We compute the error of lifting a plane by looking at the new vertices would be generated outside of the current polyhedron. For each vertex that would be added we compute its minimum distance to the current polyhedron. The maximum of these distances is the error measure for the candidate plane. This can be seen in the side view of Figure 1. The amount of simplification that can be made to an object depends on the shape of the object and on how much error will be tolerated.
Many objects have lots of room for improvement.
The original convex hull has 176 planes, the simplified version has only 12. The performance improvement provided by using a simplified convex polyhedron depends on the application where it is used. There is not always a linear gain. Therefore the performance gain will only be proportional to the square root of the amount of mesh simplification. Highly optimal techniques such as V-Clip leave even less room for improvement.