Rating limit?

What is the limit of probabilities?

>There is no rating limit. And how to know it: Read the source Luke, read the source

Close, but the limit IS in the source. You even link to the right file.
github.com/ornicar/lila/blob/b8a6745f9871f624570048953a266fcf611a1a64/modules/rating/src/main/Glicko.scala#L35

def sanityCheck =
rating > 0 &&
rating < 4000 &&
deviation > 0 &&
deviation < 1000 &&
volatility > 0 &&
volatility < (Glicko.maxVolatility * 2)

There are other limits too, lower down in the file

There is no theoretical limit, but in practice as rating increases, you would need to play against other people with similar ratings. Let's say hypothetically there was a single player with a 3500 rating, and the other top players are all 2800-2900s. The 3500 player wouldn't get many points for a win, and as the rating gap increasesam it's possible for the higher-rated player to get 0 rating points for a win.

So, for rating to increase indefinitely, you'd need a group of players to move up together, possibly only playing each other. It would become very difficult for ratings to increase beyond a point.

@TBest I did find that one but Idid not find any call to it from that file. Yes there is a call to it in other file. Syntax of scala makes it hard to understand how itis used but it will clip on 3999.

Despite the fact there's some bots matchs where one of them reach 14K 1+0 rtg... So, what do u mean by limit? #12
(Search on forum something like highest rating all time and ull found the link)

at #12 is correctly notices that there functions that makes sensibility of rating calculation which is used to decide is calculated rating is storred. If rating IN LICHESS exceeds 4000 it will not be strored. Probably not implemented as rating limit but safety catch agains programming errors in rating calculation,

If there is a stationary probability distribution behind the rating computation algorithm, whether mathematically proven or empirically observed, then Sargon's comment makes sense, and the question might be better formulated as what is the 99% confidence interval (that is where 99% of population is within). Maybe that could be even calculated from the same lichess data showing those smooth but wavy above 2000 , weekly distributions. I am curious about which binning would show noise.

from the average one could expand a ball and compute area under the curve until the relative increase becomes below a certain threshold and qualify that limit.

But that is likely what the op meant anyway. Clearer question at least, than mine.

well that got me curious, and i gathered the courage to go start to read a statistical paper, might even be by Glickmann, to get a taste for the kind of mathematical object. and its assumptions. It seemed to have been developed with OTB tournaments times frames and assumed an interaction between player activity rate (# games per time frame), and some play quality drift in precision, the more sustained the activity over some time frame bigger than that which defines activity level, the less uncertainty increase for the individual player.

I have not finished reading. And it is actually well explained (and the dependency on earlier non-stated models are clearly referred to, if one gets overwhelmed with doubts).

Being of Bayesian approach, it does not posit a ruling distribution. but an information gain upon games experience, so if you start with a rating probability density attached to your head in your busy chess life at a given instant (you have an instantaneous #games per unit time computed for you somewhere, and it fights against information entropy) you need to keep playing to keep your attached rating probability distribution from flattening. Each games will inform it to some extent, etc...

not done reading. but that is what i get from what i read. pitting rating probability against your opponent's makes for a population of rating clouds expanding and shrinking, and that seems to be where the posited hypotheses happen. not about the resulting population level limit distribution.

somewhere i expect that the iterative process of game pairings with large population to behave with time (?) and mostly with large numbers, without having to specify a parameterized limit distribution, just that it will. distribution of what? well not of individual ratings, but of their posited rating averages and standard deviation trajectories, as each rating blob is assumed to follow normal density with some time dependent also posited spread. that's how far i read for now.

Anybody in the know, is my caricature somewhat valid.... (because i have more of it in store, if not completely off base).

Basically, I am glad to have finally gotten some sense of the foundation of such rating blobs (ever evolving amoeba).
Progression of the average, but also fluctuation of the deviation.... in a huge ensemble of different game collision rates..

@petri999 > I did find that one but Idid not find any call to it from that file

Yeah don't ask me where it is called 😅
Maybe it's here : github.com/ornicar/lila/blob/85d76db9a3f25059be5bb9cdfb731b791d646a4f/modules/rating/src/main/Perf.scala#L32

But yeah, I am neither scala proficient or familiar with the codebase really

But is there any rating limit at other chessites? For example chess.com and so on??