Catan: when to buy development cards?
Whenever you buy a development card, it increase your options because:

Development Cards solve your problems.


Get a resource you couldn't otherwise, with Monopoly, Year of Plenty, or stealing using a Knight.
Get more resources by getting the Robber off your land. (Remember you can do this before you roll!)
Slow down an opponent by putting the Robber on their land.
Build roads quickly to cut someone off or reach a settlement first, with Road Building.


And they don't, on average, actually cost 3 resources. Monopoly, Year of Plenty, and Knight all gain you at least one back, which you can choose (even somewhat when stealing with the knight). Road Building is worth 4 resources. Even if you get a victory point, how many resources do other victory points cost? Settlement is 4, City is 5. Longest Road is a lot.

Because of the low effective cost of development cards, and the gains you get from them, buying development cards actually banks your resources in a fairly fluid way, yet out of your hand so you don't have too many cards.

In short, when should you buy development cards? Anytime you can and you don't have something else you'd rather build THAT TURN. Buying the card means all the better chance of building whatever you want next turn. I buy Development Cards whenever I can.

One last note, if you are richest in sheep, development cards are probably your shortest path to victory (combined with some expansion/cities).