What is the added value of numbering Notification Badges?

Notification Badges are all over our mobile devices, all of the most common apps we use everyday have them. They keep us hooked onto an app and let us know when something new happens.

My question is about the effect on user engagement when numbering badges.

Is there any difference in user engagement between notification badges with numbers and badges without numbers?

And to a further extent what arguments are there for not using a numbered badge and instead just using a red badge without a number?