I have studied recent ATLAS plots that compare binned MC data to the pdf that is fitted unbinned to the same MC data. For pdfs with a peaking structure, like a Gaussian or Crystal Ball function, there is a characteristic and very annoying wiggle in the residuals, which is quite unnecessary. In addition, the large residuals contribute to unrealistically large values of \chi^2. The \chi^2 is not used in the unbinned fits, so this is a presentation problem rather than a fitting problem.
I think I have traced the source of the large values of \chi^2 to a few lines of code in RooCurve::chiSquare and RooCurve::average. If I have understood the code correctly, the data in each histogram bin is compared to a trapezoidal approximation of the integral of the fitted pdf in that bin, where each bin is split in two and separate trapezoids for each half-bin are integrated. This gives an effective weighted average of I= { \Delta x\over 2}{(y_l+2y_c+y_r)\over 2}, where \Delta x is the bin width and y_i,y_c, y_r are the respective values of the pdf at the left edge, center, and right edge of the bin.
The residuals (and \chi^2) can be reduced by 1-2 orders of magnitude (the only way to eliminate the bias in the residuals is with a precise integral of the pdf per bin) by using a slightly different weighted average, the one given by Simpson’s 1/3 rule: I = {\Delta x\over 6} (y_l + 4y_c + y_r). It would not require very much coding or computational load to implement this.
I presented this in December at an ATLAS Plenary statistics meeting and got support from the ATLAS Statistics Committee to propose this improvement. There is no real data in my presentation, so I can ask ATLAS if it is OK to share my slides here, if that would be helpful.
Cheers, Alex Read (Oslo)