This is topic Equations for the two new Growth rates? in forum Research Lab at The Azure Heights Forum.

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Posted by Team Rocket Elite (Member # 3154) on 01-12-2003, 03:15 AM:

In RBYGSC, there were four different Growth rates:
800000 to Lv100- Fast
1000000 to Lv100- Medium
1059860 to Lv100- Parabolic
1250000 to Lv100- Slow

RS introduces 600000 and 1640000. I was wondering if anybody here knew the equations for these two Growth Rates. I've named the 600000 Growth Rate as Erratic Growth becuase the rate of growth speeds up and slows down erraticly, especially above Lv70. I call the 1640000 Growth Rate Fluctuating Growth because after Lv35, the exp needed fluctuates between high and very high. I've determined a few of the Pokemon with these two Growth Rates. For example Volbeat has a max exp of 600000 and Illumise has a max exp of 1640000.

Experence per level charts:
Erratic Growth
Level--Total------Next
2------15----------+37
3------52----------+70
4------122--------+115
5------237--------+169
6------406--------+231
7------637--------+305
8------942--------+384
9------1326------+474
10----1800------+569
11----2369------+672
12----3041------+781
13----3822------+897
14----4719------+1018
15----5737------+1144
16----6881------+1274
17----8155------+1409
18----9564------+1547
19----11111----+1689
20----12800----+1832
21----14632----+1978
22----16610----+2127
23----18737----+2275
24----21012----+2425
25----23437----+2575
26----26012----+2725
27----28737----+2873
28----31610----+3022
29----34632----+3168
30----37800----+3311
31----41111----+3453
32----44564----+3591
33----48155----+3726
34----51881----+3856
35----55737----+3982
36----59719----+4103
37----63822----+4219
38----68041----+4328
39----72369----+4431
40----76800----+4526
41----81326----+4616
42----85942----+4695
43----90637----+4769
44----95406----+4831
45----100273--+4885
46----105122--+4930
47----110052--+4963
48----115015--+4986
49----120001--+4999
50----125000--+6324
51----131324--+6471
52----137795--+6615
53----144410--+6755
54----151165--+6891
55----158056--+7023
56----165079--+7150
57----172229--+7274
58----179503--+7391
59----186894--+7506
60----194400--+7613
61----202013--+7715
62----209728--+7812
63----217540--+7903
64----225443--+7988
65----233431--+8065
66----241496--+8137
67----249633--+8201
68----257834--+9572
69----267406--+9052
70----276458--+9870
71----286328--+10030
72----296358--+9409
73----305767--+10307
74----316074--+10457
75----326531--+9724
76----336255--+10710
77----346965--+10847
78----357812--+9995
79----367807--+11073
80----378880--+11197
81----390077--+10216
82----400293--+11393
83----411686--+11504
84----423190--+10382
85----433572--+11667
86----445239--+11762
87----457001--+10488
88----467489--+11889
89----479378--+11968
90----491346--+10532
91----501878--+12056
92----513934--+12115
93----526049--+10508
94----536557--+12163
95----548720--+12202
96----560922--+10411
97----571333--+12206
98----583539--+8343
99----591882--+8118
100--600000

Fluctuating Growth
Level--Total--------Next
1------1--------------+3
2------4--------------+9
3------13------------+19
4------32------------+33
5------65------------+47
6------112----------+66
7------178----------+98
8------276----------+117
9------393----------+147
10----540----------+205
11----745----------+222
12----967----------+263
13----1230--------+361
14----1591--------+366
15----1957--------+500
16----2457--------+589
17----3046--------+686
18----3732--------+794
19----4526--------+914
20----5440--------+1042
21----6482--------+1184
22----7666--------+1337
23----9003--------+1503
24----10506------+1681
25----12187------+1873
26----14060------+2080
27----16140------+2299
28----18438------+2535
29----20974------+2786
30----23760------+3051
31----26811------+3335
32----30146------+3634
33----33780------+3951
34----37731------+4286
35----42017------+4639
36----46656------+3997
37----50653------+5316
38----55969------+4536
39----60505------+6055
40----66560------+5117
41----71677------+6856
42----78533------+5744
43----84277------+7721
44----91998------+6417
45----98415------+8654
46----107069----+7136
47----114205----+9658
48----123863----+7903
49----131766----+10734
50----142500----+8722
51----151222----+11883
52----163105----+9592
53----172697----+13110
54----185807----+10515
55----196322----+14417
56----210739----+11492
57----222231----+15805
58----238036----+12526
59----250562----+17278
60----267840----+13616
61----281456----+18837
62----300293----+14766
63----315059----+20485
64----335544----+15976
65----351520----+22224
66----373744----+17247
67----390991----+25059
68----415050----+18581
69----433631----+25989
70----459620----+19980
71----479600----+28017
72----507617----+21446
73----529063----+30146
74----559209----+22978
75----582187----+32379
76----614566----+24580
77----639146----+34717
78----673863----+26252
79----700115----+37165
80----737280----+27996
81----765275----+39722
82----804997----+29812
83----834809----+42392
84----877201----+31704
85----908905----+45179
86----954084----+33670
87----987754----+48083
88----1035837--+35715
89----1071552--+51108
90----1122660--+37839
91----1160499--+54254
92----1214753--+40043
93----1254796--+57526
94----1312322--+42330
95----1354652--+60925
96----1415577--+44699
97----1460276--+64455
98----1524731--+47153
99----1571884--+68116
100--1640000

Posted by LanderZRPG (Member # 1615) on 01-12-2003, 11:23 AM:

Bah, I can't make left from right of it...

I mean, if it was a subtraction of powers, then it would pinnacle at one point, and then continue to either be smaller or larger (Like a parabola), but the Erratic one peaks around 50, then makes a huge jump again. It doesn't make sense for a single formula to do that around a given number.

As for the Fluctuating... Bleh. Why it changes at 35, I wouldn't know, but if it just kept getting smaller, it'd be alright, but since it keeps changing... maybe it has something to do with Sin/Cos/Tan? It has one up (in gains to XP), then one down:

87----987754----+48083
88----1035837--+35715
89----1071552--+51108
90----1122660--+37839
91----1160499--+54254
92----1214753--+40043
93----1254796--+57526
94----1312322--+42330
95----1354652--+60925
96----1415577--+44699
97----1460276--+64455
98----1524731--+47153
99----1571884--+68116

50k, to 35k, to 55k, to 40k, to 57k, to 42k.... There is a definite relation, but the only thing I could think of to match that pattern would be one of the lovely trig graphs, going on a diagnol, upwards. Either that, or the variable changes for odd/evem, which isn't supported in the lower numbers.

Posted by Lunair (Member # 681) on 01-12-2003, 12:35 PM:

The differences in required exp. for a level gains above level 50 look to me (at first glance) like a rotated sinusoidal graph, and so the peaks and troughs would be the number of exp. that Monster X needs to go from level M to N.

Here come some SWAGs (Scientific Wild Guesses; the A is silent :p) for some graph that Nintendo/Game Freak made into a table in the ROM is somethin' like this:
Between levels 2 and 20, there's one quadratic equation (A*X^Y + B); from 20 to 50, there's another one; from 50 onward, there's some sort of a sine graph (A*sin[B(X-H)] + K; may even have X to some power) that is magically rotated, and the evenly-spaced levels (as they are integers) are what gives the erratic growth rate its… erraticism? Or something.

Rip it to shreds, kids!
-Lunair

Posted by LanderZRPG (Member # 1615) on 01-12-2003, 11:25 PM:

I thought of an idea on how the jumpy thing at the end of the Fluctuating chart could work...

int((lvl^3)/2) or squareroot, etc.

Then, multiply by level.

Since 90/2 is 45, *90 = 45*90.
int(91/2) is 45, *91 = 45*91.
92/2 is 46, *92 = 46*92.
int(93/2) is 46, *93 = 46*93.

Possibly works, but I don't see why it differs in the beginning of the formula.

I think it's probably several different formulas (boooo! Stupid lazy people not wanting to make one that works!)....

Posted by John (Member # 3143) on 01-18-2003, 02:17 PM:

It might help if you added the difference of the exp increase last level and the exp increase for the current level to the chart.

Then again, it might not.

[ 01-18-2003, 02:19 PM: Message edited by: John ]

Posted by Uiru (Member # 437) on 03-06-2003, 02:40 PM:

600 000 exp *fap fap fap* 1 640 000 exp *weep*

I want to know exactly who needs 600 000/1 640 000 exp to Lv. 100. Now.
~Uiru

Posted by Rolken (Member # 7) on 03-12-2003, 11:39 AM:

Wow, can't believe I missed this. I remember regressing the original "Parabolic" curve... back in the day... ::sniff::

I still take issue with it being named Parabolic, btw.

Anyway, the first one's piecewise defined, and probably the second as well; the multiples of ten look nice and neat up till about 50, where they start getting wilder again, which is suspicious.

E = -1/50*l^4 + 2*l^3 for l<=50.
Looks like you transposed 45 - it ought to be 100237.

I'll figure out the rest... um... later. I don't think they'd use a lookup table... it's silly when they can just use a formula.

Oh, and death to UBB, which accuses my parentheses of being HTML and forces me to reformat and wait two minutes to tell me it's found something else to take issue with.

Posted by ShadowHawk (Member # 3287) on 03-27-2003, 05:09 PM:

Ok, I've run the numbers for the first one (erratic) through MATLAB a bit, and have reached a few conclusions.

1) Please rename Parabolic growth to Cubic growth immediately.
2) Erratic growth is NOT a polynomial of 5th degree or less. While there absolutely exists a polynomial of 98th degree or less that satisfies the points exactly (since there are 99 points on the graph), it is unlikely I'll be able to compute it anytime soon, since even using 64 bit integer arrays will cause MATLAB to overflow.
3) For Fluctuating growth, I suspect we can attain a fairly close approximation by using a fourier series summed with a polynomial, since it appears to be semiharmonic.

[ 03-29-2003, 04:00 AM: Message edited by: ShadowHawk ]

Posted by pika (Member # 1908) on 09-09-2004, 04:24 PM:

Umm sorry to bump this old thread again but I messed around a bit bit this today and I proudly present you:

Perfect Erratic 0-50 Formula:
f(x)=-0,02x^4+2x^3 (0=<x<=50)

Posted by Rolken (Member # 7) on 09-10-2004, 05:17 PM:

So do I. ;[
quote:
Originally posted by Rolken:
E = -1/50*l^4 + 2*l^3 for l<=50.

Posted by pika (Member # 1908) on 09-10-2004, 05:56 PM:

uh sorry i messed up. Maybe I should have re-read the whole topic again before posting.

Karpe Diem