It has been proven by research and several studies like this, that optimistic, enthusiastic and positive people are more likely to succeed than those that are not. This could be one of the things that happen with the believers on the LOA; they are effectively being optimistic, enthusiastic and positive about what they want to achieve and therefore they are more likely to achieve what they want as the result of their increased mental focus.
Another things to bear in mind is that focusing on what we want and being positive and believing it will come to us, is also a way to remove the negative thoughts that can cloud our mind in the search for a goal or situation. A lot have been studied and researched about the damaging effect of negative thinking, by believing in the LOA, we are aiding our mind to removing negative thoughts and focusing on only what we want.