Science of Chess: Winning Streaks, Losing Streaks, and Skill

@Rockiron said in #2:
> Right around 1400 there is a weird borderline. First the joy of passing it, then sliding beneath it. I also wondered how I could lose several in a row, when just passing 1400. There might be similar around other levels too, but breaking 1400 is "finally I know something about chess!"

Chess is one of those many activities where then you will hit 1800 and think you're just some opening theory away from being Kasparov. Then you hit 2200 and realize you know nothing again. Probably easier to understand now a days when you can click on a rando stream and watch somebody like Nakamura doing a puzzle rush and realize that there's a wee bit more going on than just some openings.

@OhNoMyPants said in #10:
> I think the higher streakiness between beginners is pretty interesting. I'd hypothesize a simple explanation. Ratings reflect relative strength, but not objective strength. In practice this results in a system where real strength differences are greater at higher ratings. This makes perfect sense if you view playing strength as distributed on something like a power law curve.
>
> What this means is that the difference in objective playing strength between a 2400 and 2800 is far greater than that between a 1000 and a 1400, even though it's just 400 relative points in both cases. So if running hot can add a relatively comparable amount of 'objective' strength to both beginners and strong players, it'd have a much larger influence on the results of beginners, because it'd be a much larger increase in relative strength (or ELO) than it would be for a strong player.
>
> The only way this wouldn't be true is if running hot added a much higher amount of 'objective strength' to stronger players, and I see no logical reason to think that even *might* be true.

Thanks for reading! This does sound very sensible to me - the idea of nudging objective strength up or down by some fixed amount is a neat way to think about the impact of wins and losses. I keep meaning to set aside time to really read up on different rating systems and relative vs. objective estimates of playing strength, but it seems like one could probably build a quick simulation of your idea even if you just used a relative strength (ELO bump). Not perfect, but it may capture some of the main results here.