The BEST metric to monitor the risk associated with changes deployed to production is the...

Changes deployed to production are those that affect the functionality, performance, or security of the system in a way that is visible or accessible to the end users1. These changes can introduce new risks or vulnerabilities, such as errors, bugs, compatibility issues, or unauthorized access2. Therefore, it is important to monitor the risk associated with these changes and measure how often they cause incidents in production.

One metric that can be used to monitor this risk is the percentage of changes that cause incidents in production. This metric indicates how effective the change management process is and how well the organization can prevent or mitigate potential problems caused by changes3. A high percentage of incidents indicates a high level of risk and a need for improvement in the change management process.

References = IT Change Management for SOC: Process and Best Practices, Determining and Managing Risk when Deploying Code, 6 Deployment Risks and How To Mitigate Them