Current average chess rating

Actually that would be interesting to check. We can probably expect the averages to go down due to CORVID.

No because the players here at 1700 are mostly only 1550 elo max in my experience and the 1600 only 1450 elo...but most 1000 and 1150 are 1200+

And, you know, Elo and Glicko are the names of the mathematicians who came up with the formulas, and they're used in other places besides chess. They're not perfect, but my point is they're high quality.

Exactly! here i never got above 1824 but elsewhere i got very easily 2100+

One way to set a... sort of "true" average, is if playing new players only affected their rating, not yours.

And games against them don't affect anyone's rating until they stabilize but...

Obviously this is enormously impractical.

Arpad Elo, a Hungarian-American physics professor.

Wow, come on mathematicians, you let some physics guy beat you

Mathematicians were to busy solving the catalan conjecture.

Elo was a chess master. By the 1930s he was the strongest chess player in Milwaukee, then one of the nation's leading chess cities. He won the Wisconsin State Championship eight times.^[

Yes, I know how to read Wikipedia.

Here, I made an easy way to visualize it.

Try to guess what will happen, then I'll post the answer below

For the first picture, the blue is the ratings of an established group of 5000 players, they've been playing a while and their average is at 1500.

The red is the true strength (not the rating) of a group of 500 players who join. They're new so their ratings will be adjusted quickly.

However, for the purposes of this illustration, we're going to start these strong 500 players at a below average rating. Here's the same picture but this time the red is the starting rating of the new players.

Now I run the simulation for 5 million games.

If the rating formula works (and it does) then this is sufficiently long for the group of new players to reach their proper rating.

But here's the question: Before the players joined, the average was 1500.

What do you think the new average rating will be after all the games have been played?

(The answer may surprise you)

Ok, here's the graph after 5 million games. We can see the rating system has done a good job.

But what's the average?

It hasn't changed!

We see the average started at 1502 and after the games is 1500.

Why?

It's because as the red group moved right through the graph, eventually their high RD disappeared. When their RD was about the same as everyone else, at that moment the new average was set. The red group continues to move to the right, but the average will be unchanged. I could run it for 500 million games and it wouldn't change the average.

Pretty cool isn't it?

Oops, in the first graph, it's blue and red true strength (not rating) when it was supposed to be blue's established ratings and red's strength. The way it's set up though it's extremely close. Blue had been playing so for blue there's an average difference of only about +/-50 rating points between strength and rating, so it's still a reasonable graph for this illustration purpose.

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So do strong players move the average up? Yes.

But the big question is... how quickly can your system (with the starting rating and initial period) move that player to their correct rating?

The "true" average of my example "should" have been just under 1550 after the games finished. It was lower because we started the new group low and they weren't able to climb quickly enough.

But how many did read it?

I'm sure no one except you.

I get that all rating systems are confined to their own pools, but this sites own rating system rates their own "beginner" category at 1000 which is only slight below their own average player.  Start a new account and choose "beginner", you'll be 1000 which is this sites average player.  

I don't know if the names they selected are good or not.

But trying to label them correctly would be a big mistake. What you want is for people who know nothing about ratings (or at least nothing about where they fit in to chess.com) to choose a rating close to what they will eventually be.

So as long as the words they used trick people into getting close, they were successful.

I mean, if people could be trusted to rate themselves, they'd just have a box where you enter a rating.

I mean, there's probably some interesting psychology... maybe the names hardly matter at all... if I recall 3 of them are synonyms (beginner, novice, new).

People don't want to say they're terrible, so when faced with 3 synonyms people will usually choose one of the higher ones... and if the two higher ones straddle your average then most new users will be put there... which is statistically what you want.

Then the last 2 are something like "intermediate" and "advanced"

Intermediate is perhaps the OTB average (in the United States at least) of ~1500 which may be ~1700 on this site.

Then they choose advanced to balance the distribution (whatever it is).

Again, maybe I'm over thinking stuff, but it's kinda of fun to think about.

Some physics guy!? How could you, his forename is virtually universal in modern technology, especially with Generation Z? Give some credit to his name, it's much a similar to the iPad. Arpad literally prognosticated the invention of the iPad.

Ok, but I mean... mathematicians are sort of famous for coming up with solutions 100+ years early, before people even knew there was a problem to be solved at all.

I know very little about both the theory behind statistics and economics... but doing this little program made me think they're connected.

Imagine you have a certain amount of gold. Its value depends on the market you enter, and commodities fluctuate day to day like a person's rating shadows their true skill.

In other words there were practical problems related to this since the dawn of civilization. So I'm surprised a mathematician didn't come up with something similar to Elo 1000 years ago