I feel that llama's graphs are really good, though it can't exactly distinguish time taken in making a good move from an ordinary move. You never know, someone who appears to "take a long time to think" could well be playing other games like Roblox or something else rather than focusing his time into chess.
Blueemu's accuracy then comes into play, but even then it's going to be hard to tell how a player would manage his time (apart from the obvious time taken based on llama's software).
I wonder, why does everyone seem to make so many fast moves in rapid? I never never instantly play a move in rapid unless it's opening theory or a line I've already calculated. Even if the opponent blundered mate in one I take a couple seconds to verify that it actually is mate.
Anyways, could you do my games? Any time control is fine.
I'm tellin' ya man, everyone looks the same. Doesn't matter if you think you take your time 
Here's your 600-some rapid games (I remove games with fewer than 10 moves and some other stuff, so the exact numbers wont match).
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About 39% of your moves were made in 3 seconds or less.
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I feel that llama's graphs are really good, though it can't exactly distinguish time taken in making a good move from an ordinary move. You never know, someone who appears to "take a long time to think" could well be playing other games like Roblox or something else rather than focusing his time into chess.
Blueemu's accuracy then comes into play, but even then it's going to be hard to tell how a player would manage his time (apart from the obvious time taken based on llama's software).
Being distracted doesn't matter. When I graphed my simul games it was the same shape (although longer times were more populated, i.e. a higher standard deviation).
The important idea is not that cheaters take more or less time, it's that they take a non-human amount of time. Meaning a very low standard deviation or bimodal graph.
As for what insights it can give us about time management, I think that's an interesting angle, especially for OTB. It seems that chess is a game where ~30% of moves are obvious enough to be played quickly. Knowing that might help set certain pacing benchmarks.
BTW one thing I haven't gotten to talk about is how I graphed the time for banned cheater's games, but instead of the cheater I graphed the time of the opponent. This was interesting because it was pretty much always bimodal with roughly equal peaks... and the 2nd peak was the same as the cheater's engine peak... the interpretation is that about half of the moves were played matching the opponent's pace.
Moves don't equal players, but my interpretation of this is that people tend to follow the opponent's pace, meaning in a game between two humans, the faster player will slow down a little, and the slower player will speed up a little. It's something obvious once you think about it, but once you're aware that (it seems) we all do this subconsciously, you might use that knowledge to consciously change your pace, either to manipulate your opponent's or to not be manipulated.
Given that I usually blitz out ten moves a game in the opening, yeah that makes sense. Why was I surprised lol, I was thinking about middle game positions where no one makes a move in 1 second
it flattens out kinda slowly though or is that just my imagination?
Yeah, your tail is a bit fat so to speak heh.
If they are mostly 10|0 games then you're a bit slower than average, but I'm guessing there were a fair number of increment games in there or in any case games longer than 10|0.
llama do you think you can give an example of a cheater's pace?
Post #44 is a really interesting one to me... shows a person playing honestly, but then as their rating gets higher they decide to mix in engine moves for a while, then they go back to playing honestly, then they cheat again, etc... at least that's my interpretation.
Here's a screenshot from my post (#44 in this topic) of when their graph turns bimodal (2 peaks)
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The other type of graph that I interpret as cheating has all the moves clumped together.
Here's a piece of a picture from when I was comparing "ted" to honest users (ted was eventually banned).
I color some of his graph red to show how 74% of his moves fell within a 3 second window (and I displayed some other graphs colored the same way so people could quickly see how this was not common).
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More goofing around. These are collections of 1000 blitz games, normalized, and I was wondering if an exponential PDF (in red) would be a good fit... it's not so good, but it's fun how consistent the shapes are.
The shape for @alphaous isn't as consistent... the equation for the red line is affected by the proportion of the highest blue bar... the higher the blue, the steeper the red. I was trying to get a good fit.
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Also, after looking at a handful of people like this, I have a silly theory 
Ok, so it's the lower your average moves per game, the more room you have for improvement.
Hikaru and I have a pretty high move / game average, so under my idea we can't improve much.
Noobs have like... a 20 move per game average (have you ever looked at a new player? It's probably more like 15 moves on average).
People in the middle seem to follow this trend... at least my whole 4-5 data points lol. It's an interesting idea anyway.
Also, after looking at a handful of people like this, I have a silly theory
Ok, so it's the lower your average moves per game, the more room you have for improvement.
Hikaru and I have a pretty high move / game average, so under my idea we can't improve much.
Noobs have like... a 20 move per game average (have you ever looked at a new player? It's probably more like 15 moves on average).
People in the middle seem to follow this trend... at least my whole 4-5 data points lol. It's an interesting idea anyway.
I play Danish gambit in which opponent gets checkmated in 18 moves. I know once I pass a certain threshold my opponents will punish me badly for giving away central pawns so easily.
Also, after looking at a handful of people like this, I have a silly theory
Ok, so it's the lower your average moves per game, the more room you have for improvement.
Hikaru and I have a pretty high move / game average, so under my idea we can't improve much.
Noobs have like... a 20 move per game average (have you ever looked at a new player? It's probably more like 15 moves on average).
People in the middle seem to follow this trend... at least my whole 4-5 data points lol. It's an interesting idea anyway.
I play Danish gambit in which opponent gets checkmated in 18 moves. I know once I pass a certain threshold my opponents will punish me badly for giving away central pawns so easily.
Yeah, I mean... some people have risky openings, and some people like boring safe games that reach an endgame, so my idea might not be very good hah.
But I thought it was interesting.
Mine please!
i dont play frequently at all but why not lol(rapid)
Rapid games.
The animation isn't very long with only 190-ish games.
very jumpy is the animation
also the height of the move bars grows with the rating bar and doesnt change shape, but premoves go way down(since i disabled premoves in the middle)
i dont play frequently at all but why not lol(rapid)
Rapid games.
The animation isn't very long with only 190-ish games.
start charging 5 dollars per person, haha
i dont play frequently at all but why not lol(rapid)
Rapid games.
The animation isn't very long with only 190-ish games.
start charging 5 dollars per person, haha
Heh 
I'm kinda having fun with this. Maybe this week I'll make a goal of automating the download process.
i dont play frequently at all but why not lol(rapid)
Rapid games.
The animation isn't very long with only 190-ish games.
start charging 5 dollars per person, haha
Heh
I'm kinda having fun with this. Maybe this week I'll make a goal of automating the download process.
Thanks again for doing this! These graphs are so much fun that you might be able to pitch these to Chess.com as a feature, for a small fee of course.
i dont play frequently at all but why not lol(rapid)
Rapid games.
The animation isn't very long with only 190-ish games.
start charging 5 dollars per person, haha
Heh
I'm kinda having fun with this. Maybe this week I'll make a goal of automating the download process.
Thanks again for doing this! These graphs are so much fun that you might be able to pitch these to Chess.com as a feature, for a small fee of course.
They're pretty big dorks when it comes to upgrading things, but the code to maintain a website on several platforms is enormously harder than this. They're not going to pay me for something they could write in under an hour
And as for using statistics to find dishonesty, they've invested into that too, and have a good system. One big drawback of what I'm enjoying is it requires lots of games.
i dont play frequently at all but why not lol(rapid)
Rapid games.
The animation isn't very long with only 190-ish games.
start charging 5 dollars per person, haha
Heh
I'm kinda having fun with this. Maybe this week I'll make a goal of automating the download process.
Thanks again for doing this! These graphs are so much fun that you might be able to pitch these to Chess.com as a feature, for a small fee of course.
They're pretty big dorks when it comes to upgrading things, but the code to maintain a website on several platforms is enormously harder than this. They're not going to pay me for something they could write in under an hour
And as for using statistics to find dishonesty, they've invested into that too, and have a good system. One big drawback of what I'm enjoying is it requires lots of games.
Makes sense. If they are able to code the immensely complex Insights feature, then this should be no problem for them. No offense, of course, as what you're doing is absolutely awesome.
I wonder, why does everyone seem to make so many fast moves in rapid? I never never instantly play a move in rapid unless it's opening theory or a line I've already calculated. Even if the opponent blundered mate in one I take a couple seconds to verify that it actually is mate.
Anyways, could you do my games? Any time control is fine.
Imagine you are already up in material. Your opponent does not wish to resign, but wishes to play to mate. Say this happens.
(Edited)
You have a pretty obvious checkmate here. Well...who won't blitz out the moves? But in blitzing out the moves, we added the number of "fast moves" made in rapid to the tally. As such, we tend to have more "fast moves" than others because of this.
Also, not everyone treats rapid equally. Some wish to play seriously (living example: you). Some wish to play it just like blitz (living example: me). And others view it in perhaps yet another manner.
Still, I'm sure your graph will look similar to mine since llama already disproved my thoughts of having a unique graph.