It's all numbers game. On average, you can expect 2-3% response rate and ~30 callbacks for 1 completed deal. So I think 4444 leads can realistically lead to 4 completed deals. The questions then becomes, how many deals do you want? If you want 4, then the size list you have seems appropriate. A couple of things to consider...
1) Can you handle the call volume? If you send out that list today and only 1% calls you back that's ~44 calls. At 3%, that ~133 calls. Each call involves some combination of analysis, inspecting the property, negotiation and putting together a deal; aka time and effort beyond picking up the phone.
2) You need to hit your list multiple times. You will likely not get any deals off your first mailings but your odds increase with multiple mailings.
3) Past experience does not equal future results. Make sure you're only spending money that you can stand to lose. In other words, make your peace with the idea that those ~4K leads can result in 0 or more deals.
4) Make sure your list makes sense. What filters are you using on ListSource? If you have a list of 4K un-motivated sellers, you're likely not going to close any deals.
Let us know how your campaign turns out. Good luck!