
You're quite right; assuming normal fertility, the size of the litter is determined by the number of eggs the bitch releases and whether the mating/s are at the optimum day. One mating on the right day (which varies from bitch to bitch and season to season) will produce the maximum number of pups, but if it's too early or too late then it won't. That's why many people opt for repeated matings every two days for as long as the bitch will stand to ensure they catch the right day.
The dog releases millions of sperms each time, and those in the second or third matings will be 'fresher' and possibly more potent.