College Freshman looking for a decent gaming laptop under 1500$?

I'm looking for a nice gaming laptop to bring with me to college. I know that a desktop PC is the way to go for gaming. But I need to bring it from class to class to type out notes, PowerPoint, spreadsheets, and etc. Obviously any laptop will do that but now that I'm in the budget for something nicer I would like a decently powerful machine. I'm not well educated in Computer technology being that I've been a console gamer all of my life. So I guess my best benchmark that I can give is that I would want it to run games better than its ps4 counterpart. Because if it doesn't look better than the ps4 then I might as well just get a laptop with just the necessities for school work and stick to console gaming for the next four years.
I realize this might be unrealistic for a laptop on my budget, but I really have no clue. If it could run games like the witcher 3 which seems to be the most demanding game right now, that would be great. So yeah, most powerful laptop that I can get for 1500$ or less, and want it to look better than that of my ps4. Thanks!

Added (1). Right now I've been looking into the Lenovo Y-Series as well as this one

http://www.bestbuy.com/...Id=3572056

Your ps4 is about hd 7850 equivalent and full functioning cpu instead of those aimed at battery management.
http://www.videocardbenchmark.net/gpu_list.php
Radeon HD 78503739
PS4 would score about 4000.
To beat it, GTX 970M
Laptop quad core i7
Lenovo only gets to GTX 960M
Gaming to GPU in a slow loading table of a lot of data
http://www.notebookcheck.net/...849.0.html

You can telephone or browse xoticpc.com and cyberpowerpc.com to see what they offer.
newegg.com shows 5
http://www.newegg.com/...6834152554
$1204:
MSI GT Series GT70 Dominator-895 Gaming Laptop Intel Core i7 4800MQ (2.70GHz) 8GB Memory 1TB HDD NVIDIA GeForce GTX 870M 3GB 17.3" Windows 8.1 64-Bit

http://www.newegg.com/...6834233059
$1149
GIGABYTE P35Wv2-SP1 Gaming Laptop Intel Core i7 4710HQ (2.50GHz) 8GB Memory 1TB HDD 128GB SSD NVIDIA GeForce GTX 870M 3 GB GDDR5 15.6" Windows 8.1

http://www.newegg.com/...6834232423
$1249
ASUS ROG G751JL-DS71 Gaming Laptop Intel Core i7 4720HQ (2.60GHz) 16GB Memory 1TB HDD NVIDIA GeForce GTX 965M 2 GB GDDR5 17.3" Windows 8.1 64-Bit
Free ASUS ROG GX950 gaming mouse w/ purchase, limited offer

http://www.newegg.com/...6834233092
$1355
GIGABYTE P34K-CF1 Gaming Laptop Intel Core i7 4720HQ (2.60GHz) 8GB Memory 1TB HDD 128GB SSD NVIDIA GeForce GTX 965M 4 GB GDDR5 14.0" Windows 8.1 64-Bit

http://www.newegg.com/...6834232202
$1400
ASUS ROG G751 Series G751JT-CH71 Gaming Laptop Intel Core i7 4710HQ (2.50GHz) 16GB Memory 1TB HDD NVIDIA GeForce GTX 970M 3GB 17.3" Windows 8.1 64-Bit
Free ASUS ROG GX950 gaming mouse w/ purchase, limited offer
This one at rank 15 gpu does exceed a ps4 and is 17.3" 1080p
Surprised BestBuy has a competing. GS70-459 is ok
Newegg collects sales tax as shipped to California, NJ, TN
They will perform about the same. Look for reviews.