Just to put my 2c worth into this debate My Masters was on stretching and a lot of the confusion about stretching comes from differences in definitions of stretching and flexibility, sometimes questionable research design and implementation of different stretching interventions. For example, stiffness and flexibility are biomechanical terms related to the gradient of load deformation curves. Range of Motion is assumed to be a direct measure of flexibility but it is affected my other things like joint structure, connective tissue, ligaments, nerves etc. so is not always the case. Consensus now is that static stretching before exercise might be detrimental to immediate performance (average of 5%) and might predispose injury. There are benefits to including some dynamic stretching (controlled through range movements) as part of a warm up in some sports, although I don't remember reading anything relating directly to cycling. Stretching after exercise and outside of activity periods has been shown to be beneficial in many studies. Generally injury risk in subsequent sessions is reduced and performance is increased if 20 - 30 seconds static stretching per major muscle group is performed post-exercise as part of the cool down. People also reported feeling looser when they stretched compared to when they didn't. To put in practical terms, after cycling or running, I would cool down a bit then do 20 - 30 seconds stretching of calves, hamstrings, quads, hip flexors, gluts, and hip abductors. I also find stiffness and niggles creep in if I neglect this because of time or anything else.
