Elo Distribution W4PCC 2022

I originally wanted to make this post to show that there is not much use in opening the qualifiers below 2.5k elo because nobody that low will qualify, but with the qualification of @Indipendenza I guess I was proven wrong.

The graphic that you can see above is the accumulated elo distribution of the 15 qualifiers. (Lars is excluded)
I took everybody's elo not as a single data point but as a Gauß-Curve and added those up. 

The number you can see on the left can be interpreted as the probability that a player plays at that certain elo. I added those probabilities up for 100-elo-steps to see how likely it is that a player is in a certain elo range:

As you can see, there is a 20% chance that we see some 2200-2300 elo play. So you might argue there is a small chance that someone in this elo range does qualify. But as players vary in their strength this is just the worse performance of the weaker players who are ranging around 2500 elo.

If you are wondering why some data points are above 100% or why these numbers ad up to 1500%: We have 15 players. Those are the added probabilities.

I still believe there is not much use in opening qualifiers below 2500 elo, even if 2 players below that did qualify.

But this post I made primarily for you to marvel at the beauty of mathematics.

Cheers
Michael

Nope Mike, you were in fact NOT wrong

You forgot 2 things:

a) the events are not independent , I mean it's much easier to qualify in the event number X (16 in my case) if X-1 players can't play anymore. In addition, all that has been polluted greatly by the fact the first 4 (!) qualifiers were done with even 1800 players.

b) I'm currently rated 2350, as after the Big Reform I had to accept many low level games where I lost a lot of points; but in fact I'm usually between 2480 and 2600, and was for 2650 some time.

On Saturday I won this game: https://www.chess.com/variants/old-standard/game/27435277/87/2, all three other players were 2900-3100, in the world Top 10. (Yes it was thanks to a huge mistake of Liquid, but still, not just any 2300 would exploit it correctly).

(And I fully agree, the qualifiers under their current form shouldn't have been opened to LL players, it should begin at least at 2200, but 2500 that you spoke about wouldn't have shocked me at all. Cf. anyway some proposals here: https://www.chess.com/clubs/forum/view/a-proposal-for-2023-championship).

you forget how partners can effect the game.  ive seen noobs beat some pretty impressive players.   plus farming is wide open here.  nothing is done,  so rating will never really mean a whole lot to those that know the deal.  i qualified 3 times,  once i wasn't notified of the next match and was bumped out along with many others.  and 2 times my partners dropped out.  so 4pc needs to be looked at a little differently i think.  also a wild card slot was added for this 3rd W4PCC,  not many liked seeing that show up last minute being we weren't even told we had moved on.  many questions,  few answers. 

as long as we can't take over for a disconnected partner,  we just have to "take our chances and hope they have a good one." is what i was told,  i don't thing ratings should come into play AT ALL, EVER.  i have lost more games to disconnects than some people will ever play.  (14,500 currently is my total games played in 4pc teams)  so, if i had those 2000 games back what would my rating be?  10,000 maybe?  LOL. yea,  i been here  a while and some things need to be looked at a little harder.  this is sillyness. 

I have a lot of questions now...

Who are you?

Do you know how elo rating works?

Do you know how 4PC works?

What do you mean by "i qualified 3 times"?

What wild card slot?

He is referring to teams??

Due to @a1t19 replacing @yasmin-er-vatar the distribution did change.

Note how @Indipendenza's Bell-Curve is almost completely detached from the rest of the field.

This is how the distribution would look like if @EyeoftheTiger1204 instead of @Indipendenza would have qualified.

Imagine you open the qualifier for 2200 and nobody is even remotely close to that...

Amount of players below 2500:
0,02 Players

Absolutely, there should've been a threshold, I would say 2400 or 2500. The luck factor is otherwise too big.

And I think you said your peak rating was 2650 right?

So I guess if you really wanted to participate if you grind before the Championship you could have hit 2.5k to participate.

Empty, a) if after the reform I played only normal 2400+ games instead of accepting the BS available to play, I would've remained where I were: between 2450 and 2550 ; b) if I didn't participate, I wouldn't have killed myself, sincerely ; c) there were several low level games during the qualifiers, and yes I believe a minimal threshold was necessary, and Neo and myself spoke about that above well before the beginning, but nobody cared ; d) hence my proposals for next year that you saw maybe.