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Is league of legends more structurally sound with Dynamic Queue than with Solo Queue?

Critkeeper··24 votes·1,916 views

Lets start with an analogy to communicate the gestalt of what follows before diving into the math.

You could randomly fortify a structure in 15 places, but remove a critical pillar and the whole thing comes crashing down. In a very real sense, the critical pillar is more valuable to the structural integrity of the overall structure than the other 15 combined.

Now humor this viewpoint and think of the game from that perspective. Does the following goal seem intelligent?

  • "Giving potential players the things they want causes them to play. The value of league of legends increases as the number of players increases."

Each player added improves the game by a specific amount-- a player may marginally reduce queue times by playing games regularly, can offer their own sort of insight into ways of playing champions, may create content, could spread a positive vibe and so on. On the other hand, a few players may be toxic, spread negativity and so forth. In other words a player adds a certain value V (positive or negative) to the game.

Now I put forth a question. Is the total value of a set of players the sum of their individual values? Is it person for a person to display qualities that make him more valuable to the game in the presence of specific other people, like his friends? I think it is. And I think that is the rational behind dynamic queue.

In other words, if two players have values V₁, V₂, independently, it is possible that the value of them playing together is greater than V₁ + V₂. If it is not simple addition, then what function represents their value together? Whatever it is, we can call that function E.

Let the value of playing together be E (a, b).

#Axioms

It would be helpful to establish a set of axioms (assumptions) about E. I will provide some justification about why these assumptions are reasonable, but being assumptions they do not need proof-- if they seem unreasonable despite the rationale provided, you probably won't find any reason in the proofs that leverage them.

Note that E is commutative:

  • The order of the arguments is irrelevant because the function operates on a combination of two players, not a permutation, therefore E is a commutative operator; in other words, a pair of players is the same regardless of how you order them, and the value for the pair is the same. E (a, b) = E (b, a)

Note that E is associative:

  • The order in which players join a group does not affect the group's value, thus E is an associative operator. E (a, E (b, c)) = E (E (a, b), c)

Note that E has an additive inverse:

  • Notice that it is possible for the value a player creates to be completely cancelled by the toxicity another player creates. E (b, c) = 0 is possible. We could denote the value of c as the value of -b. Writing E (b, -b) expresses the idea that a player b is grouped with some other player who cancels out player b's value.

Note that E has an additive identity:

  • The value of a player who doesn't play, create content, and who isn't involved with the game at all is obviously neither positive nor negative, thus it must be zero. I take for granted the idea that people who do not even know what league of legends is provide zero value to the game.

Therefore, even though E is not addition, it follows the same algebraic rules that addition follows. So we can justify defining addition of players as an alias to E, and represent it as the more familiar +.

a + b = b + a

(a + b) + c = a + (b + c)

a + (-a) = 0

a + 0 = a

Note that the transitive properties are NOT met:

  • Just imagine that the value of player A is greater than player B, and A and B play well together, but C and B argue. A > B and A + B > A does not imply C + A > C + B or C + A + B > C + A. This is strange. Numerical values are such that 4 + n > 3 + n with 4 > 3, but apparently this doesn't hold with player values. This is something to watch out for!

We can use these axioms to deduce properties about the game. First a trivial example:

#Hypothesis:

Acquiring more players will increase the total value of league of legends.

#Counterexample:

Let the value of league of legends be V.

Let the players of league of legends be A, B, C...

Suppose there is a player D such that D < 0.

Obviously:

A + B + C ... + D < A + B + C ....

In other words, adding a player who is so toxic he has negative value reduces the value of league of legends.

Now for something less trivial:

#Hypothesis:

Acquiring more players will increase the total value of league of legends if the players added are not toxic.

#Counterexample:

Let the value of league of legends be V.

Let the players of league of legends be A, B, C...

Suppose there is a player D such that D > 0.

Suppose player D and A play fine separately, but don't get along at all. A + D < A

(A + D) + B + C ... < A + B + C ....

#Hypothesis: If Dynamic queue causes N players to play ranked and M players to stop playing ranked, and N > M, then the value of league is greater with dynamic queue than it is without.

#Counterexample: Just take for instance the set of players so that the total value of the M players is greater than the total value of the N players. I'd like to point out that the top 1% of players on average has more value than any other 1%, and possibly more value than 20 times the middle 1%. This is because the top 1% hosts a larger portion of its people as those that make guides, stream for a living, play professionally and act as leaders. These actions increase the game's longevity by keeping it publicly relevant. If a tiny fraction of the highest level players stop playing and X times that amount of middle tier players start playing, the change in value could still be negative. So this counter example is realistic.

#Conclusion So what do the most valuable players want? Do they value team work or individual agency more? How much toxicity are they willing to tolerate in exchange for increased agency or team work or some other metric? What is the optimal set of qualities (Agency, Teamwork, Toxicity, ...) so that the value of the game is maximized?

Some players are willing to tolerate less Teamwork for more Agency, others the reverse. Some are willing to tolerate Toxicity if it means having more Fairness.

I speculate that the most valuable players desire a combination of (Agency, Teamwork, Toxicity, Fairness, ... ) that is different than the combination that RIOT is pushing. I think the most valuable players want more Agency so that they leverage their commitment to the game against those who have less commitment. I think the most valuable players are even willing to tolerate a higher degree of Toxicity for more Fairness. However, this combination must be balanced with the desires of less valuable players insofar as they outnumber the more valuable players.

  • There is a set of (Agency, Teamwork, Toxicity, Fairness, ... ) that optimally slices all potential players to maximize value.

  • There is a set of (Agency, Teamwork, Toxicity, Fairness, ... ) that optimally slices all potential pairs of buddy players to maximize value.

  • There is a set of (Agency, Teamwork, Toxicity, Fairness, ... ) that optimally slices all potential triplets of buddy players to maximize value.

...

These sets of metrics are incongruent with each other. Buddies might desire higher Teamwork at the cost of lower Agency for example. The set of metrics optimized for dynamic queue is certainly not equivalent to the set of metrics optimized for solo queue.

A solo-first-class system will have different properties than a buddy-first-class system. In all but that targeted for solo queue, your optimal value is tied to people other than yourself, so if those people stop playing then you are offering less value than you would if they were. One player leaving could cause the value of the game to increase or decrease by an amount equal to many multiples of his own independent value. This makes the value of the game more volatile.

The increased volatility does not pair well with the fact that dynamic queue cannot function without an ample supply of solo players, who are second class in the system and so are less likely to be retained. So the system is both more volatile and less reliable.

29 Comments

lofi n chillhop9 votes

you need a tldr. I got the gist of it and agree though, so I thumbs'd it up :)

AATTRROOXX7 votes

Math fandom unite!

ThePartyLeader5 votes

I don't disagree with your math, hypothesis, etc. The rage about dynamic though is mostly about perceived value of rank decreased since everyone and there mother thinks that everyone else got carried by a premade, and the ease of blaming premades for losses where as before you had to blame a troll or feeder.

So you show why riot would like to perfect this system over solo, the problem lies in culture and execution not in the theory of the processes and systems.

Daen3 votes

Not sure if you were the OP there, but this is literally copypasted directly from reddit. As with that thread, the math here makes a lot of assumptions that have no statistical basis or are overly simplistic. Consider the following:

Buddies will desire higher Teamwork at the cost of lower Agency for example

The key to acknowledge here is that many players don't just queue via one method. I queue as both solo and premade in Ranked Draft, and yet my opinions remain the same.

If I were to use the four qualities mentioned in the thread, I would say that my optimal order is Fairness >>>>>> Agency > Toxicity > Teamwork. I feel that a fair rating system is the absolute most important possible thing for ranked play, and that all other variables are handled under Fairness at some point.

Critkeeper1 votes

{quoted}

Not sure if you were the OP there, but this is literally copypasted directly from reddit. As with that thread, the math here makes a lot of assumptions that have no statistical basis or are overly simplistic. Consider the following:

The key to acknowledge here is that many players don't just queue via one method. I queue as both solo and premade in Ranked Draft, and yet my opinions remain the same.

If I were to use the four qualities mentioned in the thread, I would say that my optimal order is Fairness >>>>>> Agency > Toxicity > Teamwork. I feel that a fair rating system is the absolute most important possible thing for ranked play, and that all other variables are handled under Fairness at some point.

All that is important is that differences exist between the sets of criteria for slicing with respect to solos or groups for the average.

I don't think that a single criteria exists which optimizes for both solos and groups. The differences between those optimized for dynamic queue versus solo queue, whatever they are, big or small, create tension in the system.

Daen2 votes

{quoted}

All that is important is that differences exist between the sets of criteria for slicing with respect to solos or groups for the average.

I don't think that a single criteria exists which optimizes for both solos and groups. The differences between those optimized for dynamic queue versus solo queue, whatever they are, big or small, create tension in the system.

I would argue that optimizing for both solos and groups isn't necessarily the whole puzzle. There is something to said for maintaining competitive integrity despite the fact there are people that prefer an easier or less specialized system, and a great example of this concept is Old School RuneScape. In OSRS every change is polled, and unless the change reaches a supermajority of 75% in favor it doesn't get pushed to the live game.

That being said, Jagex has on occasion decided to override the popular vote in favor of game integrity. A specific example of this is with something called 6 hour AFKing. For quite a while, at least a year, it was possible to start attacking a mob with a specific setup such that you'd never kill it and could literally go to sleep while your character trains free stats. Jagex polled the removal of this "feature" and it failed, but they decided to remove it anyway because it affects the integrity of the game as a whole from the perspectives of leaderboards and general atmosphere.

This is a very close parallel to Dynamic Queue, in the sense that it's something where the integrity of ranked play has to be taken into account despite popular opinion. I'm not necessarily saying Dynamic Queue threatens the integrity of League of Legends, but it is absolutely a factor when considering a change that is this core to the competitive experience.

Critkeeper1 votes

{quoted}

I would argue that optimizing for both solos and groups isn't necessarily the whole puzzle. There is something to said for maintaining competitive integrity despite the fact there are people that prefer an easier or less specialized system, and a great example of this concept is Old School RuneScape. In OSRS every change is polled, and unless the change reaches a supermajority of 75% in favor it doesn't get pushed to the live game.

That being said, Jagex has on occasion decided to override the popular vote in favor of game integrity. A specific example of this is with something called 6 hour AFKing. For quite a while, at least a year, it was possible to start attacking a mob with a specific setup such that you'd never kill it and could literally go to sleep while your character trains free stats. Jagex polled the removal of this "feature" and it failed, but they decided to remove it anyway because it affects the integrity of the game as a whole from the perspectives of leaderboards and general atmosphere.

This is a very close parallel to Dynamic Queue, in the sense that it's something where the integrity of ranked play has to be taken into account despite popular opinion. I'm not necessarily saying Dynamic Queue threatens the integrity of League of Legends, but it is absolutely a factor when considering a change that is this core to the competitive experience.

i agree with that, upvoted.

franticFurball2 votes

Structurally sound in a game = Game is fun to me.

Dynamic Garbage != Fun to me.

So the answer is no. Don't need 2 pages to know that ^^

jaymc11302 votes

You really could not have said it much better. The last paragraph quite accurately sums up the state of League at the moment. The solo players, the most valuable members of the community in terms of what Dynamic queue needs to function, are the players most hurt by Dynamic Queue and are also the players leaving the game now which will ultimately result with the complete failure of Dynamic queue since it requires solo players in order to function (and we use the term "function" here very loosely).

It really cannot be better stated. Dynamic queue is the death of League if it remains.

TauntyArmordillo2 votes

You failed to mention the (fallacious) lemma which your whole argument stands on, namely that the value of individual players in a set is constant, invariant, and/or independent, instead of being a function of the members in the set. You are essentially simplifying the entirety of the player base as a linear system in the general sense.

Critkeeper2 votes

{quoted}

You failed to mention the (fallacious) lemma which your whole argument stands on, namely that the value of individual players in a set is constant, invariant, and/or independent, instead of being a function of the members in the set. You are essentially simplifying the entirety of the player base as a linear system in the general sense.

no, i define a nonlinear function E to handle the nonlinear aspect of grouping players.

Now I put forth a question. Is the total value of a set of players the sum of their individual values? Is it person for a person to display qualities that make him more valuable to the game in the presence of specific other people, like his friends? I think it is. And I think that is the rational behind dynamic queue.

I used some rationale to justify taking some of its properties as axioms. The axioms I took were specifically selected so that E would match the algebraic properties of addition. I pointed out that not all the familiar properties of arithmetic were met, for example the transitive rule fails.

If the axioms I took are disagreeable, then you can throw everything out the window. If they are agreeable, then so is anything deduced from them. I took special care in the way I made the proofs to avoid any use of familiar properties that do not apply to this specific system, like the transitive rule.

TauntyArmordillo2 votes

I'm using the term "linear system" loosely (and perhaps quite incorrectly) to describe the seemingly monotonic property that your described function implies. The function may be "nonlinear" in the sense that it is not a directly proportional relation, inasmuch as a simple quadratic equation is not, however it does not account for the full description of what a nonlinear system can be.

The main flaw in your model is the lack of dependence between variables themselves, i.e. you have a vector argument rather than a tensor. This is at least my intuitive opinion when I approached your argument. I confess that I do not have a rigorous mathematics background, my specialty is physics, so my terminology may not be as precise at times.

Naut1 votes

Stop giving me Discrete Mathematics PTSD.

WTFRWARDS1 votes

Downvoting you because you clearly attempted to come off as some pompous egotistical dick with EVERY word you decided to use here. WP Sir. TLDR wouldnt even help

Arakadia4 votes

So your downvoting him because of the way he wrote it and not what he wrote?

Ralimak3 votes

HOW you say something is often much more important than WHAT you say.

Arakadia1 votes

I do agree that it is very important, not as important necessarily. However, he was being nitpicky, close minded, and believed it was more important I think.

Ralimak2 votes

It just depends on the person. For some people, how you say something doesn't really matter - for others, it's a huge deal.

Doctor Dyment1 votes

While I agree with the post, I must say that you really didn't need to add as much as you did. The math, the wording, and no summary at the end makes this post kind of difficult to read through. Without wanting to be overly rude, its just kind of dull. I kept reading because I wanted to see your opinion on dynamic queue, not because the post itself was particularly funny, exciting, or really anything else that could be counted as a hook. Pure logistics/math and logic do have their places, but you can't just make that the central pillar of your post and add nothing else. Most players won't want to get through your writing. I'm just leaving my two cents, so I won't upvote or downvote your post. Have a nice day.

Kenioshi2 sequel1 votes

TL;DR

Hyrum Graff1 votes

Bookmarked, will read in the morning when I have functioning brain cells.

CerealBoxOfDoom1 votes

didnt read all that but what's the definition of "value" here

I is Illiterate1 votes

For what it's worth, this post entertained me greatly. +1

Quepha1 votes

Being able to play with friends is a critical pillar for the game. Solo queue was the structurally unsound option and the game will be better off in the long run without it.

Eevee In A Jar1 votes

People seem to mistake the fact that Solo Q lovers don't do well in team environment. This is stupid and one that shows how ignorant you are. Solo Q players work well with everyone, including strangers. That shows more teamwork than being in the same premade and getting carried by the team. No matter what team you go on, you're an asset to the team and you contribute to the win. Whereas you're only an asset on few teams in the other while a dark horse liability in every other scenarios. There was no proven chance to say you deserve the rank you are at with Dynamic Queue thus there is no incentive to even say it is competitive and promotes teamwork when it restricts it. And when premades are with strangers in the same team, they don't always work together that will bring the win. They could have used an ult to save YOU, the stranger, but they use it on some random premade group they are with because they are butt buddies and now all 4 of them are reporting you.

3rd Age1 votes

AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

Yuri By Mail1 votes

Yes. It is.

Lirik1 votes

missing alot of values and its based on obscur pressomption of "toxicity levels"

The Deckowner1 votes

Great post, here is your TL;DR

Dynamic queue is not good

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