ratings stats distribution graph glitch?

say, why do the stats suggest the games get easier when approaching each hundred mark, and then normalises again, and then get easier before the next hundred mark... ad infinitum. (the distribution curve peaks at each 100 after 1500, and then troughs again before approaching each following 100 !)

all I can think of is that there is a glitch in the algorithm when matching players? maybe for some reason towards each hundred mark the algorithm has a bias towards picking matched players that are currently having a good run and who maybe have a generally lower rating normally (hence a bit easier to win against), and then when the 100 mark is reached the matching is back to random?? (hence progressively more difficult again). although, before that point in time, I'm also one of those people having a good run - but idk, something doesn't feel right.

I mean, that's all I can think of. I'd like to think I'm wrong, as that would lead to misleading ratings, but I wonder what it actually is??

this might be all in my head, but I'm sure that I've felt like games actually do get easier when approaching each 100 milestone. Does anyone else have the same experience? If you look at my profile, you'll see that when achieving my recent 1700 rating, on the way there I won 19 out of 24 games (3 losses and 1 draw) - which doesn't seem to add up - and now I'm really struggling again, losing way more than 50pc of the games. This seems to be a trend. it's all very odd, but the ratings distribution graphics do seem to confirm this.

hope this makes sense.

by the way, I only play rapid, if that makes a difference.

any thoughts?

The thing that's flawed here is the human mind. It likes round numbers.

You don't stop playing at 1698, you play on until you break that 1700 barrier. So that's where you stop (and rest longer).

@nadjarostowa said in #2:
> The thing that's flawed here is the human mind. It likes round numbers.
>
> You don't stop playing at 1698, you play on until you break that 1700 barrier. So that's where you stop (and rest longer).

I think I see what you mean? so there are proportionately more fatigued people when approaching each hundred mark, making the games slightly easier for rested players to win. - although, when I was playing the games approaching 1700, I wasn't rested and was really overplayed - no different to the other fatigued players, yet I won 19 out of 24. so that still doesn't make sense. I see your point, but by that reasoning I should still only be winning just a fair amount more than 50 50, but 19 / 24...?? don't forget I was one of those unrested players too.

also, the distribution chart doesn't have these peaks and troughs on chess.com - the charts are more smoothly curved. If it was down to the point at which people generally rested (and played while fatigued), it wouldn't be particular to lichess. but it is.

although, there's probably more truth to your idea than my previous postulations. neither really makes entire sense tbh.

I don't think it's about fatigue.
It's about breaking and enjoying, maybe even starting a new account to not endanger the success of the old one.
Rate sitting and rate quitting :)

Are you referring to the distributions given here lichess.org/stat/rating/distribution/blitz? The popular human mind theories are bogus. Do you think with more than 700k players playing blitz last week, with varying conditions (age, styles, number of games, ...), you would get such nice peaks precisely at every multiple of hundred due to some kind of human mind glitch? Observe that the curve has points plotted at every 25. It is very likely a glitch in putting rating frequencies in buckets.

stats.stackexchange.com/questions/560742/why-are-rating-distributions-smoother-when-there-are-more-players You can use lichess code to simulate million games (similar to the above link) and use lichess rating formula and plotting code, and you will likely observe these peaks without any "human mind glitches". It is quite likely that certain parameters in rating calculation change at every multiple of 100.

Well, I can explain it to you, but I cannot understand it for you.

People tend to take longer breaks after having achieved their rating goal, which usually is 1500, 1600, 1700, 1800, ... or slightly above it.

There are many of these players. Now their rating is longer on that level (or in that bucket), then in the others. Which is equivalent to having more player at these buckets.

There is no magic fatigue at those levels, and no other magic going on. It just reflects human tendency to make a pause at just those levels. Even if the break is short, this will be measurable, and some people actually manage to stop their addiction at that point...

You could check with the games databases. Like examining rest times to their next game.

@kajalmaya said in #6:
> It is quite likely that certain parameters in rating calculation change at every multiple of 100.
I consider this very unlikely. Given that computers calculate with binary numbers, some human coder would have had to enter these round numbers into the code to make it special.

At #1 and #3.

You say "also, the distribution chart doesn't have these peaks and troughs on chess.com - the charts are more smoothly curved."

What graph are you looking at over there? The one I can see is much less detailed than the one here on lichess. It only shows numbers for multiples of 100 and it wouldn't surprise me if it just a smoothed graph of buckets of size 100, so then any 'spiky effect' at multiples of 100 will be hidden.

It is clear that many people giving opinions here have no idea of statistics, mathematics or computing. Hence I don't have to make them understand either. You don't see such precisely defined peaks in the distributions because of some vaguely defined things like many people take rest or people are happy to cross a milestone so they sit or quit, etc. These are fantastic pseudo-scientific, simplistic explanations. But such a thing can happen due to a precisely defined, systematic computation, for example, the way rating changes are calculated at different ratings. What is happening is a purely computational artifact, and not any computational error or glitch in the code either. chess.com has a different rating calculation. Just to give you an example if the k factor changes at certain steps in ratings, the rating gain or loss above those ratings will be different. The link I sent above has discussions about it, and example code to show how to simulate it (by people who know statistics and mathematics). Read the discussion on statistics stackexchange if you are capable of reading and understanding.