Delve into daemonheim xp

[Thai_tong]

Hey, I've interested in finding formulae relating your skill level and the amount of xp you receive for completing a daily challenge. Some challenges are different so there is lots to investigate. I am most interested in the delve into daemonheim challenge because that is certainly the most rewarding at high levels so I think this is a good place to start. Of course I cannot test every level myself so I'm looking for your help in collecting a list of the xp at different levels. I wont need to know it at every level, just enough so that I can find a formula for it.

 

At the moment I've collected these figures

 

70 dungeoneering- 50699 xp

80 dungeoneering 67681 xp

88 dungeoneering- 83915 xp

91 dungeoneering- 93012 xp

93 dungeoneering- 97822 xp

96 dungeoneering- 102000 xp

97 dungeoneering- 107993 xp

98 dungeoneering- 107993 xp

99 dungeoneering- 113364 xo

100 dungeoneering- 113364 xp

104 dungeoneering- 124k xp

112 dungeoneering- 149944 xp

113 dungeoneering- 156823 xp

115 dungeoneering- 163k xp

116 dungeoneering- 163943 xp

120 dungeoneering- 178932 xp

 

I would prefer if you could give exact figures instead of rounding it to the neared 1000xp but it wont matter too much if the formula is a little off :)

Edited April 12, 2013 by Thai_tong

[Dax]

At 97 Dungeoneering I gain around 102K exp per day, I'll update you in 20 minutes or so as to the exact number.

[Leik]

Level 70: 50,699

Level 88: 83,915

Level 93: 97,822

Level 100: 113,364

Level 112: 149,944

Level 113: 156,823

[Dax]

97: 107,993.

 

96 is 102,something thousand.

[Thai_tong]

Thank you guys! :D

[baileydafrog]

89 is 88k something

[Quyneax]

I'll post the exact xp at 115 later, and 116 in a couple of days if nobody beats me to it.

[Thai_tong]

Ok I've got it :D

I am still looking for xp rewards data to improve this estimate, particularly at low levels.

The reward xp is related to the base xp you would get for doing your highest floor. This makes sense because Jagex's plan was to make challenge rewards similar xp to what you would normally do. Grimy has the base xp for each floor in his dungeoneering xp spreadsheet https://docs.google....NDdXpKaGc#gid=3

He has manually entered values up to floor 40 and then used a formula to relate floor number and base xp for higher floors but it is a differential equation which clearly Jagex would not use. His formula predicted values must be close though because there is a very strong relationship between his figures and the reward xp (R²=0.9995 which should be 1 for a perfect relationship)

The relationship is Reward= 891.11+ 7.599B

Where B is the base xp for your highest floor. From the data you guys have provided this is off by a max of 2435 xp. A quadratic fit does not produce much better results so I'm sticking to a linear fit.

In the case where your dungoneering level is an even number, for example 80 then your highest floor is 40.5. Taking the average of floor 40 and 41 gives almost the same result as just floor 40.5

 

Grimy's formula is difficult to work with so I tried to use a polynomial to relate floor number and base xp. Neither a linear or quadratic relationship work well. I don't expect Jagex to use a higher order relationship than quadratic but it turns out that a cubic or quartic (degree 4) relationship work much better. To me this indicates that they don't use a polynomial but instead might have a formula like the one for the xp needed for a certain level. The best-fit cubic relationship is base xp= 6.536+ 54.35F+ 0.8515F²+ 0.07736F³. Where F is the floor number. This is off by a maximum of 66xp.

The best-fit quartic relationship is base xp= 82.59+ 31.14F+ 2.531F²+ 0.03477F³+ 0.0003491F⁴. This is off by a maximum of 13xp.

 

Combining these equations of reward as a function of base xp and base xp as a function of floor, and taking floor=(level+1)/2 the equation for reward xp becomes

Reward= 1641.91+128.04L+4.901L²+0.033692L³+0.00016581L⁴

Where L is level.

Comparing the predicted rewards to the data here I find that the prediction is off by a maximum of 7724xp at level 108. This is quite large but all the other errors are less than 2500xp.

 

Or for the cubic fit

Reward= 1149+209.97L+1.83817L²+0.734858L³

The predictions made by this are surprisingly far off

 

You may have thought that I could just fit a polynomial to the original data collected on this thread but that polynomial would be skewed because all the data here is for high levels. I tired this and the results for low levels is either ridiculously high or negative. The intermediate step of using Grimy's floor data which includes low levels reduces the bias to high levels.

[Troacctid]

93012 xp at 91.

[thingummywut]

From the limited data sample that we have, it seems that there is always a jump in XP after a new floor is unlocked.

 

That leads me to believe that highest possible Dungeoneering prestige bonus is involved in the formula. How exactly prestige works isn't known either, as far as I know, so it might be nearly impossible to find out this formula.

 

Why do people always search for polynomial formulas anyway? A lot of formulas in RS are of exponential nature.

 

By the way, you can get pretty close matches with stuff like a*level*2^(level/40)+b where a and b are constants.

[Quyneax]

163943 xp at 116. I'm not sure that is even an increase over the xp at 115 (which I forgot to note -.-).

[Fallstar]

I don't think the xp gained through dg daily challenges changes from 117-120.

 

Also it increases every odd level (or new floor), but I'm not sure why this does not happen at 119.

[Thai_tong]

It would make perfect sense if there was a jump when a floor was unlocked.

 

Why do people always search for polynomial formulas anyway? A lot of formulas in RS are of exponential nature.

 

By the way, you can get pretty close matches with stuff like a*level*2^(level/40)+b where a and b are constants.

I tried an exponential relationship of the form a*b^(c*level) but that didnt fit. I will try it again with a constant added. I don't know any exponential formulae in runescape that weren't added in EoC except for the effigy drop rate formula. High order polynomials should be a good approximation to any function because any function can be expressed as a polynomial.

 

Edit. I generally don't search for non polynomial functions because I don't expect Jagex to use anything more than simple functions. When I can't find an exact solution then a high order polynomial will be a good approximation.

[Sy_Accursed]

I know it isn't an exact formula but from myself, friends and dungeoneerers from clan the xp for the task seems to be roughly tied to a perfect 5 man large with max prestige of your top floor in dg. Hence why there is a pattern where by odd levels (floor unlocks) to even levels don't move much whilst even levels to odd levels jump a fair bit (new floor)

[thingummywut]

It would make perfect sense if there was a jump when a floor was unlocked.

 

Why do people always search for polynomial formulas anyway? A lot of formulas in RS are of exponential nature.

 

By the way, you can get pretty close matches with stuff like a*level*2^(level/40)+b where a and b are constants.

I tried an exponential relationship of the form a*b^(c*level) but that didnt fit. I will try it again with a constant added. I don't know any exponential formulae in runescape that weren't added in EoC except for the effigy drop rate formula. High order polynomials should be a good approximation to any function because any function can be expressed as a polynomial.

 

Edit. I generally don't search for non polynomial functions because I don't expect Jagex to use anything more than simple functions. When I can't find an exact solution then a high order polynomial will be a good approximation.

 

XP required for a level formula, for example, is an exponential one. That could be very closely related to the formula you're looking for.

 

Polynomials can be fit for a finite number of points in a plane. Not all functions can be represented as polynomials. A lot of functions can be represented as power series, though (especially locally).

 

My problem with polynomial approximations is that it yields very silly-looking formulas, in lines of 0.89738497984736434x^2+6757.3579454x-46.46234786935237. There is no way that it was coded in like that; it's probably just exponential or something else.

 

I think Sy_Accursed's answer might be the right one; that's how Jagex supposedly balanced it.

[Thai_tong]

The xp formula is not exponential it is this http://www.mirekw.com/rs/RSDOnline/Guides/guide.aspx?file=Experience%20formula.html

 

Using Taylor series any differentiable function can be represented as an infinite polynomial (or well approximated with a high order polynomial).

We all realise that Jagex don't use high order polynomials, if I could find a simple function I would use it but I can't so I'll use a polynomial instead. Being a little off the true answer doesn't matter for my uses and polynomials are also easier to use than a summation. Finding the xp gotten from this task is quite a niche use so it isn't much to ask someone to type 8 digit numbers when they need it.

The xp from a perfect floor is a multiple of the base xp so we wont need to test every level for a perfect floor, we can continue using grimy's figures :)

[derekreader]

I got 67k at 80dung, can't remember the exact amount.

[Ammako]

67,681 at 80 dungeoneering, to be exact.

[Dax]

Though I know you've already determined it goes up with a new floor, it's still 107,993 at 98.

[Kleinbus]

113,364 at 99.

[Thai_tong]

Since we now know xp only increases every 2^nd floor I took another look at the

 

I took a closer look at grimy's data and where he uses a formula to predict floor xp for higher floors based on data for lower floors is a bit off. I took another look at the data comparing max floor xp and challenge xp. The challenge xp was nearly constantly 8 times the floor xp. I am removing the level 108 info someone provided because it sticks out like a sore thumb.

 

This is a graph of the difference between the previous floor xp http://puu.sh/2yRDb

 

So grimy's predictions seem to be off by almost a fixed amount.

 

It turns out that him underestimating by 247xp gives figures that best match the trend of [challenge xp]= 8*[base floor xp] so from now on I will use that figure to adjust floors 42+

We could even work backwards and get better figures for base xp by dividing the challenge xp by 8.

 

The tricky part still remains, to find the function relating floor and base xp. The graph for it is here http://puu.sh/2yTtW

I'm open to suggestions.

[Quyneax]

171310 xp at 117.

[Thai_tong]

Cheers. So it does increase from 117 to 119

[Faststrike The Naabe]

Now it's double the old, rs2014, viswaxscape