Do I need to stretch before my run?

No. Static stretching has been shown to temporarily reduce muscle force output. Muscles work through the cross bridging of two proteins—myosin and actin. While stretched, myosin can not quite reach actin as well and this leads to a reduction in overall force for a short period after stretching. Because of this, static stretching (meaning the traditional stretch of holding a position where your feel a “pull” for a long duration of time) is not typically recommended prior to physical activity. 

Now, this does not mean you don’t need to warm-up. Warming up before your run is one of the most important things you can do to protect against injury. It lubricates your joint surfaces, initiates blood flow and nutrition to your working muscles, prepares your heart. Part of warming up includes mobility; I.e. moving joints through their range of motion to prepare them for activity. It can also include dynamic stretching and body weight strength activities to start to bring blood flow to the area before actually running. A proper warm-up also extends to the run itself where at least the first mile should be done at an easier effort while the body is adapting to activity.