Stats actually do mean something. Here's why.
Too often, I've come across statements like
"Winrate means nothing" "lol you're citing meaningless stats, <champion X> is garbage tier and should never be banned unless you're bronze for life!!!" "what a scrub, you don't know anything!"
Unfortunately for these people, the stats actually do mean something.
For example, here's what you'll see when you load up champion.gg and check the highest winrate that's prominently featured at the front. http://i.imgur.com/e07iznY.png
And if you're uninitiated, you'll go "wow! this site sucks! jarvan 4 as the best toplaner??? wtf man" and immediately dismiss any further information. But you have to look closer. It's not just winrate that matters, it's also playrate, and banrate in conjunction.
Lets look at Jarvan IV, to start with.
http://i.imgur.com/a2hctkK.png
While it is true that J4 technically has the highest winrate among toplaners at the moment, you also have to look at the banrate and playrate. After observing these stats, you notice 2 things: -He has a very small playrate. -Practically no banrate at all.
Noting these two things, I can assert that Jarvan is a decent counterpick in specific matchups rather than a great overall pick. If I look further down the page at the matchups section (where the champions that Jarvan players usually pick into are listed), I'll see that Jarvan is picked the most against Riven, Gangplank, and Nasus. It appears that Top Laners usually play Jarvan into those matchups simply to counterpick, rather than actually pick because he's broken OP.
Next, I'll move down to Vi, who is listed as the top Jungler at the moment.
http://i.imgur.com/ouyN5Yw.png
Vi has the highest winrate among all Jungling champions. Furthermore, she is sporting both a high playrate AND banrate. Her high banrate combined with a high playrate suggests that players are playing her even when they aren't very experienced with her. Her winrate still being nearly 55% even after that fact suggests to me that she is busted as fuck.
Ziggs has most of the same attributes as Vi, although not nearly as inflated playrate and banrates. I'd still classify Ziggs as banworthy.
Kogmaw has the highest winrate for ADC, but nobody plays him. Kogmaw would not be worth a ban due to low playrate.
Janna is an interesting case. She has both a high winrate and playrate, but a low banrate. Players seem unwilling to ban a support even though her mere presence in games appears to be warping games in her favor. I've sat here for 30 minutes thinking of any suggestions for her, but all I can say is just try to work around her or pick her on your team. Ban her only if you have no idea of what else to ban.
TL;DR: Stats are important. Winrate, playrate, AND banrate are to be taken in conjunction with each other. So when people complain about how much a champion wins, look at their playrate/banrates before telling people off for "being a scrubs" and ignorantly telling them that "winrate means nothing."
