binomial standard deviation with weights

I'm trying to figure out the standard deviation for a football pool. Assuming the probability of success is .5 for all games which are either won or lost on the point spread. There are weights assigned to each game: 16, 16, 12, 12, 12, 10, 10, 10, 7, 7, 7, 7, 4, 3, 2, 1. The expected value is 68 (half of the total points. But what would the standard deviation of the total score be? The SD of wins is two, but if I take the average of the points above I would get a lower SD, correct? Thank you.