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Hello folks!
Have you ever thought about champion scaling in LoL? Many people discuss it, but there isn't much objective and statistical evidence available. So, I defined new scaling indicators and analyzed which champions scale the best and the worst. I shared my findings with my Japanese friends on Twitter, but I only received 2 likes. It seems that there isn't much interest in statistics and scaling in Japan. Therefore, I decided to share this on Reddit in English. I'm Japanese, so my English might not be perfect. I apologize for any inconvenience.
Firstly, let me clarify the definition of "scaling." In this post, “scaling” specifically refers to the scaling of win rates. For example, Illaoi has impressive base stats scaling, but she doesn’t have a high win rate in the late game. Therefore, in this context, Illaoi does not have good scaling.
Secondly, how can we define the indicators of scaling? I used statistical data from Lolalytics for this analysis. To ensure a comprehensive dataset, I utilized match data from patch 14.15, covering all rank tiers.
Many people assess scaling by looking at the win rate in the late game, such as the win rate after 35 minutes. However, I believe this approach is not entirely accurate because it is heavily influenced by the champion's overall average win rate. For instance, K’Sante has good scaling, but his average win rate across all ranks is low, so his win rate after 35 minutes is estimated to be around 48%, which doesn’t reflect his true scaling potential. To evaluate scaling more accurately, I first standardized the champions' win rates. For example, if the average win rate is 52%, I adjust the win rates at all time points by scaling them relative to 50/52. Additionally, I used standardized win rate differentials at various game times to assess scaling.
First, I created a scatter plot using standardized win rates. In this chart, the horizontal axis represents the win rate before 20 minutes, while the vertical axis represents the win rate after 35 minutes. Champions who scale well throughout the game (with increasing win rates as the game progresses) are positioned in the top right, while those who scale poorly are in the bottom left. Additionally, champions that are strong only in the mid-game are found in the bottom right, and those that struggle only in the mid-game are in the top left.
Next, I created a chart using two types of win rate differences. This method is likely intuitive way to understand scaling. In this chart, the horizontal axis represents the difference in win rate between 20 minutes and 35 minutes (Scale1), while the vertical axis represents the difference in win rate between 25 minutes and 30 minutes (Scale2). Champions with significant scaling (whose win rates increase as the game progresses) are positioned in the top right, while those with minimal scaling are in the bottom left.
Based on these results, it seems that our understanding of champion scaling could change. I was previously a Kayle main in Japan and believed that Kayle had the highest scaling. However, these results suggest otherwise. It appears that Aurelion Sol is the champion with the highest scaling. Additionally, Nasus and Kog'Maw do not seem to have particularly good scaling based on these results. I was also surprised to find that Annie and Rengar have such strong scaling.
Anyway, thank you for taking the time to read this. I’m not very familiar with mathematics or statistics, so if you have any suggestions or corrections, please feel free to share. I would also appreciate any feedback or opinions you might have.
For those who want to delve into more details, I’ve included graphs showing win rate changes at various time points. In the previous discussion, I focused on scaling indicators based on early and late-game win rate differences, which may have led to mid-game scaling being overlooked. These graphs should help you understand how win rates change at different stages of the game.
Also, the champion images overlap too much, making the central part of the image difficult to see. Therefore, I also attach a list of the scaling values for clarity. (I couldn't add more attachments, so I used image links instead.)
https://imgur.com/73gSW9A
*As someone pointed out, some champions, especially ADCs, were not included in the data.(tristana,
sivir, xayah, vayne, nilah, twitch, missfortune, jinx, jhin) I'm working on creating a corrected image, so please bear with me for a bit.