Strength training can improve muscle strength.  What would be the specific benefit from strengthening particular muscle groups? 

One may want to estimate benefit from changing the shape or magnitude of a strength function (for example, pedaling by pushing sooner and reaching maximum effort for a longer portion of a pedal stroke).  The Pedaling Modal may be able to help you decide if the training you are contemplating is going to meet your expectations. The following examples illustrate the concept.

"Quads" Only
Suppose we want to study the effect of pedaling using different muscle groups. For example, suppose that we wanted to study the effect of pedaling only with the shin extensors, the "quads."  The following table gives power from pedaling with "quads" only:

This is a very large difference. (These values are hypothetical. With more developed "quads" or less developed thigh extensors, the results could be very different.) In the above table, the base case was evaluated with default values for Thigh and Shin Extensor and Flexor Fit Points. In the test case, Shin Extensor Fit Points were at default value and Thigh Extensor and Flexor and Shin Flexor Fit Points were set to {0,0,0,0}.

"Pushing" Only
We read anecdotal comments that a rider can only pedal by pushing on the pedals. How does power from "pushing only" compare with pedaling using all the muscles?

The relatively small difference would show that "pulling up" is not nearly as important as "pushing down," but "pushing only" neglects an important source of power. (These values are hypothetical. your results could be very different.) In the above table, the base model was evaluated with default values for Thigh and Shin Extensor and Flexor Fit Points. In the "pushing only" case, Thigh and Shin Extensor Fit Points were at their default values and Thigh and Shin Flexor Fit Points were set to {0,0,0,0}.

Strength Training
So, you're going to work real hard in the gym this winter, build up those quads, look like a real biker when you're done. What results can you expect? The following table shows the before and after results from changes to thigh and shin extensor and flexor strength functions. 

For example, suppose a rider improves the strength of the shin extensors (quads) by 50%. How much will this change a rider's theoretical power output? This table shows the results of 50% stronger Quads:

Same 50% increase but in the thigh extensors:

Results based on your data could be very different.