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General Guide by ketsi027

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League of Legends Build Guide Author ketsi027

Probability calculations behind the league

ketsi027 Last updated on May 31, 2014
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Updates.

Work in progress!
Need data!
Lolnexus screenshots of normal soloQ or ranked soloQ are welcome.
Not yet tested for higher ELO tiers WIP.


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Introduction.

These calculations are only just probability. So don't rely only on them. You should always try your best. But I hope you'll find em interesting. any remarks, errors, new ideas or help is always welcome so please PM me or leave a comment in the discussion section.
HF!


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Basic idea explained.

So imagine you just played a normal game and you lost. we are for now neglecting lane matchups and the concept of ELO/MMR.
MMR and ELO are basically 1 and the same thing. Now because you lost you have a theoretical higher chance of winning the next game. Note the word theoretical. now we can calculate that chance if we have your personal Avg. win/loss ratio. Let`s assume u have a good win/loss ratio let`s take 55%. that means that you probably win 55% and lose 45% (100% - 55% = 45%). We can represent this as 2 roads the win (W) road and the loss (L) road. So if we call the win percentage x then the loss percentage is 1-x, agree? since the previous events don't mess with the variables the chances of 2 wins in a row are x^2. And what I mean with "they don`t mess with the variables" is that for example: You have 10 cards in a pile (5 blue and 5 purple) you take a card, the chances of taking a blue or purple card equal, 1/2. You look at the card and it is blue what that means is that if you`re going to take another card that the chances of taking a blue card are not 1/2 but 4/9 because there only remain 4 blues and 5 purple cards. This is not the case with league so the win ratios are defined as followed taking in consideration that your last game was a loss, 1 win streak = x^1, 2 win streak = x^2, 3 win streak = x^3..., and loss ratios are defined as 1-x as we said before. For calculating the loss ratios we take in consideration that your last game was a win, the loss ratios follow as such, 1 loss streak = 1 - (x^1), 2 loss streak = 1 - (x^2), 3 loss streak = 1 - (x^3)...
Now that I cleared up the basic idea lets move on to a more complex version because remember its a 5 Vs. 5 not you alone.


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chances of a team: MRR/ lane matchups excluded

This is easy. for notations sake we`ll call player 1 p1, player 2 p2 etc. And the chances of them winning x1, x2, etc... We are assuming a fairly standard match-up at the moment. Witch is Top (p1), Jungler (p2), Mid (p3), ADC (p4), Supp (p5). just calculate x1, x2, x3, (x4+x5)/2.
I`ll refer to x4+x5 as x45 from now on. so now you have calculated all those individual chances Just do (x1 + x2 + x3 + x45)/4 = t1 ; t1 is the Avg. chances of the team to win. don`t be suprised when you get a fairly low value. it just means there is a great chance of mistakes to happen wich mostly means a loss at high ELO tiers. But don`t be saddened by the low numbers. You have to take in consideration that the enemy team has such low numbers to. It is even quiet exceptional to get Avgs above 0.5; Btw t2 = 1 - t1 does not apply here. use t1 </> t2 to know who`s in favor. but as you might see this technique is quiet inaccurate when u put it to the test. But no worries we are getting there. Read on to refine your skills.
Fortune doesn't favor fools.


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Chances of a team: MRR included lane matchups excluded

Here it becomes again a little more complex. I`ll introduce you here to MRR. first and foremost to those that do not know what MRR is here is the a link to the wiki page LoLWiki WikiPedia. now the basic idea with includes MRR in to the scene is that if you have a higher MRR then the rest of your team. as an effect of you having a higher MRR you`ll be a better player thus having a more important role. so the chances of you winning should in turn commit more to the average chance of your team winning. We can easily incorporate this all we need to do is count up the MRR of p1,2,3,4,5. we will call the MRR of p1, m1 and the total MRR mt. so we just need to do m1+m2+m3+m4+m5=mt. Let`s say we want to know for how much p1 accounts for mt. we just do m1/mt and we get a % easy as that.


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