as you can see from my scores listed below I just paid off 3 small collections (under $1k) and mine went up some 40 something points in a couple months. I have 7 year old collections to fall off next month ( 1 real baddie, 1 not so bad). Very anxiuosto see how that changes my score. Plus I got a $500 unsecured CC from my CU with a 10.99% interest rate...so I'm hoping that has a positvie impact also. (fingers and eyes crossed!)
Starting Score: 
There are many different factors that would have to go into play to determine this. Were they affecting your util? Are these your only baddies? Do you have any positive TLs to make your CR healthy?
July 2013 score: EQ FICO 819, TU08 778, EX "806 lender pull 07/26/2013
Goal Score: All Scores 760+, Newest goal 800+
Take the myFICO Fitness Challenge
Current scores after adding $81K in CLs and 2 new cars since July 2013
EQ:809 TU 777 EX 790 Now it's just garden time!
June 2017 update: All scores over 820, just pure gardening now.
If they were revolving accounts and with the OC and figuring into your util. Then I could see that. 20 points is doable. 
July 2013 score: EQ FICO 819, TU08 778, EX "806 lender pull 07/26/2013
Goal Score: All Scores 760+, Newest goal 800+
Take the myFICO Fitness Challenge
Current scores after adding $81K in CLs and 2 new cars since July 2013
EQ:809 TU 777 EX 790 Now it's just garden time!
June 2017 update: All scores over 820, just pure gardening now.
I don't see a significant jump just because they were paid, but I've seen stranger things happen so we will hope for the best. In the mean time, since they are paid now, start the GW process.
July 2013 score: EQ FICO 819, TU08 778, EX "806 lender pull 07/26/2013
Goal Score: All Scores 760+, Newest goal 800+
Take the myFICO Fitness Challenge
Current scores after adding $81K in CLs and 2 new cars since July 2013
EQ:809 TU 777 EX 790 Now it's just garden time!
June 2017 update: All scores over 820, just pure gardening now.