TL;DR I trained a machine learning model to figure out which champions are banned more than their performance and popularity deserves. The top 5 most over-banned/hated champions are Samira, Darius, Morgana, Zed, and Yone. The bottom 5 are Jhin, Ezreal, Ashe, Kaisa, and Thresh.

The process:

• Data taken is for Plat+, global player-base, patch 10.21. Data is collected from lolalytics.com.
• For each champion, we record their pick-rate, ban-rate, and win-rate.
• We train a multivariate linear regression model with the data. The model is trained such that it tries to predict the ban-rate as a function of the win-rate and play-rate of a champion.
• Actually, ban-rate and play-rate are log'd first, then put into the regression model.
• For each champion, the model will predict a ban-rate based on their win/play rates. We take the difference between the predict ban-rate and the actual ban-rate. If the actual ban-rate is significantly higher, it indicates that a champion is being banned more than their stats deserve.
• I admit this method has its weaknesses; i.e. it assumes that the relationship between the different variables are in fact linear. Upon inspection, ban-rate does appear to be a linear function of pick-rate. However, it is difficult to say exactly whether ban-rate is a linear function of win-rate, since the relationship between the two is surprisingly weak to begin with.
• Another concern is whether the win-rate and play-rate are correlated with each other, since you ideally want independent features for multivariate regression. Win-rate and play-rate are in fact not correlated with each other (p-value=0.92).

Champions towards the top of the list are widely hated, with ban-rates significantly higher than their play-rate and win-rates would justify. Champions at the bottom are they opposite: They tend to be popular, yet have ban-rates much lower than normal for their pick-rate and win-rate. Champions at the middle aren't really liked or disliked; people are generally ambivalent about them.

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Below is the complete list of (

) values for each champion.
Samira:63.05 Darius:33.33 Morgana:29.93 Zed:29.23 Yone:23.49 Yasuo:21.41 Evelynn:20.76 Hecarim:19.83 Akali:19.35 Pantheon:16.32 Kassadin:16.17 Yuumi:13.39 Lillia:10.77 Master Yi:9.90 Renekton:8.57 Lulu:8.21 Vladimir:8.01 Irelia:7.41 Lucian:7.26 Blitzcrank:7.19 Fizz:6.98 Fiora:6.08 Karthus:6.04 Nautilus:6.00 Ekko:5.96 Graves:5.83 Caitlyn:5.01 Elise:4.92 Jax:4.79 LeBlanc:4.59 Sylas:3.96 Rammus:3.83 Leona:3.67 Shaco:3.65 Mordekaiser:3.25 Kha'Zix:3.00 Fiddlesticks:2.95 Rengar:2.64 Katarina:2.40 Sett:2.31 Malphite:2.26 Garen:2.25 Illaoi:2.11 Pyke:1.96 Zoe:1.95 Malzahar:1.90 Volibear:1.65 Olaf:1.64 Tryndamere:1.64 Nidalee:1.62 Cassiopeia:1.53 Quinn:1.41 Diana:1.29 Teemo:1.24 Draven:1.04 Nasus:0.97 Talon:0.93 Rek'Sai:0.85 Urgot:0.81 Nocturne:0.75 Zac:0.75 Swain:0.73 Vayne:0.62 Brand:0.61 Kled:0.42 Heimerdinger:0.26 Yorick:0.23 Tahm Kench:0.23 Kayn:0.23 Aatrox:0.21 Dr. Mundo:0.18 Nunu:0.16 Qiyana:0.14 Jayce:0.13 Xerath:0.09 Gangplank:0.08 Trundle:0.07 Poppy:0.03 Anivia:0.03 Taliyah:0.02 Lissandra:0.01 Rumble:0.00 Syndra:-0.01 Ivern:-0.03 Neeko:-0.04 Azir:-0.06 Aurelion Sol:-0.08 Maokai:-0.09 Cho'Gath:-0.09 Vel'Koz:-0.10 Kog'Maw:-0.11 Taric:-0.11 Corki:-0.12 Veigar:-0.12 Zyra:-0.14 Shyvana:-0.14 Varus:-0.15 Kennen:-0.15 Wukong:-0.16 Skarner:-0.17 Gnar:-0.17 Kalista:-0.18 Sejuani:-0.20 Ziggs:-0.20 Udyr:-0.24 Amumu:-0.31 Gragas:-0.34 Viktor:-0.34 Annie:-0.35 Galio:-0.40 Zilean:-0.42 Warwick:-0.43 Aphelios:-0.45 Xin Zhao:-0.45 Sivir:-0.51 Singed:-0.52 Xayah:-0.53 Senna:-0.57 Braum:-0.61 Kayle:-0.64 Ryze:-0.64 Sona:-0.71 Camille:-0.79 Jarvan IV:-0.82 Shen:-0.94 Tristana:-1.00 Kindred:-1.03 Twitch:-1.06 Sion:-1.07 Riven:-1.11 Ornn:-1.36 Vi:-1.38 Twisted Fate:-1.71 Soraka:-2.15 Rakan:-2.29 Ahri:-2.31 Karma:-2.44 Alistar:-2.64 Nami:-2.71 Lux:-2.96 Bard:-3.00 Jinx:-3.35 Janna:-4.85 Lee Sin:-5.79 Miss Fortune:-5.93 Orianna:-6.12 Thresh:-9.45 Kai'Sa:-10.87 Ashe:-17.44 Ezreal:-25.13 Jhin:-35.18