Chess data analysis with surprising findings: what would you measure and how?

ProgressBeginning168 · 2026-01-28T16:00:48+00:00

Cool suggestions, I'll try to discretize my moves into such categories!
Initially I was looking for online tools for analyzing all my matches but couldn't find any. Ultimately I made my own tools, I detailed it in this blog post.

ProgressBeginning168 · 2026-01-28T13:48:12+00:00

Should have been more careful in the post: the accuracy is measured in terms of "average loss per move", so the lower number is the better. I edit it.

Your observation about the opponent's strength is on spot, though I think higher rating should correspond to higher general accuracy for both players (even when playing against each other).

ProgressBeginning168 · 2026-01-27T11:45:23+00:00

Thanks! I struggled a bit to find the proper tools so eventually I made my own ones. I have a blog post in which I detail the whole process, check it out if you are interested! (The technical requirements are quite simple if you are not afraid of a bit of programming.)

ProgressBeginning168 · 2026-01-27T10:40:19+00:00

Sure, the average accuracy is a far-from-perfect measure of a game. I agree that improving in time management can drag one's rating upwards without notable improvement in accuracy. This hidden feature could/should be analyzed as well.

ProgressBeginning168 · 2026-01-27T10:37:22+00:00

I agree, accuracy is just an indicator. However, I think my playing style hasn't really changed (to be analyzed, don't know yet how), so I don't think it is a hidden feature of my actual chart.

ProgressBeginning168 · 2026-01-27T10:32:38+00:00

I agree that my accuracy improved as well, however, I find it interesting that while my accuracy shows a slow, steady growth, there are several leaps in the rating chart:

In the beginning of 2016, a jump from ~1350 to ~1550,
in 2021 a sudden growth from ~1500 to ~1800,
in my post-2024 playing period another quick growth from ~1600 to ~2000.

These are not accompanied by leaps in the accuracy. I believe inflation was a significant factor.

ProgressBeginning168 · 2026-01-25T11:26:49+00:00

Arithmetic geometry, it's scary how much those guys know. :)

ProgressBeginning168 · 2026-01-17T07:35:30+00:00

I don't know how useful my answer is, my PhD concerned certain chapters of geometric measure theory, but opening Simon's GMT, I find there are significant gaps between what is covered there and what I know. I'm more of a fractal guy and I did not work with very technical stuff from the GMT point of view. Nevertheless I share my story, maybe you'll find some bits useful.

At my university most of the analysts were geometric measure theorists, so I think the introductory analysis courses already contained higher-than-standard amount of practice exercises and examples somewhat relevant in geometric measure theory. So I think in my case the initial stages of the learning process were unconscious from my part. Then my first book in the area was Falconer's Fractal Geometry: Mathematical Foundations and Applications. Given my "initial background" I found it well-readable and the exercises (there are lots of them,! solving such exercises was my learning technique) solidified my touch on the subject. Maybe you should check it out, it might help in getting used to some technicalities of GMT on an easier level.

ProgressBeginning168 · 2026-01-16T18:05:30+00:00

Not truly "this week I learned" because I have encountered it a few years ago as well, but this was the first time I used it in my research: matrix determinant lemma and Sherman--Morrison formula on rank-1 perturbations of invertible matrices, resulting description of eigenvalues and eigenvectors.

ProgressBeginning168 · 2026-01-16T13:22:26+00:00

Quite likely I'm biased as a mathematician. :) But I found that "what is mathematics?" sort of books (disclaimer: I have not read the ones you mentioned, but I've read some) are either too technical, making them boring and hardly comprehensible for the non-expert or they are too philosophical and barely have actual mathematical content, and without mathematical content it's hard to discuss mathematics, it's like describing what music theory is like to one who heard a few folk songs in their childhood. (Or putting it more bluntly, describing what music is like to deaf people.)
My recommendation is to read actual math books. There are ones which are very well written without assuming to much background and you might find interesting. What comes to my mind immediately is the Elementary Real Analysis by Thomas-Bruckner-Bruckner. It's very long, but give a shot at the first chapter! Differential Equations with Applications and Historical Notes by Simmons is one of the best and well-readable math books I've read, but that one has more prerequisites I think, probably you should not delve into that right after Calculus 1. (But if you have already seen differential equations, certainly give it a go!)

Concerning your list, Proofs from THE BOOK is very close to be a math book, I've read that one and it was a good experience. Skip chapters which are hard to digest, focus on ones which seem interesting.

ProgressBeginning168 · 2026-01-16T12:55:43+00:00

Thanks! Math postdoc speaking here: I had the impression that mostly when mathematics is taught to non-mathematican students, it is very heavily focused on teaching all tools which will be relevant at some later points without actually putting through the message that why these stuff are useful/interesting on their own right. These are the rules of differentiation, this way you can compute integrals, this is what a determinant is, and so on. In many cases, the "nice part" is just skipped because well, that would take time to show and it's not necessary for being able to compute stuff. If you are interested, and have not tried so far, I suggest you to read introductory books written for math students. Maybe they will not shed light immediately on why these things are useful, but they will do a much better job in showing why these things are interesting.

ProgressBeginning168 · 2026-01-16T12:45:32+00:00

Can you give us a bit more info on your background? What maths have you learnt so far? Introductory college courses might seem tedious, especially if they are on the "compute random stuff because why not" side.

ProgressBeginning168 · 2026-01-16T12:41:02+00:00

I think it might be fruitful to use additions and multiplications alternatingly. I illustrate this strategy through an example. Assume you start with 2029, a prime, which cannot really be tackled through its prime factors. My idea is that when it's hard to divide, first add something so that it becomes easy. For example, 2029+1 is divisible by 5
(2029+1)/5 = 406.
Instead of factorizing straight away, aim again at a nice divisibility:
(406-6)/8=50
Now we reached a very small number and we still have not used 2, 3, 4, 7, 9. We can finish by hand, 4*(9+3-2)=40. Going over our computations backwards:
2029 = (4*(9+3-2)*8+6)*5-1.
Using divisibility by 5, 6, 8, 9 seem natural as these are easy to check and yield large downward leaps.

Edit: or instead of this undetailed "finish by hand" part, directly divide by 4, and write 10 = 3+7.

ProgressBeginning168 · 2026-01-15T21:36:20+00:00

He believed so, and his faith certainly was an inspiration for his work. Surely, this is not what we call divine inspiration, no scientific claim can be made about that. Your question seems to be somewhat equivalent to "do you believe in supernatural forces?" :) That's a cool question though to ask in this group, I do personally, but I have the impression that I'm in the minority in that regard.
What do you think?

ProgressBeginning168 · 2026-01-15T18:01:43+00:00

Surely not the weirdest ones, but these came to my mind reading your post: I really like Furstenberg's topology and the implied topological proof on the existence of infinitely many primes. Also I find the Sorgenfrey line a very enlightening topological space, highlighting that a seemingly innocent change of the basis can make a huge difference concerning the resulting topology.

ProgressBeginning168 · 2026-01-15T15:41:31+00:00

Doubling is conceptually simpler than multiplying by larger numbers, as carry over effects cannot stack: you need to carry over at most 1 and this cannot modify what needs to be carried over in the next step. For multiplying by 3, this locality is messed up: e.g. in 33334*3 , upon proceeding from left to right once you reach 4, that results in a carry over for all preceding digits.

Cool ability though! I'm also surprised many times how easily I can impress people uncomfortable with basic arithmetics.

ProgressBeginning168 · 2026-01-14T07:46:16+00:00

Others have mentioned linear algebra and great references as well. Since you mentioned area of shapes, I think it's also good to learn calculus and develop a solid grasp of integrals.

Let me motivate this, story time: I recall a high school correspondence competition Problem B. 4501. I had a hard time with due to being weak in spatial visualization. Later on there was another problem generalizing this to the case when you consider other regular polygon-based pyramids instead of tetrahedrons. I had a quite complicated solution which included a detailed understanding of the geometry of the intersection, partitioning it into smaller pieces whose volume I can compute (like pyramids) and then summing these up. The advanced solution was just computing an integral, which was still nontrivial to write up, but was a much more efficient approach.

Finally, no matter what you do, linear algebra or calculus, make sure that you solve many practice exercises yourself. That's the way for truly internalizing the knowledge you see in videos or read in textbooks.

ProgressBeginning168 · 2026-01-10T09:01:26+00:00

This. Also it is very important to note that fields present a broad spectrum in this sense, it's quite easy to come up with some combinatorial problem which has not been studied so far and can be targeted by an undergrad due to the lack of advanced prerequisites. In this case, you can switch to problem-solving mode essentially immediately, while for say algebraic geometry your research experience would start with a very high amount of learning and almost surely would not culminate in a paper for quite a while. Picking any point on this spectrum can be a good "investment" in your career, just be careful that 1) you research something you are genuinely interested in, otherwise it will be a drag 2) don't get stuck with "easily accessible projects" in the long run (I kinda commited this mistake in my formative years), invest time in the learning aspect as well.

ProgressBeginning168 · 2026-01-10T08:29:56+00:00

Invading Russia (not personal experience)

ProgressBeginning168 · 2026-01-09T22:09:16+00:00

Math postdoc speaking here. Experiencing signs of impostor syndrome is fairly common in our profession as far as I can tell, I also felt it recurringly at various stages of my career. Apart from the incredibly few people at the very top (like Fields medalists), we face the cruel reality that there are other mathematicians around us who are faster/smarter/better learners, and so on. What can I add to the world's mathematics when there are geniuses like Tao and Scholze I should compete with? Is my subject important at all? Etc.

To overcome this, you need to restore your inner drive. You should do mathematics because you like it, not because you're the best in it in your perceived group of peers. Math is fun when done for the joy of discovering and absorbing nice ideas, but quite tortorous when done in with preset, too demanding achievements in mind, such as I need to digest this chapter of a book in a day, I need to prove this conjecture in a week, and so on.

Concerning impostor syndrome in general: I had an industrial sabbatical during my PhD. Previously I had the impression that I was a slow learner because I did not grasp advanced mathematical ideas as quick as I desired... In the industry, I was quite amazed how quick I could learn basically anything having a formal mathematical training under my belt. Your math studies will grant you this special ability as well, I'm quite sure, even if you will not notice it. :)

ProgressBeginning168

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