The User Stats module only has a dev version for D7 (I'm assuming this question is about D7). However, your question seems like a perfect usecase for the Goals module (disclosure: I'm the maintainer of it). Below is a possible configuration for your specific case, using Goals.
Configure a goal
Navigate to the relative path
admin/config/goals/manage and use the link "Add a goal" to define just 1 goal, with a description (say):
Make X number of posts (core forum topics or/and replies).
To achieve the goal "make X number of posts (core forum topics or/and replies)", define the Task(s) to be completed.
- Post a certain number of core forum topics.
- Post a certain number of replies.
A more advanced way to use (configure) Goals, is to configure tasks like so:
- some tasks might have to be repeated multiple times.
- some tasks may require some amount of time to expire in between any 2 similar tasks (eg: if a task is performed multiple times a day, only the first one counts).
- ... (there are others ...).
Track progress while performing tasks
To track the progress made by a single user to complete some task, you only have to write the appropriate rules, using the Rules module, to record relevant events happening in your site, which are related to the completion of the various tasks.
For the goals/tasks described above as an example, you'd only need 2 (extremely basic) rules, which would be triggered like so:
- After posting a core forum topic.
- After posting a reply.
Note that these 2 rules can be re-used to measure progress on multiple goals (eg if your goal has a task like "after posting 1 reply", and a 2nd goal haS a task like "after posting 10 replies").
Moreover, the above challenges are pretty straight forward (basic) as examples of Challenges. But you can do this for virtually any entity for which you can think of a way to track them via the Rules module.
Use Rules to process completed goals
After all tasks specific to a goal are completed by a user, the goal is automagically marked as completed. But, there is more: you can also create additional rules that will be triggered (Rules Event) when a goal is completed by a user. With that, the answer to your question is extremely easy: perform a Rules Action to "... change the user to a different role" ... which is exactly what your question is about, no?
More of the same
Instead of the (boring) description of the goal above, you could have used a goal description like (say) "Participating User" instead. Which BTW could be a nice description of the role to be granted also.
If you then define (say) 3 more (similar) goals, with each of them an appropriate set of tasks to be completed, you could use the very same technique for goals (and/or roles) labeled something like so (if they sound familiar to something on Drupal.SE, that's purely be accident):
- Loyal User.
- Established User.
- Trusted User.
Refer to my answer to "How to implement gamification in a Drupal site and award incentives?" for additional details about the Goals module.
Note: Using Goals only requires typical administration tasks (configuration), though it does come with various hooks also for custom module development (if you want to).