Expectancy is the feeling in the air when everyone knows something is coming. It is waiting plus a little lean-forward — usually pleasant or exciting, sometimes just tense. It is an uncountable, rather literary word, and it almost never stands alone: you meet it in 'a feeling of expectancy', 'an air of expectancy', 'the room was full of expectancy'. You would find it in a novel or a news report describing a crowd, not in a text message to a friend. The other place you will meet this word — and honestly it is the more common one — is inside the fixed phrase 'life expectancy', which means how many years a person is expected to live. There the word has no feeling in it at all; it is a cold statistic. Same word, two lives: one poetic, one from a government report. Note also that 'expectancy' is the feeling of waiting, while 'expectation' is the particular thing you think will happen ('my expectation was that she would win'). English keeps both, and they are not swappable.