Rating/Percentile distribution of different time controls

I am really confused by the percentile vs rating distributions betwen different time controls and I'm wondering if anyone have some insights on the topic?

For example: being 2200 rapid means you're in the 98th percentile, while the same rating in bullet is only the 93rd. And the same rating again, in Blitz, will have you in the 96th. With this many players those are some very statistically significant differences.

First I thought it might be due to the amount of players, but bullet and rapid are fairly similar in that regard and yet they are the furthest apart, while blitz is the outlier with almost twice the amount of weekly players somehow lands between the two others.

And the percentile also really conflicts with my personal experience. 2200 should by percentile be by far the hardest in Rapid as only 2% of players achieve this, but to me that felt quite manageable. And 2200 bullet should be comparatively a lot easier since you basically have to meassure up against 5% less of the very best players. But to me that was by far the biggest struggle of my chess journey. And worst of all is blitz which by looking at percentiles should be somewhere in between but I've only once managed to hit even 2100, and I can't seem to find a satisfying explanation for it.

Of course my personal experience is anectdotal and this will vary drastically for other players. But I'm still left feeling like I'm missing something obvious. Any thoughts?

@CheckingOnYou said in #1:
> But I'm still left feeling like I'm missing something obvious

I think the consideration you are missing is to take into account that the player pools are very different. Both in overall strength, and also in the balance (or lack thereof) between beginner and experienced players.

For example, on this site very good players very rarely play classical, so they are underrepresented in the classical pool.
And bullet , on the other hand, is a bit pointless for absolute beginners, so players <1200 or so are likely underrepresented.

Different skews in the pools will affect the percentiles I guess.

Ooooh That's a very interesting point! As someone who fairly consistently plays all time controls except classical I guess I assumed that most people play at least a bit of each and that a pool of hundreds of thousands would reflect that, but then I do remember running into players in the rapid pool with 50k rapid games and not a single blitz or bullet game.

I am not sure the theory of fewer lower rated players quite holds water though, as removing any part of a dynamic bell curve should shift it towards that direction right? And thus the bullet percentiles should technically be lower as a result, not higher. For example if only GMs were allowed to play on lichess, and the same rating system was implemented, the bell curve would still be centered around 1500 even if the player pool was vastly stronger.

However I think your theory might be good for a different reason. Like you said a lot of strong players play shorter time controls, and bullet particularly has a unique draw due to the different pre-move implementations of lichess and chess.com. Ofcourse this is the inverted problem, adding to a dynamic bell curve should push it the other direction and also drive the average lower. However, importantly, a new account does not affect the curve proportionately because of how initial and volatile rating is implemented. And thus an influx of strong players that easily skyrocket their ratings will skew the percentiles in the way we see in the stats.

Thank you for your response, I hadn't thought of it that way and I definitely think that is a major part of the reason for why the graphs are so different!

Blitz fans keep repeating that "the blitz pool is stronger" but IMHO the problem rather is that it's essentially impossible to objectively compare the strength in different time controls. And it makes absolutely no sense to try to do such comparison based on how ratings of one selected player differ. Some players are - relatively to the overall population - stronger in longer time controls, others perform better in short time controls.

In other words, different ratings of a particular player only reflect that player's style and preferences. And different percentiles only mean that the normal distribution (which is pretty good approximation for all of them) has bigger or smaller standard deviation, nothing more. We might ask why there is a bigger difference between e.g. top 2% and top 20% in bullet than in rapid but it has nothing to do with "strength of the pool". (My hypothesis would be that it's because much fewer players are able to play a meaningful chess game at the pace needed for bullet.)