Can I random walk myself to 2300?

Follow-up,

if you assume that the rating fluctuations are the result of a Orstein-Uhlenbeck process (a random walk with mean-reversion). We can find that the long-run expected rating probability distribution is a Gaussian distribution centered around the 'true skill level' (R_real) corresponding to the invariant measure of the OU process.

This refers to the probability density graph of ratings that you were trying to prove is Gaussian..

Follow-up, if you assume that the rating fluctuations are the result of a Orstein-Uhlenbeck process (a random walk with mean-reversion). We can find that the long-run expected rating probability distribution is a Gaussian distribution centered around the 'true skill level' (R_real) corresponding to the invariant measure of the OU process. This refers to the probability density graph of ratings that you were trying to prove is Gaussian..

Draw_a_la_comensa

#12

@otb_analysis_account said in #11:

Follow-up,

if you assume that the rating fluctuations are the result of a Orstein-Uhlenbeck process (a random walk with mean-reversion). We can find that the long-run expected rating probability distribution is a Gaussian distribution centered around the 'true skill level' (R_real) corresponding to the invariant measure of the OU process.

This refers to the probability density graph of ratings that you were trying to prove is Gaussian..

First of all, OU is the continuous version of the process. The AR(1) would be the discrete version you are interested in here. Second, this process is clearly not an AR(1) process thanks to the nonlinear drift term. However, as the previous commenter said, it is ~linear near the intercept R_real and hence the stationary distribution would probably be well approximated by a Gaussian in this region, but its tails would deviate.

@otb_analysis_account said in #11: > Follow-up, > > if you assume that the rating fluctuations are the result of a Orstein-Uhlenbeck process (a random walk with mean-reversion). We can find that the long-run expected rating probability distribution is a Gaussian distribution centered around the 'true skill level' (R_real) corresponding to the invariant measure of the OU process. > > This refers to the probability density graph of ratings that you were trying to prove is Gaussian.. First of all, OU is the continuous version of the process. The AR(1) would be the discrete version you are interested in here. Second, this process is clearly not an AR(1) process thanks to the nonlinear drift term. However, as the previous commenter said, it is ~linear near the intercept R_real and hence the stationary distribution would probably be well approximated by a Gaussian in this region, but its tails would deviate.

Samarth1509

#13

yeah my rating was 1100 in clasical and then i always play different opning and play with stress free so my rating now is 1700

otb_analysis_account

#14

@Draw_a_la_comensa said in #12:

First of all, OU is the continuous version of the process. The AR(1) would be the discrete version you are interested in here. Second, this process is clearly not an AR(1) process thanks to the nonlinear drift term. However, as the previous commenter said, it is ~linear near the intercept R_real and hence the stationary distribution would probably be well approximated by a Gaussian in this region, but its tails would deviate.

Thanks, I missed the previous comment. You are right and I am mistaken

@Draw_a_la_comensa said in #12: > First of all, OU is the continuous version of the process. The AR(1) would be the discrete version you are interested in here. Second, this process is clearly not an AR(1) process thanks to the nonlinear drift term. However, as the previous commenter said, it is ~linear near the intercept R_real and hence the stationary distribution would probably be well approximated by a Gaussian in this region, but its tails would deviate. Thanks, I missed the previous comment. You are right and I am mistaken

Average nodir moment

@camilajenny said in #3:

I used to have a rating 2200 at bullet chess and I started playing my own nonsense b3, Bb2, Qc1, Nc3, Nd1, f3, g3, Nh3, Nhf2, 0-0 in every game. Now my rating is 2500, and if I play normally without that nonsense, I can reach max 2200-2300, my play strength didn't really go higher, so have I walked myself randomly to such a high rating?

Naah, +250 points shouldn't be randomness.

@camilajenny said in #3: > I used to have a rating 2200 at bullet chess and I started playing my own nonsense b3, Bb2, Qc1, Nc3, Nd1, f3, g3, Nh3, Nhf2, 0-0 in every game. Now my rating is 2500, and if I play normally without that nonsense, I can reach max 2200-2300, my play strength didn't really go higher, so have I walked myself randomly to such a high rating? Naah, +250 points shouldn't be randomness.

DaBassie

#17

@winnie33 said in #9:

Fun insights aside, I enjoyed the tone and the jokes of this post :)

I'm glad you liked it :)

@winnie33 said in #9: > Fun insights aside, I enjoyed the tone and the jokes of this post :) I'm glad you liked it :)

DaBassie

#18

@Draw_a_la_comensa said in #5:

While the monotonicity of tanh preserves the symmetry about R_real, and the drift guarantees a unique stationary distribution, I do not think that it is Gaussian. While there are a number of mathematical ways to try and show this, the easiest counter example is to probably just overlay the plot of your "analytic" solution with a Gaussian density with the same mean/variance (or just compute the L2 distance between them as functions over your support).

So, I'm a physicist, so I know some mathematics, but the deeper theorems are quite difficult for me...

But I have some observations I can contribute with. The distribution I calculate seems to be exactly Gaussian shaped, also at the tails. Like, I give my SD with 4 significant figured, because it's really that precise. So I'm pretty sure this really is correct. I would think any effects of the non-linear part of tanh would be visible, if they would make the shape non-Gaussian.

I tried to do some exact calculations, but I failed, the tanh-function isn't very friendly to work with, especially if you need to invert it. So if the final distribution is Gaussian, my guess is that it's not just because of this function, but rather that there exist a whole family of functions that would yield a similar result. The property f(x) = -f(-x) feels required (for symmetry), and probably there are more requirements.

Having said that, I'm happy with the things I learned. Exactly the right amount of maths for a Lichess post, perhaps too little maths for a scientific journal... That's life.

@Draw_a_la_comensa said in #5: > While the monotonicity of tanh preserves the symmetry about R_real, and the drift guarantees a unique stationary distribution, I do not think that it is Gaussian. While there are a number of mathematical ways to try and show this, the easiest counter example is to probably just overlay the plot of your "analytic" solution with a Gaussian density with the same mean/variance (or just compute the L2 distance between them as functions over your support). So, I'm a physicist, so I know some mathematics, but the deeper theorems are quite difficult for me... But I have some observations I can contribute with. The distribution I calculate seems to be exactly Gaussian shaped, also at the tails. Like, I give my SD with 4 significant figured, because it's really that precise. So I'm pretty sure this really is correct. I would think any effects of the non-linear part of tanh would be visible, if they would make the shape non-Gaussian. I tried to do some exact calculations, but I failed, the tanh-function isn't very friendly to work with, especially if you need to invert it. So if the final distribution is Gaussian, my guess is that it's not just because of this function, but rather that there exist a whole family of functions that would yield a similar result. The property f(x) = -f(-x) feels required (for symmetry), and probably there are more requirements. Having said that, I'm happy with the things I learned. Exactly the right amount of maths for a Lichess post, perhaps too little maths for a scientific journal... That's life.

elongermrenter

#19

How do you improve after becoming a cm

#20