But this does not give us an overall view. The Lottery company might wish to have a view about an expected win each week. Expectation in statistics is about taking a long term view of average likelihood. The Lottery company expects, over the long term, a certain 'average' weekly win. Insurance companies expect an 'average' rate of claims.
Investment companies expect an 'average' return on their portfolios.
Expectation theory is a way of giving a measure to our long term expected outcomes of uncertain events.