This is a bit more mathematical, but I know there are some smart guys on here. ATM straddle price = sqrt(2/pi) * S * vol * sqrt(t/T). where t = time to maturity and T = 1year in days and S = stock price This formula actually gives us the expected value of the trade. The expected value is = to the mean of a distribution. So why do people say a straddle tells us the expected standard deviation? Am I missing something? Thanks in advance.