We have developed new parameters that help to interpret multi-angle reflection data. By expressing measurement geometries in terms of so-called flake-based parameters, a physical explanation is given for several well-known colorimetric characteristics of effect coatings. The new concepts are based on expressing angles with respect to the normal vector of flakes, instead of the conventional usage of the coating normal as a reference. We discuss and give physical explanations for the usefulness and limitations of previously defined concepts such as aspecular angle, cis-versus trans-geometries, interference lines and aspecular lines. For example, it is known that the trans-15 degrees geometry has added value next to the cis+15 degrees geometry when samples are analyzed that contain colored effect pigments with large color travel, such as Colorstream, Chromaflair, or chromatic Xirallic pigments. Our results demonstrate and explain why there is much less added value in the case of samples that contain less striking chromatic effect pigments, such as metallic or mica-based effect pigments, or "white" Xirallic pigments. Further, interference lines are shown to be suitable for characterizing effect pigments because they selectively sample the reflectance values of flakes as a function of the angle of incidence with respect to the flake normal. In another example, the similarity between an off-plane measurement geometry and several in-plane geometries is investigated. The results are clearly explained when referring to the corresponding values of the flake-based parameters. (C) 2011 Wiley Periodicals, Inc. Col Res Appl, 37, 186-198, 2012; Published online 13 July 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/col.20679