Season One Draft Order Mistake

First Riot Post
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Makbeth

Member

06-23-2010

I apologize, I forgot that i posted this in two different sections. I will draw up a full explanation for you shortly.


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sturgeon

Member

06-23-2010

Quote:
Originally Posted by RiotMarcou View Post
Keep in mind that with bans, the format looks like this:

[--Bans--Picks---------]
ABBA ABBAABBAAB
Why have you chosen to go with ABBA bans? Most other MOBAs use an ABAB system of bans.


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Dreampod

Senior Member

06-23-2010

Quote:
Originally Posted by sturgeon View Post
Why have you chosen to go with ABBA bans? Most other MOBAs use an ABAB system of bans.
In general I don't think order matters for bans particularly as there is very little advantage in banning first or last. After all if the enemy bans a champion you were intending to ban it just allows you to choose another one that you'd like to get rid of and you can't prevent the enemy from banning a champion you want to use (like a pick does). Very rarely does a ban choice reveal a composition plan either since there are few hard counters to try to remove.


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Makbeth

Member

06-23-2010

Okay. Here is a brief explanation, but the most I am willing to type out without explaining it on the telephone. I'm not being paid, after all.



You may look at balancing in two different mathematical ways, as an arithmetic selection process or as a geometric one. An arithmetic process assumes that each pick is of equal value; i.e. the fourth pick is as important as the 7th pick. A geometric one assumes that each pick becomes increasingly more important than the last. This selection process is somewhat geometric because of the knowledge each player gains as a choice is made. Should team 1 choose five physical DPS players, team 2's last player would likely choose someone with the most armor. This is what we call a "real life" version of an exponential advantage. Lucky for us, both schools of thought (arithmetic and geometric) have the same outcome here.



Here is a simple rock paper-scissor-selection model for what you call the "snake draft":

(Team): (Pick)

1: Rock (random)

2: Paper (counters pick 1)

2: Rock (random)

1: Paper (counters pick 3)

1: Paper (random)

2: Scissor (counters pick 5)

2: Paper (random)

1: Scissor(counters pick 7)

1: Rock (random)

2: Paper (counters pick 9)


Notice that team 2 will receive three counters, while team 1 will receive only two. This is a strong advantage, as team two will always win the game 100% of the time with this model. A game with 50 champions is more complicated, but it would take a year of explaining game theory models to prove a 10% advantage.

You must, in any game theory model, assume each pick's quality is equal. That is to say, each champion is exactly balanced. I'm doubtful that a mathematician is proofing your balancing, but nonetheless we will assume it to be as true as humanly possible. As such, the first pick is not an advantage. Any player selecting a champion randomly will be as equally successful as a person who really really really really wants to play a jungling warwick (something I hate Riot for, by the way!). The last pick, therefore, has the absolute most value.









If you are willing to accept this as fact, we can move on to my suggestions for simplest selection process without making life impossibly difficult to the game designers:



1. Champion selection remains 1-2-2-2-2-1, but the champion itself is not revealed. The champion's primary/secondary roles are listed instead (tank/support), (fighter/support), etc. as well as listing the player's primary mastery spec. Should a player be 9/0/21 or whatever, it will say something like this:

Mastery - - - Champion

(Utility) - - - (Tank / Support)




2. If the anonymity of the first selection process doesn't sit right, I completely understand. Another option would be to make the selection process exactly the same up until the last pick on each team, both of which must remain completely anonymous. This allows both teams to choose two counters, without providing nearly as strong an advantage to either team.


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Panzerfaust

Emissary of the League

06-23-2010

Quote:
Originally Posted by Makbeth View Post
Here is a simple rock paper-scissor-selection model for what you call the "snake draft":

(Team): (Pick)

1: Rock (random)

2: Paper (counters pick 1)

2: Rock (random)

1: Paper (counters pick 3)

1: Paper (random)

2: Scissor (counters pick 5)

2: Paper (random)

1: Scissor(counters pick 7)

1: Rock (random)

2: Paper (counters pick 9)

So you are saying that champions picked as a counter have no viable counters to them? (I pick rock and you pick paper to counter, and another random. Could I not pick scissors to counter your paper, as well as whatever counters your random champion?)

Draft doesn't work with anonymity unless you scrap exclusivity.

The limited revelation you mentioned is basically blind pick, but you either don't know enough to pick against, or you know enough that you know who they're playing. The only thing it would prevent is all tank teams or something of the like.

If you're correct about 1-2-2-2-2-1 favoring T2, then what about a system that was something like 1-2-1-2-3-1? But that might favor T1, so maybe 1-1-1-2-3-2? You get the idea though.


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FuYA

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Senior Member

06-23-2010

Makbeth I see the point your trying to make. The Rock Paper Scissors model works for that instance. But it doesn't work in the model created by this game. In Your model Picking First you are pretty much saying that the pick is Random and are forgetting exclusivity. And i will explain this as best as I can Using a base of exactly 14 Champions. This while not being exact it does Explain the point and can later be expanded.

The champions will be

Ezrael
Ashe
Ryze
Blitzcrank
Morgana
Pantheon
Soraka
Janna
Tristana
Shaco
Morde
Shen
Sion
Master YI

4 Tanks/ 3 Ranged Carries/ 3 Melee DPS/ 2 support champ/ 1 Bursters with disables

The 14 champs could be applied in a various ammount of combinations in order to make a winning team. You really just need to make sure you get a tank and a Carry and then you can add some other parts to make a whole.

So lets start with the bans.

A - Ezrael
B- Ashe
B- Janna
A - Blitzcrank

Now you are left with a pool of

Ryze
Morgana
Tristana
Pantheon
Soraka
Shaco
Morde
Sion
Shen
Master Yi

The Picks

Looking at this pool team now can get Pick 1. If you look at this pool who would YOU pick. Team A Needs a Ranged Carry and there is only 1 left needs a Tank Shen is still in the pool along with SIon and Morde so that might not be too urgent. Disables are found on Morgana and Ryze, Morgana can also play mid effectively. Pantheon is a decent Burster and Is also a DPS he can also play mid if it comes to that. The only clear pick that I wont take is probably Master Yi as that role is not essential. BUt what does come to mind is only 1 Ranged Carry left which is a counter all by itself. And I probably set that up by not Banning Tristana and istead Banning Blitzcrank in the first place. I do have to consider that the reason i didnt Ban Shen is that I wanted shen on my Team but being able to deprive the opposition with thier only chance for a Ranged Carry with which to play mid and be able to kite with Red Buff is a small advantage. But Taking Shen also leaves Team B scrambling to get the a decent Tank leaving several options later and Morgana can always mid properly so Shen it is which is also the clear TOp pick. Just being able to pick shen is ALSO a counter all Alone.

Team A Shen

Team B is now left with a choice. They can try to hard coutner Shen but they also have to choose a champ that can tackle mid without seriously hurting the team and letting mid grow unhindered. They could try and take Morgana for a Mid role later or take tristana Now. Maybe Morde could be a choice for mid later aswell. Maybe they want to take the only healer left in the pool. Maybe Team B knows that Team didnt Ban Shen cause they really want to play him and that they messed up and now should be looking at the only other tanks in the pool which are Morde and Sion. Sion also has a Stun which can be useful in team fights. So team B now concludes that they need a tank so they go for Sion. Now theres a problem however that The Ranged carry team B wanted to have was Ezrael and Tristana is a clear downgrade. But they really need a mid Champ so they take that Tristana and Counter team A which was planning to get her.

Team B Sion
Team B Tristana

Now Team A has a smaller pool of 7 heroes These are Ryze, Morgana, Pantheon, Soraka, Shaco, Morde and Master Yi. Well Team had Tristana Stolen Morgana, and Ryze are range champs with disables that can easily make up for not having tristana also, it would make the last champ with a Stun of sorts to be Pantheon. However the team isnt too happy picking ryze as Ryze is really squishy and will just be countered by a shaco pick. So the answer is of course to take Shaco himself who is a great counter to Tristana aswell. Also Shaco is a champ that can load up Madreds and take down Morde and Sion if they decide to horde the Fat in the next pick. So it actually becomes clear which to get.

Team A Shaco
Team A Morgana

Team B now has less choices. They need some more fat to be able to hold down some shaco damage and need some burst to be able to deal with morgana constantly stunning immobalizing people and black shielding everybody in sight. Team B already has a kiter that can take care of Melee DPS leaving Team A with those is not a bad deal. But also it would be nice to be able to heal taking soraka. But that would leave Team A with the possibility of taking Ryze who has the last available CC and so far Team B only has Sion in disable mode while Team A has a Taunt an immobilize a Team Stun and a Slow. So Ryze it is. Also Team B needs to consider if Taking Morde to horde the last fatty or Take Pantheon for more damage and some map control. They take Morde to keep the fat to themselves.

Team B MOrde
Team B Ryze

Team now is seening 3 picks of Pantheon, Soraka, Master yi. They take Pantheon and Soraka. Seeing as Yi will probably just get kited by Tristana every other fight and would rather have Pantheon cause a player on thier team is really good with Panth and is almost psychic about where he needs to drop. Soraka being the last Healer is a good plus to have with the awesome tankness that is shen aswell.

Team A Soraka
Team A Pantheon

Team B in this case is stuck with Master YI. And ill explain at the end why this is relevant. However do note that Master Yi is not a bad champ in this case. he could potentially be a treat to towers with backdooring and then running real fast. And can carry some decent DPS smack people down like mad. But is actually quite subpar and I put him in the pool for a reason. Again ill explain in a bit.

Team B Master Yi


So team Comps come down to

Team A

Shen
Shaco
Morgana
Soraka
Pantheon

Pretty Balanced team but having Shen could push them over the edge.

team B
Sion
Morde
Tristana
Ryze
Master yi

Also Pretty balanced and Having Tristana is a Strong Factor

So what happened here. Each and every pick was a counter to every pick the other team was taking starting at Pick 1. Infact it started at Ban 1 when Team A decided to Ban Ezrael cause they knew the other team would take him. Team B Banned janna and ashe cause Janna is annoyingly Op in the right conditions and Ashe can be really tough to counter at Mid with any champ and you dont want Team A first picking her. Blitzcrank was just another way of taking out a champ that can just wreck a single champ on a team each time he launches that rocket grab. And seeing as Team B didnt Ban shen you might aswell ban thier best Tank and First pick your best tank afterwards.

Now of course there are 50+ champs in the game and you will most likely not get stuck with Master Yi or whatever at the end. But getting the very last pick could actually leave a team member with little choices to pick from especially if you happen to have a teammate with fewer champion buys than others. I personally am only missing 18 champs from the entire roster. But what about people that only have 20 or so champs. Even if they have a plan on what to take they will probably not even have a champ that can effectively counter the last pick Team A makes. And thats why that is relevant. Even with 5 people and you can leave the guy with the most options for last he still has 13 less options and that is a disadvantage that is inherent with every situation were you pick last.

Also there is one more thing that I want to point out. Picking Bans is also important and is something you didnt include in your very good Post. In a world were people dont scout the opposition it might not matter but scouting will happen, as it happens in every tournament out there. People will Scout out the other teams best players and check theyre most used and available champs and Ban Accordingly. Information is gonna become a very powerful tool as it already did in past TT Draft tournaments. For example in one match that I saw, one team going First chose not to ban Janna eventhough Janna is clearly OP in TT. And the Voice chat made it clear why they did this. As one player said PLayer X has Janna but he is really bad with her and PLayer Y and Player Z are gonna pick these 2 other champs that they picked last time. So lets Ban Ezrael and Jax which are the other 2 champs Player X would use and First pick Shaco which is his only real other choice. Going first gave them all the advantage they needed. Player X ended up picking Janna because it was the clear choice of the champs he had left and they went on to lose that match. Even though it appeared to me that he was doing alright, the opponents chatting made it clear that they were all real happy about how bad he was doing with Janna and that they engineered that particular set of events starting at Ban 1. In fact I was at 1 point wondering why there were only 2 Bans on Summoners Rift per team. The Current Ban format having team A Ban Last and Pick First is like giving team A an extra Ban since picks are exclusive.

So if we take this into account in your Rock Paper Scissor Model it would be like saying You know Opponent wants to pick Rock but I ban him from ever doing so. Not just that you get to see what 2 bans the other team makes and can make a good conclusion as to what you should ban that and Also I go first so im gonna pick the clear best pick from the entire pool and make sure you dont get it which is like Banning yet another time from you. And not just that you now have to counter my First pick and i can counter both your picks with 2 of mine and again later. so if you put it this way and include all this info into your R-P-S model we can conclude that the Very First pick is a great coutner pick. You also have to consider that i need to fill my team with at least 3 of the NEEDED roles in order for my team to be succesfull.

So we get in real dumbed down fashion (and In case you didnt want to READ ALL oF that WALL of TEXT that I actually hope not that many people read cause its Booooring)

A First pick counter "best pick overall"
B Countering pick 1
B Second Best Champ Overall
A Counter pick 2
A Counter Pick 3
B Counter Pick 4
B Counter Pick 5
A Counter Pick 6
A Counter Pick 7
B Counter Pick 8 or 9 but not both


As far as I see this is 4 counters to each side and it would seem to me that team 1 actually gets a slight advantage. Of course you could say you dont want to counter Pick 8 or 9 and just pick a Champ you cant counter. But that means I have two picks that went un-countered AND i get the best champ available.

Better way to explain why i think team A gets 2 counters in a row is with Rock Paper Scissors Lizard Spock.

A Rock
B Paper Counters Rock
B Scissors
A Lizard Counters Paper
A Spock Counters Scissors
Invent 5 more and you get the same result for 10

of course you then have to consider that Rock also Counters Scissors and was probably taken accordingly.


TL;DR If you take all the factors into consideration This system is pretty well balanced and in fact it might be slightly favored towards team one.


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FuYA

This user has referred a friend to League of Legends, click for more information

Senior Member

06-23-2010

In case you didn't catch it in my long boring post. I Don't think 2 bans on each team on Summoners rift is the correct number of bans. I believe it should be 3 per team. But also having 6 champs banned with less than 60 champs available is probably a bit nutty. I still think though that the Ban format should be ABBAAB to avoid the inherent advantage of being able to ban last and Pick first. And TT Banning should probably be handled in ABAB Fashion.


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Dreampod

Senior Member

06-23-2010

Quote:
Originally Posted by Makbeth View Post
Okay. Here is a brief explanation, but the most I am willing to type out without explaining it on the telephone. I'm not being paid, after all.

You may look at balancing in two different mathematical ways, as an arithmetic selection process or as a geometric one. An arithmetic process assumes that each pick is of equal value; i.e. the fourth pick is as important as the 7th pick. A geometric one assumes that each pick becomes increasingly more important than the last. This selection process is somewhat geometric because of the knowledge each player gains as a choice is made. Should team 1 choose five physical DPS players, team 2's last player would likely choose someone with the most armor. This is what we call a "real life" version of an exponential advantage. Lucky for us, both schools of thought (arithmetic and geometric) have the same outcome here.
Quote:
Originally Posted by Makbeth View Post
You must, in any game theory model, assume each pick's quality is equal. That is to say, each champion is exactly balanced. I'm doubtful that a mathematician is proofing your balancing, but nonetheless we will assume it to be as true as humanly possible. As such, the first pick is not an advantage. Any player selecting a champion randomly will be as equally successful as a person who really really really really wants to play a jungling warwick (something I hate Riot for, by the way!). The last pick, therefore, has the absolute most value.
I think there are several logical flaws in how you are thinking about the draft that lead your game theory premise being incorrect.

The first is that you are trying to apply game theory to the real world. While game theory can be illustrative it comes with some inherent weaknesses. The prime of which you summarize quite well saying 'You must, in any game theory model, assume each pick's quality is equal.' While that may be true (I disagree though, unbalanced options appear in many forms of game theory) it assumes that simply because game theory says so that the real world will conform to those rules as well. Which brings me to the second flaw.

The second is that you are not treating the champions as having inherent differences, or to be more precise 'Champions are not fungible'. Even in a perfectly balanced game (which is an impossibility in this genre) the capacities of individual champions will suit them more to different roles. Thus unlike rock, paper, scissors there is an intrinsic reason to value one balanced champion over another. Which in turn leads to the ultimate failure in your theory.

The third is that you are only considering the draft in terms of countering the opposing team. However you will also be choosing picks for the strategy your team is pursuing, balanced composition, and player talents and preferences. This gives 4 different basis for making selections and if your team focus' on one it will be detrimental to your success.

First pick strongly benefits from being able to serve those alternate reasons to select a champion. Additionally it can potentially grant the team the ability to prevent the opposing team from accessing three champions, rather than just their two bans, due to the exclusivity (assuming you want that 3rd champion yourself).


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Makbeth

Member

06-24-2010

Several logic flaws? The post is a strong simplification because I'm not interested in investing dozens of hours on the subject, but I assure you that a consultation with anyone else in the profession of theoretical mathematics or game theory (instead of a troll who wants to put in his two cents) will reach a consensus view.

Tell you what. Please put in a special exception just for me. I'd like to always be placed on Team 2. No more arguments from this end.


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Dreampod

Senior Member

06-24-2010

Yes I'm the troll, you caught me. Blast how my politely discussing the issue using facts and logic prevents legitamate discussion. Next time I will make sure to follow your approach of dismissive appeals to authority and ignoring the substance of what is posted - that should lead to productive discussion.

I may not be a professional game theoretician but I have taken some game theory and logic classes which is enough to allow me to see the gaping flaws in your premise. I don't expect a dissertation but a response that is in effect saying 'nuh uh' is too far at the opposite end of the spectrum. However it should take no more than 5 minutes to respond to the actual points I made with some reasoning as to why they are irrelevant or outweighed by your premise.


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