how accurate is the bom?

Often when involved in an important outdoor event, I'll check the weather on BOM 3-4 days out and then check it again each day until the actual day itself.

I find that (on the eastern seaboard) when rain is predicted, or not, 3-4 days out from an event, the predictions are very often completely wrong. The BOM will obviously refine their predictions each day until the actual day/time of the weather, when it is obviously accurate, because that is actually what is happening.

Last week was a great example in Sydney, where the heavy rain was predicted to begin on Thursday and then to continue building through the weekend. What ended up happening was that we did not really see any rain on Thursday and only spots during the day on Friday - obviously it finally hit the fan on the weekend.

Clearly the BOM have a difficult job and certain areas (e.g. Sydney) in close proximity to the ocean and also enclosed by mountains, make weather prediction difficult and obviously there is also far more to the BOM than predictions of rain or shine, but with annual BOM budgets in the $100's of millions, I'm wondering just how much is spent on the sorts of predictions that end up being a toss of a coin.

I wonder if there is a site that graphs how accurate the rain/sunny BOM predictions are X days out from the actual date? Would be interesting to see just how accurate they are, particularly when it comes to predicting rain when it ends up being sunny and vice versa.