It’s definitely a tricky question. I imagine you would need a variety of different indicators in order to arrive at a fuzzy level of ‘innovation’. There’s a freakonomics post about the question of measuring innovation more broadly which is pretty interesting.
One kind of parallel you could look at would be something like impact factor in the academic world, except instead of citations, you could measure a kind of ‘usefulness factor’ where a project whose code/design elements are used in other open source projects gets a higher rating.
However we don’t tend to track usage in the open source world. For example in software, most F/LOSS projects have no idea how many users they have, let alone how many other projects are using their code. You can estimate it based on downloads, page views, activity on the code repository or community forum, but there’s no helpful spyware telling you what people are doing with the software.
There are a lot of new plans afoot for being able to track and attribute digital assets using the BLOCKCHAIN which could be interesting if people are using open source licenses, but it could also lead to some kind of corporate-controlled dystopia where Big Brother knows all and you need to sign a EULA before you make a cup of tea.
Anyway, although you can’t easily measure use, one advantage of open source projects is that you can measure development, because the plans are open and they are (you would hope) regularly updated. Again, using software as an example, Openhub tracks the git repositories of most major F/LOSS projects - this the video editor that I use: Kdenlive.
Here you can see the whole history of the project’s code, how many people have contributed to the codebase over the years. You can also see the worrying period between June and December 2013 when the main developer burned out and went AWOL, and there were no commits. Not such an innovative time. (he’s back now, and things are going really well for the project, if you were wondering )