Can we get an approximate formula to convert CAPS to estimated elo? I'm trying to work one out, but don't have a really great one yet. If I find some sort of secret sauce I might write a blog post about it.
This is the old system when it came out but the new Game Review changed things.
https://www.chess.com/article/view/better-than-ratings-chess-com-s-new-caps-system
Can we get an approximate formula to convert CAPS to estimated elo? I'm trying to work one out, but don't have a really great one yet. If I find some sort of secret sauce I might write a blog post about it.
This is the old system when it came out but the new Game Review changed things.
https://www.chess.com/article/view/better-than-ratings-chess-com-s-new-caps-system
Yeah I know, but those are guidelines and not a (approximate) formula.
Using the table you can do a linear regression. You get Estimated rating= CAPS*60.2-3375
Btw, using linear regression is pretty problematic for this.
Notice that the formula would give you a rating of -3375 at 0% accuracy which makes very little sense. In fact, any accuracy below 56% gives a negative rating. Basically, this model gives a horrible downward skew to values lower than the dataset chesscom provided.
It is better to model with a polynomial recognizing that no elo values less than 0 should be given. This gives you something more like
Re = 2.05+12.9*Acc-0.256*acc^2+0.00401*acc^3.
Where Re is the estimated rating and Acc is the CAPS accuracy score. This seems to be a much better conversion.
This model is still pretty imperfect and pretty far from Chesscom's data right at 1200 elo, however, it seems like a much better overall model.
Hey @ScootyMcScrooty
Above is what I came up with. It isn't super accurate, but I haven't found anything better. However, as Martin indicated, this probably doesn't mean much anymore as chess com has changed the way things are calculated.
Using the table you can do a linear regression. You get Estimated rating= CAPS*60.2-3375
Btw, using linear regression is pretty problematic for this.
Notice that the formula would give you a rating of -3375 at 0% accuracy which makes very little sense. In fact, any accuracy below 56% gives a negative rating. Basically, this model gives a horrible downward skew to values lower than the dataset chesscom provided.
It is better to model with a polynomial recognizing that no elo values less than 0 should be given. This gives you something more like
Re = 2.05+12.9*Acc-0.256*acc^2+0.00401*acc^3.
Where Re is the estimated rating and Acc is the CAPS accuracy score. This seems to be a much better conversion.
This model is still pretty imperfect and pretty far from Chesscom's data right at 1200 elo, however, it seems like a much better overall model.
Hey @ScootyMcScrooty
Above is what I came up with. It isn't super accurate, but I haven't found anything better. However, as Martin indicated, this probably doesn't mean much anymore as chess com has changed the way things are calculated.
I actually checked it out earlier with some data I got, that works fairly well for ratings between 1600 and 2800 but I am confident I have found a better way. I'll write a post when I cook something up! My goal is a working function for ratings between 1000 and 3000 over a sufficiently large number of games.
Using the table you can do a linear regression. You get Estimated rating= CAPS*60.2-3375
Btw, using linear regression is pretty problematic for this.
Notice that the formula would give you a rating of -3375 at 0% accuracy which makes very little sense. In fact, any accuracy below 56% gives a negative rating. Basically, this model gives a horrible downward skew to values lower than the dataset chesscom provided.
It is better to model with a polynomial recognizing that no elo values less than 0 should be given. This gives you something more like
Re = 2.05+12.9*Acc-0.256*acc^2+0.00401*acc^3.
Where Re is the estimated rating and Acc is the CAPS accuracy score. This seems to be a much better conversion.
This model is still pretty imperfect and pretty far from Chesscom's data right at 1200 elo, however, it seems like a much better overall model.
Interesting. So for a beginner who is looking for CAPS numbers to shoot for on a ratings climb, what would the average CAPS be for typical 800, 900, 1000 and 1100 estimated ELO players? Asking for a friend.
800 would be 63%
900 would be 66%
1000 would be 69%
1100 would be 72%
Note that these are approximate and may not really apply since they've updated the way CAPS is calculated.
I have played around with this to make a conversion chart, which is very approximate. As you know, at times the 'Learn' menu or cell app games are missing ratings. Full disclosure, I used the CAPS conversion charts from Chess.com but they omit the low end, which I populated with some of my worst Game Review scores from very sleepy or distracted times. To validate it I compared the scores to a polynomial regression (English: Curvy line fitted to data. On Excel: Insert Scattergraph, Rightclick a dot, Add trendline, Select Polynomial, and Add Equation). The equation is y = 0.0057x^3 - 0.584x^2 + 36.34x - 646, where if you make a table with x column is Accuracy, it gives you y, CAP. Otherwise, I did not recheck anything.
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If you use the data to make a graph, it looks like this, dotted line being the polynomial.
Please don't beat me up over any inaccuracy or if you don't like it, just sharing in case useful.
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That's really only useful for the old calculations. The current version uses a much different metric that does not tie into rating so much, but can be influenced by it (accuracy is more forgiving for lower rated players). Most players are going to get between 65-90% in most of their games.
https://support.chess.com/en/articles/8708970-how-is-accuracy-in-analysis-determined
Can we get an approximate formula to convert CAPS to estimated elo? I'm trying to work one out, but don't have a really great one yet. If I find some sort of secret sauce I might write a blog post about it.