A Range calculation tip

I don't think that a lot of players in the community are aware of how to

estimate the numbers of arrows needed when you do or don't pick up your arrows.

This is what you need to do:

1) First, you need to know how much exp you need to earn.

You can use the Tip it range calculator to compute how much experience is required.

So, to go from level 79 to 80 ranging, I need 187260 range exp.

2) Second, you need to calculate how many total arrow hits are required to earn that experience.

You can use the Tip it range damage table

At level 79, Iron arrows hit for a max of about 10.

So, I'm going to assume that I average half of this max, or max/2.

We always earn Range exp equal 4 times the hit, so my average range exp per shot is max/2*4 which is

Average Range exp per arrow = 2*Max

Therefore, I need 187260/(2*10) = 9363 arrow shots.

3) Third, how many arrows do I need if I do or don't pick them up.

If I don't pick up my arrows then I need about 9363 arrows.

If I do pick them up then I am only going to be able to get a certain portion of them back and then I will reuse them.

Let's call the portion that we get back, p

(p will always be between 0 and 1)

If we get all of them back, p=1

If we get only 1/3 back, then p=0.333

If we get half back, then p=0.5

In practice, I find that I get about 3/4 back, so p=0.75

So, If I start with 1024 arrows and I shoot all of them then

if I am able to pick up 3/4 of them, I'll have 1024*3/4 = 768 remaining.

If I then shoot those 768 arrows and pick up 3/4 of them, then I'll have 576 remaining.

If I shoot those 576 and pick up 3/4 of them I'll have 432 remaining.

And so on and so on and ...

So the question is, "How many arrow shots can I get with those 1024 arrows?"

If you have been keeping score, we shot 1024+768+576+432+... arrows.

If we wrote the above sum in terms of the number of arrows, A, and the

portion that we got back, p, then the sum can be expressed as

Shots = A + A*p + A*p*p + A*p*p*p + ...

or

Shots = A*(1 + p + p^2 + p^3 + p^4 + ...)

So the issue is how do we handle the sum of these p terms that get

smaller and smaller until we run out of arrows.

Well, here I wave my magic bow and claim that

1/(1-p) = 1 + p + p^2 + p^3 + p^4 + ...

You can perform the long division above and verify that, indeed

1/(1-p) does equal the funny 1+ p + p^2 + ... sum.

So, we then have Shots = A*1/(1-p) or

A = (1-p)*Shots

So, continuing with my example,

I needed 9363 shots and I pick up 3/4 of those shots.

So I need (1-3/4)*9363 = 2341 arrows to reach my goal :D

So the equation to use is

ArrowsNeeded = (1-p)*ShotsNeeded

So, in summary

1) Use the Tip It range calculator to calculate how much exp you need

2) Use the Tip it range damage vs arrow type table to calculate how many shots you need.

It's best to do this 1 level at a time because you max hit goes up with level.

The equation is ShotsNeeded = ExperienceNeeded/(2*MaxHit)

3) Calculate the number of arrows needed as

ArrowsNeeded = (1-p)*ShotsNeeded

Or, you could put it all together in a sort of 'master range formula' as

ArrowsNeeded = ExperienceNeeded*(1-p)/(2*MaxHit)

where p=0 if you do not pick up and p is about 0.75 if you do

So, for my example I get 187260*(1-0.75)/(2*10)

or 187260*0.25/20 = 2341 as expected.

Now, keep in mind that the long term average of damage done is not always going to be Max/2

and that the portion of arrows gotten back is not always going to be 3/4.

So if you don't like my suggested values for Max hit and p then

go ahead and use your own values.

Now, at least, you have a formula that ties everything all together.

Hope this helps.

:D Good job for writting this up, maybe get some Tipit staff to incorporate this into the calculator? From what I see, quite a few Scapers wouldn't have a clue what you are speaking of.

To emphasize the usefullness of picking up your arrows,

look at how many shots you can get with 1000 arrows if you

... pick up none, you get 1000 shots

... pick up 1/4, you get 1333 shots

... pick up 1/2, you get 2000 shots

... pick up 3/4, you get 4000 shots

... pick up 80%, you get 5000 shots

... pick up 90%, you get 10000 shots

So if you can pick up your arrows, you can save

yourself a lot of time and/or money when ranging.

wow, looks like you put alot of thought into this. were you procrastinating away from real work? I tend to come up with all sorts of useful things when trying to avoid real work lol. I'm liking it, would be cool to see it in a calculator too, although, you do have to make allowances for the rude people who steal your arrows(i was training with bronze yesterday, and some 92 was picking them up lol).

...although, you do have to make allowances for the rude people who steal your arrows...

That's exactly what "p" does.

It represents the portion of your arrows that you get back.

Use whatever value seems right for your current ranging situation.

This guide is a bit hard to understand at first, but then I realized it's very useful. The only thing i found is the p=3/4.

I thought that it would change with other arrows materials like, for example, P=0,5 with bronze, up to p=0,8 to rune or something like that. What kind of arrow were you using when you got that percentage?

Congratz I believe it should be added

Sounds like you could be a good mathmatician.

... is the p=3/4.

 

I thought that it would change with other arrows materials like,

 

for example, P=0,5 with bronze, up to p=0,8 to rune or something like that.

 

What kind of arrow were you using when you got that percentage?

You raise a very good question.

I observed that I get back about 75% to 80% typically with bronze arrows against lesser demons.

I use bronze because I have 10000 of them from various drops, lol

But when I have used other arrows It seemed that the Addy arrows were gone very quickly.

So, perhaps Jagex has made higher arrows vanish more quickly.

Or, perhaps it also depends on the monsters range defense as well.

The way to answer your question would be to run an experiment

with a 100 or so of each arrow and see if there is a difference.

Lots of data from the community would be useful in that regard...

 

2) Second, you need to calculate how many total arrow hits are required to earn that experience.

 

You can use the Tip it range damage table

 

At level 79, Iron arrows hit for a max of about 10.

 

So, I'm going to assume that I average half of this max, or max/2.

 

We always earn Range exp equal 4 times the hit, so my average range exp per shot is max/2*4 which is

 

Average Range exp per arrow = 2*Max

 

Therefore, I need 187260/(2*10) = 9363 arrow shots.

 

Nice guide, however you're forgetting something.

You're assuming that all your arrows hit. This is obviously not the case.

So this will change your average range exp per arrow to:

A*2*Max,

in which A is a factor between 0 and 1, indicating your changes of hitting. (for example 0.5 means that half your shots hit).

...Nice guide, however you're forgetting something.

 

 

 

You're assuming that all your arrows hit.

No, I'm not.

Some arrows hit 0 and some arrows hit the max.

Most arrows hit somewhere between the 2 extremes.

The idea is to use an average value for all arrows shot.

So if 14 arrows hit 0, 5, 10, 1, 0, 9, 3, 8, 2, 10, 7, 4, 6, 5

The average hit of these 14 shots is 5 which is Max/2

even though 2 of the arrows hit for 0 damage.

Look at what is implied in my statement,

...So, I'm going to assume that I average half of this max, or max/2...

That means that some arrows will hit more than the average and some will hit less.

Some can even hit the max and some can hit a 0.

 

So this will change your average range exp per arrow to:

 

 

 

A*2*Max,

 

 

 

in which A is a factor between 0 and 1, indicating your changes of hitting. (for example 0.5 means that half your shots hit).

First, your use of A is confusing since I already used it to represent

the numbers of arrows involved. Better to use something like "k" to

represent the scaling that you want to indicate.

Second, we all understand that any particular arrow

is going to hit somewhere between 0 and the max.

My point of using Max/2 as the average hit per arrow is based upon

the assumption that most arrows won't hit the max, most won't hit 0,

and most will hit somewhere in between the 2 extremes with an average

hit of Max/2.

In your nomenclature, that would be a factor of 0.5

Third, the point of my post was to generate some formulas to allow

a player to estimate arrows needed and expected experience.

In the post I said,

...So if you don't like my suggested values for Max hit and p then

 

go ahead and use your own values.

In my post I showed where each term came from, so any player could

plug in any numbers that they think are better values to use.

The formula allows the user to account for the average arrow

hit and different amounts of arrows gotten back.

Hope this clears up a few things.

Whoa, what do you know, I use the EXACT same calculations on the range calculator I use on microsoft excel. I generally go with 20% break rate instead of 75, guess I'm just an optimist, eh?

But yeah, nice work taking the incentive to figure all that out, I spent a while trying to make sure my break rates were right.

The (X*.75)+((X*.75)*.75)... part was a real nuisance to write down over and over though.

..I generally go with 20% break rate instead of 75, guess I'm just an optimist, eh?...

Hmmm, the 75 value is the non-break rate.

So a 75 non-break would be 25% break rate which is close to yours.

'Course, use whatever value you think is most accurate.

you forgot to factor in the fact that as your range increases so does your max damage... for some of the lower level archers they will be increasing max damage rapidly so you are actually going to have to just recalculate for each individual leve... you probly already knew that though because in your example you did just use one level adjustment but just putting it out there for other people... please correct me if im wrong

you forgot to factor in the fact that as your range increases so does your max damage... for some of the lower level archers they will be increasing max damage rapidly so you are actually going to have to just recalculate for each individual leve... you probly already knew that though because in your example you did just use one level adjustment but just putting it out there for other people... please correct me if im wrong

No, you're absolutely right. But, thankfully, this calculator is not even close to accurate, as there are always variables when ranging. If you get teleported a bunch of times, you could stand to lose tons of arrows, or have an arrow theif grab them before you can get to them. Assuming there is no arrow income, your increasing max hit makes up for arrow losses.

No, you're absolutely right. But, thankfully, this calculator is not even close to accurate, as there are always variables when ranging. If you get teleported a bunch of times, you could stand to lose tons of arrows, or have an arrow theif grab them before you can get to them. Assuming there is no arrow income, your increasing max hit makes up for arrow losses.

well thats when the the percentage of arrows in the equation comes in, depending on how optomistic that ppl are/arent going to steal your arrows, you can raise or lower that percentage to fit what you think best for the training area

you forgot to factor in the fact that as your range increases so does your max damage...

No, I didn't

In the guide, I wrote:

...2) Use the Tip it range damage vs arrow type table to calculate how many shots you need.

 

It's best to do this 1 level at a time because you max hit goes up with level.

...But, thankfully, this calculator is not even close to accurate, as there are always variables when ranging...

I'm not exactly sure what you are trying to say here.

This is not a calculator, it's a guide that presented some formulas

on how to account for the long term effects of picking up your arrows.

Since ranging does random amounts of damage and breaks random amounts of

arrows, there is no way that you can predict in advance what is going to happen.

The best that you can do is to use estimates for the

damage done and the number of arrows gotten back.

In the guide I suggest using Max/2 for the average damage done and 75% arrows gotten back.

But I also say,

...So if you don't like my suggested values for Max hit and p then go ahead and use your own values.

So go ahead and use your own values as you see fit.

Use whatever values you think are most accurate.

The whole point of my post was to show how to include the effects of picking up your arrows when ranging.

(That was the 1/(1-p) thing)

I presented tha derivation of the formulas and clearly stated the assumptions that were used

so that players could use the best values for damage done and arrows returned to best fit their ranging situation.

The formula lets you decide what values to use for average damage and % arrows returned.

So rather then complain about "the calculator",

maybe you should go figure out what values work best for you.

The formula does all the work of putting it all together for you.

It is a good guide, and lot of efforts in to it i can tell. Well the stuffs about picking arrows is random and not much seem to really know that this guide(tip) is useful or important. I know my range is not so good, so i cant really know much, but hey its a good tip try a combat tip maybe it will attracts alot of people. :D

This is a great idea. I've seen loads of questions along these lines on the forums. I thought about writing one but it seemed like a lot of effort!

I think people need to realise that nothing like this is ever going to be 100% accurate without prior knowledge of the underlying probability distributions (max hit, arrow breakage etc.) and even then a reasonable prediction can only be made for a large number of shots.

might be useful for som people :)

I just don't really care how many arrows are needed̮̱̉̉

It'd be nice to have Tip.it'ers to psot their arrow breaking amounts, just to see if 'p' changes with the kind of arrow.

Excellent guide, should be stickied.

edit:ArrowsNeeded = ExperienceNeeded*(1-p)/(2*MaxHit)For me personally this doesnt work out, it underestimates amount of arrows needed, i just tweek the 2 to 2-2.5.

ep.[/b]

Excellent guide, should be stickied.

 

edit:ArrowsNeeded = ExperienceNeeded*(1-p)/(2*MaxHit)

 

For me personally this doesnt work out,

 

it underestimates amount of arrows needed, i just tweek the 2 to 2-2.5

Then it is working out for you.

If you can get useful results by tweaking a parameter that is meant to be

tweaked, well, then the formula is doing the job that it was designed to do ;)

Also, that's why I said

...Now, keep in mind that the long term average of damage done is not always going

 

to be Max/2 and that the portion of arrows gotten back is not always going to be 3/4.

 

So if you don't like my suggested values for Max hit

 

and p then go ahead and use your own values.

The main point of the post was to show how to account for picking up your arrows.

The formula was derived with the assumptions clearly stated and

suggestions on what to tweak to best fit your own ranging situation.

Also, some approximate Range Max hit formulas by arrow type and level are:

Bronze = (Range+14)/9

Iron = (Range+15)/9

Steel = (Range+14)/8

Mith = (Range+13.5)/7.5

Addy = (Range+16)/7

Rune = (Range+18 )/6

Hope this helps.

very nice tht must have taken u a while to think tht 1 through. if only there was some programmer who could make a nice calc to go on the main site :roll:

very nice tht must have taken u a while to think tht 1 through.

Thank you

...if only there was some programmer who could make a nice calc to go on the main site :roll:

I did suggest it in the Website Updates & Corrections Skill guide: Ranged forum.

But sometimes, older web content is slow to be corrected or updated...