League of Legends Selector User Guide

Data

League of Legends Selector's data is currently available for 3 servers(EUW, KR and NA), 2 tier ranges(Diamond+ and Master+), and 2 durations(last 7 days and last 30 days). The data is collected from the Riot Games API and updated daily.

All the example data in this guide are from actual data available on December 25th, 2023 for NA server, Diamond+ tier ranges, and last 30 days.

League of Legends Selector uses 2 different types of statistics in nature:

1. Single champion statistics

Ex) Blue team Annie's win rate is 52.49% with 4,822 total games.

Ex) Red team Annie's win rate is 50.96% with 4,829 total games.

2. Paired champions statistics

Ex) Blue team Annie's win rate with Blue team Olaf is 52.00% with 75 total games.

Ex) Red team Annie's win rate with Red team Olaf is 61.40% with 57 total games.

Ex) Blue team Annie's win rate against Red team Olaf is 38.81% with 67 total games.

Ex) Red team Annie's win rate against Blue team Olaf is 46.97% with 66 total games.

Both types of statistics consist of win rates and numbers of games and because the numbers of games differ, the magnitudes of advantage/disadvantage are not obvious to compare. Consider below 2 single champion statistics and try deciding which champion is more advantageous to play in Blue team.

1. Single champion statistics.

Ex) Blue team Zoe's win rate is 52.03% with 6,048 total games.

Ex) Blue team Neeko's win rate is 51.54% with 9,016 total games.

Zoe has a higher win rate than Neeko but Neeko has more games than Zoe. The win rate normallizes closer to 50.00% as the number of games increases due to the elo rating based matchmaking, so which champion is more advantageous is a debatable question with only win rates and numbers of games.

In order to address this ambiguity, League of Legends Selector performs binomial tests on each of the statistics to determine the statistical significance of the observed win rate and number of games. The statistical significance is represented by the Z-score(number of standard deviations the observed win rate is from expected win rate) from the test. Binomial test is a statistical test of determining whether the observed win rate is significantly different from the expected win rate.

For the single champion statistics, the null hypothesis(expected win rate) is that the champion's win rate is 50.00% and the alternative hypothesis is that the champion's win rate is not 50.00%. The formula for the Z-score of binomial test is as follows:

Z = (p - p₀) / √(p₀ * (1 - p₀) / n)

Where p is the observed win rate, p₀ is the expected win rate(50.00% or 0.5), and n is the number of games. By using this formula, the following Z-scores for the above 2 single champion statistics are obtained:

1. Single champion statistics.

Ex) Blue team Zoe's win rate is 52.03% with 6,048 total games.
Blue team Zoe's Z-score is 3.157 = (0.5203 - 0.5) / √(0.5 * (1 - 0.5) / 6048).

Ex) Blue team Neeko's win rate is 51.54% with 9,016 total games.
Blue team Neeko's Z-score is 2.924 = (0.5154 - 0.5) / √(0.5 * (1 - 0.5) / 9016).

Blue team Zoe's statistic proves to be more statistically significant than Blue team Neeko's statistic because Blue team Zoe's absolute value of the Z-score(3.1574) is higher than that(2.9245) of Blue team Neeko. Therefore, League of Legends Selector considers Zoe more advantageous to play than Neeko in Blue team based on Z-score comparison. The higher the absolute value of the Z-score, the more statistically significant the statistic is.

Now, consider below 4 paired champions statistics and try deciding which statistic hints the most advantage/disadvantage.

2. Paired champions statistics

Ex) Blue team Annie's win rate with Blue team Olaf is 52.00% with 75 total games.

Ex) Red team Annie's win rate with Red team Olaf is 61.40% with 57 total games.

Ex) Blue team Annie's win rate against Red team Olaf is 38.81% with 67 total games.

Ex) Red team Annie's win rate against Blue team Olaf is 46.97% with 66 total games.

Again, the paired champions statistics are not directly comparable because the numbers of games differ.

Unlike the single champion statistics, in which the null hypothesis(expected win rate) is that the champion's win rate is 50.00% and the alternative hypothesis is that the champion's win rate is not 50.00%, the null hypothesis(expected win rate) for the paired champions statistics is that the champions' synergy/counter statistic is equal to the weighted average of the win rates of the 2 involved champions and the alternative hypothesis is that the champions' synergy/counter statistic is not equal to the weighted average of the win rates of the 2 involved champions.

Let's take a look at the first example of the paired champions statistics(Blue team Annie's win rate with Blue team Olaf is 52.00% with 75 total games). Initially, this specific statistic could mislead summoners to believe that Blue team Annie is advantageous to play with Blue team Olaf because the win rate is higher than 50.00%. However, the null hypothesis(expected win rate) for the paired champions statistics is that the champions' synergy/counter statistic is equal to the weighted average of the win rates of the 2 involved champions, not 50.00%

Blue team Annie's win rate is 52.49% with 4,822 total games, and Blue team Olaf's win rate is 52.41% with 5,331 games. The weighted average of the win rates of Blue team Annie and Blue team Olaf is 52.45% = (52.49% * 4822 + 52.41% * 5331) / (4822 + 5331). This weighted average can be used as p₀ in the formula to calculate the Z-score of binomial test for paired champions statistics. Blue team Annie's Z-score with Blue team Olaf is -0.078 = (0.52 - 0.5245) / √(0.5245 * (1 - 0.5245) / 75).

The Z-score of -0.078 is negative, hinting disadvantage of playing Annie and Olaf together in Blue team even though the observed win rate is 52.00% because the expected win rate is 52.45%.

Listed below are the Z-score calculations for all of the above 4 paired champions statistics:

2. Paired champions statistics

Ex) Blue team Annie's win rate with Blue team Olaf is 52.00% with 75 total games.

Blue team Annie's win rate is 52.49% with 4,822 total games.
Blue team Olaf's win rate is 52.41% with 5,331 games.
The weighted average of the win rates of Blue team Annie and Blue team Olaf is 52.45% = (52.49% * 4822 + 52.41% * 5331) / (4822 + 5331).
Blue team Annie's Z-score with Blue team Olaf is -0.078 = (0.52 - 0.5245) / √(0.5245 * (1 - 0.5245) / 75).

Ex) Red team Annie's win rate with Red team Olaf is 61.40% with 57 total games.

Red team Annie's win rate is 50.96% with 4,829 games.
Red team Olaf's win rate is 50.83% with 5,467 games.
The weighted average of the win rates of Red team Annie and Red team Olaf is 50.89% = (50.96% * 4829 + 50.83% * 5467) / (4829 + 5467).
Red team Annie's Z-score with Red team Olaf is 1.587 = (0.614 - 0.5089) / √(0.5089 * (1 - 0.5089) / 57).

Ex) Blue team Annie's win rate against Red team Olaf is 38.81% with 67 total games.

Blue team Annie's win rate is 52.49% with 4,822 total games.
Red team Olaf's win rate is 50.83% with 5,467 total games. Red team Olaf's loss rate is needed instead of win rate, so Red team Olaf's loss rate of 49.17% = 1 - 50.83% is used to calculate the weighted average.
The weighted average of the win rate of Blue team Annie and loss rate of Red team Olaf is 50.72% = (52.49% * 4822 + 49.17% * 5467) / (4822 + 5467).
Blue team Annie's Z-score against Red team Olaf is -1.951 = (0.3881 - 0.5072) / √(0.5072 * (1 - 0.5072) / 67).

Ex) Red team Annie's win rate against Blue team Olaf is 46.97% with 66 total games.

Red team Annie's win rate is 50.96% with 4,829 total games.
Blue team Olaf's win rate is 52.41% with 5,331 total games. Blue team Olaf's loss rate is needed instead of win rate, so Blue team Olaf's loss rate of 47.59% = 1 - 52.41% is used to calculate the weighted average.
The weighted average of the win rate of Red team Annie and loss rate of Blue team Olaf is 49.19% = (50.96% * 4829 + 47.59% * 5331) / (4829 + 5331).
Red team Annie's Z-score against Blue team Olaf is -0.361 = (0.4697 - 0.4919) / √(0.4919 * (1 - 0.4919) / 66).

By comparing the Z-scores of the above 4 paired champions statistics(-0.078, 1.587, -1.951, -0.361), League of Legends Selector considers Red team Annie's win rate with Red team Olaf the most advantageous statistic with a Z-score value of 1.587, and Blue team Annie's win rate against Red team Olaf the most disadvantageous statistic with a Z-score value of -1.951.

The positive sign of the Z-score indicates the advantage and the negative sign of the Z-score indicates the disadvantage.

Although League of Legends Selector utilizes both single champion Z-scores and paired champions Z-scores, it heavily relies on the paired champions Z-scores over the single champion Z-scores because the general/overall strengths of single champions, which can be represented by the single champion Z-scores, are actually better reflected in the paired champions Z-scores.

Consider the following 4 single champion statistics/Z-scores:

1. Single champion statistics

Ex) Blue team Vayne's win rate is 52.36% with 29,735 games.
Blue team Vayne's Z-score is 8.139 = (0.5236 - 0.5) / √(0.5 * (1 - 0.5) / 29735).

Ex) Blue team Hecarim's win rate is 51.47% with 17,662 games.
Blue team Hecarim's Z-score is 3.907 = (0.5147 - 0.5) / √(0.5 * (1 - 0.5) / 17662).

Ex) Blue team Viego's win rate is 48.79% with 14,100 games.
Blue team Viego's Z-score is -2.874 = (0.4879 - 0.5) / √(0.5 * (1 - 0.5) / 14100).

Ex) Blue team Aphelios' win rate is 47.27% with 13,407 games.
Blue team Aphelios' Z-score is -6.322 = (0.4727 - 0.5) / √(0.5 * (1 - 0.5) / 13407).

Let's examine the synergistic paired champions statistics/Z-scores that involve the above 4 champions in Blue team:

2. Paired champions statistics

Ex) With Blue team Vayne, 102 champions have positive Z-scores totaling 104.149 and 63 champions have negative Z-scores totaling -61.350.

Ex) With Blue team Hecarim, 101 champions have positive Z-scores totaling 79.832 and 64 champions have negative Z-scores totaling -54.068.

Ex) With Blue team Viego, 67 champions have positive Z-scores totaling 50.547 and 98 champions have negative Z-scores totaling -95.659.

Ex) With Blue team Aphelios, 57 champions have positive Z-scores totaling 35.445 and 108 champions have negative Z-scores totaling -126.468.

Let's also examine the counteristic paired champions statistics/Z-scores that involve the above 4 champions in Blue team:

2. Paired champions statistics

Ex) Against Blue team Vayne, 64 champions have positive Z-scores totaling 61.113 and 101 champions have negative Z-scores totaling -114.193.

Ex) Against Blue team Hecarim, 74 champions have positive Z-scores totaling 54.191 and 91 champions have negative Z-scores totaling -88.204.

Ex) Against Blue team Viego, 107 champions have positive Z-scores totaling 94.074 and 58 champions have negative Z-scores totaling -35.311.

Ex) Against Blue team Aphelios, 124 champions have positive Z-scores totaling 139.029 and 41 champions have negative Z-scores totaling -31.072.

As illustrated by the above paired champions statiscits/Z-scores examination, the paired champions statistics/Z-scores are more informative and reliable in assessing the general/overall strengths of single champions than the single champion statistics/Z-scores.

Listed below are the results of simple data analysis performed on the single champion Z-scores and the paired champions Z-scores:

1. Single champion statistics

Minimum Z-score absolute value = 0

Maximum Z-score absolute value = 25.235

Average Z-score = 0.017

Average Z-score absolute value = 2.635

Count = 332

2. Paired champions statistics

Minimum Z-score absolute value = 0

Maximum Z-score absolute value = 7.066

Average Z-score = -0.014

Average Z-score absolute value = 0.876

Count = 110224

The average Z-score absolute value of the paired champions statistics(0.876) is significantly lower than the average Z-score absolute value of the single champion statistics(2.635). In order to place extreme emphasis on the paired champions statistics, the single champions statistics are downscaled so that each single champions statistics carry only 1% significance compared to those of each paired champions statistics.

Including the single champion statistics, even though the single champion statistics only carry such little significance, offers 2 benefits:

1. The single champion statistics can be displayed to users so that they can assess the general/overall strengths of single champions through another perspective other than the paired champions statistics.

2. The single champion statistics enable proper functioning of the application when there are no ally champions and no enemy champions selected to view the relationship with/against pickable champions.

The single champion statistics are downscaled by multiplying the Z-score of each single champion statistics by the following downscale factor:

Downscale factor = Paired Champions Average Z-score Absolute Value(0.876) / Single Champions Average Z-score Absolute Value(2.635) * 0.01

League of Legends Selector introduces a new unit of measure, "Selector-score(represented by capital letter S)", so that this single unit can be used to refer to both the downscaled Z-score of the single champion statistics and the Z-score of the paired champions statistics.

The formula for the Selector-score is as follows:

1. Single champion statistics

S = Z * Downscale factor

2. Paired champions statistics

S = Z

Listed below are the results of simple data analysis performed on the Selector-scores of the single champion statistics and the paired champions statistics:

1. Single champion statistics

Minimum Selector-score absolute value = 0

Maximum Selector-score absolute value = 0.08389

Average Selector-score = 0

Average Selector-score absolute value = 0.00876

Count = 332

2. Paired champions statistics

Minimum Selector-score absolute value = 0

Maximum Selector-score absolute value = 7.066

Average Selector-score = -0.014

Average Selector-score absolute value = 0.876

Count = 110224

League of Legends Selector represents the Selector-scores in visuals of lines and bars so that users can compare the strengths of champions and the relationships between champions by the color and the alpha(opacity) of lines and bars. Consider the following instance where the user's team is Blue team, the user has the third pick within the team, and the user has selected Darius and Rengar as allies, and Garen and Kha'Zix as enemies:

The single champion Selector-scores are represented by the circular outlines around the champions, and their values are displayed as below:

As illustrated by the green and red colorings of the circular outlines and the single champion statistics above, League of Legends Selector doesn't use the green color to represent positive Selector-score and the red color to represent negative Selector-score. Instead, League of Legends Selector uses green color to represent the Selector-scores that hint advantage to the user's team and red color to represent the Selector-scores that hint disadvantage to the user's team.

In the above instance, the user's team is Blue team so the green color represents the Selector-scores that hint advantage to the Blue team and the red color represents the Selector-scores that hint disadvantage to the Blue team.

Darius is an ally champion and has a positive Selector-score, so the circular outline around Darius is colored green.

Rengar is an ally champion and has a positive Selector-score, so the circular outline around Rengar is colored green.

Garen is an enemy champion and has a positive Selector-score, so the circular outline around Garen is colored red.

Kha'Zix is an enemy champion and has a negative Selector-score, so the circular outline around Kha'Zix is colored green.

The counteristic paired champions Selector-scores are represented by straight lines connecting an ally and an enemy:

Initially, League of Legends Selector had planned to use the green color to represent positive Selector-scores and the red color to represent negative Selector-scores, similar to how data is traditionally displayed to the summoners in most other statistical platforms. However, while deciding the visualization method for the counteristic paired champions Selector-scores, League of Legends Selector chose to use the green color to represent the Selector-scores that hint advantage to the user's team and the red color to represent the Selector-scores that hint disadvantage to the user's team.

Consider below counteristic relationship between Darius and Kha'Zix:

Above relationship can be viewed as Blue team Darius' Selector-score against Red team Kha'Zix as below:

Above relationship can also be viewed as Red team Kha'Zix's Selector-score against Blue team Darius as below:

As illustrated by the relationship between Blue team Darius and Red team Kha'Zix, the visual line can either represent Blue team Darius' Selector-score against Red team Kha'Zix or Red team Kha'Zix's Selector-score against Blue team Darius, which are additive inverses of each other(one would be positive(1.638) and the other would be negative(-1.638) with same magnitude, unless both are equal to 0). Using green color to represent positive Selector-scores and red color to represent negative Selector-scores is inappropriate for League of Legends Selector due to this reason.

However, when the two additive inverse Selector-scores of the counteristic paired champions are viewed through the perspective of the user, both Selector-scores hint advantage to the user's team.

Blue team ally Darius having a positive Selector-score against Red team enemy Kha'Zix is advantageous to the user's team.

Red team enemy Kha'Zix having a negative Selector-score against Blue team ally Darius is also advantageous to the user's team.

Since using the green color to represent the Selector-scores that hint advantage to the user's team and the red color to represent the Selector-scores that hint disadvantage to the user's team enables uniform visual representation of the counteristic paired champions Selector-scores, League of Legends uses the user's perspective in determining the colors of all the Selector-scores presented in the application.

Thus, League of Legends Selector displays the above illustrated relationship between Blue team Darius and Red team Kha'Zix in green color as below:

The synergistic paired champions Selector-scores are represented by curved lines connecting 2 allies or 2 enemies:

Ally Darius and ally Rengar's relationship is displayed as below:

Since an ally Darius having a negative Selector-score with an ally Rengar is disadvantageous to the user's team, the relationship is colored red.

Enemy Garen and enemy Kha'Zix's relationship is displayed as below:

Since an enemy Garen having a positive Selector-score with an enemy Kha'Zix is disadvantageous to the user's team, the relationship is colored red.

League of Legends Selector uses colored gradient bars to represent the sum of all the Selector-scores related to a champion, referred to as "overall Selector-score"(ΣS):

Darius' overall Selector-score is 1.475 ΣS, and it is the sum of all the visible Selector-scores related to Darius as shown below:

=

+

+

+

The gradient bar for Darius is colored green, because an ally Darius having a positive overall Selector-score is advantageous to the user's team.

Garen's overall Selector-score is 1.113 ΣS, and it is the sum of all the visible Selector-scores related to Garen as shown below:

=

+

+

+

The gradient bar for Garen is colored red, because an enemy Garen having a positive overall Selector-score is disadvantageous to the user's team.

League of Legends Selector uses overall Selector-scores to compare the statistical advantage/disadvantage of remaining pickable champions. Consider below overall Selector-scores of Azir if Azir is to be placed in Blue team with Darius and Rengar as allies and Garen and Kha'Zix as enemies:

=

+

+

+

+

Now, consider below overall Selector-scores of LeBlanc if LeBlanc is to be placed in Blue team with Darius and Rengar as allies and Garen and Kha'Zix as enemies:

=

+

+

+

+

Since the overall Selector-score of LeBlanc(2.163 ΣS) is greater than that of Azir(-5.800 ΣS), League of Legends Selector considers LeBlanc to be a better pick than Azir and places LeBlanc in higher position than Azir in the pickable champions list as below:

League of Legends Selector uses the difference between the magnitude of total advantageous Selector-scores and the magnitude of total disadvantageous Selector-scores, specified by "Σ|S| - Σ|S|" to assess the overall statistical advantage/disadvantage to the user's team of all available Selector-scores.

The difference between the magnitude of total advantageous Selector-scores and the magnitude of total disadvantageous Selector-scores is referred to as "Selector-score difference(Σ|S| - Σ|S|).

In order to compute the Selector-score difference, League of Legends Selector first computes the magnitude of total advantageous(green) Selector-scores(Σ|S|) by adding the absolute values of all the green Selector-scores available:

The magnitude of total advantageous Selector-scores(Σ|S|) is |0.001| + |0.008| + |-0.001| + |0.597| + |1.638| + |0.655| = 2.9.

League of Legends Selector then computes the magnitude of total disadvantageous(red) Selector-scores(Σ|S|) by adding the absolute values of all the red Selector-scores available:

The magnitude of total disadvantageous Selector-scores(Σ|S|) is |0.003| + |0.063| + |1.644| + |-0.761| = 2.471.

The difference between the magnitude of total advantageous Selector-scores and the magnitude of total disadvantageous Selector-scores(Σ|S| - Σ|S|) is 2.9 - 2.471 = 0.429 and this value is displayed as below:

Positive Selector-score differences(Σ|S| - Σ|S|) indicate that the user's team has overall statistical advantage over the enemy team so they are colored green, and negative Selector-score differences indicates that the user's team has overall statistical disadvantage to the enemy team so they are colored red.

The nontraditional visual representation of the Selector-scores, using green color to represent the Selector-scores that hint advantage to the user's team and red color to represent the Selector-scores that hint disadvantage to the user's team may appear unfamiliar at the early stages of using League of Legends Selector.

The following statements could help users better understand the visual representation of the Selector-scores: