x100 peaks on the ratings distribution graph continued...

thought I'd continue this topic as it got closed but wasn't resolved. some interesting chat I had about it after on someone's direct messages, but not forum.

RE: peaks at every 100 mark on the graph (the rapid ratings graph in particular) --
I just noticed that aswell as the peaks at exactly the 100 marks, it also goes towards a steep decline from exactly every 50 mark until 75, and then from 75 steeply upward. Why's there a dip there?! Lots of adamant comments about it being to do with people tending to keep going until the 100 marks and then rest, but I don't think the positioning of these precise and perfectly regular peaks and troughs illustrate this. I still really would like to get to the bottom of it though. why on Earth does this happen? There was a link that someone left re some explanation, but the forum wouldn't let me open the link, so I couldn't read it. It did look interesting though - if you're reading this, please could you briefly explain what it said. Thanks in advance.
I think regarding the common idea (misconception imo) that people tend to keep going until the 100 multiples and then rest would be more realistic if this was concerning the puzzles, bc you can just keep going until the next 100 mark if you've got time - and I definitely aim to do that sometimes (but more often I don't), but in a real game, we just don't get significantly better in one sitting, improvement is clearly a very gradual process however hard we try, - and with each game being matched, it's a 50 / 50 thing, and when improving, just slightly more than 50 50 - and there are significantly more people resting at random points other than the 100 marks, so that idea doesn't make much sense (particularly as this is no approximation). If anyone does believe that it's to do with the human will to keep going till the 100, please leave some actual evidence to illustrate this, rather than the general cyclic hearsay. One way or the other, I'd really like to understand why the graph isn't a smooth curve. To me it shows that from every 50 to 75 it gets increasingly more disproportionally difficult to win, and then disproportionally easier to win from 75 to 100 !!? that just doesn't make sense to me. Please help me put the pieces of my mind back together. appreciated.

I wish I could insert a "rolls eyes" gif here.

@MartinPlath said in #2:
> I wish I could insert a "rolls eyes" gif here.

oh for goodness sake. Just cos loads of people say one thing, doesn;t make it correct. If it's not hearsay that this curiosity is down to the will of people breaking at the 100s, show me some evidence. Don't roll your eyes at genuine inquisitiveness, it's stifling. Just contribute with something helpful or don't say anything. I roll my eyes at people that assume hearsay is evidence. that's you mate.
I genuinely got excited to see what comment someone had left.
Disappointing.

As far as I am concerned: I have done that often. After reaching a milestone I have switched to

-another profile
-created a new one
-changed the period for playing
-changed the server

-> resting and doing something different elsewhere

@Jimothy-Jangles said in #1:
> I just noticed that aswell as the peaks at exactly the 100 marks, it also goes towards a steep decline from exactly every 50 mark until 75, and then from 75 steeply upward.
Sigh... You still haven't noticed (even if someone already pointed this out in previous discussions, IIRC) that these graphs have a granularity of 25 so that your "exactly a multiple of 100" point in fact represents an interval of width 25? In other words, what you see as e.g. "exactly 1800" in fact represents (probably) the interval of [1800; 1825) and "exactly 1775" is actually everything in [1775; 1800). What you see as "steep decline from exactly every 50 mark until 75, and then from 75 steeply upward" is just a straight line connecting two points where the intermediate values have no real life interpretation.

@Jimothy-Jangles said in #1:
> To me it shows that from every 50 to 75 it gets increasingly more disproportionally difficult to win, and then disproportionally easier to win from 75 to 100 !!? that just doesn't make sense to me."

Well indeed, it doesn't make sense. The obvious explanation is that many players "rest" at the full 100 peaks, and the data in the Lichess graphs being sorted in bins of size 25. As explained above and many times before. If you have an alternative, more plausible hypothesis, please show us.

Some people insist that using these graphs with straight line segments connecting points representing discrete values (or summed over intervals) are Bad ThingTM and that bar graphs or at least isolated dots should be always used instead. I always found it a bit "Sheldony" as I believed that noone could really think that those segmented lines represent actual dependency of continuous values. I may have been wrong... :-(

@Panagrellus said in #6:
> Well indeed, it doesn't make sense. The obvious explanation is that many players "rest" at the full 100 peaks, and the data in the Lichess graphs being sorted in bins of size 25. As explained above and many times before. If you have an alternative, more plausible hypothesis, please show us.

no, I haven't got an alternative more plausible hypothesis - doesn't mean that the current hypothesis is correct though. Yes, it would be an obvious explanation about the resting thing, but surely in the grand scheme of things it wouldn't make as much of a difference as the graph suggests (ie, there would just be way too many people resting also at other rating points compared to the insignificant few resting at the 100s - yes, maybe there should be a slight peak at the 100s for that reason, but not so pronounced). Someone in the last thread (who I was talking to via direct message after it closed) kindly suggested that he'd compile a graph of resting points throughout the ratings spectrum - I really hope he does do it. That would be great evidence one way or another. at the moment this idea seems to be just that - an idea - and so many people are insisting that's the solution - but it's so far an assumption. In fact - if anyone can tell me how to see the resting points somehow? - I'll try and find time myself to do it (if I can). It sounds like a fun task. might take a while though! up for it. thanks Panagrellus

@Jimothy-Jangles I try to bring up my ratings 100 at a time and I won’t touch them untill I bring up the other ratings. I would like to maybe get 2000 in all variants and never touch any of them again besides crazyhouse. I’ll play blitz/bullet again once I hit 2200 in rapid. I’m sure it’s a common thought. Same on chess.com I hit 2000 blitz/2000rapid and I won’t touch them again untill 2000 bullet.

@mkubecek said in #5:
> Sigh... You still haven't noticed (even if someone already pointed this out in previous discussions, IIRC) that these graphs have a granularity of 25 so that your "exactly a multiple of 100" point in fact represents an interval of width 25? In other words, what you see as e.g. "exactly 1800" in fact represents (probably) the interval of [1800; 1825) and "exactly 1775" is actually everything in [1775; 1800). What you see as "steep decline from exactly every 50 mark until 75, and then from 75 steeply upward" is just a straight line connecting two points where the intermediate values have no real life interpretation.

yes, the intermediate values between each 25s have no real life interpretation - i agree, but the connecting lines should still approximate more of a curve. still doesn't explain the more pronounced dip between the 50s to 75s. I know someone pointed out the 25s in the previous discussion, but I'm saying I hadn;t noticed that the graph actually dips more between the 50 to 75. what's this area got to do with the current hypothesis of the resting points at the 100s? this is my point. why does the game get more difficult to win when I'm in the 50 to 75 zone, isn't that what the graph shows? (less people are managing to win increasingly disproportionately towards the 75s, whatever the reason for it is?).
I get your point about my use of the word "exactly" though. I'm an idiot! (i tend to be on this forum in the middle of the night when I can't sleep). I think what I mean is "disproportionately large peaks at only those points" - even if the general hypothesis about the resting point was true - it seems way too pronounced? there'd have to be a huge percentage of people doing that for the graph to look like this (this is why I'm tending not to buy into this hypothesis). - a small peak, yes, I'd agree with you all. anyway, cheers mate.