In general I say the more metrics the better. I did not see the boards, here, (I could go look, but I am going to talk generally). But it was nice that there was not domination early that got compounded at least not of the direct immediate measures (some of which derived from many games behind the sources tools in some of the function graphs). I still have a problem with heatmaps because they are not about the interactions networks of the pieces, and more about their location stability or not. Well, it is something to know for sure what things were more transient in location than others for sure. I can't vote on any. I think it is more interesting to look at all of them in parallel. Perhaps some superimposition visualization (nothing in mind, just was curious at some point to align more than one function in one figure. Although the persistant abscissa scale of the move number allowed some visual memory above and below to work well.
My point about heatmap (which is about each movable actors localisation dynamic density through whole game, if i got it right), lacking the interaction aspect, is possibly related to the follow reaction i had reading this:
"After move 45 Nepo’s piece activity was again higher (the material imbalance might be a reason for this) even though Carlsen was the one playing for the win."
As the game progressed, one can think of a gaz of 32 points that gets loose at time=0, and while the players may have plans, it is clear that the maximal crampiness will have to lose its minimal energy or maximal order or lack of mingling "information" (not talking about move sequence surprise or information here, but the board location 32 point set). In that sense, it might be that activity with the pressure bias metric being on the other territory and the king safety donut or zone (or where it might have more probabllities of going, one could talk about leading the ulitmate target at slow chess turn by turn time), might lose its total imbalance on the player to player axis (sorry but I am prudent with the word imbalance, so talking weird than might be needed, i also do not know the most usual word for that dimension which is an elephant in the discourse, not horizontal not exactly vertical but yes related, but not just of the plan dimensions). lots of ramblinjg....
So my point is that activity on the empty board, even if piecewise weighted, might be more of an early or middle game dpeth thing, as some point you might want metric of inter-mingling as it might refine notion of "space" under control. depending on the position nature.. long range highways, versus many pawn obstacles. Or bring in your not exactly turn by turn path likelyness (my word) single piece paths (not heatmap, or do they help with that). you could then modulate the 16x16 acitivity vector by the now more informed 64 small square desirablilty "density".. Sorry i come from continuous time and mostly continuous space dynamical system modelling. but that should not stop me making some sense in this discrete space and distrete time problem. I hope I do make some sense. enough to suggest the reader (and author) own better thinking about this.
I also think that some way to visualise the interaction between pieces would be better than the individual heatmaps, but I don't know what works best in this regard.
As for the activity, there are certainly problems with using it for positions with a material imbalance. I guess that one would need to look at a lot of different positions, assign them an activity score beforehand based on human reasoning and then tune the activity function to do something similar. But I currently don't have the time to do that detailed testing, so I'll have to stick to the primitive formula. I hope that I can revisit it in a couple of months when I have more time for it.
I do like this post a lot! A few thoughts: it might be useful to break accuracy into three numbers, one each for opening/book, mid game and endgame. Magnus is known for pulling endgames out of nowhere and I think that would correspond with a high accuracy, while if both players know the first twenty moves of whatever opening they are playing by heart, that will inflate the overall accuracy.
To capture more of the spirit of the game as it was played, looking at time spent per move by each player would be curious to me. Does number of possible piece moves correlate with time spent thinking? Or does depth of the primary variation sequence correlate with time spent thinking?
I like seeing the number of piece moves a lot. Something I’ve experimented with is viewing that number as something number of candidate moves, or number of possible choices open to the player. Going further, you can break each possible move into blunder best mistake etc and show the variety of options available to a player. If there is fifty moves and only one of them is playable, vs there is fifty moves and half of them are all playable with different characteristics, that’s interesting to see!
Love these posts and look forward to more of them! wdl graphs really give a good sense of the game to me.
Looking at the time spent after each move is also interesting. I didn't do it until now since it only works for games where one has the time stamps, which excludes most games played a couple of years ago. But I'll certainly include it for my analysis of current games.
In general I say the more metrics the better. I did not see the boards, here, (I could go look, but I am going to talk generally). But it was nice that there was not domination early that got compounded at least not of the direct immediate measures (some of which derived from many games behind the sources tools in some of the function graphs). I still have a problem with heatmaps because they are not about the interactions networks of the pieces, and more about their location stability or not. Well, it is something to know for sure what things were more transient in location than others for sure. I can't vote on any. I think it is more interesting to look at all of them in parallel. Perhaps some superimposition visualization (nothing in mind, just was curious at some point to align more than one function in one figure. Although the persistant abscissa scale of the move number allowed some visual memory above and below to work well.
My point about heatmap (which is about each movable actors localisation dynamic density through whole game, if i got it right), lacking the interaction aspect, is possibly related to the follow reaction i had reading this:
"After move 45 Nepo’s piece activity was again higher (the material imbalance might be a reason for this) even though Carlsen was the one playing for the win."
As the game progressed, one can think of a gaz of 32 points that gets loose at time=0, and while the players may have plans, it is clear that the maximal crampiness will have to lose its minimal energy or maximal order or lack of mingling "information" (not talking about move sequence surprise or information here, but the board location 32 point set). In that sense, it might be that activity with the pressure bias metric being on the other territory and the king safety donut or zone (or where it might have more probabllities of going, one could talk about leading the ulitmate target at slow chess turn by turn time), might lose its total imbalance on the player to player axis (sorry but I am prudent with the word imbalance, so talking weird than might be needed, i also do not know the most usual word for that dimension which is an elephant in the discourse, not horizontal not exactly vertical but yes related, but not just of the plan dimensions). lots of ramblinjg....
So my point is that activity on the empty board, even if piecewise weighted, might be more of an early or middle game dpeth thing, as some point you might want metric of inter-mingling as it might refine notion of "space" under control. depending on the position nature.. long range highways, versus many pawn obstacles. Or bring in your not exactly turn by turn path likelyness (my word) single piece paths (not heatmap, or do they help with that). you could then modulate the 16x16 acitivity vector by the now more informed 64 small square desirablilty "density".. Sorry i come from continuous time and mostly continuous space dynamical system modelling. but that should not stop me making some sense in this discrete space and distrete time problem. I hope I do make some sense. enough to suggest the reader (and author) own better thinking about this.
I also think that some way to visualise the interaction between pieces would be better than the individual heatmaps, but I don't know what works best in this regard.
As for the activity, there are certainly problems with using it for positions with a material imbalance. I guess that one would need to look at a lot of different positions, assign them an activity score beforehand based on human reasoning and then tune the activity function to do something similar. But I currently don't have the time to do that detailed testing, so I'll have to stick to the primitive formula. I hope that I can revisit it in a couple of months when I have more time for it.
Interesting concepts, love the data viz, as always!
I do like this post a lot! A few thoughts: it might be useful to break accuracy into three numbers, one each for opening/book, mid game and endgame. Magnus is known for pulling endgames out of nowhere and I think that would correspond with a high accuracy, while if both players know the first twenty moves of whatever opening they are playing by heart, that will inflate the overall accuracy.
To capture more of the spirit of the game as it was played, looking at time spent per move by each player would be curious to me. Does number of possible piece moves correlate with time spent thinking? Or does depth of the primary variation sequence correlate with time spent thinking?
I like seeing the number of piece moves a lot. Something I’ve experimented with is viewing that number as something number of candidate moves, or number of possible choices open to the player. Going further, you can break each possible move into blunder best mistake etc and show the variety of options available to a player. If there is fifty moves and only one of them is playable, vs there is fifty moves and half of them are all playable with different characteristics, that’s interesting to see!
Love these posts and look forward to more of them! wdl graphs really give a good sense of the game to me.
Thanks for all the suggestions!
Splitting the accuracy is a really good idea.
Looking at the time spent after each move is also interesting. I didn't do it until now since it only works for games where one has the time stamps, which excludes most games played a couple of years ago. But I'll certainly include it for my analysis of current games.
Looking forward to the next one!
Nice work! Now maybe try collab orating with a coach to see how these graphs could help us mortals improve our game? :)
Oops, I accidentally hit WDL for both the most and the least useful graphs 🙈