TLDR as a spoiler :

I've investigated the existence of a loser queue by averaging statistics over ~100 000 master elo matches in the last months. Overall, there is no evidence that players who lose a game are more likely to lose the next game, resulting in more defeats. Conversely, the results are very consistent with what would happen if each game were won or lost with a probability close to the overall winrate of the players in the sample, with very low dependency on the previous game played.

However, this study cannot disprove the balancing of matchmaking inside a single match. From this data, I cannot prove that game are balanced from the lobby. However, such a claim would have to be proven by the proclaimers of the loser queue, and not disproved by other people like me.

Anyway, I really enjoyed doing this exercise, and I might try it again in the future!

Introduction

Hi fellow summoners! I'm u/renecotyfanboy, a French PhD student, and I have been a League of Legends enjoyer since the beginning s4. I have mostly played this game in casual queues, and played at most 100 ranked in a s5, and barely 20 rankeds per season after, we could say I'm not a competition enjoyer. However, I do enjoy high elo League streams, and in the past 3 years, we were all exposed to the emergence of the “loser queue” concept. Whatever your formulation of loser queue is, it can be summarized as follows :

• What? Loser queue is a mechanism in matchmaking that improves player engagement by artificially enabling win and lose streaks.
• How? When losing, you get a higher probability of being matched with people that are themselves in lose streak and against players on win streaks, thus reducing your probability of winning the game.
• Why? Improving player's engagement is always good for business, and since League is a game which is hard to start to play, it is easier to retain old players to keep a good player base.
• Hints? Other companies such as EA are using Engagement Optimized Matchmaking frameworks is their competitive games such as APEX.

That's a lot to digest, and this seems really unfair and pointless to play competitive games in LoL if most of this is real. As being sceptical innately, I would have loved to see strong proof of this, but I never got to see more than high-elo players' feelings about this. Well, as I am a PhD student in astrophysics currently redacting his thesis with a lot of spare time, I decided to have a look at this by myself, using a bit of statistical inference to get things done properly.

Data, Hypothesis & Known biases

To perform this study, I used publicly available data, which I fetched with the Riot API. I gathered around ~100 000 matches in Master elo from the past months, and tracked 1000 randomly chosen master players history. Using this, I built the win/loss history of 100 games and I'll use this to test some models.

I am aware of some data qualities issues here :

• People might not be at their stationary elo, thus biasing toward long win or lose streaks while they climb or fall. There is basically nothing I can do about this since Riot doesn't give public data about the players' elo over time. Mobalytics and affiliated can show this metric because they are tracking all players on each match they make and compute this quantity over time, and I have sadly no access to this with an automated data gathering process. As a rule of thumb, I consider that after the season starts, players reach close to their elo in ~25 games, and as we study 100 games per player, it should be fairly stationary. In any case, I'm banking on the large quantity of data to soften the selection bias and instability of game histories.
• I can't verify that when you're on a losing streak, you're likely to tag with people who are also on a losing streak. This would require recursive calls to the Riot API which are already limited with my personal use key. Gathering enough data would take eons, and I have to speed up this study before I lose my mojo. In any case, a biased matchmaking would expose systematic bias in the win/lose streaks behaviour, as a departure from what would be expected from a ~50% WR matchmaking.
• The high elo sample might bias value toward large win streaks, since the early season climbing is full of winstreaks for master+ players. I still prefer to stick to master player since I think they are on average more involved in the game than lower elo players, which helps when it comes to have a stationary elo

Being aware of these biases is crucial when interpreting the results, there might be other things I didn't think about, but hey this is not a scientific article, it is a reddit post I made this weekend. Do yourself a favour and referee this post in the comments if you feel like it.

Result (i) Streak size frequency

After computing the win/loss history for the master dataset, we got an average winrate of ~55% which is positive as expected from the master player sample. The most straightforward thing to do is to investigate the frequency of the streak length in this match sample. To do so, I simply counted the win and lose streak lengths in the game sample, and computed their empirical frequencies. I also computed what histogram would be expected if each game was a pure coin flip, with the probability of win fixed to the previously computed winrate of 55%. By pure coin flip, I mean this is modelled as a Bernoulli trial, each match being completely independent of the previous one. As I would rather not do the maths, this is computed with a Monte Carlo approach with 1 million fake matches. The results are displayed in the following figure.

Frequency histogram of Win/Loss streak lengths in ordinary scale (left) and log scale (right). The expected distribution is computed for independent matches.

Many things to say about this simple figure. First, there are on average more win streaks than lose streaks, as expected in our master player sample. We see an excellent agreement with what we would expect from purely independent matches with 55% WR and the observed frequency in our sample. The biggest discrepancies occur in the largest streaks, where there is too few data to get significant constraints. As illustrated in the log-scale plot, this streak length could be modelled with a Power-Law behaviour, this is a very common pattern in science that we could have foreseen here.

For the picky scientists or data analysts that might read this, I didn't propagate any kind of dispersion and didn't compute any significance for this compatibility because of laziness. In any case, if loser queue was impacting the streak sizes, I would expect a significant excess in 3/4/5-size series, which is not visible in this sample.

So the hints provided here is that the distribution of streaks is compatible with what would appear if matches were on average independent one to another. I.E. you are not more likely to win after a win, or you are not more likely to lose after a loss. One would say “With a 55% WR, you are more likely to win after a win”, which is a true but incomplete statement as with a 55% WR, you are more likely to win in any case. This is crucial because it can point to the fact that the outcome of a given match may be fairly independent of the previous one. We will explore this in the next section.

Result (ii) Probability of losing after a loss

I am now seeking correlation between games. The most straightforward way to do this is approaching this problem by determining the transitions probabilities of a Markov Process. This is simply The idea is to judge whether we get a bigger probability to win right after a win and vice versa.

Graph depiction of a Markov process with two states : the player switches between winning and losing, with probability depending on the previous state

The transition probability can be estimated directly by computing the frequency of transitions, with proper normalisation. As before, we compare the results obtained on the true dataset and the results obtained from the simulated dataset of independent matches.

Transition matrix for the 2 states Markov process estimated for the true data and the independent simulated dataset. There is a 2% more probability of losing right after a game, which appears when compared to the true dataset.

The major difference between the simulated dataset and the true dataset is that in real game, after a loss, people tend to lose 2% more often. This is a pretty low significance discrepancy, which may be due to loser queue tilt? I would personally interpret such a low difference by more general and external factors, such as the fact that a player can be slightly tilted after a loss, which will reduce their winrate.

I continued this methodology by adding one more game, to see the win/win, win/loss, loss/win and loss/loss successions to check that there are no additional probabilities appearing. And indeed, everything is consistent to 1 or 2% as illustrated below.

Same as before but exploring the correlation with the two last games

Going further and manually inspecting all the combinations for 3-state or even more depth would be interesting at some point. I won't do it right now, since we do not have any hint toward the fact that players experience long streaks.

Result (iii) Consecutive games

I wanted to look at what happens when you play games without any break. From the data I got, it is pretty straightforward to break into series of games that are played one after the other. I studied what happens to your winrate when you play without ~1h30 break (I got some issues with the Timestamp conversions, so not sure about the exact value).

https://preview.redd.it/3udl2lznlkgb1.jpg?width=1439&format=pjpg&auto=webp&s=1c675ee10cf87e52347734f5c0ead16504af1ea3

What we see from this graph is that players hit peak performance when playing once, and that the WR tends to decrease when the number of games increases. I can't even imagine that some people can play 30 games in a row… I guess hope that these are only streamers doing marathons. Increasing error bars is due to lack of data (not many players play that much).

Conclusion

• From what we saw before, there is no such thing as an algorithmically orchestrated chain win or chain lose mechanism in master for this 100 000 match sample. The winstreak or lose streak distribution is fairly compatible with what you would expect from a coinflip biased toward the winrate of players.
• Based on this data, I can't disprove out that matchmaking for a given game is balanced. Riot may intentionally bias the matchmaking toward a given side. Since I do not have access to the history of all players in a given champ select, I cannot look at the fact that people are matched with losing people after they lost a game (or any kind of method to push the game to a given side). However, the burden of proof is on those who claim that such a mechanism exists, and until this, it's simpler to think that matchmaking is fairly balanced. Never forget the Sagan standard : Extraordinary claims require extraordinary evidence.
• If you want to perform at best, do breaks when you play. This seems natural.

This has been pretty fun to do! I hope that you enjoyed this post, and that it was clear enough. See you on the rift for more bait pings ( ͡° ͜ʖ ͡°)

--------------------------------------------------------------------------------------------------------------------------------------------

Edit 1 : I didn't export the graph properly, hope this is fixed now

Edit 2 : The database I built

https://filesender.renater.fr/?s=download&token=779baa8a-0db3-4309-a196-4b491927ce3a

• master.json contains a list of master players I fetched 3 or 5 days ago, and a list of match history for each. I used the 1000 firsts to perform this analysis.
• match_data.json contains matches which were used in this analysis, sorted by match_id.

Edit 3 : I changed "loose" to loss, since people notified me it was a French "Anglicism"

External link →