Ever heard the phrase 'generals are always fighting the last war'? It's poignant applied to France and Britain's strategy during the Second World War, when they assumed, based on WW1, that the advantage would always be to the side using a defensive strategy. That's why they constructed the 'Maginot Line' and refused to attack Germany.
Have you heard the proverb 'the past is a foreign country, they do things differently there'? This has the opposite lesson to Hegel's dictum which was posted above: that you can't just assume that the present is 'like' the past and use it to teach you lessons about what to do.
I can't give a definitive answer to a broad question like this: In other words, what is the benefit of retrospective analysis for dealing with the future on a political level?
It varies. A lot. Someone who draws the wrong lessons from history may suffer as much as he who learns nothing from it. How do you know for certain what lessons are wrong? I wish I knew.