as often as they "should", the market would converge approximate the true ratio between drop frequencies of different pieces.
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