I can answer this, to a point. If your credit score is under 650, a new derogatory mark is not going to have that big of an impact. If your score is 650-720, a new mark can drop you 40 points depending on the number of credit cards you have open, your credit utilization etc. I've seen a single bad mark drop a friend from 740 to 690. If your score is over 800, and you get a new mark, the impact will be more, but again, that depends on your credit utilization, the age of your credit and number of lines of credit. I had to deal with a hit due to my accident which dropped my score from the 810's to the 710's.
In short, it hurts.
When you pay an old debt you need to negotiate the holder to remove the mark from all your credit reports, get that in writing and then send that letter to each of the Bureaus so that the bad mark is gone.
Why care? Insurers use your credit score to assign rates (in part at least. I got a discount of 10% due solely to my credit score off my home and auto). It also helps when you need to put down security deposits, when you have to rent cars, if you need a security clearance, and some employers will make hiring decisions based on credit score. That last one, other than Finance, should not be legal, but it is what it is. Credit over 750 opens doors. Credit scores under 680 slam doors shut.