How do value investors deal with the analytical necessity to predict the unpredictable?

The only answer is conservatism. 

Since all projections are subject to error, optimistic ones tend to place investors on a precarious limb.

Virtually everything must go right, or losses may be sustained.

Conservative forecasts can be more easily met or even exceeded. 

Investors are well advised to make only conservative projections and then invest only at a substantial discount from the valuations derived therefrom.