FATALITY said:
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Actually you got it wrong, the relationship is of inverse, not direct proportionality.
Anyhow, it depends on what part of the graphics pipeline is the most stressed. In general, if AA is at a level not too close to the GPU limits, it's more likely that HALF the number of polygons, at the same level of FX and quality, DOUBLE the framerate, otherwise, if AA is pumped to the max possible, max framerate will be roughly double at half the number of pixels and that means at roughly (1/sqrt(2))*linear resolution. More in general, fps will roughly go with the inverse of resolution, but it won't be that exact value. Also, at lower screen res, it will make sense to reduce the number of polygons, and the final compromise could be a double framerate at somewhat better than half the pixels. Many compromises are possible and some are better at lower res and some at higher ones, so, in general we can say that the realationship between number of pixels and fps is of inverse proportionality, but only if the other variables can be constrained at a constant value without making the GPU meet any bottleneck as res goes up and fps down, or vice versa, the relationship will be as simple as res*fps~=K.
PS And obviously all this applies as long as graphics RAM size and throughput are enough.








, so, if a compromise is unavoidable, I can almost always choose the one that's best for my needs or my tastes.