Field sobriety exercises are "Divided Attention Tests". The theory is that a person who is impaired by alcohol or a controlled substance is unable to do both physical activities while at the same time remember what the instructions were. The divided attention tests are to see hwo well you can remember instructions while performing the requested tasks.

The problem with these "tests" is that the validity of them depends on the persons prior ability to do two things at once. The validity of the tests is also  questionable because a person in their 50's who is 60 pounds overweight is supposed to have the same balance as a 24 year old gymnast who is in perfect shape.  As a real life example, when I was in basic training in the army, some of us understood marching and turns better then other trainees. That is why so much time was spent on marching drills. Some people just take more time then others to learn.