He doesn t know. There is no magical formula available to him. Fed policy in an age of financial deregulation is such that he can t even know for sure just how much money and credit a small action by the Fed will create. It depends on the lending decisions of banks, the borrowing decisions of consumers and investors, and a hundred other factors. The only way to know for sure is to examine the money supply after the fact, and even that is rather difficult to do because there are many different ways to measure it.
All central planning is hard because central planners are attempting to do what is impossible.
They are operating outside the free market and therefore lack the basic signals like profit and loss that guide the decisions of private entrepreneurs. It enters the economy through the capital markets and spurs production in a way that would otherwise be unjustifiable. This creates an unsustainable economic boom that begins in a few sectors and then spreads to create a kind of euphoria. During the 1990s, the Fed had come to believe in its own infallibility. We all know investors who became heady in the 1990s, attributing their massive profits to their own personal savvy instead of the phenomenal bull market.