100 points higher: 66% score. e.g. 2 wins and 1 loss.
200 points higher: 75% score. e.g. 3 wins, 1 loss or 2 wins, 2 draws.
Can't remember it in anymore detail, other than to say that it's exponential, so the chances of scoring points get drastically smaller as the difference increases.
1900 and 2000 are close ratings, 1900 will probably beat a 2000 2/5ths less then a 2000 would beat a 1900, but whe the rating gap gets bigger the results also get bigger.
At the class levels, the trend would definitely be logarithmic.
It is hard to argue against the fact that a difference in "quantifiable" knowledge + skill between a 1600 player and a 1400 player is INSANELY more than the difference between a 1400 and a 1200.
A lot of players starting out make the "linear-thinking" mistake of saying "hey, my rating went from 1000 to 1400 in 2 months, so I'll be Master (2200) in no time" :)
At the class levels, the trend would definitely be logarithmic.
It is hard to argue against the fact that a difference in "quantifiable" knowledge + skill between a 1600 player and a 1400 player is INSANELY more than the difference between a 1400 and a 1200.
A lot of players starting out make the "linear-thinking" mistake of saying "hey, my rating went from 1000 to 1400 in 2 months, so I'll be Master (2200) in no time" :)
That's what I thought. Someone told me that after 1400, things begin to get really hard (improving rating). I think I heard/read someone call it the 13/1400 plateau.
That's probably true for most people, but if you start young with a coach lets say, you may say beginner to 1800 was pretty easily, but now I'm having to work at it.
Or if they're a future GM something like... I was stuck at 1800 for a few months, then a steady climb up to 2200 and that was a tough plateau for a year then I went to 2600 in the next 2 years.
So... it's all relative in my mind.
For a hobby player who started as an adult and does some work on chess now and then I think 1300/1400 would be a legitimate plateau. You're now better than about 100% of casual players and now you're facing more experienced players if you want to keep climbing.
I'd say the same for ~1600 USCF just because Dan Heisman's concept of hope chess and around this ratnig I plateaued until I changed the way I thought about moves (basically less random heh).
Oh by the way, forgot where I found this but here's the winning percentages:
That's probably true for most people, but if you start young with a coach lets say, you may say beginner to 1800 was pretty easy, but now I'm having to work at it.
Or if they're a future GM something like... I was stuck at 1800 for a few months, then a steady climb up to 2200 and that was a tough plateau for a year then I went to 2600 in the next 2 years.
So... it's all relative in my mind.
For a hobby player who started as an adult and does some work on chess now and then I think 1300/1400 would be a legitimate plateau. You're now better than about 100% of casual players and now you're facing more experienced players if you want to keep climbing.
I'd say the same for ~1600 USCF just because Dan Heisman's concept of hope chess and around this ratnig I plateaued until I changed the way I thought about moves (basically less random heh).
Oh by the way, forgot where I found this but here's the winning percentages:
That's a great table, thanks! I work really hard everyday at chess (and have been non-stop since I started last November). I am an adult, so I don't really know what that will mean for me in terms of climbing the ladder.Everyone says it will take much longer, but I just can't wrap my head around the reason for this. Some people compare it to learning a language when you are young; however, I think that is just a case of being in a submersed environment. For example, I bet if you wanted to learn spanish FAST, you would learn pretty quick by living in Mexico as opposed to practicing flash cards everyday. If you work hard everyday (maybe a few hours a day and 10-12h on the weekend), I don't see why an adult cant reach 2000 at some point in their life, as long as they remain mentally and physically healthy. Obviously, I am talking about me here, and my goals. I am 31 years old, so I actually consider myself to be somewhat young 
...lol. Maybe...But certainly at a much greater disadvantage than a 4 year old learning the game.
For me, I think each day I am seeing the board better. I can actually tell. Its small changes, but noticeable (if you eliminate my off days). I think what begins to be a challenge, is what you said before, and that is changing your thought process. That can be difficult, but you can train yourself to do it. Maybe this is why chess 960 is so popular. Another thing is trying to ID patterns quickly. I am still slow at that, but tactics are helping.
The problem is that the adult has a job. And also they know that they will die one day D:
That's what I thought. Someone told me that after 1400, things begin to get really hard (improving rating). I think I heard/read someone call it the 13/1400 plateau.
My own experience seems to back that up. I started getting "serious" about chess 2 years ago - reading books, studying problems and master games, and playing A LOT (~2000 games in 2 years) - and after the first year, I improved from, I would guess, about 900 to high 1300's. The second year has been all plateau - at standard time controls, I haven't budged from the 1360-1380 range, despite continuing to study and play constantly. It's sometimes hard to accept, but we all do have a limit to our abilities...looks like I've found mine!
That's what I thought. Someone told me that after 1400, things begin to get really hard (improving rating). I think I heard/read someone call it the 13/1400 plateau.
My own experience seems to back that up. I started getting "serious" about chess 2 years ago - reading books, studying problems and master games, and playing A LOT (~2000 games in 2 years) - and after the first year, I improved from, I would guess, about 900 to high 1300's. The second year has been all plateau - at standard time controls, I haven't budged from the 1360-1380 range, despite continuing to study and play constantly. It's sometimes hard to accept, but we all do have a limit to our abilities...looks like I've found mine!
As long as you still have fun doing it, that's all that counts. 99% of us here are not, nor will ever be masters or GM's in chess. I just love the game and Im going to do my best to break expert level.
Log base 10.
THANK YOU.
if you look at the denominator in the pic, that 400 should be glaring out at you. what it means is that a 400 point ratings difference equates to a 1 in 10 chance of winning, an 800 point difference would be 1 in 100, a 1600 point difference would be 1 in 10,000.
"if you look at the denominator in the pic, that 400 should be glaring out at you. what it means is that a 400 point ratings difference equates to a 1 in 10 chance of winning..."
Not to be too technical, but it actually equates to a 1 in 11 chance of winning: so it's worse than I thought!
1 in 10 vs. 1 in 11 makes a difference! After losing 9 in a row to someone rated 400 points more than me, I was all excited that I was "supposed" to win our next game. Now I knew I've at least one more to lose! 
Agreed. Any person of average intelligence should be able to reach 2000 if they have the time to play and study, and if their health allows.
That's probably true for most people, but if you start young with a coach lets say, you may say beginner to 1800 was pretty easily, but now I'm having to work at it.
Or if they're a future GM something like... I was stuck at 1800 for a few months, then a steady climb up to 2200 and that was a tough plateau for a year then I went to 2600 in the next 2 years.
So... it's all relative in my mind.
For a hobby player who started as an adult and does some work on chess now and then I think 1300/1400 would be a legitimate plateau. You're now better than about 100% of casual players and now you're facing more experienced players if you want to keep climbing.
I'd say the same for ~1600 USCF just because Dan Heisman's concept of hope chess and around this ratnig I plateaued until I changed the way I thought about moves (basically less random heh).
Oh by the way, forgot where I found this but here's the winning percentages:
I beat a person 375-391 above me once. That means I was in that 9%. COOL! How about draws? However, my BIGGEST was a 494 above me.
That means I was in that 4%!!!!
@naturalproduct : you're right about immersion being a decisive factor in your chess progress.
But immersion in chess is not studying : it's playing OTB and analyzing with stronger players. 
@naturalproduct : you're right about immersion being a decisive factor in your chess progress.
But immersion in chess is not studying : it's playing OTB and analyzing with stronger players.
Immersion...lol. That was the word that wasn't coming to me! Agreed. I am trying to play OTB at lease a couple times a week. Unfortunately, in my area, there is not a lot of chance to play all the time. How much do you think a "good" amatuer plays OTB chess a week?
Mike
I have a question I have been interested in recently. Maybe this will be picked up by the more mathematically inclined in the group :)
What type of mathematical trend does rating (USCF) have with respect to skill. For example,in chemistry and on the pH scale, a pH of 1 is a 10x stronger acid than an acid with a pH of 2 (and is 100x stronger than a pH of 3, etc.).The trend is logarithmic.
Since skill is a nebulous term, maybe we could compare it to win ratio. For example, is a 2000 rated player 10x stronger than a 1900 rated player (say a 1900 rated player would beat a 2000 rated player only 10% of the time, and so on)?
I have heard that as you get higher in rating it becomes much, much, more difficult to increase that rating.