Quick Math Question

[Tonko]

Got into a pretty heated debate with a friend today. It was over a drop rate issue in a game, and over two different ways of distributing the loot.

One way allows everyone in a group of 5 to roll on every drop.
The other way allows every 5th corpse to give you 100% of the loot on that corpse.

Given a static drop rate % for all items, is there a difference between the two systems regarding your personal chance to get a piece of loot?

[Howard Roark]

is there a static number of corpses?

afaict it only affects lootpools not in multiples of 5 if you go in with 5 members

[Tonko]

There's a finite # of corpses. Killing things in groups of 5 isn't the issue here though, it's the overall chance at drops. We'll say things are killed in groups of 5.

[Kaylia]

Got into a pretty heated debate with a friend today. It was over a drop rate issue in a game, and over two different ways of distributing the loot.

One way allows everyone in a group of 5 to roll on every drop.
The other way allows every 5th corpse to give you 100% of the loot on that corpse.

Given a static drop rate % for all items, is there a difference between the two systems regarding your personal chance to get a piece of loot?

The average (1 win every 5 kills) would be the same over a long period of time, the distribution however would not be the same. The 2nd method guarantee that everyone has the same number of wins (if the numbers of monsters killed is a multiple of 5), while the 2nd methods is subject to statistical fluctuation (large difference are less likely to happen, but they are still possible).

This is of course assuming that every monsters killed give you a reward. If drop rate isn't 100%, you still have the same difference between both distributions, except it's the chance to "win" an item that is distributed. Statistically, it just mean that you would have a normal distribution around the combined probability of the event (1/5 * 50% = 1/10).

Long story short, you will see most fluke appears when the combined chance to win an item is 50%. If it's 100% or 0%, everyone will get the same, and if it's 50%, it will follow a pretty bell curves.


[edit]
7am talk...I'm probably wrong, but i cant think of anything else right now.

[Apelila]

The other way allows every 5th corpse to give you 100% of the loot on that corpse.

Explain more on this.

Does everyone get to loot the 5th corpse? If not, how is who gets the drops determined? If so, does the 5th drop more in relation? The 'how' on the second part is going to play a part, but the second way still has more variables than the first.

[netz]

Explain more on this.

Does everyone get to loot the 5th corpse? If not, how is who gets the drops determined? If so, does the 5th drop more in relation? The 'how' on the second part is going to play a part, but the second way still has more variables than the first.

Every xth kill is WoW's group loot system. It makes sure people in the group get the opportunity to loot roughly the same number of corpses over the course of an instance. The only difference here is that Tonko's system is blind to the quality of loot that drops, and he has also set up a case where everybody does get to loot an equal number of corpses (this isn't always true in WoW).

I'd say there's no difference. Both are cases of discrete probability, because an item dropping doesn't alter its probability of dropping again, and your rolling and winning or losing on an item doesn't change anything about your next roll, so you should be able to multiply the probabilities together and arrive at the same probability for both of your methods.

What might be confusing the issue here is the probability of consecutive drops, which someone could be treating as the drop rate after something drops, and it isn't -- that is a different scenario entirely with a different probability. Yes, your probability of getting something after something drops is low, especially consecutively, but it doesn't change the fact that each corpse looted has its own individual probability for an item to drop, and that rate doesn't change.

[Tonko]

Explain more on this.

Does everyone get to loot the 5th corpse? If not, how is who gets the drops determined? If so, does the 5th drop more in relation? The 'how' on the second part is going to play a part, but the second way still has more variables than the first.

Simply that out of every 5 corpses, each person in the group has 100% loot privileges to everything on 1 of those 5 corpses.

Person A gets every 1st, 6th, 11th, 16th, etc
Person B ets every 2nd, 7th, 12th, 17th, etc
Person C gets every 3rd, 8th, 13th, 18th, etc
Person D gets every 4th, 9th, 14th, 19th, etc
Person E gets every 5th, 10th, 15th, 20th, etc


And so on.

And yes, this is a WoW loot issue. I had a friend swear up and down to me that changing the loot threshold to Rare, instead of Uncommon, would reduce their chances of getting a green item.

I told him he was wrong, and the only thing I was doing was eliminating the need to roll on every green that dropped. Since the corpse loot assignments are in order, you are garunteed 20% of the corpses in a kill total with a factor of 5.

[Jotaru]

Yep, in a large enough sample size, its the same.

The only time I can see it being different were if you were to kill, say, 9 mobs- now the 20% per kill vs. 1-in-5 is different. Sample size is important hurr

[Cadsuane]

For simple examples sure. You'll loot 1/5th of all corpses if you loot every fifth corpse in a group of five, in other words any particular corpse has a 1/5th chance of being yours. Beating 4 other people on a lot is a 1 in 5 shot as well, so, same odds of getting a dorp. However, it's only true if the whole drop pool goes to the same person with system A, and that everyone is lotting on the whole pool in system B. If this isn't the case it's more difficult to compare.

[Tonko]

It would only be one item possibility per corpse that we're concerned with.

[Enygma55]

Lets say all corpses drop the same item at 20% of the time.

Addressing the 1st method, everyone has a 20% chance at every time it drops.

Addressing the 2nd method, Your chance at getting said item is 20% of the time but on every 5th kill.

1st method will give you more chances at winning the item because regardless of the droprate everyone has an equal chance at winning it at every drop.

2nd method your alot more dependent on the droprate being generous on your kill.

Since your only aiming at 1 specific loot item the 1st method is more promising.

[Tonko]

Lets say all corpses drop the same item at 20% of the time.

Addressing the 1st method, everyone has a 20% chance at every time it drops.

Addressing the 2nd method, Your chance at getting said item is 20% of the time but on every 5th kill.

1st method will give you more chances at winning the item because regardless of the droprate everyone has an equal chance at winning it at every drop.

2nd method your alot more dependent on the droprate being generous on your kill.

Since your only aiming at 1 specific loot item the 1st method is more promising.

That's what he was saying, the problem is that the 1st method also depends on the item first dropping, and then you winning the roll.

Statistically given an infinite sample size with a factor of 5, the second method is exactly the same. You first need to have the corpse assigned to your loot, and the item be on it. The argument you just proposed would result in a lower number of total items dropped given the second method, and that's not the case.

At the end of the run, the same total number of items will drop. The loot method doesn't influence that at all. Again, assuming an infinite sample size, factor of 5, you'll win 20% of the rolls, OR get 20% of the corpses.

[Enygma55]

At the end of the run, the same total number of items will drop. The loot method doesn't influence that at all. Again, assuming an infinite sample size, factor of 5, you'll win 20% of the rolls, OR get 20% of the corpses.

I get what your saying and I'm in agreement, its all the same in the end.

Just some notes on how it can be seen skewwed.

The 1st method will feel more fair because the item is already present and your rolling for claim.

The 2nd method might make it feel your getting the shaft. If your 5th in the loot order and the item only seems to drop on the 4th, then 9th, then 13th, then 18th, then 57th.

You just went thru the entire run without feeling like u even had a chance when in actually your just banking on the drop being every 5th but lost.

[Suiram]

Both methods give the same chance at getting an item in the sense that if you looked at all the different possible outcomes of killing the same number of mobs (provided, of course, and as people have already said, that this number is a multiple of the number of eligible lotters) and averaged all of those outcomes weighted by their chance of occuring, then everyone's chance of getting the item will be the same as everyone else's, and it will be the same in both lotting procedures.

They are not identical, though, although the difference is not in one person's overall chance of an item, but rather in the possible sets of distributions of all of the items that drop. This is where my lack of coffee and statistics knowledge catches up to me, however, so hopefully someone will come along and elaborate upon and justify what I'm saying, or else point out the flaw, but it seems to me that the 2nd method (rotating 100% lotting privileges) will make it more likely that the loot distribution in a given run is more spread out (that is, diminish the chances of one person walking away with disproportionately more items than another). This would be obvious in the case where the mob has a 100% drop. If you kill 100 with 5 people, in the second method everyone walks away with 20 of the item, whereas in the first method there's always the chance that one person has 40 and the rest have fewer, or that one person wins all lots and nobody else gets any, however small of a chance that may be. Maybe it doesn't hold up though as the chance of an individual drop gets lower, again hopefully someone will come and confirm/rebut this.

Assuming that I'm right, though, it would seem that at least in situations where a person will want multiples of a given drop, the 2nd method is more "fair" in some sense. On the other hand, if it's the sort of thing that you only need/want/can obtain one and then you pass the rest, I don't think it would make a difference, and the first method is probably easier to enforce.

[Cadsuane]

It would only be one item possibility per corpse that we're concerned with.

Then yeah, it's identical.

You're among five people, farming a 15% drop rate.

Using method one, 15% of the corpses drop, you have a 20% (1 in 5) of winning the lot. Chances that on any particular mob you get the drop is 0.15*0.20=0.03. Or, the probability that you will win the lot given that the mob dropped is 3%.

Method two, you lot 20% of the corpses, 15% of which drop. The probability that the loot drops given that the mob is yours is still 3%.

[Komm Suesser Tod]

The problem with a system like wow is that given a small enough sample size, one person can get every drop with a roll off. I've seen it too, a run through scarlet stratholme back in the day saw our warrior get every single green drop, of which there were 12.

[Kaylia]

Then yeah, it's identical.

You're among five people, farming a 15% drop rate.

Using method one, 15% of the corpses drop, you have a 20% (1 in 5) of winning the lot. Chances that on any particular mob you get the drop is 0.15*0.20=0.03. Or, the probability that you will win the lot given that the mob dropped is 3%.

Method two, you lot 20% of the corpses, 15% of which drop. The probability that the loot drops given that the mob is yours is still 3%.

The average would obviously be the same in both case. There is no doubt about it. However, is the distribution going to be the same around that average?

[Daydreamer]

I'm just going to say that it's awesome that that example spawned this kind of discussion.

That is all.

[Khamsin]

I'd go with lot offs, because with everyone getting every xth corpse, you're assuming everyone will want what they get. With lot offs, people who don't want a particular item don't have to lot it, which allows people who do need it to have a better chance at it.

For example, I'd never do an every xth corpse system in dynamis, or I'd end up with AF for jobs I don't have, and someone else would get the AF I really wanted.

[Kaylia]

I'd go with lot offs, because with everyone getting every xth corpse, you're assuming everyone will want what they get. With lot offs, people who don't want a particular item don't have to lot it, which allows people who do need it to have a better chance at it.

For example, I'd never do an every xth corpse system in dynamis, or I'd end up with AF for jobs I don't have, and someone else would get the AF I really wanted.

They are talking about the loot you sell at the vendor for money. The good stuff is rolled normally, but low quality item are distributed with the method in question.