We discuss some properties of the point spread distribution, defined as the distribution of the difference of two independent binomial random variables with the same parameter n in- cluding exact and approximate probabilities and related optimization issues. We use various approximation techniques for different distributions, special functions, and analytic, combi- natorial and symbolic methods, such as multi-summation techniques. We prove that in case of unequal success rates, if these rates change with their difference kept fix and small, and n is appropriately bounded, then the point spread distribution only slightly changes for small point differences. We also prove that for equal success rates p, the probability of a tie is min- imized if p = 1/2. Numerical examples are included for the case with n = 12.