"10 bans doesn't mean both teams will ban the same champ"

General Esdeath ·Jul 12, 2017·151 votes·6,131 views

http://i.imgur.com/rbtTlwI.png

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127 Comments

Some Noob DudeJul 12, 201726 votes

Lmao what are the odds? (Inb4 someone actually does the math)

ExcalibaitJul 12, 201718 votes

there are currently 135 champions in the game right? then it should be:

(5 / 135) x (5/135) = 0,13717 %

General Esdeath Jul 12, 20177 votes

138* But don't forget to subtract the 10 everyone wanted to play.

ExcalibaitJul 12, 20177 votes

you start with bans, so you have to consider the entire pool, no matter the pick intents

General Esdeath Jul 12, 20172 votes

True

Mecha MaIphiteJul 12, 201775 votes

Nope. That assumes every champ has the same ban rate.

The most likely scenario would be having five bans on the top five banned champions, and you could calculate a ban rate for that; but that isn't the only scenario, and you would also have to do it for every other combination. I'm sure there's some method to get a better approximation without doing a load of work but I am neither determined nor mathematically gifted enough to figure it out.

Dr PoroJul 13, 201725 votes

That's not even correct assuming they all have the same ban rate. This calculation reflects the chance that 3 people would ban the same champion, or two people banning a specific champion.

First off, there are 137 champions since Kayn's release.

The outcome for the bans of your team doesn't matter, the only thing you have to calculate is that the other team bans the exact same 5 champions, aka 5 specific champions.

This would be (5/137) x (4/136) x (3/135) x (2/134) x (1/133) or shorter: 5! x 132! / 137! = 2.676894x10^-9 = 0.0000000027... Explanation: The first player can ban any of the 5 bans of your team 5/137. The second player has to ban one of the remaining 4, but can't ban the same as the previous one because bans have to be unique. So the entire champion pool also goes one down. same thing goes for the next players.

This whole calculation assumes that every champion has the same chance of getting banned and that no one leaves their ban open. Of course bans are left open occasionally, lowering the chance a bit, but some champions are banned a lot more often, which means that the actual chance of this happening is much much greater.

JSTIN8Jul 13, 20176 votes

NEEERRRRRRRRD

Dr PoroJul 13, 201726 votes

I mean, hey, you don't become a doctor by skipping class.

masterdomloJul 13, 20175 votes

preach brother. us so called nerds control the world

BLACK REALM GODJul 13, 20179 votes

in other words - permutations and combinations.

ShahamutJul 13, 20172 votes

still, even if you multiply that chance by 100, you get 0.00000027, which is a FAR cry from even 1% :P

Trias000Jul 13, 2017

[Edit] Nvm

SzGamer227Jul 13, 20172 votes

Exact ban compositions don't matter in this case. The only thing that matters is that each individual ban is mirrored by the enemy team. If you want to calculate the probability that a specific five ban comp is mirrored by both sides (e.g. the probability that you see the OP's exact bans) this would come into play, but not for a general analysis.

Trias000Jul 17, 20171 votes

You're right. My bad.

Trias000Jul 17, 20171 votes

Ok, so since there are 373566942 possible ban combinations and for each of those there are 373566942 possible enemy ban combinations, that means the actual probability that bans are mirrored are 373566942 * 1/(373566942 * 373566942) = 1/373566942 = 2.68 * 10^-9

SomnitsuJul 13, 20172 votes

{quoted}

there are currently 135 champions in the game right? then it should be:

(5 / 135) x (5/135) = 0,13717 %

It's actually [(1/135)(1/134)(1/133)(1/132)(1/131)]^2 = 5.77735603E-22

Which is 0.000000000000000000000577735603

But once you take into account banrates and human preference idk anymore.

General Esdeath Jul 12, 20171 votes

Well 138 champs minus the 10 that people wanted to play. 128 champs to ban.

Killed InactionJul 12, 20171 votes

133 since the teams each ban without knowledge of who the enemy team wants to pick.

So, actually... (5/133) x (5/133) = 0.141% chance.

Dr PoroJul 12, 20171 votes

But the other team can still ban the champs you want to play, so you cant even leave those 5 out. Also, most players have more than 1 champ to play, so it's quite impossible to account for that.

In the end, you also have to use each champ's individual ban rate to have the best empirical estimate.

Killed InactionJul 12, 20171 votes

I'm not entirely sure what you meant by that first sentence. If I'm reading it correctly, this is my response: The other team can still ban the champions you want to play, but that's why it's 5/133; if it were 138 that would mean the might be banning champions their own team wants, and if it were 128 that would mean they could somehow see the enemy's champion picks in order to not ban them.

Going based on averages, yes, you would have to examine each champion's ban rate. You would also have to look at each individual champion select, since you need the specifics as well as the averages.

The estimate would have to include many, many factors. For that reason, it's probably less than a 0.1% chance. But this is the best I can do, since I took Statistics 3 years ago and it wasn't my best subject then. ^.^

Skins ProjectJul 12, 20172 votes

Well first it doesn't matter.

For duplicate bans, it means that neither team wanted it, or a team had an asshole.

I suck at JhinJul 13, 20171 votes

And it's also a chance that both teams will ban exactly 5 same champions, not about player intentions, feelings and other crap, I don't get it.

It's MATH, not philosophy, you have raw numbers and use them.

Literally the problem can be formulated like this:

There are 138 champions in League of Legends. There's 10 people who can ban 1 champion each, duplicate bans are possible, neither team knows what is enemy team banning until banning phase ends, what is the chance that during the banning phase, 5 duplicate bans will occur, resulting in only 5 champions being banned?

See anything about how players pick and etc? Me neither. This probably could be shortened even more, but cba.

Skins ProjectJul 13, 20172 votes

if it were 138 that would mean the might be banning champions their own team wants,

I suck at JhinJul 13, 20171 votes

I'd ban your champ just to prove my point.

Just because you want to play it, doesn't mean that the chance of it being banned is 0.

kthx bye

Skins ProjectJul 13, 20172 votes

Not you in particular.

Perhaps in a team of 5 theres 1-2 people like you

That's another chance.

Unless your assuming all 5 players would ALL be just like you?

I suck at JhinJul 13, 20171 votes

Doesn't change the fact that any of 138 champions can still be banned at any time, available right there, on your screen, nothing prohibits you...

If you really want to argue about that, now start whining about people who have only 20 champs and it might happen that there's like 50 available champs to ban/pick from in total and that fucks with chances even more...

Skins ProjectJul 14, 20172 votes

Im saying.

Your off topic.

My point is that because it is DUP the team thing is pointless.

TeCoolMageJul 14, 20171 votes

YOU

Skins ProjectJul 14, 20171 votes

YOUUUUU

TeCoolMageJul 16, 20171 votes

NO YOUU

Skins ProjectJul 16, 20171 votes

UUUUUU

TeCoolMageJul 16, 20171 votes

UUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU

Skins ProjectJul 16, 20171 votes

TeCoolMageJul 17, 20171 votes

notice me Sin piJul 13, 20172 votes

if u assume every champion has the same ban rate, then it's actually (5/133) x (4/132) x (3/131) x (2/130) x (1/129) = 0.0000000031114%

Sraeg2013Jul 12, 20172 votes

You are like 2 months too late with that "inb4".

[click]

FantasySniperJul 13, 20178 votes

It's impossible to properly calculate the chances without peeking into exact records, but we can guess based on the ban rate of these champions. Let's assume it's Plat+ [1] [2].

| Champ ----------- | Ban% ----------- | Cumulative % Chance ----------- | Fraction |- | Zac | 68.9 | 68.9 | 2 / 3 | Fiora | 47.2 | 32.5208 | 1 / 3 | Yasuo | 39.9 | 12.9757992 | 1 / 8 | Darius | 26.6 | 3.4515625872 | 1 / 29 | Kayn | 20.9 | 0.7213765807248 | 1 / 139 | Chance of this combination.

But realistically, the chance should be slightly higher as once a teammate has locked in their ban, the chances of banning the other champions in the pool becomes more likely. (Think of how last pick was usually support or last ban was usually Kassadin) I would guess that in higher elos, 1 out of every 200 games has the same five bans, and 1 out of every 100 games has the same 4 bans.

StusauceJul 13, 20172 votes

[{quoted}](name=Lee OnLee,realm=NA,application-id=Ir7ZrJjF,discussion-id=L8g5xE83,comment-id=0000,timestamp=2017-07-12T18:21:08.530+0000)

Lmao what are the odds? (Inb4 someone actually does the math)

My psych professor would tell you the odds are 1.0 because it happened.

RikariJul 12, 201712 votes

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lmao,this actually happens more often in high elo.

TwitchInMyPantsJul 13, 20178 votes

New champ, Zac, 2 most popular toplaners, and Yasuo

Checks out

SanKakUJul 12, 20177 votes

Personally I don't see why I'd care if my opponents could see my team's bans while we were deciding on them. It wouldn't be hard to come up with some mind games, so I don't see any problem with it.

cocacolalipsJul 12, 20172 votes

it gives some information that can be used against you, you usually ban counters (besides op champions of course), if I ban say rammus, there is a good chance I wanna play an AD assassin or an auto attack heavy champion, the enemy team will see the ban, read me like a book and pick accordingly to counter said AD assassin or auto attack heavy champion anyway

if we are being honest, that won't happen like 95% of the time because people are too lazy - too bad - don't really care, but the remaining 5% of the time, especially at high elo, it will happen, and people will wait till the very last second to pick / ban stuff, which defeats the purpose of having a new ban system that supposedly goes faster and stuff.

Weight of LawJul 12, 20174 votes

but what the enemy team doesn't know is you banned rammus with the intent to pick a full ap team comp ;^)

Romans VI XXIIIJul 12, 20172 votes

They can already tell who you banned, as the bans go in order from according to who banned them. Left > RIght = Top > Bottom on the enemy side, and reverse on your side.

So changing it wouldn't change the fact that the enemy can see who you banned.

Sraeg2013Jul 12, 20173 votes

The problem is that Riot decided to do this whole blind pick free for all because "muh timers" instead of looking for a better solution that actually provides 10 bans.