There will not be one optimal size. Each affiliate will have their own needs.
Here is a list of the common sizes: http://designerstoolbox.com/designresources/banners/
I find it most helpful to send out a survey monkey poll to affiliates directly. I'd also ask your top affiliates directly. Don't rely on stats from the network panel, as many affiliates will strip off the banner and use the URL for a text link, which will skew the reporting.
Once you decide on the best sizes for your affiliates. Change your banners at least once a quarter. Ideally, create themed banners for each holiday. Changing banners frequently will drive more clicks and sales.