https://ratings.fide.com/card.phtml?event=2254174

Karjackin is drawing against Carlsen

some say he is 1300 inches

"and the transitive property does not apply fully to chess ratings"

Why exactly? It seems like you're just asserting this, not offering much of an argument. All you mention is a color analogy, which you don't put much effort into.

I don't even necessarily disagree; what you're saying has some plausibility. But you're making much of a non-argument for it. It's up to you to explain why and how the transitive property should break down.

"A 2700 will beat a 2300 (99% of the time)"

That's not what a 400 rating point difference means. It's more like a bit over 90%. And a chunk of those games will be draws.

"Even at GM level we see cases where player A usually beats higher rated player B and player B usually beats higher rated player C, yet C usually beats A."

Usually but not always. All we are asking about is a mere chance of winning.

It's the same way in sports sometimes.   Team A beats team B, B beats C, but C beats A.   I guess it has to do with how they match up against each other.   It kind of reminds me of online fantasy MMORPG's, where wizards beat melee, melee beats ranged and ranged beats wizards.  Magic works better against metal armor than it does against leather armor, apparently.   It must have to do with electrical conductivity.   

Kinda like this.  A 1300 player will lose to a 1500 player 75% of the time.  A 1300 will lose to a 1700 player 99% of the time.  A 1300 will lose to a 2700 player 99.999% of the time, etc.

That's how ELO ratings differences are explained.   Look it up.  400 ratings points equals a 99:1 ratio.

I looked it up before I made my comment. And I actually found 90.9% chance from the source I looked at if I recall correctly. 99 to 1 I have never heard of, and in practice I would say the upsets have been much more common than that. That is, from tournaments I've went to and watched.

It probably applies more to sports than in chess. No one would really say, though, that Nakamura was incapable of beating Carlsen just because he had a horrible record against him. Remember we're talking about possibility. We're not saying that if x scores well against y, who scores well against z, then x will score well against z. We're only trying to show that x could beat z.

So as an example as to how that could go: it seems that if x can beat y, there must be some skillset x has that can equal or go beyond y's. And if it's alligned right, x should be able to beat z. Maybe for some stylistic reasons this is difficult, but one would think x should at least have enough skill to have a chance at beating z.

I understand that if rock beats scissors, which can beat paper, it doesn't imply that rock can beat paper. But chess has a lot more overlap in skills than that and it can't be compared to that game. Any experienced tournament player should be able to speak to the amount of overlap in different levels of chess strength.

One response to this might be that the cause of upsets is based on players playing "like" someone else. So a 2300 beating a 2700 is because a 2300 plays like a 2700 for some particular game. Perhaps we all have ranges of strength. A 2800 can play from a range of 2400-3200, and so on. And so to explain why a 1900 can beat a 2300, it's because the 1900 can stretch to 2300 and hope the 2300 isn't having a good day. But on the other hand, a 1900 can't beat a 2300 who is playing like a 2700, because that stretch would be too much. But then again if the 1900 is playing like a 2300, they could beat a 2700 who is playing like a 2300. Speaking like this can cause a lot of confusion, it seems.

I don't know, just some incomplete thoughts. Play is variable in humans, of course. Of course, I post this at the risk of getting ad hominem attacks, because it seems like when someone makes a post about numbers, some other poster likes to call it stupid. You know, instead of trying to add to my thoughts, or add to the discussion.

I do tend to think that it's possible, for example, for a 2700 to play "like" a 2000, it's just incredibly unlikely and may not happen in the next hundred years.

If you look at "400," you see that it lines up at .91 on the expected curve, the .91 being in blue. So the person 400 points higher is expected to score about 91% against their opponent.

Ok.  It's possible that it's 800 points difference that is 99% then.   I knew that 200 points was around 75%.   

Of course there is a chance. If a Bobby Fischer has just joined the site and after a couple of games got 1300 points 

Oh, I agree with you.   I'm about a 1700 player, but sometimes I play like a 1400 and sometimes like a 2000 player.   So yeah, a range sounds about right.  So, in theory, on a good day I could beat a 2200 player (who is having a bad day), but on a bad day, I could lose to a 1200 player (who is having a good day).   I'll buy into that theory.  

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

Of course, there is a chance. When a Bob Fischer or a Michael Tal have just joined chess.com and got 1300 points after winning a couple of games. By the way. I hate the new version of chess.com. You should of called it chess.con

Of course, there is a chance. If a Bobby Fischer or Tal have just joined the site and got 1300 points after winning a couple of games

I've also known players whose playing strength seemed to vary with the opponent in a fairly consistent manner.

I've seen players who could simply sweep the bottom half of the tournament table, winning against every single player he out-ranked... but couldn't even scrape up a draw against anyone higher-ranked.

I've also seen players who only seem to play well against strong opponents. Pair them against a 1400 player and they play like a 1401 (or 1399) player.

My favorite example: Myself.

I've got an even score against World Chess Champions (thanks, GM Mikhail Tal!) but any strong CM or weak IM could crush me like a bug.

Boy, Tal must have really been slipping in his old age.   lol   Kidding, of course.  Congratulations if you really did draw against Tal.  That's pretty awesome for a strong Expert (untitled).   Was he very upset?

anything possible

just like seeing a fat lady sing

The only chance for a 1300 to win against a 2700 is when his opponent gets a heart attack or something.