Understanding Probability

[TheAncient]

[hide=Introduction]

 

Introduction

 

Half of Runescape is chance: whether youÃÆââââ¬Å¡Ã¬Ã¢ââ¬Å¾Ã¢re trying to attain a max hit, digging for 3rd age, or monster hunting for treasure. Understanding chance, or probability, will help you to better understand how often youÃÆââââ¬Å¡Ã¬Ã¢ââ¬Å¾Ã¢ll get a drop, or when you can expect to see one of those awesome DDS specs. In this guide, we will investigate weaponry, rare items, the controversial ring of wealth (ROW), and so many more unanswered questions using our understanding of probability.[/hide]

 

 

 

Drop Rates

 

[hide=Basics]

 

The Basics: Drop Rates

 

- Usually, we like to express chance using a fraction, decimal, or percent. LetÃÆââââ¬Å¡Ã¬Ã¢ââ¬Å¾Ã¢s say we have a 1 in 100 chance of getting a dragon chain from a kalphite queen. We write this as 1/100, .01, or 1% chance.

 

- We can multiply probabilities to find the chance of the same event more than one time. For example, the chance of us getting 2 dragon chains in a row is (1/100) x (1/100), or 1/10000.

 

- We have a 99/100 chance of not getting the chain. If the chance of getting the chain was 1/1000, we would have a 999/1000 chance of not getting the chain. The chance of something not happening is 1 minus the chance of that something happening, or (1 ÃÆââââ¬Å¡Ã¬Ã¢ââ¬Ãâ chance).

 

- Based on my second and third conclusions, we can say we have a (99/100) x (99/100), or (99/100)^2 chance of not getting a chain after two kalphite queens. After three KQs, our chance of not getting the chain would be (99/100)^3. After five KQs, our chance of not getting the chain would be (99/100)^5, and so on.

 

- You can also conclude we have a 1 ÃÆââââ¬Å¡Ã¬Ã¢ââ¬Ãâ (99/100)^2 chance (= .0199, or 1.99%) of getting the chain after two KQs, or 1 ÃÆââââ¬Å¡Ã¬Ã¢ââ¬Ãâ (99/100)^5 chance (= .049, or 4.9%) of getting the chain after five KQs. After killing ÃÆââââ¬Å¡Ã¬Ãâ¦Ã¢â¬ÅxÃÆââââ¬Å¡Ã¬ÃâÃ

[Ryuuka]

great stuff :thumbsup: 9/10 needs some pictures maybe a dragon chain drop

[go461]

wow that last part was helpful, thx :mrgreen:

[kemikalkadet]

Very nice, it's written in a way nearly everyone can understand too. i knew a lot of it already.. particularly about drops, but its nice to see it laid out like this. :thumbsup:

[smobo]

Yay math solves all. Here is another usefull forumla:

 

 

 

On average you will get a drop this often:

 

 

 

(1-chance)/chance

 

 

 

So, as in your example, if a d chain drop 1 in 100, the chance is 0.01. Therfore:

 

 

 

(1-0.01)/0.01 = .99/.01 = 99

 

 

 

thus on average, you get a chain every 99 kills.

 

 

 

There is a whole bunch more formula, but this is the only usefull one for this i can think of off the top of my head.

[TheAncient]

Yay math solves all. Here is another usefull forumla:

 

 

 

On average you will get a drop this often:

 

 

 

(1-chance)/chance

 

 

 

So, as in your example, if a d chain drop 1 in 100, the chance is 0.01. Therfore:

 

 

 

(1-0.01)/0.01 = .99/.01 = 99

 

 

 

thus on average, you get a chain every 99 kills.

 

 

 

There is a whole bunch more formula, but this is the only usefull one for this i can think of off the top of my head.

 

 

 

The average thing doesn't really work. Since it's hard to kill KQ, most people won't kill more than 300-400 in their RS lifetimes, usually not enough kills to get exactly (or even close to) the drop ratio. You probably need at least 1000 kills, maybe more, and you'll get something like 8-12 drops which is close enough to the actual ratio.

[The Real ET]

Nice guide, I'm going to use this as reference whenever possible. This kind of thing doesn't need pictures so 9/10, only because you can't be sure. :thumbsup:

[pokexpert]

We use the slow weapons (rune crossbow/dbow/cbow, whip) first, until we get lucky and hit a high amount.

 

Isn't the whip as fast as a dagger? :-k

[TheAncient]

We use the slow weapons (rune crossbow/dbow/cbow, whip) first, until we get lucky and hit a high amount.

 

Isn't the whip as fast as a dagger? :-k

 

 

 

DDS special is 2x as fast as whip.

[craggyp]

first of all smobo, if the drop rate of a dchain is 1/100, the average number of kills it will take you to get one is 100. the 1/100 is basically saying that out over every 100 kills, 1 drop will be a dchain.

 

 

 

if you were to look at, say 100,000 kills, we expect that over such a long period of time any inconsistencies and outlying results will cancel each other. such as not getting a dchain in 500 kills, and getting one in 5 kills. if you take this out to infinity, you'd find that the average number of kills it would take would be 100. this is dictated by the fact that the drop rate is a pre-set variable. if, after infinite kills, the rate actually was 1 every 99 kills, then we would have to assume that the drop rate within the programming is 1/99.

 

 

 

or maybe I'm looking into this too much.

 

 

 

sseli: it took me a while to understand what you meant when you said that a ddp will hit more in the medium range. then I remembered what standard deviation is. all in all, a very very nice intro to the basic statistics of the game. 8/10 for the guide :D

[mchainmail]

first of all smobo, if the drop rate of a dchain is 1/100, the average number of kills it will take you to get one is 100. the 1/100 is basically saying that out over every 100 kills, 1 drop will be a dchain.

 

 

 

 

That is not necessarily true. Assuming the drop rate is 1/100, then the odds of not getting any d-chains after 100 tries would be (1-(99/100)^100), or 63.4%. The odds of getting 1 d-chain within those 100 tries would be (1-(99/100)^99*(1/100) - (1-(99/100)^100)), or 36.2%. The odds of getting more than 1 d-chain would be 100-36.2-63.4, or .4%.

 

 

 

The drop rate can only be applied if you kill an extremely large number, such as 10,000. Otherwise, you would use these odds to determine the likelihood of getting a d-chain drop.

 

 

 

Because there is a chance of getting more than one d-chain, that skews the odds.

[meme79]

We use the slow weapons (rune crossbow/dbow/cbow, whip) first, until we get lucky and hit a high amount.

 

Isn't the whip as fast as a dagger? :-k

 

 

 

DDS special is 2x as fast as whip.

 

 

 

thats with spec, the whip's hits are only slighly longer than dagger, far less than the onthers menchoned

 

 

 

 

 

nice giude, i little difrent, 8/10

[craggyp]

yeah mchain, you're right. this is a kill-by-kill situation, and getting one chain doesn't exclude you from getting another instantly. I just didn't think that his reasoning on the "1 in 99" thing seemed right. but I freely admit I could be wrong. also, statistics tends to be a very murky field, because there are so many ways of looking at the numbers you get. what type of distribution, how much data, what is the process, etc. I think the guide does an excellent job of giving people an idea of how the numbers can work without paralyzing them via information-overload :)

[oni_link007]

One important thing to note is that the drop rate is said to be "without memory".

 

 

 

That means that the drop is independant of the earlier drops. So the odds of getting a d chain at the 259th kill is the same as getting one on the 1st kill. Is know this is not much info, but it's just to note that the probabilities are calculated in a stochastic way (i.e over a large number of drops).

 

 

 

The essence of this post is just to say that don't have your hopes too high on drops if you have been training on the same monster over and over in hopes of getting a very good drop. Having killed it 1000 times doesn't give you more chance of getting a rare drop than having killed it 10 times.

[phata_elise]

I love mathematics :P

 

 

 

Of course, the biggest problem is knowing the actual drop rate. Without that information it is very hard to make any predictions.

 

 

 

One thing that would be nice is to turn the table of drop chance versus amount of KQ into a graph. That provides as much information as the table, but is easier to understand and faster to use.

[TheAncient]

One important thing to note is that the drop rate is said to be "without memory".

 

 

 

That means that the drop is independant of the earlier drops. So the odds of getting a d chain at the 259th kill is the same as getting one on the 1st kill. Is know this is not much info, but it's just to note that the probabilities are calculated in a stochastic way (i.e over a large number of drops).

 

 

 

The essence of this post is just to say that don't have your hopes too high on drops if you have been training on the same monster over and over in hopes of getting a very good drop. Having killed it 1000 times doesn't give you more chance of getting a rare drop than having killed it 10 times.

 

 

 

Right logic, wrong conclusion. For each individual monster killed, your chances of getting a drop won't increase. However, if you look at the whole picture, a person who kills more monsters has more opportunities to get the drop, and thus has a larger chance of getting the drop.

 

 

 

I love mathematics :P

 

 

 

Of course, the biggest problem is knowing the actual drop rate. Without that information it is very hard to make any predictions.

 

 

 

The ability to calculate drop rate is one of my conclusions ;) But it would require too much organization...

[Dudecrush8]

Nice job... your the most mathamatical person I have ever met on these forums \

 

 

 

Your Expounding Evindence Compremises my Indistingishable Comprehension Abilitys...

 

 

 

Did that confuse your impressive brain?

 

 

 

10/10 :thumbsup:

[Nitemare100]

Ok i thought i was good in math (A+ student) but this really hurts.. i don't understand much of it. :x

[dkjestrup]

Ok i thought i was good in math (A+ student) but this really hurts.. i don't understand much of it. :x

 

 

 

yeah, I sort of get you, I'm only 12 :-# but I'm doing ncea maths (year 11/form 5) and I almost got mucked up with it, then I realised you mean't this.

 

 

 

X^2 as in X to the power of two. I get basically everything else, fairly good, but if you say made it simpler like below it would be better.

 

 

 

Conclusion.

 

 

 

per kill you have a 1/100 chance of a d chain from the KQ. The average amount to get a d chain is in around 60-70 kills. Of course results may vary.

[phata_elise]

I love mathematics :P

 

 

 

Of course, the biggest problem is knowing the actual drop rate. Without that information it is very hard to make any predictions.

 

 

 

The ability to calculate drop rate is one of my conclusions ;) But it would require too much organization...

 

 

 

As long as that research hasn't been done, we don't know the actual drop rate ;)

 

 

 

I like your guide (hey, i love mathematics ;)) and I read it again a bit more thoroughly this time.

 

Do you have a source for the the theory behind the ROW or is this an assumption you made? As far as I know Jagex never released the actual effect of the ROW, just that it increases your chance for "better" items.