Grits N Gravy, on 19 September 2013 - 05:10 PM, said:
There's no direct correlation to win rate and Elo scores not because one team is expected. In fact the system takes that into account and rewards you more points if you upset a better team. But because the Elo scoring has nothing to do with win and loss ratios. Elo does not equal win loss.
A person can end up with an Elo ranking of 2000 if they beat enough people with high ranks early in his career, due to the K factor. His K factor will eventually go away and he'll sit on a 50/50 win ratio at 2000 elo over a course of another 50 games. Meanwhile a player who maybe an 1400 Elo. Maybe he didn't quite pick up on things early on, but he's really developed a lot of skill, thus allowing to gain some elo points. So he might have a win/loss of 3/5. Because he's at the top of his bracket, he needs to keep up that win loss to stay there as his losses cost him more points than his wins generate, aka elo hell.
Can you start to see how there is no strong correlation to win loss and Elo rankings? Even if we looked at Elo after 20 games when K factors are still in play; People with the same win and loss will have wildly different Elo scores based on the competition they faced, as their Elo scores are derived directly from their opponents. Within the Elo scores it's reasonable to assume a totally random distribution of win loss, that trends to 50/50 the longer the person stays at that score.
I'll phrase it more clearly: there's no way we can do any of the calculations ourselves. I've poured over all their posts and fully understand how it works, but we're unable to do anything with the math they've given us.
Again, I still think that over a statistically significant period there will be a fairly narrow range of win-loss ratios for a given Elo ranking. As your Elo begins to set, I'd imagine you even get a very similar number of "expected to lose" and "expected to win" matches as those with a comparable Elo (because the matchmaker is trying to normalize good players down and bad players up).
Your examples are all fine and well for a tiny sample, but once you get 500+ matches, I'd bet money the win-loss ratio distribution for any given Elo looks a lot like a standard bell curve. Pretending there's no correlation between WLR and Elo is simply ridiculous; it's clearly not direct, but certainly you'd agree that someone with a 1.1 WLR is more likely to have a higher-than-average Elo than someone with a 0.9 WLR.