Q:

How to recover from credit score hit from paying off loan? 

My credit score recently took a dip after I paid off my student loans recently. 
When I look at the credit report via mint it shows a "not bad" rating for number of accounts opened. (" not bad" is the second worst out of 4: bad, not bad, good, excellent)
To get into the "good" range it has a range of 13+ accounts.  I currently have 4 credit cards, 1 care credit account, and 1 auto loan.  How could I ever get to 13 accounts?  I have a good income so I could apply for more credit cards, but 4 already seems very high. 
What can I do to get the highest rating in this category of account quantity? 
Note: this question is only regarding the category of quantity of open accounts in a credit score rating.  Every other category is maximized (except for age of credit, which all I can do for that is wait)

A:

First, you need to be aware that the credit score reported by Mint is Equifax Credit Score.  Equifax Credit Score, like FICO, Vantagescore, and others, is based on a proprietary formula that is not publicly available.   Every score is calculated with a different formula, and can vary from each other widely.   Lenders almost exclusively only use FICO scores, so the score number you have is likely different than the score lenders will use. 
Second, understand that the advice you see from places like Mint and Credit Karma will almost always tell you that you don't have enough credit card accounts.   The reason for this is that they make their money by referring customers to credit card applications.   They have a financial interest in telling you that you need more credit cards. 
Finally, realize that credit score is just a number, and is only useful for a limited number of things.   Higher is better to a point, and after that, you get no benefit from increasing your score.   
My advice to you is this:

Don't stress out about your credit score, especially a free score reported by Credit Karma or Mint.   If you really have a desire to find out your score, you can pay FICO to get your actual score, but it's not cheap.   You can also sometimes get your FICO score by applying for a loan and asking the lender.   I last saw my FICO scores (there were three, one from each credit bureau) when I applied for a mortgage a couple of years ago, and the mortgage rep gave them to me for free.   But honestly, knowing your score doesn't do much for you, as the best way to increase it is to simply make your payments on time and wait. 
Don't give in to bad conventional advice from places that are funded by the financial services industry.   The thing that makes your credit score go up is a long history of paying your bills on time.   Despite what you commonly read about credit scores, I'm not convinced that you can radically boost your scores by having lots of open credit card accounts.   At the time I applied for my last mortgage, I only had 2 open credit cards (still true), and the oldest open account was about 1.5 years old.   The average of my 3 scores was just over 800.   But I've been paying my bills on time for at least 20 years now.   Only get credit cards that you actually want, and close the ones you don't want. 

A:

This answer is an attempt to answer the actual question posed.  Please keep in mind that this applies specifically to the Equifax credit model that Mint uses as mentioned in the accepted answer, and that different models may react in different ways (or not at all). 
As mentioned in the comments, the number of total accounts you have does not have much bearing on your overall credit score.  If you click on Mint's "About Total Accounts" link, you get the following statement:

Total Accounts has a low impact on your score. 

Second, the way the Total Accounts score is represented is misleading.  This is not a count of the total number of accounts you have open, but rather how many accounts you have in your total history.  Mint's header under this metric is flat out wrong:

Try to have a good mix of credit lines open. 

To back up the assertion that this is looking at total accounts in your credit history rather than just those that are open, my Mint report shows 2 open accounts and 7 closed accounts, for a total of 9.  Under the Total Accounts metric, I am plotted smack dab in the middle of the "Not Bad" range, right where people with 9 would be plotted. 
So the proper advice here is to just let it be and only open new accounts as you need them.  As you amass credit history, this metric will continue to grow naturally - it should never decrease. 
You may ask, then, why did your overall score decrease when you paid off your student loans?  Most likely because your average age of credit dropped when you closed your loan account.  If you're like most people I know, your student loan is one of your oldest accounts, so closing that account will hurt your score - credit age is measured only on your open accounts.