Grandmasters blunder more often than this. I would venture to say that what correlates with blunders more so than rating is time. Error rate goes way up in Blitz and Rapid.
IMO the more interesting thing about chess skill at the top is how much way way better GMs are than everyone else.
To me, ratings at the top feel more like an exponential scale than a linear one. For example, I have beaten International Masters at chess lots of times but have never once beaten a GM.
If I studied or cared (which I don't), I think maybe it would be possible to squeeze out a lucky win once in awhile. Aspiring to be a punching bag isn't a very appealing notion though, so you can understand my lack of motivation. GMs are crazy good.
ELO ratings are constructed such that skill differences are invariant across the entire scale. A person who plays someone 200 ELO points lower is expected to win 76% of the time.
Could this analysis be a lower bound? I'm not familiar with Crafty, but given that all the games were annotated in 6 hours of wall-clock time, this analysis can't be going extremely deep into the game-tree. There may be many more moves which would qualify as blunders if analyzed as deeply as Regan's work in the other comment.
>To me, ratings at the top feel more like an exponential scale than a linear one. For example, I have beaten International Masters at chess lots of times but have never once beaten a GM.
If true this is purely psychological. You are unable to beat a GM because he's a GM and you think you're unable to beat GMs.
The strength difference between IMs and GMs simply isn't that great. Because the GM title is based on results and not ratings there are frequently IMs who are higher rated than GMs.
I think you are citing the exception(s) to the rule. Most GMs are stronger than IMs imo. I don't think it's psychological. I have played players (GM and otherwise, including other untitled players like myself) that I know are so much better than me because they win and I can't even comprehend how they arrived at making the moves that they did.
As an aside, this is kind of an issue I have with chess analysis. A computer can 'verify' that a certain move is good or bad. That's fair enough. But in the past I have seen players (of lower skill level to me) discuss analysis in for example, a battle between two bigname players.
I have sometimes wondered if these discussions are truly honest because I have seen moves made by top players that I don't even understand how they arrived at the process of deciding that was the correct move vs others. Excluding GMs, a human simply cannot prune the game tree at depth like a computer can. So discussing a few tiny branches of the game tree like one is correct and the others aren't just seems really silly for the rest of us.
Time definitely plays a huge roll in blunders. Actually if you look at the first graph there's a spike in blunders around 2800 which is entirely due to a single GM (Caruana) playing a string of blitz games this year in which he made several blunders.
Blitz games? Is your data from Blitz games played on an online server?
I like the idea of your research, but blitz games are garbage and online ratings are frequently meaningless due to abuse.
You should also look at replacing Crafty with Stockfish. Stockfish is still open source and it's around 350 points higher than Crafty which is a huge amount at this level.
IMO the more interesting thing about chess skill at the top is how much way way better GMs are than everyone else.
To me, ratings at the top feel more like an exponential scale than a linear one. For example, I have beaten International Masters at chess lots of times but have never once beaten a GM.
If I studied or cared (which I don't), I think maybe it would be possible to squeeze out a lucky win once in awhile. Aspiring to be a punching bag isn't a very appealing notion though, so you can understand my lack of motivation. GMs are crazy good.