Usually when I discuss a research paper in this blog, it’s because of some interesting chart I want to explore and remake. However, this paper, Cognitive foundations of chess performance in novice players, is remarkable because it has no charts at all. How is that possible?!
The study is about how well chess players can recall piece positions that they only saw for a few seconds. The interesting angle, which has been studied before, is how experienced players do better at recalling real game positions but are no better at recalling random positions. The study also considered a few cognitive tests in addition to chess ability. Their main model was to predict a player’s chess rating based on a cognitive test (Corsi Backward) and the number of pieces recalled correctly in each of the two conditions (real and random).
Perhaps the reason they didn’t include a chart was because they had three predictor variables. While it’s not feasible to plot the entire four-dimensional space, there are plenty of methods to look at slices of one or two variables at a time. Below is one, a Profiler plot from JMP, showing the response against each predictor. The light gray lines show how the fit’s profile moves across variation in the other predictors.
In this case, only one of the predictors has any statistically discernible effect of the response: the number of pieces correct in real chess positions. So they could have just graphed that one.
I’m more interested in the inverse question, anyway. How does chess Elo rating predict the number of pieces recalled correctly for the two conditions. Fortunately the paper did provide some data. It’s not the raw data for each trial but a summary of each participant’s 20 trials. Here’s the Number Correct vs. Elo.
It does show a potentially important result with performance accelerating for higher ratings. “Potentially” because it’s only three participants accounting for the uptick and the ratings are only rough estimates based on a ten-question chess quiz.
I found a paper for 2015, Recall of Briefly Presented Chess Positions and Its Relation to Chess Skill, which has a wider variety of players and with real Elo ratings. Here’s the same graph with that paper’s data.
While the basic structure looks the same, it’s interesting that the blue curve is now flat against real ratings. Both studies using similar positions (middle game positions with 2-25 pieces), but the participant groups were different. The first study used students who played chess and the second study had participants across all ages but generally older and higher rated than the first study.
Having a broader range of ages lets the age effect be examined.
Since age also looks significant, at least beyond 50, we can look at the interaction with a contour plot.
Interestingly, the paper did not find age to be a significant predictor, apparently because they on tested a straight line fit across all ages, which is generally flat.
