Riot removed the level cap and now you can grind till infinity. So some people took the opportunity to farm like crazy. Some already reached level 100, and even though they used bots, it's still impressive.
But in another discussion I made a comment, comparing the XP gain between Summoners Rift games and Twisted Treeline botgames. I wanted to figure out which system is better: Summoners Rift PvP or Twisted Treeline Botgames?
And this post both has the answer on which is better, aswell as the math. Let's jump straight into it!
(From now on I will call Summoners Rift "SR" and Twisted Treeline "TT")
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Let's start with the Formulas that we need to compare the XP.
According to LoLWiki, these are the the formulas for the XP gain in PvP SR games:
> Victory:
> XP = Time \* 0,11 + 6,6
> Defeat:
> XP = Time \* 0,09 +5,33
[Source](http://leagueoflegends.wikia.com/wiki/Experience_(summoner))
Now for TT, this was a bit more difficult, since I didn't really found formulas for TT. So I went ahead and calculated the formular on my own.
The formular of TT most likely resembles the formular of SR, but with different values.
> XP = Time \* Rate + Base Value
So our job is to find the Rate and Base Value. Our job is a little bit easier, because we will only need to find one formular, since you will most likely win TT botgames.
To get those values, we first need data. GPet and me played a few games and gathered following data:
(Time and game length will always be displayed in seconds from now on)
|Game length||||||||||XP gained|
|:-:||||||||||:-:|
|433||||||||||41
|561||||||||||51
|676||||||||||61
We can plot this into a graph and get this:
https://imgur.com/zep8SKV
Since the formular is a linear function _(y=mx+c)_, we can get our **Rate** and **Base Value** by calculating _m_ and _c_. _m_ is equal to our **Rate** and _c_ is equal to our **Base Value**.
We get the **Rate** with following calculations:
> **Rate** = Δy / Δx = ΔXP / ΔTime = (61 - 41) / (676 - 433) ≈ 0,0823
And now since we have the **Rate**, we can plot in one of our datapoints to calculate the **Base Value**:
> XP = Time \* Rate + Base Value => Base Value = XP - Time \* Rate
> Base Value = 61 - 676 \* 0,0823 = 61 - 55,6348 = 5,3652
Now we have our two values. We now just need to round it a little bit and create a formular:
> XP = Time \* 0,08 + 5,37
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The next thing we need to do is figuring out the average length of a SR game. I used [this source](https://www.leagueofgraphs.com/rankings/game-durations) to determine the average game length. I took the data of the Draft Ranked Flex Graph and took the average game length of all elos, from Bronze to Master. This gives us a gamelength of 1655 seconds.
Now how many TT bot games can we play in this time? As it turns out, the game has to be longer than 480 seconds, or 8 minutes, otherwise you get 0 XP. So you want to play 8 minute games. We can expect that you wont be able to get that everytime, and finish a bit later. Add to it the short queuetimes and championselect between each game, and I would say one entire game, including the time outside the game, it takes roughly 540 seconds, or 9 minutes.
> 1655 / 540 ≈ 3
This means, you play 3 TT games during the entire time of 1 SR game. Now that we know that, let's use our formulas to calculate how much average XP you gain per SR game:
> 3 TT games, 100% winrate:
> XP = (480 \* 0,08 + 5,37) *3 ≈ 131 XP
>
> 1 SR game, 100% winrate:
> XP = 1655 \* 0,11 + 6,6 ≈ 189 XP
>
> 1 SR game, 50% winrate:
> ((1655 \* 0,11 + 6,6) + (1655 \* 0,09 + 5,33)) \* 0,5 ≈ 171 XP
>
> 1 SR game, 0% winrate:
> XP = 1655 \* 0,09 + 5,33 ≈ 154 XP
As we can see from this, you get more XP from SR.
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#EDIT:
So after a few comments, people suggested TT is still better, because of XP boosts. So let's jump in and figure this one out.
There are 2 types of XP boosts, Daily XP Boosts and Per-Win XP Boosts. They work differently:
- The Daily XP Boosts double your XP. Since it just multiplies our expected XP by a constant, this isn't really interesting. SR is still the better option.
- The Per-Win XP Boost is a little bit more complicated: It adds a flat XP value of around 210 XP ontop of your XP you gain by default.
Now the second one is interesting, because it is a flat value. But this throws up a new question: You need to play 8 minute games to get your XP. But what if you play even shorter games? Of course, you don't get base XP because such matches are below 8 minutes, but because matches are shorter you can get that flat value more often. So what is more efficiant in the long run? Playing 8 minute games or playing games as short as possible?
To figure that out, we use a simmelar strategy than before: We see how many short TT games we can play during 8 minutes. After some research we find the [CLG Bot challenge](https://youtu.be/36asLS1MTSI). The context doesn't really matter, but what is important for us is that you can finish TT games in around 270 seconds, or 4 minutes and 30 seconds.
This means following:
> 480 / 270 ≈ 1,78
This means we can play 1,78 short TT games in the span of just 1 TT game. Since we get 0 XP due to the short TT game being under 8 minutes, we will only get 210 XP per short TT game. If we use that we get the following:
> Short TT game:
> XP = (0 + 210) \* 1,78 ≈ 374 XP
>
> Normal 8 minute TT game:
> XP = (480 \* 0,08 + 5,37) + 210 ≈ 254 XP
As we can see from this, you get more XP when you are using an XP Boost. If it is a Per-Win XP Boost, don't bother getting the game till minute 8 and finish it as fast as you can!
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So let's recap everything we figured out in some small, digestable sentences:
#You get more overall XP by playing Summoners Rift than playing Botgames on Twisted Treeline, but only if you don't use an XP Boost!
#If you are using a Daily XP Boost, stay with Summoners Rift.
#If you buy a Per-Win XP Boost every time you can, then you should finish the game as fast as possible! Don't bother getting above the 8 minute mark.
As long as you don't buy boosts, despite TT games being shorter and you winning all of them, SR games are generally the better option if you want to farm XP.
But this doesn't mean TT is less useful. Because TT is so easy and 99% of players wont flame you there, it may be more healthy for your psyche. Maybe you find it more relaxing and you can play TT longer than you could play SR. In this case, TT is the better option. But if you are a powerhouse who can play all day without taking a break, definetely play PvP Summoners Rift!
But if you decide to buy a boost, buy Per-Win XP Boosts and finish the game as fast as possible. This is expensive and takes alot of RP, but it is the best way to farm XP period.