Wow, imagine if you had been studying go as hard as at the beginning, you would be 80 dan by now.

The difference between Bradley-Terry and Elo is not very big. You can even "derive" the Elo formula from the Bradley-Terry formula.

Both work as P_win = 1/(1 + b/a) where b and a are measures of "skill" of both players. The rating is usually expressed as r_a = ln(a) [with some additional scaling constants], so that P_win = 1/(1 + exp(r_b - r_a))

So instead of using ratios of "skill", you get to use differences in rating, which is more convenient.

So it's true that ratings are a logarithmic scale for "skill", similar to the Decibel scale, the Richter scale and the Kardeshev scale, where a difference in those units actually means some ratio of the underlying quantities.

But when you make a plot like the one that Herman pointed to, but this time using "skill" on the vertical axis, it comes down to just transforming the vertical axis to a logarithmic scale. The plateau effect stays. So I think this rescaling doesn't really matter for the "depressing" implications of that plot.

If you're interested, I got this for the relation between Bradley-Terry "skill" (a in my previous post) and EGF rating from my previous statistical analysis of EGD data (note the logarithmic scale on the vertical axis).

The plot is not linear, because EGF ratings are based on ranks instead of P_win (like Elo ratings), but when you zoom in a bit to a smaller range of ranks, it's close to linear (especially in the kyu range):

Learning curves often follow a logistic pattern, with a slow start followed by a rapid increase with an increasing rate of growth. Then at some point the curve has an inflection point after which the curve continues to increase but the rate of growth decreases. The curve eventually approaches a horizontal asymptote at a level approximately twice the level of the inflection point. If learning go follows this pattern you could predict your maximum by observing the change in the rate of increase.

multiple reasons

Playing is not studying. It's more like writing a test but unless you review it, you'll never know where your mistakes were. Feedback-loops are essential for improving. Measuring wins, losses or your rank won't give you meaningful feedback to improve.

The perfect example for me is typing. We pretty much all do it and have invested a lot of time in it. But how many of us are actually proficient in typing (fast and steady, using every finger, not looking at the keyboard)?

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My "guide" to become stronger in Go

Nobody dares to say the main reason why some are not able to increase their go abilities over their current level. ( genan did in a polite way )

While political correct, it serves nobody. Respecting players at all levels does.

It is nice that go can be enjoyed by people at all levels.

We agree (in fact we are saying exactly the same thing) up until here:


Instead of using the log of the skill (in the Bradley-Terry sense) for the y axis, I prefer to use actual skill for the y axis, so the plot of skill as a function of effort is affine, but with the horizontal lines (representing ranks or Elo) that have exponentially increasing spacing.

Of course this illustrates exactly the same information. But to me it is much less depressing to think "I'm grinding, and of course it's getting harder to hit new ranks because they're farther apart" than to think "My ability to improve has decreased".

Gennan said more or less that go rank depends on several factors:

• Talent
• Time
• Motivation
• Learning environment

You seem to be suggesting that talent is the main factor. No problem with that, I've accepted long ago that I have no particular talent for go, but this doesn't explain what is talent. For me, talent is a combination of

1) Doing (almost) the right thing right away.
2) Being able to identify mistakes.
3) Being able to correct them.

People with ability #1 make quick progress, but it doesn't mean that other people cannot reach a good level after a lot of effort.

People without ability #2 can use the help of a teacher, but a teacher is useless if they don't have ability #3.

Coming back to my analogy with learning English as a second language, people with good listening abilities can pronounce "the" almost correctly from the very beginning. Others will go through a stage of pronouncing "ze", realize by themselves it's wrong and will improve the pronunciation after several months. Others need the help of a teacher who points out the problem and tell them to repeat "The thirty-three thieves thought that they thrilled the throne throughout Thursday" ten times. But some people, even with the help of a teacher, continue to pronounce "ze" for decades, thinking that making the effort to correct the pronunciation is not necessary and that communication is efficient anyway, even with the pronunciation defect.

If (say) some of my stones get captured at the dame-filling stage, someone could tell me "hey, didn't you count liberties? Can't you read what happens if your opponent cuts or peeps?" Well, yes I can do that. Yes I know I should do that. But no, I don't pay attention at every move of every game.

If somebody really lacks learning ability, it is fair to respect the limits. Go can be enjoyed on many levels. This is one aspect of Go I love.

(To be clear: I am not arguing that all the people not improving on go servers lack the learning ability to do so.)

Since learning can be learnt, this discussion will start going in circles soon ; )

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My "guide" to become stronger in Go

I think learning is a very complex subject in itself.

There are different learning styles. Some people are good at self-teaching while others are dependent on having a teacher whose teaching style matches their learning style (and this is where opportunity becomes important too). I think personality traits also play an important role. A hunger for knowledge, self-reflection, self-discipline and patience probably have a positive effect, but a strong ego and performance anxiety may have a negative effect.

But maybe:

strong ego = strong igo

and

strong igo = strong ego

QED and DDT

I suppose confidence often goes together with being a strong player. But learning requires an open mind. A strong ego can get in the way of self-reflection and accepting feedback from a teacher.

Probably good to have some balance: not too modest, not too arrogant - seek the truth.

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be immersed

I used to be proud, but I learned my lesson. Now I'm perfect.

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The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I stopped making progress when I reached the point where the pain of studying harder was getting bigger than the fun of being stronger.

They get married.

Don't forget children, a career and other hobbies.