A commonly overlooked variable for most cyclists is that of proper technique. In essence, proper technique presents itself as the foundation for which fitness should be laid upon. More often than not, it's the latter that gets the attention- forcing those who have poor technique to work perpetually harder as they go harder and so on. It becomes a "cat chasing its tail" scenario.
Without going into a bunch of neuro-physical jargon, here's the skinny. Muscles fire (contract) via electrical impulses from the brain through neuropathways, which then trigger very specific chemical reactions at the nerve/muscle junction, resulting in the contraction (shortening) of muscles. Now, the key word is neuropathway. This "network" of physiological communication is built upon repetition. The old saying "practice makes perfect" is true. However, practice can also apply to perfectly poor technique. Think of neuropathways as water-formed ravines that have been created over long periods of time. The more time, the deeper the ravine. If the ravine does not permit the water to travel from point A to point B in the most efficient and effective manner, then you're doing a lot more work than you need to.
So, what are the factors that instigate inefficient neuropathways (poor technique)? Poor fit to the bicycle is the most common. Others include muscular imbalance, anatomical compensations (Ex. leg length discrepancy), crossover interference (Ex. A hockey player who tries to swing a golf club often mimics the technique of the hockey swing due to the movement tasks being similar.), or just plain old bad form. Remember that the key to neuropathway development is repetition. Repeated movements with any of the above fault(s) is going to lead to perfectly polished, highly trained, non-compromised, finely tuned, bad form.
Here are some remedies to help combat poor cycling technique:
Have a proper bike fit conducted by a knowledgeable fit specialist. A good fit ensures optimal use of anatomical levers in their union with the bicycles mechanical levers.
Have an evaluation performed by an orthodics specialist. Most technique flaws start at the pedal-foot interface. A trained orthodics specialist with cycling knowledge can ensure that the origin of mistake is identified and fixed. I deal with Matt Pulisic at Richmond/Ashland Physical Therapy. He's been the most instrumental person in my recovery and success after a 2-year misalignment injury.
Focus on technique. Pay close attention to the kinetic chains (i.e. your foot-hip musculo-skeletal linkage). Make sure that it is straight- void of wobbles and kinks as it rotates the entire 360 degrees of the crank rotation. A good orthodic can vastly improve the straightness of the leg's motion through the entire crank revolution.
Work with a physical therapist or sport-related chiropractor to identify weak stabilizer or mobilizer muscles. If certain muscles are misfiring or not firing at all, then there is most likely a compensation effect by other muscles so the task can be performed. Yes, you still rotate the cranks, but under the restraints of a muscle imbalance. With a sound strength-conditioning program, the muscle balance can usually be restored with more efficient technique to follow.
Practice single leg drills. For a good portion of individuals, a muscle imbalance not only exists within the same leg, but also exists between both legs. If one leg is stronger (or more coordinated), then that leg will pick up the slack of the inferior leg. Over time the problem is exacerbated, which can then lead to either severe weakening of the non-dominant leg, or a shift in posture. Each is a discrepancy, and will ultimately become an antagonist to proper technique.
I hope these suggestions help. Even if you don't get faster, fellow cyclists on the next group ride will heckle you a lot less. Remember to ease into any riding after a change in bike fit, orthodic, or bouts of single leg drills. The human body is a dynamic organism. Give it time to adapt to the changes, then capitalize from them. Safe riding.