lichess.org
Donate

Quantifying Volatility of Chess Games

Interesting formula. We should expect higher volatility from a tactical player and from games under time pressure. I would love to see a graph with more data.

Interesting formula. We should expect higher volatility from a tactical player and from games under time pressure. I would love to see a graph with more data.

If I remember correctly (and likely I don't), Lichess' accuracy score is based upon something like this.

If I remember correctly (and likely I don't), Lichess' accuracy score is based upon something like this.

@MyPunIsTwoWeek said in #2:

Interesting formula. We should expect higher volatility from a tactical player and from games under time pressure. I would love to see a graph with more data.

As I mentioned at the end, I did some tests and realised that it depended a lot on the opponents of the players and I wasn't quite sure how to account for this. But I'll look at the game volatilities of the players in Norway Chess to get some comparisons of the players when they are playing against the same opponents.

@MyPunIsTwoWeek said in #2: > Interesting formula. We should expect higher volatility from a tactical player and from games under time pressure. I would love to see a graph with more data. As I mentioned at the end, I did some tests and realised that it depended a lot on the opponents of the players and I wasn't quite sure how to account for this. But I'll look at the game volatilities of the players in Norway Chess to get some comparisons of the players when they are playing against the same opponents.

The symbolic math comes out clearer here than on substacks (i use dark background here, maybe that is why, besides that lichess expands images to fit width by default).

It makes them stand out..

At some point the symbol for the a-th root, can be just a fractional exponent with a parenthesis on the operand.

just a presentation preference I would suggerst if you are indeed going to explore different a.. which I find possibility.

A problem here is about the meaning of this.. What can we do with volatility_a. I am curious, and IDK.

Also, I wonder about using the turn as the clock here and not the half-turn... perhaps there is something I am not aware of, or understood about the purpose of this new quantity defintion. Maybe from lack of chess culture or whatever..

The symbolic math comes out clearer here than on substacks (i use dark background here, maybe that is why, besides that lichess expands images to fit width by default). It makes them stand out.. At some point the symbol for the a-th root, can be just a fractional exponent with a parenthesis on the operand. just a presentation preference I would suggerst if you are indeed going to explore different a.. which I find possibility. A problem here is about the meaning of this.. What can we do with volatility_a. I am curious, and IDK. Also, I wonder about using the turn as the clock here and not the half-turn... perhaps there is something I am not aware of, or understood about the purpose of this new quantity defintion. Maybe from lack of chess culture or whatever..

you could have a 2 player definition and integrate on all the pairing with same player if the tournament is not too streamlined in its tiering versus pool mixing at same tier... (sorry for my chess culture words missing, but I assume you can translate).

perhaps this is related to my question of clock tick definition.. the ply or the turn (I realize that turn might mean either turn or half turn, same for move... words are a pain).

you could have a 2 player definition and integrate on all the pairing with same player if the tournament is not too streamlined in its tiering versus pool mixing at same tier... (sorry for my chess culture words missing, but I assume you can translate). perhaps this is related to my question of clock tick definition.. the ply or the turn (I realize that turn might mean either turn or half turn, same for move... words are a pain).

Now thinking from far, (I just went AFK, so my eye gaze could do its thing in my mind's eyes as well, jerking (lack of english vocabulary) around free of external visual focus tyranny that typing imposes)

I think the name given to this definition seems to be about capturing not the accuracy but how that accurcay swings around. Averaging over the accuracy (how close to engine god ceiliing a single halt-move is), of each move would by design smooth over that information.

So we want to accumulate the swing information... I would suggest, given my training bias to first think derivative, and then discretization scheme of that.

this beintg a 2 person factors of swing potential, one should clarify what the question is.. The game full sequence accumulated swinginess, so not considering player differences (in variation, damn words across specialisations, not a chess variation here) but adding them, then one player contributiion to that swininginess or the other player..

this is vague, but I am trying to work from what we might be interested in, given my level of chess culture and my other background (and my current decline from that perhaps).

I also find that human games at my level at least, while I have some foresight thinking and plan shenanigans that seem to explain how my game went, has nothing to do wtih the engine ceiling point of view...

It seems the currency we are swinging at each other from that point of view is just errors upon errors.. and that the real dynamics is within those errors...

I find that this search for a definition or mettric of this more human behavior might be something to consider to further explain by other means in some future research..

start characterizing human play.. since we are stuck with oracle single number point of view about whole searches for each positions, how can this tunnel vision stuck on some ceiling tool help us, get to more human useful analytical tools or measures...

This is might sound crazy to some.. If I did manage to express my idea.. I suspect this might be similar to the authors intent, maybe not, in those words. probably not in those words.

My point about integrating on the second player variable over main games in the set of games (tournament, tier, pool?), would be about the question of player style perhaps, about answering other post question about tactical style (if that is well defined or further definiable, sort of... it could actually be part of the question to further define it, although I do not see the chess argument here, but I would need to learn, what is a tactical player). Why would a player who is thinking more in terms of tight tactical foresight, more than strategic target plans objective setting, or more positional instinct, result in .. I see by tactical one means agressive and lots of captures per unit time (ply).?

I think we need to discuss some chess here about this non engine typical human profilie when goggled from engine point of view..

Now thinking from far, (I just went AFK, so my eye gaze could do its thing in my mind's eyes as well, jerking (lack of english vocabulary) around free of external visual focus tyranny that typing imposes) I think the name given to this definition seems to be about capturing not the accuracy but how that accurcay swings around. Averaging over the accuracy (how close to engine god ceiliing a single halt-move is), of each move would by design smooth over that information. So we want to accumulate the swing information... I would suggest, given my training bias to first think derivative, and then discretization scheme of that. this beintg a 2 person factors of swing potential, one should clarify what the question is.. The game full sequence accumulated swinginess, so not considering player differences (in variation, damn words across specialisations, not a chess variation here) but adding them, then one player contributiion to that swininginess or the other player.. this is vague, but I am trying to work from what we might be interested in, given my level of chess culture and my other background (and my current decline from that perhaps). I also find that human games at my level at least, while I have some foresight thinking and plan shenanigans that seem to explain how my game went, has nothing to do wtih the engine ceiling point of view... It seems the currency we are swinging at each other from that point of view is just errors upon errors.. and that the real dynamics is within those errors... I find that this search for a definition or mettric of this more human behavior might be something to consider to further explain by other means in some future research.. start characterizing human play.. since we are stuck with oracle single number point of view about whole searches for each positions, how can this tunnel vision stuck on some ceiling tool help us, get to more human useful analytical tools or measures... This is might sound crazy to some.. If I did manage to express my idea.. I suspect this might be similar to the authors intent, maybe not, in those words. probably not in those words. My point about integrating on the second player variable over main games in the set of games (tournament, tier, pool?), would be about the question of player style perhaps, about answering other post question about tactical style (if that is well defined or further definiable, sort of... it could actually be part of the question to further define it, although I do not see the chess argument here, but I would need to learn, what is a tactical player). Why would a player who is thinking more in terms of tight tactical foresight, more than strategic target plans objective setting, or more positional instinct, result in .. I see by tactical one means agressive and lots of captures per unit time (ply).? I think we need to discuss some chess here about this non engine typical human profilie when goggled from engine point of view..

suggestion: grind the last post with some language crunching machine. It might make more sense than my own intended meaning anyway....

suggestion: grind the last post with some language crunching machine. It might make more sense than my own intended meaning anyway....

I do agree that if one is target characterization of the game sequence of half turns (sorry until I know for sure what turn etc.. means I will write in weirdness). not the player style or behavior over a pool of pairings, but the game characteristics aspect called here volatility (and what one might mean proposing such word, which does have other domain precise definition, like in stock market time series, or rating belief-probability densities, in glicko, but here we are searching for something meaningful in human chess thinking as traceable from played moves in single games.

Then I agree that using same rating pairs would reduce the number of factors of variation (floating uncontrolled noise).

so much verbiage. I have this floating variable of who might be reading my ramblings. This is not really like a real physical conversation where we know something about who is listening.... but we act as if it was. The internet illusion (worse with chat bots.. that is the epitomy of the illusion).

I do agree that if one is target characterization of the game sequence of half turns (sorry until I know for sure what turn etc.. means I will write in weirdness). not the player style or behavior over a pool of pairings, but the game characteristics aspect called here volatility (and what one might mean proposing such word, which does have other domain precise definition, like in stock market time series, or rating belief-probability densities, in glicko, but here we are searching for something meaningful in human chess thinking as traceable from played moves in single games. Then I agree that using same rating pairs would reduce the number of factors of variation (floating uncontrolled noise). so much verbiage. I have this floating variable of who might be reading my ramblings. This is not really like a real physical conversation where we know something about who is listening.... but we act as if it was. The internet illusion (worse with chat bots.. that is the epitomy of the illusion).

so how do you define xs(n) exactly? If it's a computer evaluation, then why do you call it "expected game score"?

so how do you define xs(n) exactly? If it's a computer evaluation, then why do you call it "expected game score"?