by Caden Pascual (capascual@ucsd.edu)
League of Legends is a Video Game where players play in a team of 5 players, versus another team of 5 players, with the objective being to kill the opponents base. Currently, there are 169+ "champions" in the game, with each of them possessing a unique set of skills and abilities they can use in battle. At the start of every match, both teams have the option to ban 5 characters from being played that match, with two teams, leaving up to 10 champions from being banned. Then both teams draft or pick champions to use during the game from the pool of champions that aren't banned or haven't already been picked. There are more details as to what happens during the game, but this analysis aims to predict the outcomes before the game even happens, so we don't need to understand those details.
The League of Legends dataset was the most intriguing to me, since it heavily relates to the field that I want to pursue, sports analytics. Similar to some types of sports, a League of Legends match is a competition between two opposing teams, with the goal of destroying the other teams base.
I think that with my analysis, using data like "damage per minute" or "total kills" may not be as interesting, as you can only fully get these statistics at the end of the match.
In League of Legends, there is a draft phase at the start of the game, where teams ban and pick different characters to use in the game. My goal is to be able to accurately predict the outcome of the game by just using this data.
If we take a look at different matches and the ban + pick% of the characters used (higher meaning they're more popular or meta), can we conclude that certain characters can expect higher win percentages, or that a matches outcome isn't that affected by the "meta", and that it really depends on the players skill/teamwork instead.
We're going to be using the dataset taken from the website Oracle’s Elixir using match data from 2022. The original dataframe has 150,180 rows and 161 columns, with each column being a single players data in a single match. The match is a 5 versus 5, so for every match there are 10 designated rows, for some matches, there are also 2 extra rows with the sum of all stats of a team.
There are lots of statistical columns ranging from damage dealt, first kill, and the % of damage you have on your team. However, these are stats that are calculated after the game starts. We're trying to predict the outcome of the game before it starts, and after the draft, so these columns are irrelevant to our calculations. If we want to, we can predict these columns using the draft data, but I want to specifically focus on the outcome of the match, not the total "dps" of a team or who will take the first tower.
The main columns that we're going to be working with are the 'ban' and 'pick' columns. In each game of League of Legends, there is a draft before the game starts, where both teams can ban 5 different champions from being played that match. Then each team starts "drafting", or picking the champions they want to use. A champion can't be picked if it has already been pick or it has been banned, but the same character can be banned by both teams. If each team has 5 unique brawlers they drafted + 5-10 unique brawlers banned. In total for every match there are 15-20 different champions that are picked/banned.
Other important columns include
- 'gameid', which categorizes every game with a unique ID
- 'result', 1 if your team wins, 0 if your team loses
- 'date' and 'patch', which gives a specific time and patch (update) that the game is played
- 'champion', the specific champion the player is playing, empty if the row is the 'team data'.
- 'league', the competitive league the match is played in.
<iframe src="assets/playoff_chart.html" width="800" height="600" frameborder="0" ></iframe>
The above plot is the distribution of non-playoff vs playoff games. There are much more "non-playoff" games since the playoffs are a specific subset of games, only for the best teams, to play against each other for the final championship. We can group by "playoff" and "non-playoff" games in our analysis to see if it may be easier or harder to guess the outcome of a game based off if it is a playoff game or not.
<iframe src="assets/patch_chart.html" width="800" height="600" frameborder="0" ></iframe>Above is the distribution of games played for every patch (game update). There are less games played in certain patches since the time that certain patches were up may have been less than others. We can verify this by plotting the amount of games played per month. There are 9 games that aren't assigned a patch. We will figure out what patch they are in and the reason later.
<iframe src="assets/month_chart.html" width="800" height="600" frameborder="0" ></iframe>The distribution of games played per month has a very similar shape to the patch notes graph. We can assume many things, maybe there are big tournaments around Feb-March and June-August.
<iframe src="assets/first_pick_chart.html" width="800" height="600" frameborder="0" ></iframe>There is a slightly positive correlation between a "popular" first pick and winning, but even the most popular first pick, Jinx, only has a win pctg of 51%, which isn't that high above average. Let's take a look at the chart with all possible first picks (min 25 times picked, since the data for such champions is always skewed).
<iframe src="assets/all_first_pick_scatter.html" width="800" height="600" frameborder="0" ></iframe>There isn't a strong visible correlation between win % and the how popular the first pick is, we have to look futher into this, maybe some characters are stronger during some patches, and after they get nerfed (the game devs lower their stats or make their abilities worse to make them fairer), their win percentages drop.
With the previous Bivariate examples in mind, let's see what an aggregation of ALL champions, regardless of when they're picked, and their win rates.
<iframe src="assets/win_rate_scatter.html" width="800" height="600" frameborder="0" ></iframe>Most champions win rates hover around the 50% line. This is what we should be expecting, since we haven't looked at any of the banned statistics, we can expect that all the strongest champions are being banned (meaning they can't be picked in matches).
I don't believe there is a column in the dataset I'm using that is NMAR. There is a column in my dataset that is named "datacompleteness", so there should be some column in the dataset that is missing based off this column. That wouldn't be NMAR data however, since the missingness would depend on the "datacompleteness" column. In a LoL game, there isn't any way for a player to "hide" a specific stat. Sure, there are competitive matches that may not be in this dataset. Not all games are public, but for these games we wouldn't be left with only some of the stats, we wouldn't see the row altogether.
"Each 'gameid' corresponds to up to 12 rows – one for each of the 5 players on both teams and 2 containing summary data for the two teams." The summary data for both teams usually contains the champions picked for the whole team, although some of the picks are missing in these rows. Some competitive 'leagues' may not be as mainstream as others, let's see if this data is missing dependent on the league.
<iframe src="assets/picks_missing_graph.html" width="800" height="600" frameborder="0" ></iframe>As we can see, 6/50 of the leagues have all their draft data missing. Let's see if this is statistically possible, or if the draft data missing is actually dependent on the league with permutations.
Null Hypothesis: The missingness of pick_missing is independent of the column 'league'.
Alternative Hypothesis: The missingness of pick_missing depends on the column 'league'.
Our p-value is 0.0, which is under the threshold 0.05, so we reject the Null Hypothesis, meaning that pick_missing depends on the column "league". Let's check another column that pick_missing ISN'T dependent on, such as 'side' (the current game in the series).
Null Hypothesis: High-ban-rate champions do not have a statistically significantly higher mean win rate than the average champion.
Alternative Hypothesis: High-ban-rate champions have a statistically significantly higher mean win rate than the average champion.
Test Statistic: Difference in Means
P-Value: 0.0439
Now that we have all the ban rates, lets categorize our champions by how high their ban rates are.
<iframe src="assets/ban_freq_chart.html" width="800" height="600" frameborder="0" ></iframe>This is the average win rate of characters that have a 'high' ban rate (above the median) vs a 'low' ban rate (below the median). The difference in means ends up being around 0.023, which is a signifigant enough difference to give us a p_value of 0.0439 under permutation testing. Our p_value is under the significance level of 0.05, so we are able to Reject the null hypothesis, leading us to the conclusion that High-ban-rate champions have a statistically significantly higher win rate according to our data.
We're going to be using the ban/pick rate data that we made to predict the outcome of a game (win or loss) through Classification (1 = win, 0 = loss). The only data we want to use is before the match starts, but after the draft. Therefore, the feature we'll be using will only be related to the draft.
The columns we used from the original data + new ones that I created were
- 'gameid': a unique ID for every match.
- 'result': 1 if your team wins, 0 if your team loses.
- 'pick_rate': the percentage of matches that the champion was picked to play (0-1).
- 'ban_rate': the percentage of matches that the champion was banned in (0-1).
- 'win_rate': the percentage of matches that a champion has won (0-1).
- 'patch': the current version of the game (changes when game is updated).
- 'position': the position that the current player is playing (top, bot, jng, mid, sup).
My baseline model is very simple, use the ban rates and pick rates of each champion and the original result data to Classify which team should win and which should lose. Both of these features are quantitative, on a scale from 0-1, with 0 being "never" picked/banned and 1 being "always" picked/banned. The ban and pick rate data wasn't in the original data set, I had to create it myself. Here's the process I had to go through to create this data.
The 'pick_rate' was easier to find, I had to take the value counts of all champions in the 'champion' column and divide the counts by the total number of games played. For the 'ban_rate', there was no 'banned_champion' column that had the specific champion that each player banned in the match, instead there were 5 different ban columns for the whole team. For 'ban_rate' we also have to account for duplicate bans from both sides. A champion can't be picked to play in game by multiple players, but both teams can ban the same champion in a single match, meaning that if we just take the value counts of all the ban columns, we might be overestimating the ban rates of some champions. If in all games, both teams ban the same champion, calculating it that way would give us a ban rate of 200%, which is obviously impossible. I had to find a way to get around this by grouping all the bans in each game, and taking all the unique values, getting rid of duplicates.
Using these two features under a Standard Scalar, the accuracy score of this model ended up being around 51.86%, which is just a little higher than guessing at random. This baseline model isn't very good, but I didn't expect too much out of it with such little features.
For my final model, I looked into adding more features, such as adding the 'win_rates' (quantitative data) of the champions in addition to the ban and pick rates. This raised the accuracy to around 52.57%, which isn't very significant. I also added "position", which is a nominal feature, to see if your role on the team played any significance in whether you won or not. It didn't do much, raising the accuracy to 52.60%.
Then I had an idea. I thought about filtering the data I already had by the current "patch" (an ordinal feature) or update. Whenever the game gets updated, the developers "buff" (increase stats) or "nerf" (decrease stats) certain champions that are too strong or not powerful enough. It might be harder to set a prediction if we're using data from the whole year, since a characters usage rate changes over each patch. If we filter our ban and pick rates by the current patch, we might be able to more accurately predict the outcome of matches. And I did just that.
I created a whole new data set, finding the win, ban, and pick rates for all champions in each individual patch, and then merging the original data frame with the new statistics. Using these new statistics (updated 'ban rate' and 'pick rate' based on patch), as well as the two other features I added after the baseline model ('win rate based on patch', 'position'), I ended up with a final accuracy score of 55.65%, which is signifigant enough to say that my Final model improved from the original Baseline model.
This section checks if our model performs worse for a certain group of individuals. The two groups we'll be looking at are ones we formed in our Hypothesis Testing. People using 'high-ban-rate' champions and people who aren't
- Null Hypothesis: Our model is fair. Its precision for high and low ban rate champions are roughly the same, and any differences are due to random chance.
- Alternative Hypothesis: Our model is unfair. Its precision for low ban rate champions is higher than its precision for high ban rate champions.
- Test Statistic: Accuracy
- P Value: 0.0
Our p value falls below the signifigance level of 0.05, meaning that our models precision is unfair, and the precision for low ban rate champions is higher than the precision for high ban rate champions.