Advance paid rates are supposed to be cheaper, but they are not always: if the hotel thinks that it will have a massive demand for a specific date, rates might be high (and sometimes get much cheaper a few days before the actual date, if the hotel has rooms left and demand is not so high).

I am not quite sure than booking more than one year in advance is a good strategy, as yield management is not precise at that time (read: the hotel cannot precisely forecast the demand, and might be tempted to have a higher rate than 2-3 months in advance).