Position Influence Statistics: Where are they?

There are plenty of statistics online, but I can't seem to find statistics that provide an objective measure of the influence of positions.

There are plenty of opinions on which roles have the most/least influence on the game. Supports are said to have the least influence on the game, but there aren't any actual statistics I can find to talk about that in an objective manner. It's all opinion. There isn't any statistic that maps outperforming your counterpart into game win rate.

For example, ADCs do the most damage in the game. So you might think that ADCs have the most influence, but where are the statistics that say if you out damage the other ADC, then you will win x% of the time?

Other players will use the 20% argument. That says that you are one of five players and therefore you can only influence 20% of the game. But that isn't statistics! That's BS disguised as statistics. It wasn't gathered from any actual game data. It was manufactured by someone making guesses about how the game works!

Some sites will give you data that allows you to personally compare your performance on a champion with the performance of other players on the same champion. This is great because, for example, if you play Zac, you aren't expected to die much (because of Zac passive). That means if you play Zac and say, "Well, I'm not dying much, I must be doing really well, but I can't get an S." You might find that you aren't expected to die much and you are actually still under performing (possibly in other ways).

But despite the wealth of information out there, I can't find statistics that map influence by position. How do we actually know that some positions have more influence over the game? How do we know that supports out performing their counterparts aren't a stronger indicator of victory than mid laners outperforming their counterparts? We don't. All we have is reasoned opinion and some strong players who talk about the best position to carry a game from. Where are the statistics that back up the conventional wisdom on how much influence positions actually have over the game?