changing the pixel dimensions has no effect on file size. Am I missing something here?
Yep, some basic math.
Files size is measured in bits. So size will be determined by a fairly simple formula. Bits per second x number of seconds. That's it. Frame rate, resolution, interlaced or progressive, all are irrelevant.
There is some overhead with any file and that may vary with the type of file you're creating, such as an AVI or an MP4. But those differences will be fairly small. Bitrate x duration is the key to file size.
So there is no connection between the number of bits and the number of pixels?
There is, but only when dealing with codecs that don't have fixed or user-specified bit rates; visually lossless codecs would be one example, and so would uncompressed/raw formats. Such codecs/formats "use what they need" to encode to a specific quality level, rather than a given quantity (as in file size).
I guess I don't get it.
Here's a visual for you that might help explain it. Say you have a t-shirt that fits a 140-pound person perfectly well; the amount of material in that t-shirt is the bitrate of your encoded video. Let's say there is 2 yards of material in that t-shirt (I'm making this up); in video terms, let's say that is 2 megabits (mbps) per second. Now, a 600-pound sumo wrestler puts on that t-shirt. Do you have more t-shirt now to fit over the--ahem--larger frame (assuming the t-shirt hasn't ripped apart)? No--the t-shirt stretches, and the amount of material is exactly the same.
Now, think about the same in terms of bitrate: if you encode a frame of video that is 720x480 at 2mbps, that frame "weighs" the same as a 1920x1080 frame at 2mbps. You've limited the amount of "material" you have to work with (bitrate), so you're simply stretching it out over a larger frame. So long as the bitrate is the same, practically speaking, one video of a specific frame dimension will be the same file size as another video with different frame dimensions.
I thought that by redoucing the pixel dimensions I could make the file size smaller and thus easier for my clients to stream,
While the lesson of "datarate is datarte" is important, don't get distracted from Colin's original message of "don't worry" about file size. Vimeo is going to redo the video. Upload your large file. Vimeo will provide an appropriate rate.
I posted my comment before you posted this.
it seems like a smaller pixel count/size would give a better quality image.
For the same datarate, yes. but you are going to vimeo, and they will provide a useable datarate for your full frame. If you use a smaller frame size, Vimeo will not have the full size to work with. Your image will NOT look as good.
So we are capping how big the final file can be frame by frame. In that case it seems like a smaller pixel count/size would give a better quality image.
Yes, on both counts. Any time you see the word "rate" applied to something to do with video, you're dealing with an amount per unit of time. So, with "bit rate," you're saying "this is how much data I let my output video use for each division of time." If you're not changing the amount of data, and you're not changing the amount of time, the only qualitative difference you can make is to adjust the frame size; within these parameters, you're not making any quantitative (file size) changes.
I use the provided presets for Vimeo uploads and get quite good results; I recommend using them.