An intuitive fit measure for a binary choice / logistic regression model

Hi,

I am looking for an intuitive fit measure for a binary choice /
logistic regression model. Is there anything similar to R^2 for
logistic regression? One possibility is this:

R^2 = 1 - sum (y_i - phat_i)^2 / sum (y_i - pbar)^2

where y_i is 0 or 1 depending on the outcome; phat_i is the predicted
probability; and pbar is the number of times the even occurred divided
by the number of observations.

While this seems to make sense to me, I have never seen this used, so
I am wondering if there is some reason that this cannot be used.

Besides this idea, are there other measures that are actually used?

Thanks.

.

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