it is true that a given game has a certain amount of chance or luck involved. Also, your true average performance can never be known. However, we can use solo queue and statistics to become extremely confident that our estimate of your performance over the course of a large number of games is close to your true performance.
The way we can do this is through the use of a concept known as Regression toward the Mean. The idea is that as sample size N increases, the probability that the sample mean, Xbar, is close to the population mean, mu, increases. So, as we play more games of solo queue, we become more confident that the performance measured in the games in solo q accurately represents the total performance.
We can use Xbar as a Point Estimate; this point estimate is your current Elo. However, a Point Estimate is only a guess. It could be right, but it is much more likely to be wrong. So in this sense, it's true that Xbar (your current elo) is probably wrong. Fortunately, we can use Confidence Intervals to create a range that we are very confident that mu lies within. Even better, we can control HOW confident we are that mu is within the range by altering the width of the Confidence Interval. Without access to the data behind league and league systems, I couldn't tell you exactly how confident I could be that you're within 50 LP of your true Elo after say, 100 games. However, I can tell you about what it will look like. After a large number of games- which could be 100, 250, or 1000 depending upon Variance, but is likely to be close to 100-250 in my opinion- I'd expect to be at least 95% confident that Xbar was within +/- 50 LP of mu. Further, I'd expect to be at least 99.999999% confident that Xbar was within +/- 500 LP (difference between silver/gold, ect). At that confidence level, I'd expect 3 players per 300,000,000 ranked players to be off by 500 LP or more after that given large number of games. I consider this pretty conservative, as it's entirely plausible that I would be order of magnitude more confident about each of these cases than I've described. I would be very surprised to find that the confidence interval were less precise than I have described here.
Additionally, given that trolls/unskilled players are randomly occurring, and assuming that you are not unskilled or a troll, this estimate is actually biased in your favor. The probability of your team getting one or more trolls is given by:
1-[1-(Probability of a Given Player Being A Troll)]^4.
The probability of your team getting one or more trolls is given by:
1-[1-(Probability of a Given Player Being a Troll)]^5.
The first number will always be less than the second, because YOU are guaranteed to not be a troll, thus biasing the result in your favor. So in conclusion, while you are correct that an individual game is partially a game of chance, over the course of a large number of games this chance is mitigated to the point of being irrelevant.
If the wikipedia articles are too archaic for you, and you'd like to understand what I'm talkign about, I'd recommend Khan Academy. There are serveral videos there on the relevant topics that are quite good and easy to understand.