XP Evolution (III)

[LucaBlack]

Hi everyone,

Original Topic [FR Forum] : http://forum.sfgame.fr/showthread.php?t=14920

I have launched a few days ago a new study about XP evolution on the french forum. Since it goes well enough for me, I'm now coming here to share and ask help from a greater community.

I won't recap everything, so if you want to hear the full story of these studies here you can read the first post about:

XP Evolution: https://forum-int.sfgame.net/showthread.php?t=5253

The second study was a failure since the curve found for levels 1-393 was no more than a basic exponential and even the developper published it (without values) on the DE forum.

I now want to know what's happening from level 393 to 500... Don't you? Maths say if devs wants to keep the same "XP difficulty evolution" [...]

MATHS:

First, what's I call "XP difficulty evolution"?
Something simple but harder to explain... How to say... First, let's just talk about what I call "XP difficulty":

Imagine you're level 300. You need a certain amount of XP to level up and you earn a certain medium amount of XP by quests, academy and arena. We can define XP difficulty: ([Amount_of_medium_quests] OR [Amount_of_Academy_Earnings] OR [Amount_of_Arena_Earnings]) / (XP_Needed)

note: I will call the different ways to earn XP as a "work".

So... Higher level is, more work you need to do, harder it's to level up, higher the XP difficulty is.

As we just said, higher your level is, higher the XP difficulty are, but there is an other thing to notice about. XP difficulty can be shown as a multiplier:
Level up when 300= X amount of "work" to level up;
Level up when 301= X amount of "work" to level up multiplied by Y, the XP difficulty

If Y=1.02 (+2%), you need an average of 2% more "work" to level up when you are 301 than when you are 300.

What's the real value? Well it's actually impossible to know (or if you hack the game and steal back the values...), and that's probably a developper's secret we won't ever know about. But we can observe easily the "XP difficulty evolution":

Level up when 300= X
Level up when 301= X*Y
Level up when 302= (X*Y)*Y ???

This is a theory, but if this is correct, the XP difficulty stays always the same. In fact that's to answer this I have launched this study.
Anyway I can define "XP difficulty evolution" by:
[Level_up_When_X] / [Level_up_When_X+1]
X are a level so here, X are 301 and X+1 are 302.

If " Level up when 302= (X*Y)*Y " are true, let's check what appends with random values. For example X=10000 and Y=1.08
1) 10000
2) 10800
3) 11664
4) 12597
5) 13605
[...]

Continue for a lot of values, put this on a curve, you'll see an exponential curbe. And that's exactly what happend in the game from level 1 to 393. So the XP difficulty evolution are exactly the same for every level (and that's why my second study here about was completely obvious)

Now comes the real question:
We know from level 1 to 393.
But we know too that after level 393 you don't need more XP to level up, there is a cap at 1.500.000.000.
And all the higher players will tell that after 393, for every level up, you earn a bit less XP.
So what? A cap appears, and now we earn less XP? The formula of XP evolution have changed. How it looks? That's precisely the aim of that study.

Theory:
The XP difficulty evolution are the same from level 1 to 393... After 393 you earn less XP, but you don't need more to level up. So the XP difficulty keep increasing... So, maybe the XP difficulty evolution can be just the same after level 393?

If the theory are true, we will observe a simple decreasing right. We won't know how fast the right have to decrease but we'll know that it have to, and that it have to be a right.

So let's just see, uh?

If you want to help me, it's simple. I explain again what to do here and now. All you need is have a character with a level 393 or higher and take 2min of your time.
I need:
-Your character's level;
-The level of his academy
-The amount of XP that academy produce in one hour. [click on it to see]

PLEASE don't give away the XP that the academy can stock. I don't want it!

Example: 435/15/303.626
level 435, academy level 15, 303.626 XP per hour.


Lastest results here /!\ Big Screen /!\

TABLE:
Lvl. | Exp.
393 | 2,884·10⁴
394 | 2,860·10⁴
397 | 2,787·10⁴
400 | 2,717·10⁴
401 | 2,694·10⁴
403 | 2,648·10⁴
405 | 2,604·10⁴
407 | 2,560·10⁴
412 | 2,454·10⁴
416 | 2,373·10⁴
417 | 2,353·10⁴
418 | 2,333·10⁴
419 | 2,314·10⁴
420 | 2,294·10⁴
421 | 2,275·10⁴
423 | 2,237·10⁴
428 | 2,146·10⁴
433 | 2,058·10⁴
435 | 2,024·10⁴
437 | 1,991·10⁴
439 | 1,958·10⁴
440 | 1,942·10⁴
441 | 1,926·10⁴
442 | 1,910·10⁴
456 | 1,702·10⁴
457 | 1,688·10⁴
458 | 1,674·10⁴
459 | 1,661·10⁴
460 | 1,647·10⁴
461 | 1,634·10⁴
462 | 1,620·10⁴
463 | 1,607·10⁴
464 | 1,594·10⁴
465 | 1,581·10⁴
466 | 1,568·10⁴

Last Update: Octo./22/17 11:35 PM

I will edit this post later to explain for those who don't understand how to read the curve. And of course sorry for the French therms, but since it's maths vocabulary, I'm not sure to be able to translate them all accurately.

Please leave a "thanks" if you like my work, and PM me if I made language mistakes. I'm far from bilingual lol.

LucaBlack,
The Orange.

[Valkyra]

405/13/338.501

[sharshooter]

Playing 100% exp with accademy. More later (i have to 393 so far):



Lvl Exp [mln] Gold [mln]
320 128,3 30,8
321 121,1 49,6
322 129,1 65,6
323 118,7 44,8
324 134,7 46,9
325 138,3 51,4
327 133,0 62,1
328 136,1 43,9
329 140,6 53,1
330 137,4 47,3
331 136,2 54,8
332 141,2 53,1
333 144,2 60,1
334 140,3 64,9
335 136,4 65,3
336 143,7 66,6
337 144,7 44,7
338 146,5 63,7
339 147,2 61,0
341 143,7 68,9
342 151,0 62,3
343 148,1 83,0
344 151,9 81,5
345 154,8 66,4
346 155,0 70,3
348 151,9 75,8
350 154,2 80,9
351 158,3 94,6
352 151,9 100,0
353 158,4 77,0
354 164,6 94,8
355 161,1 90,0
356 165,8 99,7
357 165,2 80,2
358 164,0 78,0
359 168,4 99,8
360 167,2 94,7
361 166,2 89,0
362 167,8 98,8

[LucaBlack]

I don't really understand your curve, sharshooter, what is "mln"?

[sharshooter]

I don't really understand your curve, sharshooter, what is "mln"?

mln - 10^6

This curve shows total exp per lvl (academy, arena, thirst). Soon I will add more data (to 400 lvl).

[LucaBlack]

I don't know where your values came from but it's false, it has been prooven that the curve from level 1 to 393 are no more than a basic exponential, the developper themselves agreed...

[sharshooter]

I don't know where your values came from but it's false, it has been prooven that the curve from level 1 to 393 are no more than a basic exponential, the developper themselves agreed...

And you believe it ? Those values are from the game, I jot down starting exp/gold before I start play and jot down ending exp/gold values after whole day. It doesn't look like exponential for me, it looks like polynomial. As far as I know it will be f(x)=-ax^2 +bc +c .When you calculate derivative in X=393 you will get 0. That means f(x) for x=393 has maximum. When I collect all data (lets say to 410 or more) I can fit the right curve to the data. And we will see how fast exp is decreasing after 393 (if it's simple ax^2+bx+c it should be same like increasing before 393).

PS. Why on your previous curve from lvl 275 to 300 your exp from Academy drops so hard? As far as I remember I was always getting more and more exp/h.

[dfps]

I just passed the twister big barrier so ill be able to help you fast because im lvling up much faster and im still on twister 630.
So im lvl 455 and my lvl 20 academy gives me 343 184 per hour
Btw arena xp keeps on decreasing too... But already done the 10 atacks today.

[Leander]

Thanks for your continued work and contribution!

[sharshooter]

I still don't understand previous calulcations (1-394). How come from 275 to 300 exp/h drops so hard?

[LucaBlack]

Because it was in the past, the curve of my first study are no longer reflecting the reality. It was before when there was XP brakes... Devs removed them if I remember well enough... When the fortress was introduced. Of course, now, there is no more drops and XP just increase from level 1 to 393.

Point of history, the first time I heard about the XP brakes was with a French study made in 2009 or 2010. The guy used quests XP to trace his curve, and used thousands of values to be accurate. The curve are just right here:

I can translate for you it's written: daily progression in millions of XP for 100 thirst, no mount, full XP quests, without any scrapbook/guild bonuses.

But again, the XP brakes exist no more uh ^^

Now let's talk about the present.
And if you really want to see, curve that I havn't published here caus the study about was quickly obvious and no one asked:

/!\ Big Screen /!\

This is the amount of XP you earn with a level 1 academy for different levels now.
And no need to tell about, I have proven that academy XP is directly linked to quests -and also arena- XP, so there is no problem about.
Well, a lot of values are missing but it's clear... A basic exponential as I said. So yes the devs told it plus my study proven it and everyone around he FR community agreed with that, there is no doubt possible ^^

I don't understand how you made your curve but I insist to say there is a problem on it...


I think your problem can be statistic. You said you used quests XP to build up your curve. But quests XP are A LOT... What's the word... Let's say the reward move a lot. To be accurate you'll need easy thousands of quests for every level (end of cours without changing any bonus). And doing this alone well, good luck 3:
And of course for every level you have to take your values with the same XP bonuses too... So good luck again, lol.

Plus you said you're using academy XP. But academy XP depends not only on your level... but too on the level of the academy.

Plus you said you're using academy XP AND quests XP. That makes a huge mistake. Caus quesks XP change with your XP bonuses when academy XP don't care and only varies with your level. Same with arena XP, through.

So if you daily record all the XP earning you can get, cumulate them all and put the result on your curve... The mistake become really massive. That could explain why your curve goes up and down all the time.

[sharshooter]

Why do you assume that exp from quests drops same like exp from academy?

[LucaBlack]

It's simple:
-From level 1 to 393, for every level up you earn more XP, the devs themselves said it, the FR community agreed with that and it's exactly the same with academy and arena. Not so hard to observe because for every level up you need a lot more XP, or the time needed to level up increase slower. So you earn more XP.
-After level 393, for every level up you earn less XP, It's observed since the first time people have reached this high levels (even before the remove of XP brakes) and continues today... Again, same with academy and XP;
-If you calculate how much time you need to level up with a certain level of your academy, for higher levels it will be always longer, same with quests and arena.

For me that's enough; I havn't studied XP in quests and in academy together because I will need thousands of values to get accurate numbers about the quests. And the real fact of why I study the academy it's exactly because every value are accurate, so one value for every level are enough.

[slasker]

439/20/391.612

[dfps]

Lvld up...lvl 456 xp academy lvl 20: 340 379