Optimising League of Legends draft resource allocation for individual player

Before the start of any MOBA game between 2 teams, in our case LoL(League of Legends), there is a drafting phase, where teams exchange pick and bans to select best of playable characters for the upcoming match. This phase consists of 5 bans and 5 picks for each team. Each team uses their draft resources to get the best possible champions for their players in every position: top, jungle, mid, ADC and support. As there are finite draft resources at every team’s disposal, it is imperative to spend them wisely. Draft resources encompass multiple actions, for example prioritising and picking the best champions for your carries early or saving counter-picks for your most versatile players. However, in this article we will be considering bans as a sole draft resource and look at how best they can be utilised to enable or shut down certain players. To accomplish this, we will look at bans for and against each individual player in their position considering them separately, link the bans for and against a player to the win rate of the player and calculate the change of win rate per ban, categorise players into different buckets of draft flexibility depending on the gradient calculated above and try to assemble an example team of 5 pro players optimising for draft resources.

The following assumptions have been used throughout the investigation:

1. Bans considered as the only draft resource
2. No individual champion proficiency is considered
3. All 5 bans are assumed to be taking place at the same time at the beginning of champ select (in reality 3 bans are at the start and 2 in the middle of the drafting phase)
4. No flexing, every champion is considered to be assigned to the role which they have appeared in most in a given time period
5. No coupling is considered between the players on the same team during the analysis
6. Bans are considered on positional basis, meaning that a ban for or against a player at a certain position is always accredited to the player in that role, within role interactions are not considered
7. All conclusions are drawn from the Oracle data of LEC Summer 2022 regular seasons, without considering play-offs

Meta-adjusted bans

LoL and by proxy most modern games operate on meta cycles, where the developers can change the power level of certain champions, leading to changes to how the game and therefore drafting is executed. Usually this causes an imbalance in the number of bans used for different positions, meaning that those bans are dictated by the meta and not the player themselves. The goal of the investigation is to classify players in different buckets without considering the meta constraints. To achieve that a multiplier for each role is calculated which assigns varying importance to the bans in that position. The numbers used can be found below:

We can see that the importance for ADC is much lower than the one for Top, this is because ADCs are considered to be strong in this meta (Kalista, Zeri, Sivir, etc.) and therefore get banned more frequently when compared to Top, meaning that Top bans are more likely to be directed to or for a player rather than the champion. Going forward all the analyses will use these multipliers.

Bans for and against a player

Most important concepts that need to be differentiated is the bans made by the player’s team to enable him or the bans made against the player by the opposition to shut him down. It is important to know that players draw bans for different reasons, for example, a team might ban many Top champions in order to shut down a player with a small champion pull or they it could be because they are scared of a niche pocket-pick or a potential counter. However, we are interested in draft resources that a player demands from their own team or the opposition, therefore the reasoning for the ban is not important.

Position of the bans for and against each player is considered and the changes in the win rates by each ban is recorded. An example distribution is given below:

Win ratio per ban gradient

Once we have the win rate for each player with the number of bans in their position, we can calculate how the win rate of the player changes per ban, so the gradient of the distribution. For each player we are able to obtain 2 different gradients, change of win rate with respect to bans for that player and the change of win rate with respect to bans against the said player.

In general we would expect the bans against gradient to be negative as the player has less options to win the game and bans for to be positive as it shuts down the opposition. However, as we will see, this is not always the case, as a ban for or against one player means 1 less bans for the rest of the team, creating an inter-dependency between different positions which we will not explore further in this article.

We will call the players who can easily be enabled or shutdown by the bans “Sensitive” and ones that seem to be unaffected as “Insensitive”. We also differentiate players who can be enabled by draft, but not shutdown as “Inducible” and one that can be shutdown but not enabled as “Vulnerable”. Top 5 Inducible and Vulnerable players can be found in the tables below:

Draft optimal players and where to find them

Now that the hard part is done we can have some fun!

The gradients defined above is all we need to find the most draft flexible players and try to build a 5 person team with only draft data in mind.

Below is a plot of win rate for and win rate against gradients for every player in the league:

Each dot on the scatter plot represents an individual player, the color of the dot represents the bucket each player has been placed in and the size of the dot is the amount of bans that player has attracted throughout the season.

Players on the far right are the ones who have the highest probability of winning the game if the bans are used for their advantage and the ones one the low end are the ones who get shut down if the bans are directed towards them.

We see the coupling effect discussed earlier in full swing here. For example, Dajor seems to have a big increase in his win rate more bans he attracts which on the surface does not make much sense, but if we look deeper we will see that Dajor is in the Inducible bucket meaning that he is not easily shut down by target bans, whereas his teammates Jezu, Vizicsacsi and Xerxe are Vulnerable. So more bans Dajor attracts to himself, less bans there are left for the rest of his team, leading to higher win chance.

In theory, opposition teams should look to ban out players in blue and green (Vulnerable and sensitives), which will increase their probability of winning, however we see that in reality that is not always the case. We see a lot of bans going to players like Alphari, Haru and Finn who are not affected by them according to our calculations. This fact is very important when trying to build the most optimal draft team.

Example draft-optimised roster

The idea is that we can build a team of high win rate players that can be easily enabled but not shut down (Inducible and top end of Sensitives) and compliment them with players who tend to attract high amount of bans, but not be affected by them (Insensitives).

Firstly, lets look for players that use most of draft resources, but are likely to win you the game. A great example of such players would be Wunder and Patrik. They are both at the right side of the graph which makes it beneficial to spend bans for them, but they are also high enough that the bans against them should not have an impact.

Now we need find a Support, Mid and Jungle form the Insensitives who also attract a lot of bans. An example of such a trio could be Targamas, Haru and caPs. So our team would look something like this:

• Wunder, Haru, caPs, Patrik, Targamas

Limitations and further investigation

I wanted to take a moment to thank you all for reading this article and congratulate you on reaching the end! The goal of this article was to investigate the drafting process and see how it can be improved by simple data analysis and I hope we managed that. it is important to point out that this is a valuable thought experiment but is too simplified to be directly translated to the real world.

In the final section I wanted to outline certain limitations on this analysis as well as suggest improvements for the future.

1. With the maximum of 18 games played per player on different patches the data is indeed sparse, meaning that the gradient estimation is not accurate.
2. Other draft resources outlined in the description are arguably more valuable than bans, so this model does not provide the full picture.
3. Meta-adjustment devised was useful for this given discussion, but it fails to fully eradicate the effect of the meta on bans.
4. Further investigation can be completed to decouple players from their teams.
5. This kind of analysis is interesting to perform retrospectively at the end of the season, but it might be a lot harder to dissect mid-season where the data is even more sparse.