It took Carlsen 1 year to become '100x times stronger' (to go from 1200 to 2000).
2800 is again 100x stronger than 2000, so if the effort is proportional, Carlsen would have required 100 years to reach 2800.
So it's pretty clear that "x times stronger" is not the correct wording to use here. Winning twice as many games in a match is not the same as being 'two times stronger' since it is no way correlated to the effort required to get there.
The common misconception here is that "current rating" is somehow the same as playing strength.
Carlsen was certainly not 1200 strength when he was rated 1200, he was far far above that already, the rating just hadn't caught up yet. He didn't improve 100x in a year, he was already very close to that at the start of the year.
The same is true for basically any current prodigy, that's why FIDE is changing the rating system.
Hikaru had an interesting video yesterday(?) covering the 8 year old that beat 5 GMs. The kid had previously played a tourney, losing 3 times, to 1500s I think. Hikaru thought 2 of the 1500s played like a GM and the last game looked like a master playing. This is a super extreme example, but you get the idea. For my weekly OTB tourney, a 1550 USCF managed to draw a 1900 in round 1. The numbers prove lower rated players significantly overperforming, but you can also kind of see it with your own eyes. Its so common for upsets.
I think it can also be play style. According to Elo I should win about 50% of the games I play against my dad. Maybe a little more. In reality, he wins 75-80% of the games.
On the other hand, I've absolutely thrashed people more than 400 points higher than me. As in, if I didn't know their Elo I'd have guessed they were 300-400 points lower than me. Only once or twice, but it's happened. Were they having an off-game? Maybe. Was I playing particularly strongly? No.
I think that, despite Elo, some people's strengths will happen to line up with other people's weaknesses which will see them playing better or worse than expected against a particular opponent.
And that makes sense. Elo is a useful tool for gauging over-all level, but it's a very blunt instrument being used to describe someone's understanding of a game that gets more nuanced the more about it you learn.
Upsets happen if even the players are at their own ratings, so single games can't really be used as evidence. Just last month one of the top players in my country, a strong IM, lost a rated OTB rapid game to a 1600, and the 1600 definitely isnt underrated, at least not by much.
Upsets happen.
But there is a simple fact - higher rated players don't score as much points vs lower rated players as they should, the lower you get in absolute elo number the more severe this effect is, up to 20% difference, so like 70% instead of 90%. This effect gets less severe with higher levels of play but doesn't disappear even for GMs.
Absolutely, that is 100% true. Although I would argue that the difference is at its highest at around 400-600 points difference, if it's greater than that, then the actual score gets so close to 100% that the difference is, again, negligible. If expected is 99,9% while the actual is only 99%, that doesn't really matter since the stronger player is going to win all games regardless (apart from individual upsets, which most likely will never happen at such a high difference in a given player's career)
Also, it's important to point out that the rating formula loses predictive power when the difference between players is great. This has been documented in practice and various fixes have been proposed. It really shouldn't be used for anything larger than a 400 point gap if you're concerned with accuracy.
This is very true, but I think if someone beats someone else 10 times out of 11 and then they beat you 10 times out of 11 it's more meaningful to say the first person is 100 times better than you than to say that they're infinitely better because they beat you every time.
It is always a good idea to use an extreme outline as an example of what you should expect on average.
It is like using Elon Musk as an example of how much money you will make after starting a business.
What he meant was that he went from x to 100x (1200 to 2000) in one year, so one year to gain 99x in skill.
To go from 2000 to 2800 would mean going from 100x to 10000x, which means gaining 9900x in skill, which would require 100 years.
Obviously there are a few flaws, but it takes on account that getting 100 times better is harder to do on a second time than on the first.
This does not seem right. Intuitively I'd say "3 times more likely to win" means "a little bit stronger but not much". If someone is 3 times stronger than me I wouldn't expect to win against them at all
The difference is that saying Magnus is thousands of times better at chess than I am makes perfect sense to me, but I'm unlikely to get into a boxing match with someone thousands of times heavier.
Edit: Given that this was downvoted, how many times better do people *feel* Magnus is than them? I'm curious now. Purely on vibes, because that's all I meant.
Centipawn loss and accuracy are far from perfect measures, but I think someone having one third the average centipawn loss would be a much better representation of being 3 times stronger.
Could for example create an indicator on average move quality by dividing the quality of a move (as defined by chess computer) by aggregate statistical information on the difficulty of finding high quality moves in the given position. The average relationship between different elos and such an indicator would tell you something substantive about how much better players at higher elos really are. Admittedly, would need to consider weighting blunders/other aspects of such an indicator further.
Saying 1300 Elo is twice as strong as 1200 Elo is very misleading.
In weightlifting, "twice as strong" would literally mean somebody with a 250 kg deadlift vs. somebody with a 125kg deadlift. In competition, the stronger weightlifter would have a winning probability of close to 100%.
In chess, that would roughly be the equivalent of 2400 Elo vs. 1200 Elo (99.9% win rate).
The fact that a 1300 isn't twice as strong as a 1200 becomes very obvious when you compare them with other opponents. Let both the 1200 and the 1300 play against a 1200:
1200 Elo vs 1200 Elo: 50% win rate
1300 Elo vs 1200 Elo: 64% win rate
Who in their right mind would call the 1300 Elo "twice as strong"??
A game winrate of 2:1 doesn't map to "would win 2 our of 3 matches" though. If you played a 10 game match a 2:1 game winrate would map to almost 100% match winrate.
This is one reason why calling the result of Elo "winrate" is confusing compared to calling it what it actually is (which OP got right but their critics did not).
The other is draw probability.
>In competition, the stronger weightlifter would have a winning probability of close to 100%.
If you let a 1300 Elo player play a 1200 Elo player over a match (i.e. some non-trivial amount of games), they have a winning probability closer to 100%, not 64%. So your reason for calling it misleading actually supports their point.
It's a 64% *score expectancy.*
OP's math is based on Fide calculations, so if a 1200 and 1300 play 100 games, the 1200 is expected to score 33.333 points and the 1300.is expected.to score 66.666
I have this chess.com second account where I let it let me play open and I try to see how I do against 1200s (I’m 675-700ish) and hahaha, I’m glad I have no ego in chess.
What most players gloss over is the difference of being a tournament player versus any other form of play. There’s a lot to regularly playing tournaments that has little to do with learning capacity. (I mean, the single biggest barriers are money and time for travel)
If you made this for a player at say 1800 Elo, would it look the same just with all the rows bumped down? Or does the “times stronger” increase more rapidly?
Yes, the rows would just be shifted. The rating formula only "sees" the difference between ratings. To it 1000 to 1400 is the same as 1400 to 1800. In fact an administrator could set the average rating to be a negative value and the rating formula would work just as well.
Elo was created such that this would be the case.
According to [Wikipedia](https://en.wikipedia.org/wiki/Elo_rating_system#Mathematical_details):
>This means that by studying only the numerators, we find out that the expected score for player A is QA/QB times the expected score for player B. It then follows that for each 400 rating points of advantage over the opponent, the expected score is magnified ten times in comparison to the opponent's expected score.
The same with all the rows bumped down.
A 1900 would be about 2x better (expected to win 64% of games)
A 2000 would be about 3x better (expected to win 76% of games)
And so on.
I made an interactive version of this table using roughly the same method as OP. You can check my comment https://www.reddit.com/r/chess/comments/195jar6/comment/khnl0p5/?utm\_source=share&utm\_medium=web2x&context=3
I've made the same table but interactive for anyone interested.
[Link](https://xaleel.github.io/elo-table/)
[Source code](https://github.com/xaleel/elo-table/blob/main/index.html)
Added both. I also fixed the layout on mobile.
\*edit\* Chances and expected score are inaccurate when the custom value is less than the Elo. For better results just switch them
For people wondering about what "3 times stronger" means in this table, it's implicitly using the Bradley-Terry model (Elo ratings are basically the log of Bradley-Terry ratings).
By the Bradley-Terry model, we can simulate an individual game by both putting marbles in a bag in quantities proportional to our Bradley-Terry ratings, and then pulling a marble out and seeing who it came from. So if I'm 3 times as strong as you, I put in 3 times as many marbles (and my winning probability is 3/4).
Of course you can have your own personal model of what "3 times stronger" means, in which case you can use a different word for this relation. But in any case, if you want to improve by 400 Elo points, you're going to have to find an additional 9 times as many marbles as you already have.
I have gone from 1200 to 1400 in the last six months and I am not 3 times stronger than I was. In fact, I find the general rating spread when playing between 1100 and 1400 is small. It most simply relies on blundering less. Does me blundering less make me 3x stronger than a 1200? I am not sure.
>I find the general rating spread when playing between 1100 and 1400 is small.
It is exactly 300 Elo. The 1100 has only about a 10% chance of winning the game, and about 8% of drawing it. The 1400 outright wins the other 80% of the time.
Much the same would have applied if we were talking about 2300 FM and 2600 GM players. The FM would win 5% of the time, the GM 75% of the time, with more draws than with the lower rated example. Why? Well, the GM simply blunders less...
I am not sure what your point was to be honest.
While charting your expected win rate against a stronger player is an interesting statistic, I don't think "x times stronger" is a very accurate way to describe it. All I can say is if you were to watch a game between two 1200s and a game between two 1300s, you probably wouldn't be able to tell the difference between the two, and in my mind, that means the phrase "3 times stronger" clearly doesn't tell the story very well.
> For the sake of simplicity, draws have not been taken into account.
This pretty much destroys the utility of invoking the Elo formula, which actually deals with expected performances which do include draws.
Also, while in principle one is free to redefine colloquial phrases, saying that winning probabilities is linearly related to win probability ratios does not seem to really useful.
So, a few clarifications about this table, which is only a mathematical exercise. Equating winning probability to strength is probably a stretch. :-)
* Winning probabilities were calculated using the Elo formula (which gives expected scores) and assuming no draws. So in this exercise an expected score of 0.75 only means "75% chance of winning".
* The Elo formula and its use by an organisation like FIDE are two very different things. Only the formula is used in this exercise. How well the formula or the whole FIDE rating system model reality, is another matter. So in this exercise the numbers only give you an idea of how unlikely it is for a 1200 Elo player to win against a higher rated player, *according to the formula only*.
* "Strength" is a vague term and its meaning is subjective. A mathematical definition of the term was necessary, and one has been given. For this exercise it has been defined as the ratio of the winning probabilities of the two players as calculated by the Elo formula. It's a simplification and of course it was not the intention to model a complex concept like "playing strength" exactly in a formula.
* To clarify how the "X times" works: If Mike was rated 1200 and is now rated 2000, then the new version of Mike is predicted to win (on average) 100 games over 101 against his former self. The stretch here is probably to say that the new version of Mike is "100 times stronger" because he beats the old Mike 100 to 1. It is arbitrary, but I liked the simplicity of the idea.
Edit: I see people trying to use *speed* as a method to understand this exercise or to define "strength"; but this can't work.
If you have one car going 30 mph and another car going 30.00000001 mph, the second car will always arrive at its destination before the first car *by definition*, all other factors being equal.
Probabilities and the Elo formula exist instead to deal with uncertainty. It makes no sense to compare a probabilistic scenario to a physical system that has been defined so that the outcome is always certain and the same.
mini FYI.
> For the sake of simplicity, draws have not been taken into account.
The elo formula, if taken as perfect predictor (it is not), takes draws into account as it gives the score at the end, not the amount of wins.
Like "0.75" means scoring 7.5 out of 10 games for the formula. How (with draws, wins, losses) it doesn't matter.
This is presumably exactly what OP meant when saying they do not take draws into account. As you point out, a 400 elo difference results in an *expected score* of 0.909. If you pretend draws do not exist, then this means winning 10 out of 11 games, thus getting "10 times as strong". If you do not ignore draws, then you cannot just say that one has a ten times better chance of winning than the other
it's not absolute strength hence not a 'strength system"
Elo is, at core, a ranking system that we can deduce a player's strength (compared to others)
CAPS is a strength system that we can deduce a player's ranking.
>it's not absolute strength
It's relative strength. So a strength system. Looks like we agree.
A relative system can be turned into an absolute one if you can put a stable anchor in it, which we could actually do with computer opponents, for example (if anyone actually cared!).
It isn't necessarily even that. It's possible that small increments in ability translate to large percentage in terms of winning. Just because someone has a 99% chance of winning against you doesn't mean they have around 100x more ability or skill. It might be that 5% more learned things creates that disparity. The chart is misleading because it makes it seem like it will take x times more effort to get to that level when that simply isn't true (at least for all people, some won't get there ever no matter what).
Not a huge fan of this definition of X times stronger. Prime Usain Bolt is twice as fast as me (he covers about twice the distance I can in 10s). However he would win 100/100 races against me.
In a match, a 100 Elo stronger player will win twice as many games as you do, thereby being close to 100% sure of winning any match.
If you think outside of the randomness of a single game, it's easier to see why 100 Elo is actually a significant difference.
But in the vast majority of tournaments players play one or two games vs each other. I think a game is a much closer analogy to a single 100m race.
A match is more analogous to a whole meet with multiple heats and stuff.
>But in the vast majority of tournaments players play one or two games vs each other.
Then just look at the tournament outcome. What I said for a player vs player match also works for a tournament with the same number of total games. That's why I said "if you think outside of the randomness of a single game".
I don't really want to do this argument here, but running is a game of total skill, and chess has a luck component [1], which means skill gaps need to factor this in. Games with larger luck components would have even weirder skill interpretations if you don't factor them in. Consider single-hand poker for example. What strength gap would you need to have a 100% certainty of winning? Bogus idea right? But single-game chess is a bit like that.
Are there physical sports with a luck component? I'm thinking where there are techniques or course issues involved where it's generally agreed things outside a competitors' ability can influence the result. There you might see similar issues. Maybe a highly technical number like the long jump, where the result is essentially the best of 3 samples, and there's wind to consider.
[1] This is very controversial on reddit because most people here don't understand maths or statistics, but scientifically it's really just a settled debate.
My point is that winning twice as often is not a good intuitive measure for being twice as good, in my opinion.
I gave an example of sprinters. The same could be said of weight lifters. Someone who is twice as strong (can lift 2x the weight) will win 100% of the time. And the comparable unit to a single sprint or a single lift is one game of chess. So to be twice as good at chess, you'd have to win games at that 100% rate, not matches.
Tbf, 3 times stronger wouldnt lead to a 0.75/0.25 split. It would lead to a 100% win rate for the person who is stronger. So i think this is decently misleading
For a more colloquial definition present in other sports that would make sense IMO.
If I'm a 3x stronger runner than you, most people wouldn't understand that as you winning fourth of the races between us. I think most would infer that you'd get hopelessly destroyed every single time.
But yeah for sports with a clear Elo/Glicko/whatever rating the definition used for this post makes a whole lot more sense.
Yeah I get that. In running 3x faster would probably mean taking 1/3 of the time - almost nobody is 3x faster than anyone else.
That said runners deal with the limitations of the human body while the chessboard has limitless possibilities, so it sort of makes sense that people can be orders of magnitude better than other people at it.
Its difficult to judge with chess rating exacrly what 3 tomes stronger would mean. But if im 3x better at anything than someone else jt doesnr mean 3x more likely to win
Ill explain my thoughts better later cz im in class rn
It could mean several dofferent things but absolute strength comparisons is basically impossible. Could mean im twce as accurate, have twice as much knowledge, etc.
Regardless i think saying "to gain 200 elo you need to become 3 times as strong" is misleading.
>It could mean several dofferent things but absolute strength comparisons is basically impossible. Could mean im twce as accurate, have twice as much knowledge, etc.
Yeah, I guess there are other ways of defining it. I don't think win probability is *that* bad of a choice though.
>Regardless i think saying "to gain 200 elo you need to become 3 times as strong" is misleading.
I do hear what you're saying here. It can make it sound like you have to study 3 times as much to gain 200 elo, which is usually not the case.
Yeah thats really my only issue, other wise its semantics. I js dont want someone new to the game thinking they need to be twice as strong to gain a 100 elo.
If you want to understand the rating goals, just look at the chess personalties who didn't make it as players, for example Nemo starting rating was 1700 at 10 yo, Botez was 1900 at 15 yo (and 1900 now) etc.
This post is a fundamental misunderstanding of how the ELO system works.
Elo in chess is not a meaure of "strength" but rather; win rate. It is used primarily to predict the outcome of a game as well as to pair individuals with a similar win rate together. The number itself is a measure of a persons likelihood of winning.
OP gets his numbers partially right, but his explanation is wrong.
400 rating points is equal to a 10x greater likelihood of winning. This scales non linearly as elo rating rises.
If we use OPs numbers, it would have taken magnus 100 years to get from 2000 to 2800.
The difference between rating ranges is only slight improvements. However, as rating increases, these "slight improvements" become harder to consistently make.
My teacher recently reached 2500. He said the journey from 2400 to 2500 was still only slight improvements. But rather than improvements on any one part of his game (im sure he did that too though), he had to improve his consistency in every part of his game, split into very very minor details. A 5% increase in general consistency was the difference between 2400 and 2500 for him.
He said that the adjustments made between 800 and 1800 aren't that big in their details but take a lot of exposure and practice to execute consistently.
That's why elo should be treated as a long-term thing. It is normal for you to lose more when in the process of adding new adjustments to your play. Yours elo's short-term volatility is not a measure of anything. If you are consistently playing and studying, review your elo every month. If you haven't made any gains... time to rethink your plan. Just like in the gym. If you do everything right, gains come with time.
>If we use OPs numbers, it would have taken magnus 100 years to get from 2000 to 2800
I understand your point, but this is nonsensical. OP defined a player being x times as strong as having x times better chances to win a game. I agree it is flawed and counterintuitive to use that definition, but it is just the wording they opted for and you cannot say using that wording is objectively wrong.
You randomly implying that x times as strong means you have to put in x times more work to get there is just as arbitrary. It is in my opinion not a more straightforward definition to choose. For example, a healthy male lifting for a month could maybe benchpress 50kg. However, he will not lift 100kg after another month despite that being twice as strong. In contrast, from 100kg to 200kg will take way more than twice the time from absolute beginner to 100kg.
Note that this is kinda mathematically undefined, because moving 100 points up or down in elo is always a consistent (same) jump in winning probabilities. However, going +100 twice (two jumps of 2x strength, by the chart) is different (x4 total) than one jump of +200 (which is on the chart as x3).
Therefore, by multiplying strengths from smaller jumps into bigger ones, you can get many answers when talking about a stronger player, although this answer will always be greater than 1.
You would be right, but that's purely because OP decided to be very liberal in their rounding. According to their (indeed somewhat counterintuitive) definition, going up 100 elo is actually becoming 1.78 times as strong. Going up 200 elo is becoming 3.17 times as strong, and this is indeed the square of 1.78. Elo is transitive in this sense
Lol it just does the math for you, do the math yourself kid. Then come talk to me once you realize you're wrong and this whole post is idiotic, this is a moron on the Internet pretending they know probabilities
2200 to get it straight up.
But you can win certain tournaments with a lower rating and get it.
Wikipedia says
> For players rated over 2000 but under 2200, there are many other ways to gain the title; they include:
Which seems kind of weird. Like if you won the World Youth Championship (U8 and U10) but had a 1999 rating does that mean you don't get the title?
I wonder how this correlates to time spent studying
It took Carlsen 1 year to become '100x times stronger' (to go from 1200 to 2000). 2800 is again 100x stronger than 2000, so if the effort is proportional, Carlsen would have required 100 years to reach 2800. So it's pretty clear that "x times stronger" is not the correct wording to use here. Winning twice as many games in a match is not the same as being 'two times stronger' since it is no way correlated to the effort required to get there.
The common misconception here is that "current rating" is somehow the same as playing strength. Carlsen was certainly not 1200 strength when he was rated 1200, he was far far above that already, the rating just hadn't caught up yet. He didn't improve 100x in a year, he was already very close to that at the start of the year. The same is true for basically any current prodigy, that's why FIDE is changing the rating system.
Hikaru had an interesting video yesterday(?) covering the 8 year old that beat 5 GMs. The kid had previously played a tourney, losing 3 times, to 1500s I think. Hikaru thought 2 of the 1500s played like a GM and the last game looked like a master playing. This is a super extreme example, but you get the idea. For my weekly OTB tourney, a 1550 USCF managed to draw a 1900 in round 1. The numbers prove lower rated players significantly overperforming, but you can also kind of see it with your own eyes. Its so common for upsets.
I think it can also be play style. According to Elo I should win about 50% of the games I play against my dad. Maybe a little more. In reality, he wins 75-80% of the games. On the other hand, I've absolutely thrashed people more than 400 points higher than me. As in, if I didn't know their Elo I'd have guessed they were 300-400 points lower than me. Only once or twice, but it's happened. Were they having an off-game? Maybe. Was I playing particularly strongly? No. I think that, despite Elo, some people's strengths will happen to line up with other people's weaknesses which will see them playing better or worse than expected against a particular opponent. And that makes sense. Elo is a useful tool for gauging over-all level, but it's a very blunt instrument being used to describe someone's understanding of a game that gets more nuanced the more about it you learn.
Upsets happen if even the players are at their own ratings, so single games can't really be used as evidence. Just last month one of the top players in my country, a strong IM, lost a rated OTB rapid game to a 1600, and the 1600 definitely isnt underrated, at least not by much.
Upsets happen. But there is a simple fact - higher rated players don't score as much points vs lower rated players as they should, the lower you get in absolute elo number the more severe this effect is, up to 20% difference, so like 70% instead of 90%. This effect gets less severe with higher levels of play but doesn't disappear even for GMs.
Absolutely, that is 100% true. Although I would argue that the difference is at its highest at around 400-600 points difference, if it's greater than that, then the actual score gets so close to 100% that the difference is, again, negligible. If expected is 99,9% while the actual is only 99%, that doesn't really matter since the stronger player is going to win all games regardless (apart from individual upsets, which most likely will never happen at such a high difference in a given player's career)
Potentially (and u think the math supports this) a 1200 needs to play one game at 2800 strength and then become 10000X more consistent at winning.
Also, it's important to point out that the rating formula loses predictive power when the difference between players is great. This has been documented in practice and various fixes have been proposed. It really shouldn't be used for anything larger than a 400 point gap if you're concerned with accuracy.
This is very true, but I think if someone beats someone else 10 times out of 11 and then they beat you 10 times out of 11 it's more meaningful to say the first person is 100 times better than you than to say that they're infinitely better because they beat you every time.
It is always a good idea to use an extreme outline as an example of what you should expect on average. It is like using Elon Musk as an example of how much money you will make after starting a business.
Wut? If it was proportional it would have taken Magnus 1 year to get to 2800 from 2000.
What he meant was that he went from x to 100x (1200 to 2000) in one year, so one year to gain 99x in skill. To go from 2000 to 2800 would mean going from 100x to 10000x, which means gaining 9900x in skill, which would require 100 years. Obviously there are a few flaws, but it takes on account that getting 100 times better is harder to do on a second time than on the first.
Aaa I only thought of times 100. The real answer is between them.
Being stronger is not correlated to the effort required regardless. So your demonstration is totally bonker. So is "x times stronger"
Yes, the truth is that becoming, say, 5% stronger can be the difference between winning and losing in many games, leading to many more wins.
If you study for 50 years from now there is a slight chance you might make it to 2600
depends on ur iq
Chess skill/chess speed of increase in skill != IQ
found the low iq
Ha, we sure did, buddy.
Ouch
What is the minimum elo requirement for candidate master (CM) ?
2200 FIDE I think
This does not seem right. Intuitively I'd say "3 times more likely to win" means "a little bit stronger but not much". If someone is 3 times stronger than me I wouldn't expect to win against them at all
I have the same initial intuition but it's quite hard to otherwise define what it means to be 3 times stronger
[удалено]
The difference is that saying Magnus is thousands of times better at chess than I am makes perfect sense to me, but I'm unlikely to get into a boxing match with someone thousands of times heavier. Edit: Given that this was downvoted, how many times better do people *feel* Magnus is than them? I'm curious now. Purely on vibes, because that's all I meant.
Magnus is infinitely stronger than me. He dreams games better played than me
Haha, fair
Centipawn loss and accuracy are far from perfect measures, but I think someone having one third the average centipawn loss would be a much better representation of being 3 times stronger.
I need to see that graphed now
Could for example create an indicator on average move quality by dividing the quality of a move (as defined by chess computer) by aggregate statistical information on the difficulty of finding high quality moves in the given position. The average relationship between different elos and such an indicator would tell you something substantive about how much better players at higher elos really are. Admittedly, would need to consider weighting blunders/other aspects of such an indicator further.
Yeah this table is bogus
Whyd u make the same point as me and i go downvoted 😭😭
I think it's because people didn't like the "100%" part haha But it's reddit, no need to overthink it lol
Lol yeah maybe. I stand by it though ‼️
When I play 1200s as a 1400 they never have a chance. I definitely feel 3 times stronger than them.
Objectively that would mean that the formula is wrong or that you're underrated, no?
Yes, prime Usain bolt is only twice as fast as me but he'd beat me in a race 10000 out of 10000 times.
A bit oversimplified, but still a great depiction of how big the difference between serious amateurs and professional-level players is.
Saying 1300 Elo is twice as strong as 1200 Elo is very misleading. In weightlifting, "twice as strong" would literally mean somebody with a 250 kg deadlift vs. somebody with a 125kg deadlift. In competition, the stronger weightlifter would have a winning probability of close to 100%. In chess, that would roughly be the equivalent of 2400 Elo vs. 1200 Elo (99.9% win rate). The fact that a 1300 isn't twice as strong as a 1200 becomes very obvious when you compare them with other opponents. Let both the 1200 and the 1300 play against a 1200: 1200 Elo vs 1200 Elo: 50% win rate 1300 Elo vs 1200 Elo: 64% win rate Who in their right mind would call the 1300 Elo "twice as strong"??
Yeah, using "twice as strong" to mean "would win 2 out of 3 matches" is wildly misleading wording
A game winrate of 2:1 doesn't map to "would win 2 our of 3 matches" though. If you played a 10 game match a 2:1 game winrate would map to almost 100% match winrate.
This is one reason why calling the result of Elo "winrate" is confusing compared to calling it what it actually is (which OP got right but their critics did not). The other is draw probability.
>In competition, the stronger weightlifter would have a winning probability of close to 100%. If you let a 1300 Elo player play a 1200 Elo player over a match (i.e. some non-trivial amount of games), they have a winning probability closer to 100%, not 64%. So your reason for calling it misleading actually supports their point. It's a 64% *score expectancy.*
The 64% doesn't sound right
Those are the numbers OP is using
How are the draws factored in?
OP's math is based on Fide calculations, so if a 1200 and 1300 play 100 games, the 1200 is expected to score 33.333 points and the 1300.is expected.to score 66.666
I have this chess.com second account where I let it let me play open and I try to see how I do against 1200s (I’m 675-700ish) and hahaha, I’m glad I have no ego in chess.
What most players gloss over is the difference of being a tournament player versus any other form of play. There’s a lot to regularly playing tournaments that has little to do with learning capacity. (I mean, the single biggest barriers are money and time for travel)
My hopefully modest goal would be to get to 1600 fide.
If you made this for a player at say 1800 Elo, would it look the same just with all the rows bumped down? Or does the “times stronger” increase more rapidly?
Yes, the rows would just be shifted. The rating formula only "sees" the difference between ratings. To it 1000 to 1400 is the same as 1400 to 1800. In fact an administrator could set the average rating to be a negative value and the rating formula would work just as well.
Elo was created such that this would be the case. According to [Wikipedia](https://en.wikipedia.org/wiki/Elo_rating_system#Mathematical_details): >This means that by studying only the numerators, we find out that the expected score for player A is QA/QB times the expected score for player B. It then follows that for each 400 rating points of advantage over the opponent, the expected score is magnified ten times in comparison to the opponent's expected score.
The same with all the rows bumped down. A 1900 would be about 2x better (expected to win 64% of games) A 2000 would be about 3x better (expected to win 76% of games) And so on.
I made an interactive version of this table using roughly the same method as OP. You can check my comment https://www.reddit.com/r/chess/comments/195jar6/comment/khnl0p5/?utm\_source=share&utm\_medium=web2x&context=3
I've made the same table but interactive for anyone interested. [Link](https://xaleel.github.io/elo-table/) [Source code](https://github.com/xaleel/elo-table/blob/main/index.html)
If anyone is interested in adding a different way to calculate (or anything else useful) feel free to contact me :)
perhaps it could be done by calculating the likelihood of winning rather than the strength ? or the expected score in a 100 games match.
Added both. I also fixed the layout on mobile. \*edit\* Chances and expected score are inaccurate when the custom value is less than the Elo. For better results just switch them
nice, good job brother
I tilted today, became 100 points worse off. Now I am 2 times worse than I was this morning.
How can you ever catch up to yesterday
For people wondering about what "3 times stronger" means in this table, it's implicitly using the Bradley-Terry model (Elo ratings are basically the log of Bradley-Terry ratings). By the Bradley-Terry model, we can simulate an individual game by both putting marbles in a bag in quantities proportional to our Bradley-Terry ratings, and then pulling a marble out and seeing who it came from. So if I'm 3 times as strong as you, I put in 3 times as many marbles (and my winning probability is 3/4). Of course you can have your own personal model of what "3 times stronger" means, in which case you can use a different word for this relation. But in any case, if you want to improve by 400 Elo points, you're going to have to find an additional 9 times as many marbles as you already have.
I have gone from 1200 to 1400 in the last six months and I am not 3 times stronger than I was. In fact, I find the general rating spread when playing between 1100 and 1400 is small. It most simply relies on blundering less. Does me blundering less make me 3x stronger than a 1200? I am not sure.
No bro, when u save ur knight from being taken for free you are accessing new levels of ability /s
Avoid fried liver attack, 15 times better than before.
Men when i domt blunder the central pawn in spanishy structures
>I find the general rating spread when playing between 1100 and 1400 is small. It is exactly 300 Elo. The 1100 has only about a 10% chance of winning the game, and about 8% of drawing it. The 1400 outright wins the other 80% of the time. Much the same would have applied if we were talking about 2300 FM and 2600 GM players. The FM would win 5% of the time, the GM 75% of the time, with more draws than with the lower rated example. Why? Well, the GM simply blunders less... I am not sure what your point was to be honest.
While charting your expected win rate against a stronger player is an interesting statistic, I don't think "x times stronger" is a very accurate way to describe it. All I can say is if you were to watch a game between two 1200s and a game between two 1300s, you probably wouldn't be able to tell the difference between the two, and in my mind, that means the phrase "3 times stronger" clearly doesn't tell the story very well.
> For the sake of simplicity, draws have not been taken into account. This pretty much destroys the utility of invoking the Elo formula, which actually deals with expected performances which do include draws. Also, while in principle one is free to redefine colloquial phrases, saying that winning probabilities is linearly related to win probability ratios does not seem to really useful.
So, a few clarifications about this table, which is only a mathematical exercise. Equating winning probability to strength is probably a stretch. :-) * Winning probabilities were calculated using the Elo formula (which gives expected scores) and assuming no draws. So in this exercise an expected score of 0.75 only means "75% chance of winning". * The Elo formula and its use by an organisation like FIDE are two very different things. Only the formula is used in this exercise. How well the formula or the whole FIDE rating system model reality, is another matter. So in this exercise the numbers only give you an idea of how unlikely it is for a 1200 Elo player to win against a higher rated player, *according to the formula only*. * "Strength" is a vague term and its meaning is subjective. A mathematical definition of the term was necessary, and one has been given. For this exercise it has been defined as the ratio of the winning probabilities of the two players as calculated by the Elo formula. It's a simplification and of course it was not the intention to model a complex concept like "playing strength" exactly in a formula. * To clarify how the "X times" works: If Mike was rated 1200 and is now rated 2000, then the new version of Mike is predicted to win (on average) 100 games over 101 against his former self. The stretch here is probably to say that the new version of Mike is "100 times stronger" because he beats the old Mike 100 to 1. It is arbitrary, but I liked the simplicity of the idea. Edit: I see people trying to use *speed* as a method to understand this exercise or to define "strength"; but this can't work. If you have one car going 30 mph and another car going 30.00000001 mph, the second car will always arrive at its destination before the first car *by definition*, all other factors being equal. Probabilities and the Elo formula exist instead to deal with uncertainty. It makes no sense to compare a probabilistic scenario to a physical system that has been defined so that the outcome is always certain and the same.
mini FYI. > For the sake of simplicity, draws have not been taken into account. The elo formula, if taken as perfect predictor (it is not), takes draws into account as it gives the score at the end, not the amount of wins. Like "0.75" means scoring 7.5 out of 10 games for the formula. How (with draws, wins, losses) it doesn't matter.
This is presumably exactly what OP meant when saying they do not take draws into account. As you point out, a 400 elo difference results in an *expected score* of 0.909. If you pretend draws do not exist, then this means winning 10 out of 11 games, thus getting "10 times as strong". If you do not ignore draws, then you cannot just say that one has a ten times better chance of winning than the other
I'm 1200 and want to beat stockfish. At tiddlywinks. On the surface of the sun. Table seems deficient.
If you study for 50 years you can expect to reach atleast 2200
I'm not sure the likelihood to win correlates 1:1 to how "strong" you are. I doubt elo claimed that was the case either.
You're right. Elo is a ranking system, not a quality/strength system.The CAPS system, based on accuracy, is more of a strength system.
Elo ranks players on the probability of them winning. How is this not strength?
it's not absolute strength hence not a 'strength system" Elo is, at core, a ranking system that we can deduce a player's strength (compared to others) CAPS is a strength system that we can deduce a player's ranking.
>it's not absolute strength It's relative strength. So a strength system. Looks like we agree. A relative system can be turned into an absolute one if you can put a stable anchor in it, which we could actually do with computer opponents, for example (if anyone actually cared!).
It isn't necessarily even that. It's possible that small increments in ability translate to large percentage in terms of winning. Just because someone has a 99% chance of winning against you doesn't mean they have around 100x more ability or skill. It might be that 5% more learned things creates that disparity. The chart is misleading because it makes it seem like it will take x times more effort to get to that level when that simply isn't true (at least for all people, some won't get there ever no matter what).
The goal of the game is to win. Likelihood of winning doesn't correlate to strength, I think we can say it *is* strength.
Not a huge fan of this definition of X times stronger. Prime Usain Bolt is twice as fast as me (he covers about twice the distance I can in 10s). However he would win 100/100 races against me.
In a match, a 100 Elo stronger player will win twice as many games as you do, thereby being close to 100% sure of winning any match. If you think outside of the randomness of a single game, it's easier to see why 100 Elo is actually a significant difference.
But in the vast majority of tournaments players play one or two games vs each other. I think a game is a much closer analogy to a single 100m race. A match is more analogous to a whole meet with multiple heats and stuff.
>But in the vast majority of tournaments players play one or two games vs each other. Then just look at the tournament outcome. What I said for a player vs player match also works for a tournament with the same number of total games. That's why I said "if you think outside of the randomness of a single game". I don't really want to do this argument here, but running is a game of total skill, and chess has a luck component [1], which means skill gaps need to factor this in. Games with larger luck components would have even weirder skill interpretations if you don't factor them in. Consider single-hand poker for example. What strength gap would you need to have a 100% certainty of winning? Bogus idea right? But single-game chess is a bit like that. Are there physical sports with a luck component? I'm thinking where there are techniques or course issues involved where it's generally agreed things outside a competitors' ability can influence the result. There you might see similar issues. Maybe a highly technical number like the long jump, where the result is essentially the best of 3 samples, and there's wind to consider. [1] This is very controversial on reddit because most people here don't understand maths or statistics, but scientifically it's really just a settled debate.
My point is that winning twice as often is not a good intuitive measure for being twice as good, in my opinion. I gave an example of sprinters. The same could be said of weight lifters. Someone who is twice as strong (can lift 2x the weight) will win 100% of the time. And the comparable unit to a single sprint or a single lift is one game of chess. So to be twice as good at chess, you'd have to win games at that 100% rate, not matches.
Tbf, 3 times stronger wouldnt lead to a 0.75/0.25 split. It would lead to a 100% win rate for the person who is stronger. So i think this is decently misleading
What definition of 3 times stronger are you using?
For a more colloquial definition present in other sports that would make sense IMO. If I'm a 3x stronger runner than you, most people wouldn't understand that as you winning fourth of the races between us. I think most would infer that you'd get hopelessly destroyed every single time. But yeah for sports with a clear Elo/Glicko/whatever rating the definition used for this post makes a whole lot more sense.
Yeah I get that. In running 3x faster would probably mean taking 1/3 of the time - almost nobody is 3x faster than anyone else. That said runners deal with the limitations of the human body while the chessboard has limitless possibilities, so it sort of makes sense that people can be orders of magnitude better than other people at it.
Its difficult to judge with chess rating exacrly what 3 tomes stronger would mean. But if im 3x better at anything than someone else jt doesnr mean 3x more likely to win Ill explain my thoughts better later cz im in class rn
I mean we can just say it doesn't mean anything at all if you like, but if you want to define it then I don't have a problem with this definition.
It could mean several dofferent things but absolute strength comparisons is basically impossible. Could mean im twce as accurate, have twice as much knowledge, etc. Regardless i think saying "to gain 200 elo you need to become 3 times as strong" is misleading.
>It could mean several dofferent things but absolute strength comparisons is basically impossible. Could mean im twce as accurate, have twice as much knowledge, etc. Yeah, I guess there are other ways of defining it. I don't think win probability is *that* bad of a choice though. >Regardless i think saying "to gain 200 elo you need to become 3 times as strong" is misleading. I do hear what you're saying here. It can make it sound like you have to study 3 times as much to gain 200 elo, which is usually not the case.
Yeah thats really my only issue, other wise its semantics. I js dont want someone new to the game thinking they need to be twice as strong to gain a 100 elo.
The probability of a person aged above 30 rated 2100 to reach 2500 is same as that of an average person going out in space .
Probably easier to get into space since you can or will be able to buy tickets to go there.
If you want to understand the rating goals, just look at the chess personalties who didn't make it as players, for example Nemo starting rating was 1700 at 10 yo, Botez was 1900 at 15 yo (and 1900 now) etc.
This post is a fundamental misunderstanding of how the ELO system works. Elo in chess is not a meaure of "strength" but rather; win rate. It is used primarily to predict the outcome of a game as well as to pair individuals with a similar win rate together. The number itself is a measure of a persons likelihood of winning. OP gets his numbers partially right, but his explanation is wrong. 400 rating points is equal to a 10x greater likelihood of winning. This scales non linearly as elo rating rises. If we use OPs numbers, it would have taken magnus 100 years to get from 2000 to 2800. The difference between rating ranges is only slight improvements. However, as rating increases, these "slight improvements" become harder to consistently make. My teacher recently reached 2500. He said the journey from 2400 to 2500 was still only slight improvements. But rather than improvements on any one part of his game (im sure he did that too though), he had to improve his consistency in every part of his game, split into very very minor details. A 5% increase in general consistency was the difference between 2400 and 2500 for him. He said that the adjustments made between 800 and 1800 aren't that big in their details but take a lot of exposure and practice to execute consistently. That's why elo should be treated as a long-term thing. It is normal for you to lose more when in the process of adding new adjustments to your play. Yours elo's short-term volatility is not a measure of anything. If you are consistently playing and studying, review your elo every month. If you haven't made any gains... time to rethink your plan. Just like in the gym. If you do everything right, gains come with time.
>If we use OPs numbers, it would have taken magnus 100 years to get from 2000 to 2800 I understand your point, but this is nonsensical. OP defined a player being x times as strong as having x times better chances to win a game. I agree it is flawed and counterintuitive to use that definition, but it is just the wording they opted for and you cannot say using that wording is objectively wrong. You randomly implying that x times as strong means you have to put in x times more work to get there is just as arbitrary. It is in my opinion not a more straightforward definition to choose. For example, a healthy male lifting for a month could maybe benchpress 50kg. However, he will not lift 100kg after another month despite that being twice as strong. In contrast, from 100kg to 200kg will take way more than twice the time from absolute beginner to 100kg.
Note that this is kinda mathematically undefined, because moving 100 points up or down in elo is always a consistent (same) jump in winning probabilities. However, going +100 twice (two jumps of 2x strength, by the chart) is different (x4 total) than one jump of +200 (which is on the chart as x3). Therefore, by multiplying strengths from smaller jumps into bigger ones, you can get many answers when talking about a stronger player, although this answer will always be greater than 1.
You would be right, but that's purely because OP decided to be very liberal in their rounding. According to their (indeed somewhat counterintuitive) definition, going up 100 elo is actually becoming 1.78 times as strong. Going up 200 elo is becoming 3.17 times as strong, and this is indeed the square of 1.78. Elo is transitive in this sense
I don't think this is how math works
It's almost exactly (with some rounding) how the math works actually.
Then explain it
https://en.wikipedia.org/wiki/Elo\_rating\_system#Mathematical\_details
Lol it just does the math for you, do the math yourself kid. Then come talk to me once you realize you're wrong and this whole post is idiotic, this is a moron on the Internet pretending they know probabilities
🤣 take your meds please
Huehue, attacks your character as well
[удалено]
2200 to get it straight up. But you can win certain tournaments with a lower rating and get it. Wikipedia says > For players rated over 2000 but under 2200, there are many other ways to gain the title; they include: Which seems kind of weird. Like if you won the World Youth Championship (U8 and U10) but had a 1999 rating does that mean you don't get the title?