I need help making a point again (stats, odds)

Factual Questions
1

I play a game where everyone gets rated based on how much they win and lose. This game uses the Elo rating system to place you in a rank. This game is 5v5, so when you win or lose it is not always because of your skill, as 9 other people can affect the outcome.

There is this common misconception among low ranking people that ive been trying to argue against. Many people at low ranks say that their Elo is almost independent of their play, and it is very heavily based on other people in their games. The most common complaint is that people leave mid game or play badly on their team, which gives them a lot of losses.

My arguments against this viewpoint are that given it is a 10 person game, and that you are better than your Elo says you are, and that you dont leave in the middle of games or play poorly, the game is skewed heavily in your favour.

The reasoning is you are matched with players worse than yourself, and to paraphrase another argument I have read, if everyone is all dice and 600 Elo players always roll 1-3, and you are a 900 elo player you always roll a 2-4, you are likely to have a higher roll as a team majority of the time.

Now even ignoring that part, the other big complaint for losing is that people leave or “troll” in games, meaning they play poorly and throw the odds against you. I explain that because you as a player never do this, and you make up one of the five possible people on your team who CAN do this, your team is 20% less likely to have a player throw the game than the other team is. This again is another thing which boosts your position and gives you a larger advantage in the matchmaking.

Now, I have a person who has stopped arguing against this, and started completely ignoring that kind of logic and is only posting a comment something along the lines of “It takes from 250 to 1000 games to reach your true Elo,” and even went as far as to say “statistical analysis says this.”

Now, I am no stats major, but Ive taken a few courses at university a few years back. I want to point out in the most simple way possible that my above points are correct, and that his new argument of

is a complete joke and that he has no clue what hes talking about. He has no stats background so this has to be done very simply. I am not the best with stats but I know enough to understand that his point is very wrong and he simply made it up.

How can I prove this to him, and any other people who are unfortunate enough to read his writings? I appreciate anyone who takes the time to help me cure a fundamental case of confirmation bias fueled by his ego.

His comments about failing to understand math are so ironic that its killing me and forcing me to beat this horse until it is dead.

2

More information (which may not be readily available) is needed. There is no finite number of games after which you can be assured of actually reaching your “true” rating level: Rather, you’ll asymptotically approach it. There is, of course, some number of games after which you can be assumed to be “close enough” to your true rating, but that number depends on what your standard is for “close enough”. And what a reasonable standard is for that probably depends on how much variation in genuine skill there is in the game, which is something that can’t be easily determined.

EDIT:
The simplest solution for you is to just ask him for the statistical analysis. If he’s so confident in his statements, clearly, he knows what the arguments are. At the very least, he has to be quoting the results from someone else. It’s not like it’s “Hey, I just ran into Statistical Analysis the other day, and I asked him about the game. He said that it takes a thousand games to determine a rating. No, I won’t give you Statistical Analysis’s phone number to ask yourself-- He’s a very private person.”