Is there any chance that a 1300 rated player can beat a 2700 rated player?

"The rating system is an estimate based on incomplete information."

"I'm saying in reality, if we knew everything, we could see there are units of information that let you play correctly in specific situations. If you have enough units, you play correctly in all the situations a 1300 can generate."

And this seems to just be a baseless assumption. It's not unreasonable to say that what we consider covering all the units is really just our inability to understand what thousands of games is really like, and the kinds of odd things that can happen with so many. I can't really grasp it either, but I don't pretend I can. You can't just dismiss that just because we casually observe that 2700s make very few unforced errors. How many games do we look at to base our decision? Maybe dozens? That's not close to enough. When we see hundreds of quality moves we get absorbed in that. But we're not talking hundreds of moves. We're talking about hundreds of thousands of moves. The 1300 only needs a tiny percentage of opportunities to win a tiny percentage of the time.

I haven't been saying 2700 vs 1300 here actually, I'm just saying theoretically why it makes sense a player can have an expected score of 100% even if the rating system will always give some very small decimal just above zero.

As for "unforced errors" I think we need more specific terminology. When a 1300 makes an error it means they lost a rook. When a 2000 player makes an error they lost a tempo. When a 2700 player makes an error...

And also "unforced." Carlsen plays 20 "best" moves in a row and even if the position is equal his opponent can be pressured into a mistake. Is that unforced? Would Nakamura make the same "unforced" error against a 1300?

Ok, so I understand there is a random nature to chess. No one can see to the end, so (other than just uncharacteristic blunders) we can get into positions whose evaluation we didn't expect.

Still, it's not so random that this evaluation is off by an enormous amount. If you want to say a 1300 has a non-zero chance, ok, I can't prove it either way. But I think you can argue a basis for there being a 100% chance in some cases.

That's why I make the distinction "unforced" in the first place. In your Carlsen example, the opponent would be making a "forced" error because they were under pressure.

"I haven't been saying 2700 vs 1300 here actually, I'm just saying theoretically why it makes sense a player can have an expected score of 100% even if the rating system will always give some very small decimal just above zero."

I don't really disagree here. My problem is not that the expected score being 100% simply can't be, but that people don't really give a good reason for this to be believed. It could be true, but why should I think so? What I believe doesn't require as much dreaming. I'm just saying 2700s make fewer mistakes, so there are fewer chances to lose, it's the same thing that makes you go up to any higher rating. I'm better off going by the rating system than making up my own theory that I just pulled right out of my ass.

"we can get into positions whose evaluation we didn't expect."

Right. It's not just random blunders. The above point is a much more realistic scenario. Still super unlikely, but nevertheless. Maybe one game in a thousand between the 2700 and 1300 will feature some closed up position where the 1300 doesn't have to play great moves to hold together. Even here the 1300 is extremely likely to lose, but it's probably not a negligible chance that they would draw or win (maybe the 2700 overpresses, maybe the 1300 is feeling inspired and finds better ideas). Remember that at the end of the day the 1300 and 2700 are both human, even if they're in good form.

Yes, I guess that's the basic argument. The randomness in chess due to humans not seeing to the end on top of the randomness of humans in general (bad day, in a mood to play too fancy, stuff like this).

So you can say there is some non-zero chance.

But it's all a bit silly in practice. The position not being what you expect and being in a odd mood is something you might see in a 700 point upset, not a 1400 point upset. The higher the difference in skill, the more extreme the randomness will have to be.

So is the randomness great enough to cover the skill gap? I think the answer is yes or no, but I also think we'll only ever be able to answer maybe. (I feel like bizarre blunders like hanging a mate in 1, while possible, betray the spirit of the question.)

As for pulling a theory out of an ass, I'm just giving one structure to it. I.e. that for each position there exists knowledge and ability to play it correctly and that individuals have an incomplete collection of this knowledge. Also any two players have a finite set of positions they can generate. Given this model some players will always beat other players when every position they can generate can be played correctly by one of them.

Sure the rating system may be the best we have, but we only use statistics because we have incomplete information. If we know everything it's only yes or no. Much like the real eval of a position (win/draw/loss) or is chess a draw with best play.

100% doesnt exist in reality. The 1300 could play the best moves by guessing . There is always something.

Then there is no 0% in reality. And the 1300 cannot make a "pure" guess. I.e. the method and reasoning will always be non-random.

My POV gets into deterministic stuff, which I'm not informed enough to have a strong stance either way.

Ah, in that model complete information to play a position correctly would only exist for very simple positions. Very strong players play complicated positions well, but not perfectly.

It wouldn't be hard to say any set of knowledge and ability is incomplete enough that there is never a 100% chance.

This is all intuitive of course, but it's fun (for me) trying to organize the thoughts and write/type them out. Sometimes making the effort you reach an unintuitive conclusion.

Actually, an exact answer to this question can be given, at least from a statistical standpoint.  The rating system is based on a bell curve with a standard deviation of 200√2, which is a little less than 283.  With a 1400 point rating difference, the mathematical expectation for the lower rated player is .000000372.  This means if 2.7 million games are played between an 1300 and a 2700 player, the 1300 player can be expected to pick up one point.

@ OBIT

Post #76, 2 years ago.

leiph18: I agree with that two-year-old post from theSicilianDragon that the ELO-system math breaks down when the rating disparity is large.  When the rating difference is less than 400 points, the ELO math fits the normal bell curve pretty well.  However, then discrepancies start to creep in, and the bigger the rating difference, the worse the discrepancies get.  To give some concrete examples:

When the rating difference is 200 points, the ELO calculation gives the stronger player a .76 expectation.  I get the same answer with a normal bell curve: 200 points =  200/283 = .71 standard deviations = .76 probability.

When the rating difference is 400 points, the ELO calculation gives the stronger player a .91 expectation, while I get .92 with a normal bell curve, still pretty good.

However, at 850 points (i.e. 3 standard deviations), the ELO calculation gives the stronger player a .993  expectation, while it is..999 with a normal bell curve.  So, if 1,000 games are played, ELO predicts the weaker player will pick up seven points, while the normal curve predicts the weaker player only gets one. 

Now, at 1400 points... yeh, this is just too big a discrepancy for the ELO math to be meaningful.  And, I suppose it could be argued the normal curve math is suspect as well.  Statistics work very nicely for the data that falls in the fat area of the bell curve, but not so well for the extreme cases.  That's why, for example, an IQ measurement of 115 sounds reasonable, but anyone claiming to have an IQ over 145 is just spouting BS.    

In my experience, a GM's ability to coordinate minor pieces is too much for anyone under expert.  Playing GM Shabalov once, he happlily gave me his Q for 3 minor pieces and a pawn at the back end, and there was nothing I could do.  I imagine this sort of thing, as well as the ability to find resources, etc., makes it effectively impossible for GM that is in his or her right mind and paying any kind of attention to lose to such a player.

One other point: I have heard that the idea behind the USCF rating system (all rating systems, maybe?) is that a 400-point difference is supposed to mean that there is no realistic likelihood of the lower player beating the higher or the game ending in a draw, if the rating difference is truly 400 points.   

Sadly I lost, recently, to a player who at the time was about 500 points lower than me :( He played a good game too. Chess is strange sometimes.

400 points should be a 95% score I believe.

So the worse player should win 5 in 100, or draw 10, or a combination.

It always seems like the chances of the lower player winning (against me for instance) are higher than 5%, even with those kinds of rating differences. I play in swiss tournaments and I'll usually play two or three people 300-400 points lower, and 1 or 2 players slightly stronger than me. While I don't lose/draw often to the lower players, it doesn't seem rare either, certainly not 5% rare. I guess it's just my imagination.

I guess it depends whether you're playing someone who has been sitting at that rating, or someone who is better than that but their rating lags behind.

For an improving player, they will generally play stronger than their rating.

Among the  good kids this difference often are several houndred points.

Statistical analysis is next to worthless when you are talking about the elite of the elite. During the years of the thread, the number of players rated over 2700 has varied from 45 to 50.

The discussion, however, has focused on the general strength of Grandmasters without the recognition that 2700s win almost every game against GMs below 2650.

1300s have no chance. That is, the chance of a rank beginner is less than the fraction of a tenth of a percent that might be predicted from statistical analysis.

That's a long way from no chance though. Of course that's arguing over semantics.