*** EDIT: A couple of patches ago--right after this post *facepalm*--they changed the IP/XP payouts, so some of this will be inaccurate, but I'm not doing this all again, haha. The ratio is still the same, but the amount/game is a bit off. Expect to level up a bit faster than this says. ***

Hey guys, when I started playing league I couldn't really find a good answer for this, so I catalogued a lot of my games to try to give a good one. I also will break down how XP is calculated and how many games it takes to go from level to level.

First, it took me 89 days, 309 normal games, 4 practice games, and approximately 210 hours of game play. I ended 9 wins up, which saved me about about 3 games or so. The average game time (from LoLbase.net) appears to be about 36 minutes, I tend to avoid surrendering and try for the comeback so I average about 40.8 minutes per game. Had I hit the average, I would have saved myself about 25 hours.

Every win up is saves about .4 games, so you save about 1 hour for every 4 wins up you are.

In order to crack how XP was calculated I collected data from about 175 games. I have every game from level 20 on, and I started a smurf to get a couple low level games in there so I could be interpolating the middle, rather than extrapolating one side.

It's stupidly simple: XP is proportional to your IP.

There are two exceptions. The First Win of the Day bonus does not give you any XP benefit, and there is a very small difference that rounding error doesn't quite account for--I'll get into what that is later (it's cool!).

Here is the (approximate) equation to calculate XP based on IP and your level:

XP = IP * ( LVL * 0.0315 + 0.832)

Assuming a 50/50 win with an average game length, here is the # of games needed per level. The first column show how many games from your current level are needed to get the next. The middle shows the total normal games you need to play to get to any level. And the final column is probably the most helpful, because it shows you about how many games you have left to lvl 30, based on what level you are now.

01) __ 1.18 __ 1.18 __ 315
02) __ 1.24 __ 2.41 __ 314
03) __ 1.28 __ 3.70 __ 313
04) __ 1.33 __ 5.03 __ 312
05) __ 5.12 __ 10.1 __ 310
06) __ 5.27 __ 15.4 __ 305
07) __ 5.41 __ 20.8 __ 300
08) __ 5.55 __ 26.4 __ 294
09) __ 5.67 __ 32.0 __ 289
10) __ 10.3 __ 42.4 __ 283
11) __ 10.5 __ 52.9 __ 237
12) __ 10.7 __ 63.7 __ 262
13) __ 10.9 __ 74.6 __ 252
14) __ 11.1 __ 85.7 __ 241
15) __ 11.3 __ 96.9 __ 230
16) __ 11.4 __ 108 _._ 218
17) __ 11.6 __ 120 _._ 207
18) __ 11.7 __ 132 _._ 295
19) __ 11.8 __ 143 _._ 284
20) __ 16.5 __ 160 _._ 272
21) __ 16.6 __ 177 _._ 155
22) __ 16.8 __ 193 _._ 139
23) __ 17.0 __ 210 _._ 122
24) __ 17.1 __ 228 _._ 105
25) __ 17.3 __ 145 _._ 87.7
26) __ 17.4 __ 262 _._ 70.4
27) __ 17.5 __ 280 _._ 53
28) __ 17.7 __ 297 _._ 35.5
29) __ 17.8 __ 315 _._ 17.8

Ta da! It's approximate, but very close. And remember, practice games will throw this off (they are worth about 80% of a normal game). For a break down of how I made this table and other factors that affect IP, check out this post (http://www.leagueoflegends.com/board/showthread.php?p=5975250#post5896908). I mostly just used correlation analysis and linear regression to do the overall analysis, but I felt this post was long enough without going into all those details. However, if you are curious, I break it down in this post (http://www.leagueoflegends.com/board/showthread.php?p=5975250#post5975250).

Now. The final thing is the rounding error. There's just slightly too much variation left over after the equation to account if just rounding. There's something else. I ran correlation on Kills, Deaths, Assists, Gold, Turrets, Time, and Minions. Nothing. But I had another guess. I got about 63% correlation to Wins. So I'm pretty sure that this is sort of a sneak look at the Elo system at work. I consistently lost games that gave more XP than expected, and consistently won games that gave less. This means that using this formula you can sort of predict your odds of having won a game. And it boils down to: You get slightly more XP from tougher games. I may look into this further with my smurf account.

That's all. Please keep those comments civil, and I'll gladly clear up any questions!

Hmm...Did you account for win of the days? I don't remember it taking me this long, though I had many wins/losses.

Hmm the numbers are a bit clumped together. Maybe something like

1) + 1.12 // = 1.12
2) + 1.24 // = 2.41

Right here I notice that the numbers are a bit off, 1.12+1.24 should be 2.36 no? (Hence the // between the first number and the equals sign.)

The factors that affect IP from wins.

(cough cough)
Streak without leaving: max +23IP
Quick Victory/Long Defense: ? IP
Boost: +100%, +200% if both boosts.
Custom game: -10%
Twisted Treeline: -30%
Uneven teams: -100%
>6th win/'day' in Custom if(lvl>10): -100%

Also, you should add the calculations you used, so that those who understand it can comment on where you might have gone wrong.

From experience by watching my friends list, it's between 160-190 wins. I don't remember if wins of the day affect XP, but I don't recall that they did.

333 games ~= 166.5 wins, so that falls within my observations. Obviously different ratios of wins to losses and number of custom games affect this number, but I can guarantee that by 200 wins everyone will be lvl 30.

Answered: First win of the day doesn't affect XP.

It's been too long since I've had to deal with xp.

Does the streak w/o leaving still affect XP?

Nice suggestion on the format btw, it's too bad that simple tabbing can't be done. Implemented.

And good catch, the first number was a typo, and I have fixed it. I also double checked all the rest, so they should all be correct now..



I had no leaves on my account, and ignored this factor, because, hey, leavers are lame. I counted the first games on my smurf account to see how long it takes to earn this bonus, and it takes 7 games. This means a leave sets you back about 3/4 of a game.



My next post will be to show the time intervals that earn the different point counts (I have it figured out, just have to write it up). But essentially the average person earns about 7 per game, and that's how it's factored in above. But this is slightly variable.



Saves you one or two games each.




Other factors for custom games are: You cannot lose (hopefully), you do not gain time bonus, and you do not gain non-leaver bonus. So you always get 71 IP. Assuming an average IP per game for 50/50 is around 88.5 IP, this is where I got the practice games = 80% of a normal game.


To keep my data pure, I avoided balanced practice games (4) and 3v3 games (1). So I can't really speak to these. Maybe my smurf account will have to check this out.



These are pretty self explanatory.


Will do. The major analysis I will leave for when I have more time, and I will break down how I got the table here:

Loss = 47+7+14 = 68
Win = 79+7+23 = 109
Average = 88.5

XP needed to level up:

1) 90
2) 98
3) 105
4) 113
5) 448
6) 476
7) 504
8) 532
9) 560
10) 1050
11) 1100
12) 1150
13) 1200
14) 1250
15) 1300
16) 1350
17) 1400
18) 1450
19) 1500
20) 2131
21) 2200
22) 2269
23) 2338
24) 2406
25) 2475
26) 2544
27) 2613
28) 2681
29) 2750

Using the formula XP = IP * (0.0315 * LVL + .832) we can solve these all out. As an example, level 1 would be:

90 = (# of games) * 88.5 * (.0315 * 1 +.832)

90 = (# of games) * 76.42

# of games = 90 / 76.42 = 1.18

The real use of the table is not to see if you are on track, or reverse engineer how many types of games you've played, but to figure out how many games you have left, since the growing XP per level throws off those estimates. I may reverse the cumulative column to highlight this.

Cheers!

Alrighty, for those of you who are interested, here's a more in depth look at how I came to the conclusions above. Beware, math ahead! Also, while I'm pretty good at math/statistics, there are probably those of you better at what I'm trying to do here, so please pitch in if you see a way to help!

First off, I collected data from, like I said before, around 175 games. The factors I collected where: Win/Loss, Surrender, Level, XP, Base IP, Time IP, Leaver IP, FWotD IP, Total IP, Kills, Deaths, Assists, Minions, Turrets, and Gold. These were the stats that I figured would have the highest correlation to XP.

Then at specific levels, I ran correlation on XP and a few of the factors. For example, I played 17 games at level 27, and here are the correlation results:

Kills: -24%
Deaths: -38%
Assists: 48%
Minions: -29%
Turrets: 61%
Gold: 5%
Base IP: 97.6%
Base IP + Time IP: 97.6%
Base IP + Time IP + Leaver IP: 99.99%

Looking at these numbers, it was pretty obvious that the real factors involved here were IP, omitting FWotD. The high correlation to Assists and Turrets is due to covariance with wins, which have a strong impact on IP, and therefore XP. Simply put: If you win, you get more IP and XP, AND if you won, you probably killed more towers. Therefore turret kills are important for winning, but not for calculating XP directly.

From here, I was hoping for the following result: I wanted the equation to be modeled by XP = IP * ( LVL * m + b), because this is very simple. Simple for me means simple for Riot, so I figured I had a decent shot. But, to be sure this is how they did it, I had to rule out some other possibilities.

For example, running a Linear regression on Level 27, with IP on the x-axis and XP on the y-axis, I got the first graph.

Wins and losses sort themselves, to the right and left respectively, and you can see how well they fit the trend line. However, the fact that the equation is "y = 1.6487x+2.8688" is a problem. To keep our final equation simple, we must have the form "y=mx."

So, what I had to determine was if the 2.8688 value was not zero due to randomness. To cut a long story short, I made graphs like this for each level, then ran a correlation between the the intercept value and the level. The results were uncorrelated, which means they are likely due to randomness. They didn't quite center around zero, but they were close enough to ignore.

The next thing I had to show was that the IP and XP ratio per level increased in a linear fashion. What I had to rule out was other trend lines (like square, cubic, exponential... etc) and more importantly, stair step patterns like what is used for XP per level. I created a scatter plot with level on the x-axis and all the XP/IP proportions on the y-axis, and got the second graph.

Now, it's unfortunate that I have no data at the center of this graph, but I think the trend line pretty obviously works and works well. There is no evidence of stair stepping. There does seem to be a slight curve to the graph, but the second order polynomial equation is "y = 0.0001x^2+ 0.0272x + 0.8559" which has a laughably small x^2 factor, which pretty much shows that, if it's there, it's ignorable. So, this is the end of the analysis, we can just use the trend line as our estimation equation.

I already went over how I used the equation to build the table of games needed per level, and it gave results close enough that I felt the approximation was good enough.

I don't really have much to add on the Elo system hypothesis, because it's mostly just a guess right now, and my analysis has pretty much been restricted to what I stated in my previous post. So, I'll leave that to another day, and probably another thread.

This probably isn't all as clear as I want it to be, but please ask questions and I'll answer them. I'll also try to make edits based on questions to make things clearer for the next interested person.

That's all I've got for now. When I have a chance, I'll post my next thread about how much IP you get based on game time.

huehue

Most definitely in deserving of a

bump