I'm presenting how DevOps practices reduce the risk of outages due to mistakes during manual deployments. Curious to know if there are any reduced outages due to changes within organizations that adopt DevOps vs. those that deploy manually. Is there any Gartner literature or research about the number of outages caused by changes that have gone wrong?

While I have not seen any hard metrics like the ones quoted by Vanshul, here is a good article that describes the benefits of change automation from a Site Reliability Engineering perspective.  https://sre.google/sre-book/automation-at-google/ 

The actual time savings you get will depend on the risk and recovery time from a faulty deployment.

I’m not aware of Gardner numbers but regarding to literature there are a few books that exemplify the improvements you can gain with the use of DevOps . The Phoenix Project, Accelerate, Continuous delivery and the DevOps handbook.
They all touch on the benefits of DevOps and what other practices nned to exist to make it successful

I’m not aware of any useful literature from Gartner, etc. that compares pre-DevOps to post-DevOps.

My experience has been that automation—not synonymous with DevOps—and improved change management (documentation, approval, post deployment validation, links to incident management) are beneficial. But they are only as good as the people setting up the configuration and deployment settings. It also does not eliminate the need to perform appropriate testing after the deployment.

50% reduction of outages for organizations doing daily deployments.
30% reduction of outages for organizations doing weekly deployments. 
20% reduction of outages for organizations doing monthly deployments.