I love to solve puzzles, and I love to treat every little complication, obstacle, and issue as a new puzzle to be solved. For me its kind of like being a detective. When things are unclear and nobody knows how to proceed, then we get to pull out the drawing board and start having fun.
So why exactly is drawing the right way to go? Well a quote that is unrelated to analysis and problem solving sums it up perfectly.
A Picture Is Worth A Thousand Words
In other words, you can draw a picture or you can write out a thousand words. The problem with words is that they can be subject to interpretation. Pictures on the other hand are very hard to misunderstand. Here is a pretty easy example...
Here are a bunch of words explaining what a business analyst does
Here is a picture of what a business analyst does...
In one simple picture, you basically get the entire scope of what a business analyst does, who they interact with, and they're overall relationship to other pieces of the puzzle.
Using this diagram, I can easily explain to someone what a business analyst is and they can easily understand what a business analyst is and more importantly, I can answer the all important question, "What is the difference between what a project manager does and what a business analyst does"
For me personally I use pictures in the form of wireframes when I need to explain why or how something works a certain way or will fail if it works a certain way. I use diagrams and decision trees to explain intricate or complex concepts like multi-layer permissions structures in a web application. Concept maps or mind maps are great for getting a grasp on scope. Flow diagrams are great for explaining or document issues in a current process or getting decision that need to be made around a particular change.
Any business analyst who can put his or her words into pictures...and in our world, pictures mean diagrams, models, wireframes, you name it... will be wildly successful. First, because you are verifying that you truly understand the topic. Second, because you will be ensuring all of your stakeholders do too.