Let's do a breakdown...
So for simplicity sake we will assume you are getting 10/10 up/down
Quoted from their recommended settings:
Quote
An internet speed of 6Mbps is enough to have a smooth gaming experience for League Of Legends. Other recommendations are to have a minimum upload speed of 1Mbps and a maximum ping rate of 100 to 150ms.
Ok so you might think, ok then I'm good I meet or beat all of that...
Well now let's dig a little deeper...
You need to assume that you are getting 80% of your reported speed from Speedtest.net, that is nothing against them personally, but they are known to test against optimal performance against your ISP. You should test your speed against FAST.COM which is sponsored by Netflix and gives a very acurate real world representation of your connection speed.
Notice how the optimal server for you in CA is over 150 miles away? So that means the nearest NID that you are banking against is no where near you. If you are playing on a West Coast server, this might not be such a big deal, but the LOL servers are in Chicago, IL. So you are hitting a NID 150 miles away (If you are lucky, you could be routed somewhere entirely else if there is heavy load there) and then, assuming no hop points (Which I guarantee there are, but lets ignore them for now as that is a lesson for another time.) You are then running another 2100 miles away. You can then look at this from a measurable perspective of the speed of a signal through fibre or copper is approx 127,000 miles per second.
Add on a few ms per each hop (routers, switches etc) and you get around 25-30 miliseconds ping (your response between point a and point

THIS IS WITH EVERYTHING BEING PERFECT
Now you said that you were on wifi. I will tell you that unless you have configured your wifi router yourself to be optimized for speed and connectivity, you are getting 65% efficiency right off the bat, and it only gets worse the further you get and the more devices that are connected.
Lets assume you are getting 75%, that does not mean that you are going to get Perfect/.75...you have to also factor in the additional jump points, and that adds a whole mess of additional math that I couldn't get into without more info.
TL:DR - Your internet sucks, wired might be better, but it's a band-aid for a broken arm.