I got this for the whole graph:

1.5538741396718431e + 005 * 1
-2.0726906237136008e + 005 * lvl
7.7968795667479819e + 004 * lvl^2
-1.3252622239114222e + 004 * lvl^3
1.2325391601252900e + 003 ...
-6.8684496150716839e + 001
2.3941671034184275e + 000
-5.2676805857932843e - 002
7.1189934729830242e - 004
-5.4087557358274731e - 006
1.7743212012601356e - 008

From that it's fair to say that the graph is changing curve from Level 53 to 61

Edited 10/21/2015 16:13:09

Pretty sure it's not polynomial, it's exponential. All of you doing polynomial fits are doing it wrong

With Жұқтыру's predictions we have finally completed the list! Thanks to everyone who helped out.

Edit: Added graphs and a list of the total points.

Edited 10/22/2015 02:21:22

quick, go make an alt and get it to level 66 to prove the numbers, and get a new data point.

Said no one ever.

3 – 4......7 700 ... Prediction by Жұқтыру

It contradicts the data provided by Vatsug.

7800 points needed to level from 3 to 4

Edited 10/22/2015 06:34:38

I wonder how long would it take for an average player to level up to a certain level. It'll be good for someone to post some estimations as I'm eager to know how long before I could host Custom scenarios in multiplayer games:)

depends on what games you play and how often you play, there is a lot of variables, like do you play RT or MD, do you play in coin games? Ladder games, lotteries, diplos etc

I advanced in two months from level 3 to level 50 by winning more or less 3, 4 games a day (any type basically).
Base is 5000 points from winning a 1vs1 with player of the same level (and next 5k for each defeated player like that) points so you can roughly estimate how many of them you need to win for a certain level. Then of course there are achievements, tournaments, lower/higher lvls etc

Don't take my predictions as truth. I threw out all "guesses" of how many points when I was making it, and it can only be accurate to a point (pun intent).

L55+ model predicted 19 982 100 for L66, actual (thanks ALE) is 20 556 000, so that's a 2.8% mistake.

L1-L54 model:

L4: Predicted 7 700, actual is 7 800; 1.2% mistake (nitpicker detected: inquisitor)
L26: 23 900; 0% mistake.
L36: 39 900, actual is 39 800; 0.3% mistake.
L41: 51 400; 0% mistake.

More comparisons with predicted and actual will be made (when we get new data).

Updated data:

2 7000
4 7800
5 8100
6 8600
7 9100
8 9500
9 10000
11 11100
12 11700
13 12300
15 13600
16 14300
17 15100
18 15900
19 16700
20 17600
21 18500
22 19400
23 20500
24 21600
25 22700
26 23900
27 25100
28 26400
29 27900
30 29300
32 32500
33 34200
34 35900
35 37900
36 39800
37 41900
38 44200
39 46400
40 48900
41 51400
42 54100
43 57000
46 66400
47 69900
48 73600
49 77400
50 81500
51 85800
52 90300
53 95000
54 100000
55 220400
56 479000
57 830600
58 1308500
59 1957900
60 2840700
61 4040300
62 5670900
64 10898900
66 20556000

L1-L54 (99.99984% accuracy; expected mistake: practically none):

f(x) = 6.2961779967347329e+003 * x^0
+ 3.4739037512150043e+002 * x^1
+ 9.3986208776861435e-001 * x^2
+ 1.2433076952717417e+000 * x^3
+ -9.4588562454441028e-002 * x^4
+ 5.5571052739860219e-003 * x^5
+ -2.3015111620582036e-004 * x^6
+ 7.1832855351275776e-006 * x^7
+ -1.6144853896790169e-007 * x^8
+ 2.3921746115947811e-009 * x^9
+ -2.0405122934764914e-011 * x^10
+ 7.4932982236045076e-014 * x^11

L55+ (99.9999982% accuracy; expected mistake: 900; no accounting for deceleration of growth)

f(x) = 3.6232139431422749e+009 * x^0
+ -4.0620148796677458e+008 * x^1
+ 1.4802895242423024e+007 * x^2
+ -1.5305287367823487e+005 * x^3
+ -2.3482469548877129e+003 * x^4
+ 4.8250827259657868e+001 * x^5
+ 2.0967134879291541e-001 * x^6
+ -7.5678763220053090e-003 * x^7
+ 1.6465505353084485e-005 * x^8
+ 2.0553937987640950e-007 * x^9

New predictions:

3: 7 300
10: 10 500
14: 12 900
31: 30 800
36: 39 800
44: 60 000
45: 63 100
63: 7 884 500
67: 28 053 200

Also, I see the jump at L54-L55, not L53. Look at the actual data:

48 73600 (5.0% growth from last number)
49 77400 (4.9%)
50 81500 (5.0%)
51 85800 (5.0%)
52 90300 (5.0%)
53 95000 (4.9%)
54 100000 (5% exact; also, notice the roundness of the number)
55 220400 (54.6%)
56 479000 (54.0%)
57 830600 (42.3%)
58 1308500 (36.5%)
59 1957900 (33.2%)
60 2840700 (31.1%)

Criticise my polynomial regression all you like, but your logarithms failed to see this?

I think I might build a polynomial regression later based on per cent growths, later.

Also, Catus, when you build your graphs, do either with two separate for 1-54 and 55+ or just put on logarithmic scale (first y line is 10k, next is 100k, third is 1m, so on). But they're very hard to read right now except for really high levels.

Edited 10/23/2015 04:20:01

46-->47 69,900

Can confirm

56 – 57....830 600

is correct :)

I noticed you used Жұқтыру's estimation rather than the numbers I provided. Anyway, here's the proof of what I posted earlier ;) 7800 needed from level 3-4

http://i62.tinypic.com/qxt7hk.png

Edited 10/23/2015 09:18:58

It's probably exponential or derived from an exponential. As far as I remember, Fizzer confirmed this vaguely at one point or another (I think in the early stages of the introduction of points when the first people started to reach the high levels.)

Thus, a polynomial fit will give decent predictions within the scope of the data, but will be bad at extrapolating. The reason a polynomial fit works within the scope of the data, is simply because an exponential function can be reasonably locally approximated by a polynomial (see: Taylor series).

So, agree with Ameter. Feel free to not believe me, but maybe look at the first word in my name first?

So, we know it's exponential, but it's not simple.
Time to get a long sheet of paper...

13:50

9 numbers to 8th diff. Currently got 281000-8*(level2to3).

Would currently mean nothing...

Edited 10/23/2015 13:02:04

With regards to the percentages, we need more data, my current prediction is that the curve will have a second drop and then soon become constant(ish) again.

Sorry, link is too long.

Edited 10/23/2015 13:08:35

Okay, I changed 3-4 to 7800

Can someone do an alt for 2-3?

I was never levels 2-8, i won a lottery as my first game.

Edited 10/23/2015 13:36:53

My alt just skipped 2-3 so ya....

Make two alts, and get them to play each other...should work.

I was never levels 2-8, i won a lottery as my first game.

lol