Hi John,
I'll be honest--this question is a difficult one for me, but I'll attempt to answer it to the best of my ability. The number of sprites that can be rendered on the screen has many different variables to consider.
For reference, keep in mind that a bitmap is just a list of bits (or bytes technically) that represent certain colors in a specific order; whereas a sprite is an object that references the bitmap to have some sort of appearance onscreen with a set of coordinates, as well as a few other features.
First we have to consider a few things about the bitmap itself. Bit depth and resolution are the main contributors here in terms of size. 16-Bit bitmaps of a certain resolution will always be two times larger than an 8-Bit bitmap of the same resolution. Then we must consider the resolution of each individual bitmap as this will impact how many bits will be used by said bitmap. If you would like to figure out the size of a specific sprite you are working with, you can use Arduino's built in sizeof() function which returns the number of bytes that a specific instance of a data type or object is using.
Now we can look into actual sprites rather than bitmaps. There is a possibility of all sprite objects having unique bitmaps, therefore causing significantly more memory to be used as the number of sprites increases. There is also the possibility of having multiple sprite objects use the same bitmap (such as identical enemies onscreen). If the latter is the case, then each sprite doesn't use as much total memory as mentioned in the former. Technically, all sprite objects are the same size; however, by reusing bitmaps for these sprites, you will decrease the overall memory footprint.
I hope you can understand why this question is rather difficult for me to answer, as there are many possible variances that impact the answer to your question.
If you are curious as to how much program storage space is still available on your TinyArcade, you can go to File > Preferences within the Arduino IDE, and select the check-boxes under "Show verbose output during" and next to "compilation" and "upload" then click "OK" to save these changes. Now whenever you verify or upload your sketch, the IDE will tell you what percentage of memory space was used.
Although I wasn't able to fully answer your question, I hope that this in some way assisted you in understanding some of the limitations of the TinyArcade hardware. Overall, you shouldn't have to worry too much about it.
-Hunter
