# Is a logit model with a pseudo-R^2 of less than 0.5 a worse model than a coin toss?

I have recently encountered the remark that if a logit model's pseudo $R^2$ is lower than $0.5$ the result is completely worthless because a coin toss is a better model. Is this interpretation correct? If not, what is wrong with it?

$R^2 = \frac{\text{#Correct}}{\text{Total count}}$

• This would depend on your definition of your pseudo R^2. For example, are you using a Count R^2? Efron's? McFadden's? The choice affects the interpretation. Mar 27, 2015 at 14:57
• That would be the plain count $R^2$. Mar 27, 2015 at 15:06
• Plain count R^2 is number correct out of total. So if your model gets the answer right less than 50% of the time, then I'd agree with that interpretation if you are basing decisions off of rounding the outcomes to binary responses, e.g. p < 0.5 versus p>=0.5. However, the model provides more information than a coin flip in that perhaps near p = 0.5 your decision is a third response, e.g. that the results are indefinite. In some cases this would improve overall results. Mar 27, 2015 at 15:11