I was curious as to what the difference between web and worker dynos is on Heroku. They give a one sentence explanation on their pricing page, but this just left me confused
A number of people have mentioned that there is no known ratio and that the ratio of web workers to 'background' workers you will want is dependent on how you designed your application - that is correct. However I thought it might be useful to add that as a general rule of thumb, you want your web workers - and thus the controller actions they are serving - to be lightning quick and very lightweight, to reduce latency in response times from browser actions. If there is some browser action that would require more than, say, about a half a second of real time to serve, then you will probably want to architect some sort of system that pushes the bulk of that action on to a queue.
You would then design an offline worker dyno(s) that will service this queue. They can take much longer because there are no HTTP responses pending on their output. Perhaps the page you rendered from the initial browser request that pushed the action will serve some Javascript that starts a thread that checks to see if the request has finished every 5 seconds, or something along those lines.
I still can't give you a ratio to work with for the same reason others have given, but hopefully this helps you decide how to architect your app. (I should also mention this is just one design out of many valid ones.)