R2 is more simply explained as the share of the error variance explained by the model out of the share of the error explained by the best guess, which is, in this case 0.5.
Guessing 0.5 will have you wrong wrong by 0.5 100% of the time. SST is 25 for a 100 sample example.
Guessing 0.55 for the 0.55 state will have you wrong by 0.45 55% of the time and 0.55 45% of the time for the other. SSE is 24.75
1- 24.75 / 25 = 0.01
Looking at it this way it’s not too hard to see why the R2 is bad. It barely explains any more difference in the individual behavior than the basic guess.
R2 is not a great metric for percentages or classification problems like this.
> Looking at it this way it’s not too hard to see why the R2 is bad. It barely explains any more difference in the individual behavior than the basic guess.
Right. R² is 1% because the prediction is bad - only marginally better than the basic guess.
> R2 is not a great metric for percentages or classification problems like this.
Using a different metric won't improve the prediction.
Is the Brier score a great metric for problems like this?
The Brier score for the model is 0.2475.
The Brier score for the "basic guess" is 0.25.
The improvement in the Brier score for the model relative to the basic guess is 1%.
Guessing 0.5 will have you wrong wrong by 0.5 100% of the time. SST is 25 for a 100 sample example.
Guessing 0.55 for the 0.55 state will have you wrong by 0.45 55% of the time and 0.55 45% of the time for the other. SSE is 24.75
1- 24.75 / 25 = 0.01
Looking at it this way it’s not too hard to see why the R2 is bad. It barely explains any more difference in the individual behavior than the basic guess.
R2 is not a great metric for percentages or classification problems like this.